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Report Overview
Summary of Alignment & Usability: Math Nation | Math
Math 6-8
The materials reviewed for Math Nation Grades 6-8 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. In Gateway 3, the materials meet expectations for Usability.
6th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
7th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
8th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
Report for 7th Grade
Alignment Summary
The materials reviewed for Math Nation Grade 7 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence, and in Gateway 2, the materials meet expectations for rigor and practice-content connections.
7th Grade
Alignment (Gateway 1 & 2)
Usability (Gateway 3)
Overview of Gateway 1
Focus & Coherence
The materials reviewed for Math Nation Grade 7 meet expectations for focus and coherence. For focus, the materials assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials are coherent and consistent with the CCSSM.
Gateway 1
v1.5
Criterion 1.1: Focus
Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.
The materials reviewed for Math Nation Grade 7 meet expectations for focus as they assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.
Indicator 1A
Materials assess the grade-level content and, if applicable, content from earlier grades.
The materials reviewed for Math Nation Grade 7 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.
The curriculum consists of nine units, including one optional unit. Assessments include Cool-down Tasks, Mid-Unit Assessments, and End-of-Unit Assessments. Examples of assessment items aligned to grade-level standards include:
Unit 2, Lesson 1, Cool-down, “Here are three different recipes for Orangey-Pineapple Juice. Two of these mixtures taste the same and one tastes different. Recipe 1: Mix 4 cups of orange juice with 6 cups of pineapple juice. Recipe 2: Mix 6 cups of orange juice with 9 cups of pineapple juice. Recipe 3: Mix 9 cups of orange juice with 12 cups of pineapple juice. Which two recipes will taste the same, and which one will taste different? Explain or show your reasoning.” (7.RP.2)
Unit 3, End-of-Unit Assessment (A), Question 2, “The shape is composed of three squares and two semicircles. Select all the expressions that correctly calculate the perimeter of the shape. A. 40+20𝞹; B. 80+20𝞹; C. 120+20𝞹; D. 300+100𝞹; E.10+10+10𝞹+10+10+10𝞹 .” (7.G.4)
Unit 6, Mid-Unit Assessment (A), Question 3, “At practice, Diego does twice as many push-ups as Noah, and also 40 jumping jacks. He does 62 exercises in total. The equation 2x + 40 = 62 describes this situation. What does the variable x represent? A. The number of jumping jacks Diego does B. The number of push-ups Diego does C. The number of jumping jacks Noah does D. The number of push-ups Noah does” (7.EE.4)
Indicator 1B
Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.
The materials reviewed for Math Nation Grade 7 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.
The materials present opportunities for students to engage in extensive work and the full intent of most Grade 7 standards. Each lesson contains a Warm-Up, a minimum of one Exploration Activity, a Lesson Summary, Practice Problems, and three Check Your Understanding Questions. Each unit provides a Readiness Check and a Test Yourself! practice tool. Examples of full intent include:
Unit 1, Lesson 7, 1.7.2 Exploration Activity, engages students with the full intent of 7.G.1 (Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale). Students use a diagram to complete a table of values involving scale drawings to compute actual dimensions. “Your teacher will give you a scale drawing of a basketball court. The drawing does not have any measurements labeled, but it says that 1 centimeter represents 2 meters. 1. Measure the distances on the scale drawing that are labeled a-d to the nearest tenth of a centimeter. Record your results in the first row of the table. 2. The statement ‘1 cm represents 2 m’ is the scale of the drawing. It can also be expressed as ‘1 cm to 2 m,’ or ‘1 cm for every 2 m.’ What do you think the scale tells us? 3. How long would each measurement from the first question be on an actual basketball court? Explain or show your reasoning. 4. On an actual basketball court, the bench area is typically 9 meters long. a. Without measuring, determine how long the bench area should be on the scale drawing. b. Check your answer by measuring the bench area on the scale drawing. Did your prediction match your measurement?” Students are provided a table with two rows labeled, “scale drawing” and “actual court,” and four rows labeled “(a) length of court,” “(b) width of court,” “(c) hoop to hoop,” and “(d) 3 point line to sideline,” respectively.
Unit 5, Lesson 13, 5.13.3, Exploration Activity, engages students with the full intent of 7.NS.A (Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers). Students complete a table of values using the four operations and fractional values to add, subtract, multiply, and divide rational numbers. For example, “For each set of values for a and b, evaluate the given expressions and record your answers in the table.”
Unit 6, Lesson 13, 6.13.2 Exploration Activity, engages students with the full intent of 7.EE.4b (Solve word problems leading to inequalities of the form or , where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. Students analyze an inequality, explain their reasoning, and graph the results. “A sign next to a roller coaster at an amusement park says, ‘You must be at least 60 inches tall to ride.’ Noah is happy to know that he is tall enough to ride. 1. Noah is x inches tall. Which of the following can be true: , , or ? Explain how you know. 2. Noah's friend is 2 inches shorter than Noah. Can you tell if Noah's friend is tall enough to go on the ride? Explain or show your reasoning. 3. List one possible height for Noah that means that his friend is tall enough to go on the ride, and another that means that his friend is too short for the ride. 4. On the number line below, show all the possible heights that Noah's friend could be.”
The materials present opportunities for students to engage with extensive work with grade-level problems. Examples of extensive work include:
Unit 5, Lesson 14, Exploration Activity, Check Your Understanding, and Practice Problems, engage students in extensive work with 7.RP.2 (Recognize and represent proportional relationships between quantities). In 5.14.2 Exploration Activity, students use proportional knowledge to figure out how long it takes a tank to drain. “A tank of water is being drained. Due to a problem, the sensor does not start working until some time into the draining process. The sensor starts its recording at time zero when there are 770 liters in the tank. 1. Given that the drain empties the tank at a constant rate of 14 liters per minute, complete the table: 2. Later, someone wants to use the data to find out how long the tank had been draining before the sensor started. Complete this table: 3. If the sensor started working 15 minutes into the tank draining, how much was in the tank to begin with?” In 5.14.6 Practice Problem, Question 3, students use proportional knowledge to figure out how much water is in a tank after five minutes. “A large aquarium of water is being filled with a hose. Due to a problem, the sensor does not start working until some time into the filling process. The sensor starts its recording at the time zero minutes. The sensor initially detects the tank has 225 liters of water in it. A. The hose fills the aquarium at a constant rate of 15 liters per minute. What will the sensor read at the time 5 minutes? B. Later, someone wants to use the data to find the amount of water at times before the sensor started. What should the sensor have read at the time −7 minutes?” In 5.14.7 Check Your Understanding, Question 2, students work with proportional knowledge to calculate the total mileage of a runner. “Caroline is training for a half-marathon race and ran 10.1 miles on Monday, 4.3 miles on Tuesday, and 9.9 miles on Thursday. Her friend Xander is also training and he ran of Caroline’s total mileage. How many miles did Xander run? Express your answer as a decimal.”
Unit 7, Lesson 13, Lesson 15, and Lesson 16, engages students in extensive work with 7.G.6 (Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms). Lesson 13, 7.13.2 Exploration Activity, students solve problems in context using three-dimensional objects. “A box of chocolates is a prism with a base in the shape of a heart and a height of 2 inches. Here are the measurements of the base (picture given). To calculate the volume of the box, three different students each have drawn line segments showing how they plan on finding the area of the heart-shaped box (picture given) students use three-dimensional objects to calculate volume. 1. For each student’s plan, describe the shapes the student must find the area of and the operations they must use to calculate the total area. 2. Although all three methods could work, one of them requires measurements that are not provided. Which one is it?” Lesson 15, 7.15.5 Exploration Activity, students calculate the volume required to fill an object and the area that is left over once the contents are removed. “A wheelbarrow is being used to carry wet concrete. (Picture with dimensions are given) 1. What volume of concrete would it take to fill the tray? 2. After dumping the wet concrete, you notice that a thin film is left on the inside of the tray. What is the area of the concrete coating the tray? (Remember, there is no top.)” Lesson 16, 7.16.2 Exploration Activity, in this activity students work in pairs to solve a real-world problem that involves finding the volume and surface area of a play structure by decomposing the structure into prisms. “At a daycare, Kiran sees children climbing on this foam play structure. (Picture with dimensions are given) Kiran is thinking about building a structure like this for his younger cousins to play on. 1. The entire structure is made out of soft foam so the children don’t hurt themselves. How much foam would Kiran need to build this play structure? 2. The entire structure is covered with vinyl so it is easy to wipe clean. How much vinyl would Kiran need to build this play structure? 3. The foam costs 0.8¢ per in3. Here is a table that lists the costs for different amounts of vinyl. What is the total cost for all the foam and vinyl needed to build this play structure?”
Unit 8, Lesson 1, Warm-Up, Practice Problems, and Check Your Understanding, engage students in extensive work with 7.SP.6 (Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability). In 8.1.1 Warm-Up, students find the probability of an event to make predictions. “Andre and his dad have been fishing for 2 hours. In that time, they have caught 0 bluegills and 1 yellow perch. The next time Andre gets a bite, what kind of fish do you think it will be? Explain your reasoning.” In 8.1.5 Practice Problems, Question 1, students explain their reasoning in approximating the probability of a chance event. “Lin is interested in how many of her classmates watch her favorite TV show, so she starts asking around at lunch. She gets the following responses: [yes, no], [yes, no], [yes, no], [no, yes], [no, no], [no, no], [no, no]. If she asks one more person randomly in the cafeteria, do you think they will say "yes" or "no"? Explain your reasoning.” In 8.1.6 Check Your Understanding, Question 2, students use probability to determine the probability in students preference in selecting a dog or a cat. “Sam asked some of his classmates if they preferred cats or dogs. Table shows the following responses: [cat, dog], [dog, cat], [dog, cat], [cat, dog], [dog, cat], [dog, cat]. If Sam continues to ask his classmates, which statement is true based on the table? (A) The next person he asks will prefer dogs since more prefer dogs. (B) The next person he asks will prefer cats since more prefer dogs and it needs to be even. (C) The next person he asks will prefer cats since more prefer cats. (D) The preference to dogs or cats is not able to be determined based on the responses.”
The materials do not provide opportunities for students to meet the full intent of the following standard:
While students engage with 7.RP.1 (Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.), students have no opportunities to work with unit rates as fractional lengths in regards to areas to meet the full intent of the grade-level standards.
Criterion 1.2: Coherence
Each grade’s materials are coherent and consistent with the Standards.
The materials reviewed for Math Nation Grade 7 meet expectations for coherence. The materials: address the major clusters of the grade, have supporting content connected to major work, make connections between clusters and domains, and have content from prior and future grades connected to grade-level work.
Indicator 1C
When implemented as designed, the majority of the materials address the major clusters of each grade.
The materials reviewed for Math Nation Grade 7 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.
To determine the amount of time spent on major work, the number of units, the number of lessons, and the number of days were examined. Assessment days are included. Any lesson, assessment, or unit marked optional was excluded.
The approximate number of units devoted to major work of the grade (including supporting work connected to the major work) is 4 out of 8, which is approximately 50%.
The approximate number of lessons devoted to major work (including assessments and supporting work connected to the major work) is 81 out of 125, which is approximately 65%.
The approximate number of days devoted to major work of the grade (including supporting work connected to the major work) is 81 out of 125, which is approximately 65%.
A lesson-level analysis is most representative of the materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each unit. As a result, approximately 65% of the materials focus on major work of the grade.
Indicator 1D
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The materials reviewed for Math Nation Grade 7 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
Materials are designed to connect supporting standards/clusters to the grade’s major standards/clusters. Examples of connections include:
Unit 2, Lesson 8, 2.8.3 Exploration Activity, connects the supporting work of 7.G.6 (Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms) to the major work of 7.RP.2 (Recognize and represent proportional relationships between quantities). Students find and write equations for the total edge length, surface area, and volume while determining and explaining which relationships are proportional. “Here are some cubes with different side lengths. Complete each table. Be prepared to explain your reasoning. 1. How long is the total edge length of each cube? 2. What is the surface area of each cube? 3. What is the volume of each cube? 4. Which of these relationships is proportional? Explain how you know. 5. Write equations for the total edge length E, total surface area A, and volume V of a cube with side length s. Total edge length: E = ___ Total surface area: A = ___ Volume: V = ___.” Students are shown a picture of three cubes of side lengths 3, 5, and . For Questions 1-3 students answer the question for the cubes listed above in addition to a cube of side length s.
Unit 3, Lesson 4, 3.4.3 Exploration Activity, connects the supporting work of 7.G.4 (Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle) to the major cluster of 7.NS.2 (Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers). Students use the formulas for area and circumference of a circle to answer questions about a running track. “The field inside a running track is made up of a rectangle that is 84.39 m long and 73 m wide, together with a half-circle at each end. 1. What is the distance around the inside of the track? Explain or show your reasoning. 2. The track is 9.76 m wide all the way around. What is the distance around the outside of the track? Explain or show your reasoning.” A diagram of the track is provided for students.
Unit 8, Lesson 1, 8.1.5 Practice Problems, Question 3, connects the supporting work of 7.SP.6 (Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.) to the major work of 7.RP.1 (Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.). Students make predictions using probability to solve real-world problems. "A company tests two new products to make sure they last for more than a year. Product 1 had 950 out of 1,000 test items last for more than a year. Product 2 had 150 out of 200 last for more than a year. If you had to choose one of these two products to use for more than a year, which one is more likely to last? Explain your reasoning."
Unit 8, Lesson 16, 8.16.2 Exploration Activity, connects the supporting work of 7.SP.2 (Use data from a random sample to draw inferences about a population with an unknown characteristic of interest) to the major work of 7.NS.2 (Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers). Students use a random sample to solve proportion problems. “The track coach at a high school needs a student whose reaction time is less than 0.4 seconds to help out at track meets. All the twelfth graders in the school measured their reaction times. Your teacher will give you a bag of papers that list their results. 1. Work with your partner to select a random sample of 20 reaction times, and record them in the table. 2. What proportion of your sample is less than 0.4 seconds? 3. Estimate the proportion of all twelfth graders at this school who have a reaction time of less than 0.4 seconds. Explain your reasoning. 4. There are 120 twelfth graders at this school. Estimate how many of them have a reaction time of less than 0.4 seconds. 5. Suppose another group in your class comes up with a different estimate than yours for the previous question. a. What is another estimate that would be reasonable? b. What is an estimate you would consider unreasonable?”
Indicator 1E
Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.
The materials reviewed for Math Nation Grade 7 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.
There are connections from supporting work to supporting work and/or major work to major work throughout the grade-level materials, when appropriate. Examples include:
Unit 1, Lesson 6, 1.6.6 Practice Problems, Question 3, connects the supporting work of 7.G.A (Draw, construct, and describe geometrical figures and describe relationships between them) to the supporting work of 7.G.B (Solve real-life and mathematical problems involving angle measure, area, surface area, and volume). Students analyze the relationship between scaled figures, “Diego drew a scaled version of a Polygon P and labeled it Q. If the area of Polygon P is 72 square units, what scale factor did Diego use to go from P to Q? Explain your reasoning.” Students are given an image of Diego drawing.
Unit 3, Lesson 6, 3.6.2 Exploration Activity, connects the supporting work of 7.G.A (Draw, construct, and describe geometrical figures and describe relationships between them) to the supporting work of 7.G.B (Solve real-life and mathematical problems involving angle measure, area, surface area, and volume). Students approximate the area of a home given a provided floor plan. “Here is a floor plan of a house. Approximate lengths of the walls are given. What is the approximate area of the home, including the balcony? Explain or show your reasoning.” Students are provided a floor plan of the house with numerous section measurements shown in feet.
Unit 4, Lesson 3, 4.3.3 Exploration Activity, connects the major cluster of 7.RP.A (Analyze proportional relationships and use them to solve real-world and mathematical problems) to the major work of 7.EE.B (Solve real-life and mathematical problems using numerical and algebraic expressions and equations). Students use proportional relationships to solve problems. “1. Tyler swims at a constant speed, 5 meters every 4 seconds. How long does it take him to swim 114 meters? 2. A factory produces 3 bottles of sparkling water for every 8 bottles of plain water. How many bottles of sparkling water does the company produce when it produces 600 bottles of plain water? 3. A certain shade of light blue paint is made by mixing quarts of blue paint with 5 quarts of white paint. How much white paint would you need to mix with 4 quarts of blue paint? 4. For each of the previous three situations, write an equation to represent the proportional relationship.”
Unit 6, Lesson 9, 6.9.5 Practice Problems, Question 3, connects the major cluster of 7.NS.A (Apply and extend previous understandings of operations with fractions) to the major work of 7.EE.A (Use properties of operations to generate equivalent statements). Students identify equations that match a tape diagram. “Select all the equations that match the diagram.” The equations listed are the following: ; ; C ; ; .” The image of a tape diagram split into three sections with the equation, , is shown with the sum of all three pieces equal to 18.
The following connections are entirely absent from the materials:
No connections are made between the supporting work of 7.G (Geometry) and the supporting work of 7.SP (Statistics & Probability). It is mathematically reasonable that the materials do not connect these two domains to each other. (Note: As shown above, there are instances where supporting clusters within the same domain have connections to each other.)
Indicator 1F
Content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.
The materials reviewed for Math Nation Grade 7 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.
Grade-level concepts related explicitly to prior knowledge from earlier grades along with content from future grades is identified and related to grade-level work in the Teacher Edition. Generally, explicit connections are found in the Course Guide or the Full Lesson Plan.
Examples of connections to future grades include:
Unit 2, Lesson 2, Full Lesson Plan, Lesson Narrative, connects 7.RP.2, 7.RP.2a, and 7.RP.2b to F-IF.1. “The purpose of this lesson is to introduce the concept of a proportional relationship by looking at tables of equivalent ratios. Students learn that all entries in one column of the table can be obtained by multiplying entries in the other column by the same number. This number is called the constant of proportionality…it prepares students for later work on functions, where they will think of x as the independent variable and y as the dependent variable.”
Unit 2, Lesson 10, Full Lesson Plan, 2.10.3 Classroom activity, connects 7.RP.2 to 8.EE.6. “Students sort the graphs and justify their sorting schemes. Then, they compare the way they sorted their graphs with a different group. The purpose of this activity is to illustrate the idea that the graph of a proportional relationships is a line through the origin. Students will not have the tools for a formal explanation until grade 8.”
Unit 7, Lesson 6, Full Lesson Plan, Lesson Narrative, connects 7.G.2 to 8.G.A and G-CO.B. “This lesson is the first in a series of lessons in which students create shapes with given conditions. During these lessons students think about what conditions are needed to determine a unique figure, in preparation for future work with congruence in grade 8 and high school.”
Examples of connections to prior knowledge include:
Unit 2, Lesson 4, Full Lesson Plan, 2.4.3 Classroom activity, builds on 6.RP.3b and connects to 7.RP.2c. “As part of this activity, students calculate distance and speed. Students should know from grade 6 that speed is the quotient of distance traveled by amount of time elapsed, so they can divide 915 by 1.5 to get the speed. Students that do not begin the problem in that way can be directed back to the similar task in previous lessons to make connections and correct themselves. Once students have the speed, which is constant throughout this problem, they identify this as the constant of proportionality and use it to find the missing values.”
Unit 4, Lesson 3, Full Lesson Plan, Lesson Narrative, builds on 6.RP.3 and connects to 7.RP.2. “In grade 6 students solved ratio problems by reasoning about scale factors or unit rates. In grade 7 they see the two quantities in a set of equivalent ratios as being in a proportional relationship and move towards using the constant of proportionality to find missing numbers…In this lesson students move toward solving problems involving proportional relationships by more efficient methods, especially by setting up and reasoning about a two-row table of equivalent ratios. This method encourages them to use the constant of proportionality rather than equivalent ratios.”
Unit 5, Lesson 15, Full Lesson Plan, Lesson Narrative, builds on 6.EE.5 and connects to 7.NS.A and 7.EE.B. “The purpose of this lesson is to get students thinking about how to solve equations involving rational numbers. In grade 6, students solved equations of the form and and saw that additive and multiplicative inverses (opposites and reciprocals) were useful for solving them. However, that work in grade 6 did not include equations with negative values of p or q or with negative solutions. This lesson builds on the ideas of the last lesson and brings together the work on equations in grade 6 with the work on operations on rational numbers from earlier in grade 7.”
Indicator 1G
In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification.
The materials reviewed for Math Nation Grade 7 foster coherence between grades and cannot be completed within a regular school year with little to no modification.
The materials will require some modification to ensure there is content for the entire school year. The materials contain nine total units with the last unit being optional. Each unit contains between 11-23 lessons and begins with an optional Check-Your-Readiness Assessment and concludes with an End-of-Unit Assessment. Each lesson includes: A warm-up (5-10 minutes in length), one to three Exploration Activities (10-30 minutes in length), Lesson Synthesis (5-10 minutes in length), and Cool down (5 minutes in length). Lessons include “Are you ready for more?” extensions, but do not have specified time allotments explicitly stated in the materials. It is unclear whether the specified time allotted for the “Are you ready for more?” extension fits within the exploration activity it is paired with or if additional time would be needed beyond what is stated in the Full Lesson Plan. Two units include a Mid-Unit Assessment (one is optional).
There are approximately 25 weeks of instruction which includes 125 lesson days, including assessments.
Overview of Gateway 2
Rigor & the Mathematical Practices
The materials reviewed for Math Nation Grade 7 meet expectations for rigor and balance and practice-content connections. The materials reflect the balances in the Standards and help students develop conceptual understanding, procedural skill and fluency, and application. The materials make meaningful connections between the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).
Gateway 2
v1.5
Criterion 2.1: Rigor and Balance
Materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications.
The materials reviewed for Math Nation Grade 7 meet expectations for Rigor and Balance. The materials meet expectations for providing students opportunities in developing conceptual understanding, procedural skills, and application, and the materials also meet expectations for balancing the three aspects of Rigor.
Indicator 2A
Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
The materials reviewed for Math Nation Grade 7 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. Materials develop conceptual understanding throughout the grade level and materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade level. There are opportunities for students to develop their conceptual understanding in the various parts of each lesson: Warm-up, Exploration Activities, Lesson Synthesis, Cool Down, Check Your Understanding, and Practice Problems. Additionally, students’ conceptual understanding was assessed on Mid-Unit Assessments and End-of-Unit Assessments.
Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. Course Guide, “Concepts Develop from Concrete to Abstract, Mathematical concepts are introduced simply, concretely, and repeatedly, with complexity and abstraction developing over time. Students begin with concrete examples, and transition to diagrams and tables before relying exclusively on symbols to represent the mathematics they encounter.” Examples include:
Unit 2, Lesson 3, 2.3.3 Exploration Extension, students develop conceptual understanding by representing proportional relationships between quantities and explaining how to convert one quantity to another (7.RP.2). “1. How many square millimeters are there in a square centimeter? 2. How do you convert square centimeters to square millimeters? How do you convert the other way?”
Unit 4, Lesson 12, 4.12.1 Warm-Up, students develop conceptual understanding by using tape diagrams to solve problems involving parts of a whole within real-world contexts (7.RP.3). “What percentage of the car price is the tax? What percentage of the food cost is the tip? What percentage of the shirt cost is the discount?” A fraction tape diagram is provided for each question.
Unit 5, Lesson 1, Cool Down, students develop conceptual understanding as students place positive and negative numbers on a number line and then interpret these values within the context of different real-world scenarios (7.NS.1). “Here is a set of signed numbers: , , , , , , 1. Order the numbers from least to greatest. 2. If these numbers represent temperatures in degrees Celsius, which is the coldest? 3. If these numbers represent elevations in meters, which is the farthest away from sea level?”
The materials provide students with opportunities to engage independently with concrete and semi-concrete representations while developing conceptual understanding. Examples include:
Unit 2, Lesson 8, 2.8.5 Exploration Activity, students develop conceptual understanding as they identify proportional and non-proportional relationships represented in equations and tables (7.RP.1 and 7.RP.2). “Here are six different equations. , , , , , 1. Predict which of these equations represent a proportional relationship. 2. Complete each table using the equation that represents the relationship. 3. Do these results change your answer to the first question? Explain your reasoning. 4. What do the equations of the proportional relationships have in common?”
Unit 6, End-of-Unit Assessment (A), Question 6, students develop conceptual understanding by performing an error analysis on another student’s work and then correctly simplify the expression (7.EE.1).“Tyler is simplifying the expression . Here is his work: ; ; ; ; a. Tyler’s work is incorrect. Explain the error he made. b. Write an equivalent expression to that only has two terms.”
Unit 7, Lesson 8, 7.8.1 Warm-Up, students develop conceptual understanding by comparing and contrasting a set of triangles with given side lengths and a separate set of triangles with given angle measures (7.G.2).“Examine each set of triangles. What do you notice? What is the same about the triangles in the set? What is different?” Students are provided with two sets of triangles, the first set has six triangles, and the second set has four triangles.
Indicator 2B
Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency.
The materials reviewed for Math Nation Grade 7 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
There are opportunities for students to develop their procedural skills and fluency throughout the grade levels in each lesson, these opportunities can be found in the Warm-up, Exploration Activities, and Practice Problems. Examples include:
Unit 1, End-of-Unit Assessment (B), Question 2, students develop procedural skills and fluency as they solve problems involving scale drawings of geometric figures (7.RP.2a). “Rectangle A measures 8 inches by 2 inches. Rectangle B is a scaled copy of Rectangle A. Select all of the measurement pairs that could be the dimensions of Rectangle B. A. 40 inches by 10 inches B. 10 inches by 2.5 inches C. 9 inches by 3 inches D. 7 inches by 1 inch E. 6.4 inches by 1.6 inches”
Unit 5, Lesson 15, 5.15.2 Exploration Activity, students develop procedural skills and fluency as they solve equations involving negative numbers (7.EE.4a). “Match each equation to a value that makes it true by dragging the answer to the corresponding equation. Be prepared to explain your reasoning.” Equation options given: ; ; ; ; ; . Solution options give ; ; ; ; ; "
Unit 7, Lesson 2, 7.2.6 Practice Problems, Question 1, students develop procedural skills and fluency as they use facts about supplementary angles to solve simple equations for an unknown angle in a figure (7.G.5). “Angles A and C are supplementary. Find the measure of angle C.” An image of two angles is provided: Angle A is equal to 74°, and Angle C is unknown.
The materials provide opportunities for students to independently demonstrate procedural skills and fluency throughout the grade level. Examples include:
Unit 2, Lesson 9, 2.9.6 Practice Problems, Question 3, students calculate the resulting sides of a quadrilateral after it has a scale factor applied (7.G.1). “Quadrilateral A has side lengths 3, 4, 5, and 6. Quadrilateral B is a scaled copy of Quadrilateral A with a scale factor of 2. Select all of the following that are side lengths of Quadrilateral B.” Answer options are the following: 5, 6, 7, 8, and 9.
Unit 4, Lesson 9, Cool-down, students use proportional relationships to solve percent problems (7.RP.3). “Find each percentage of 75. Explain your reasoning. 1. What is 10% of 75? 2. What is 1% of 75? 3. What is 0.1% of 75? 4. What is 0.5% of 75?“
Unit 6, Mid-Unit Assessment (B), Problem 4, students independently demonstrate procedural skills and fluency by solving equations (7.EE.4a). “Solve each equation. 1. . .”
Indicator 2C
Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.
The materials reviewed for Math Nation Grade 7 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Materials provide opportunities for students to work with multiple routine and non-routine applications of mathematics throughout the grade level and independently. Applications of mathematics occur throughout a lesson in the exploration activities, practice problems, and assessments.
Materials include multiple routine and non-routine applications of mathematics throughout the grade level. Examples include:
Unit 2, Lesson 4, 2.4.7 Practice Problems, Question 4, students solve a routine word problem involving ratios of scale drawings (7.G.1). “A map of Colorado says that the scale is 1 inch to 20 miles or 1 to 1,267,200. Are these two ways of reporting the scale the same? Explain your reasoning.”
Unit 3, Lesson 6, 3.6.3 Exploration Activity, students estimate the area of a state through a strategy of their choosing (7.G.B). “Estimate the area of Nevada in square miles. Explain or show your reasoning.” An image of the state of Nevada is given with three measurements provided.
Unit 6, Mid-Unit Assessment (A), Question 2, students select situations that could represent a tape diagram (7.EE.4). “Select all the situations that can be represented by the tape diagram. A. Clare buys 4 bouquets, each with the same number of flowers. The florist puts an extra flower in each bouquet before she leaves. She leaves with a total of 99 flowers. B. Andre babysat 5 times this past month and earned the same amount each time. To thank him, the family gave him an extra $4 at the end of the month. Andre earned $99 from babysitting. C. A family of 5 drove to a concert. They paid $4 for parking, and all of their tickets were the same price. They paid $99 in total. D. 5 bags of marbles each contain 4 large marbles and the same number of small marbles. Altogether, the bags contain 99 marbles. E. Han is baking five batches of muffins. Each batch needs the same amount of sugar in the muffins, and each batch needs four extra teaspoons of sugar for the topping. Han uses 99 total teaspoons of sugar.”
Materials provide opportunities for students to independently demonstrate multiple routine and non-routine applications of mathematics throughout the grade level. Examples include:
Unit 2, Lesson 2, 2.2.5 Exploration Extension, students do research and use proportional relationships to determine if the value of a penny was worth more in 1982 (7.RP.2). “Pennies made before 1982 are 95% copper and weigh about 3.11 grams each. (Pennies made after that date are primarily made of zinc). Some people claim that the value of the copper in one of these pennies is greater than the face value of the penny. Find out how much copper is worth right now, and decide if this claim is true.”
Unit 5, Lesson 17, 5.17.4 Exploration Activity, students look at the difference in stock prices over a three-month time frame. (7.NS.3 and 7.EE.3). “Your teacher will give you a list of stocks. 1. Select a combination of stocks with a total value close to, but no more than, $100. 2. Using the new list, how did the total value of your selected stocks change?” Students are given a list of stock prices before answering Question 1. Then students receive a new list showing the changes in stock prices after three months before answering Question 2.
Unit 7, Lesson 16, Cool-Down, students solve a real-world problem by applying their understanding of area (7.G.6). “Andre is preparing for the school play and needs to paint the cardboard castle backdrop that measures feet by 6 feet. 1. How much cardboard does he need to paint? 2. If one bottle of paint covers an area of 40 square feet, how many bottles of paint does Andre need for his backdrop?”
Indicator 2D
The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.
The materials reviewed for Math Nation Grade 7 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade level.
All three aspects of rigor are present independently throughout each grade level. Examples include:
Unit 2, Lesson 2, 2.2.9 Check Your Understanding, Question 2, students solve a real-world application problem that requires them to work with proportions (7.RP.2a). “The table below shows the relationship between the amount of candy bought (in pounds) and the total cost of the candy (in dollars) at a movie theater. Which statement about the table is true? A. It does not have a constant of proportionality. B. The constant of proportionality is 0.36. C. The constant of proportionality is 2.75. D. The constant of proportionality is 4.”
Unit 4, Lesson 8, 4.8.7 Practice Problems, Question 3, students develop procedural skills and fluency by identifying the equation that matches a given situation (7.EE.2). “In a video game, Clare scored 50% more points than Tyler. If c is the number of points that Clare scored and is the number of points that Tyler scored, which equations are correct? Select all that apply.” Choices include: ; ; ; ;
Unit 6, Lesson 4, 6.4.2 Exploration Activity, Questions 1 and 2, students build conceptual understanding as they use tape diagrams to represent given situations (7.EE.A). “Draw a tape diagram to represent each situation. For some of the situations, you need to decide what to represent with a variable. 1. Diego has 7 packs of markers. Each pack has x markers in it. After Lin gives him 9 more markers, he has a total of 30 markers. 2. Elena is cutting a 30-foot piece of ribbon for a craft project. She cuts off 7 feet, and then cuts the remaining piece into 9 equal lengths of x feet each.”
Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study. Examples include:
Unit 2, Lesson 6, 2.6.2 Exploration Activity, students develop conceptual understanding, procedural skills and fluency, and application as they solve problems involving ticket sales for a concert (7.RP.2c). “A performer expects to sell 5,000 tickets for an upcoming concert. They want to make a total of $311,000 in sales from these tickets. 1. Assuming that all tickets have the same price, what is the price for one ticket? 2. How much will they make if they sell 7,000 tickets? 3. How much will they make if they sell 10,000 tickets? 50,000? 120,000? a million? x tickets? 4. If they make $379,420, how many tickets have they sold? 5. How many tickets will they have to sell to make $5,000,000?”
Unit 3, Lesson 4, 3.4.7 Practice Problems, Question 1, students develop procedural skills and fluency as they apply formulas to solve problems dealing with circumference (7.G.4). “Here is a picture of a Ferris wheel. It has a diameter of 80 meters. A. On the picture, draw and label a diameter. B. How far does a rider travel in one complete rotation around the Ferris wheel?”
Unit 7, Lesson 5, 7.5.4 Exploration Extension, students develop procedural and fluency and conceptual understanding as they find the exact measurement of three angles (7.G.5). “The diagram contains three squares. Three additional segments have been drawn that connect corners of the squares. We want to find the exact value of . 1. Use a protractor to measure the three angles. Use your measurements to conjecture about the value of . 2. Find the exact value of by reasoning about the diagram.”
Criterion 2.2: Math Practices
Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).
The materials reviewed for Math Nation Grade 7 meet expectations for practice-content connections. The materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).
Indicator 2E
Materials support the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for Math Nation Grade 7 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. Mathematical practices are identified in the Teacher Edition, Lesson Narrative, and Teacher Edition, Activities Narrative. Explanations are provided in terms of how the mathematical practices “come into play” within the lesson and activity narratives (Grade 7, Course Guide).
There is intentional development of MP1 to meet its full intent in connection to grade-level content. Throughout the grade level, students are required to analyze and make sense of problems, work to understand the information in problems, and use a variety of strategies to make sense of problems. Examples include:
Unit 3, Lesson 2, 3.2.1 Warm-Up, students make sense of a problem as they decide what a sketch for Figure C could look like. “Here are two figures. Figure C looks more like Figure A than like Figure B. Sketch what Figure C might look like. Explain your reasoning.” Given is a picture of Figure A and Figure B on a grind. Figure A is a square and Figure B is an oval. This problem attends to the full intent of MP1 as students need to make sense of a situation as they decide which characteristics of Figures A and B to use to satisfy the criteria for Figure C.
Unit 5, Lesson 14, 5.14.1 Warm-up, students look at a group of equations and remove the one(s) that does not belong. “Which equation does not belong? ; ; ; .” This Warm-up attends to the full intent of MP1 as students need to make sense of the equations to pick the one that does not belong.
Unit 7, Lesson 13, 7.13.1 Warm-up, students explain which solids are prisms, and draw a cross-section of the prism parallel to the base. “1. Which of these solids are prisms? Explain how you know. 2. For each of the prisms, what does the base look like? a. Shade one base in the picture. b. Draw a cross-section of the prism parallel to the base.” Students are given six shapes. This activity intentionally develops the full intent of MP1 as students need to make sense of the problem to identify which shapes would be prisms and draw the cross-sections
There is intentional development of MP2 to meet its full intent in connection to grade-level content. Throughout the grade level, students are required to represent situations symbolically, attend to the meaning of quantities, and understand relationships between problem scenarios and mathematical representations. Examples include:
Unit 1, Lesson 10, 1.10.2 Exploration Activity, students find the area of a triangle using a scale that they are assigned. “Here is a map showing a plot of land in the shape of a right triangle. 1. Your teacher will assign you a scale to use. On centimeter graph paper, make a scale drawing of the plot of land. Make sure to write your scale on your drawing. 2. What is the area of the triangle you drew? Explain or show your reasoning. 3. How many square meters are represented by 1 square centimeter in your drawing? 4. After everyone in your group is finished, order the scale drawings from largest to smallest. What do you notice about the scales when your drawings are placed in this order?” This problem attends to the full intent of MP2 as students need to reason abstractly and quantitatively as they order the scale drawings from largest to smallest and convert their scaling.
Unit 4, Lesson 2, 4.2.2 Exploration Activity, students use given information about a train to calculate the unit rate and answer questions about distance. “A train is traveling at a constant speed and goes 7.5 kilometers in 6 minutes. At that rate: 1. How far does the train go in 1 minute? 2. How far does the train go in 100 minutes?” This problem intentionally develops the full intent of MP2 as students need to reason about the meaning of quantities given the context of the problem.
Unit 6, Lesson 12, 6.12.1 Warm-Up, students select which expression(s) could represent a scenario. “An item costs x dollars and then a 20% discount is applied. Select all the expressions that could represent the price of the item after the discount. 1. 2. 3. 4. 5. 6. ” This Warm-up attends to the full intent of MP2 as students reason abstractly and quantitatively about the expression(s) that could be the price of the item after the discount.
Indicator 2F
Materials support the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for Math Nation Grade 7 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. The materials provide opportunities for students to construct viable arguments and critique the reasoning of others in whole class and small group settings (i.e. exploration activities) and independent work settings (i.e. practice problems and assessments).
There is intentional development of MP3 to meet its full intent in connection to grade-level content. Throughout the grade level, students are required to construct mathematical arguments by explaining/justifying their strategies and thinking, performing error analysis of provided student work/solutions, listening to the arguments of others and deciding if it makes sense, asking useful questions to better understand, and critiquing the reasoning of others. Examples include:
Unit 2, Lesson 7, 2.7.6 Practice Problems, Question 5, students use proportional relationships to determine whether either student has a correct argument.“Kiran and Mai are standing at one corner of a rectangular field of grass looking at the diagonally opposite corner. Kiran says that if the field were twice as long and twice as wide, then it would be twice the distance to the far corner. Mai says that it would be more than twice as far, since the diagonal is even longer than the side lengths. Do you agree with either of them?” This activity intentionally develops MP3 as students critique the reasoning of two students and decide who is correct.
Unit 3, Lesson 2, 3.2.4 Exploration Activity, students use their knowledge of circles to determine which parts of the circle three students measured. “Priya, Han, and Mai each measure one of the circular objects from earlier. Priya says that the bike wheel is 24 inches. Han says that the yo-yo trick is 24 inches. Mai says that the glow necklace is 24 inches. 1. Do you think that all these circles are the same size? 2. What part of the circle did each person measure? Explain your reasoning.” This activity intentionally develops MP3 as students critique the reasoning of three students while explaining their reasoning.
Unit 6, Lesson 2, 6.2.2 Exploration Activity, Question 2, students explain how a tape diagram represents a situation. “...With your group, decide who will go first. That person explains why the diagram represents the story. Work together to find any unknown amounts in the story. Then, switch roles for the second diagram and switch again for the third… 2. To thank her five volunteers, Mai gave each of them the same number of stickers. Then she gave them each two more stickers. Altogether, she gave them a total of 30 stickers.” Full Lesson Plan, Teacher Guidance: “Present an incorrect statement for the second situation that reflects a possible misunderstanding from the class. For example, ‘Mai gave 6 stickers to each of the volunteers because 30 divided by 5 is 6. So y is 6.’ Prompt students to identify the error, and then write a correct version. This helps students evaluate, and improve on, the written mathematical arguments of others…” This activity intentionally develops MP3 as students explain why the diagram represents the story they constructed and helps students build on their mathematical arguments.
Indicator 2G
Materials support the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for Math Nation Grade 7 meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. Mathematical practices are identified in the Teacher Edition, Lesson Narrative and Teacher Edition, Activities Narrative. Explanations are provided in terms of how the mathematical practices “come into play” within the lesson and activity narratives (Grade 7, Course Guide).
Examples where and how the materials use MPs 4 and/or 5 to enrich the mathematical content and demonstrate the full intent of the mathematical practices include:
Unit 2, Lesson 1, 2.1.1 Warm Up, students fill in a double number line and think of a situation that could be represented by the model. “Complete the double number line diagram with the missing numbers. What could each of the number lines represent? Invent a situation and label the diagram. Make sure your labels include appropriate units of measure.” This activity intentionally develops (MP4) as students use a representation to model a situation, and (MP5) as students have to use the double number line strategically in order to create an appropriate situation.
Unit 3, Lesson 6, 3.6.6 Practice Problems, Question 2, students use polygons to “cover” a map of the state of Virginia to approximate the area of the state. “A. Draw polygons on the map that could be used to approximate the area of Virginia. B. Which measurements would you need to know in order to calculate an approximation of the area of Virginia? Label the sides of the polygons whose measurements you would need. (Note: You aren't being asked to calculate anything.)” This activity intentionally develops (MP4) as students use the polygons to approximate area, and (MP5) as students have to choose the best polygons in order to have the closest estimated approximation.
Unit 6, Lesson 19, 6.19.2 Exploration Activity, students write equivalent expressions either in factored or expanded form. “In each row, write the equivalent expression. If you get stuck, use a diagram to organize your work. The first row is provided as an example. Diagrams are provided for the first three rows.” (Students are given a table with factored expressions in the left column and expanded expressions in the right column. First three rows of the factored (left) column include: , , blank row. First three rows of the expanded (right) column include: , blank row, .) This activity intentionally develops (MP4) as students write equivalent expressions in either expanded or factored form, and (MP5) as students create diagrams of their choice to assist them in correctly writing the expression.
Unit 7, Lesson 10, 7.10.6 Practice Problems, Question 1, students draw triangles to fit certain characteristics. “A triangle has sides of length 7 cm, 4 cm, and 5 cm. How many unique triangles can be drawn that fit that description? Explain or show your reasoning.” This activity intentionally develops (MP4) as students create models of the triangles that fit the criteria, and (MP5) as students are to use any tool or strategy to help them create the triangles.
Indicator 2H
Materials attend to the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for Math Nation Grade 7 meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. Mathematical practices are identified in the Teacher Edition, Lesson Narrative and Teacher Edition, Activities Narrative. Explanations are provided in terms of how the mathematical practices “come into play” within the lesson and activity narratives (Grade 7, Course Guide).
There is intentional development of MP6 to meet its full intent in connection to grade-level content and the instructional materials attend to the specialized language of mathematics. Students communicate using grade-level appropriate vocabulary and conventions and formulate clear explanations when engaging with course materials. Students must calculate accurately and efficiently, specify units of measure, and use and label tables and graphs appropriately when engaging with course materials. Teacher guidance very clearly develops the specialized language of mathematics as teachers are explicitly prompted when to introduce content-related vocabulary and use accurate definitions when communicating mathematically. Examples include:
Unit 1, Lesson 4, 1.4.1 Warm-Up, students name pairs of corresponding angles and confirm their prediction by measuring the angles. “Each of these polygons is a scaled copy of the others. 1. Name two pairs of corresponding angles. What can you say about the sizes of these angles? 2. Check your prediction by measuring at least one pair of corresponding angles using a protractor. Record your measurements to the nearest 5°.” This activity intentionally develops MP6 as students need to be precise in recording their measurements and attend to the specialized language of mathematics as students must understand the definition of corresponding angles.
Unit 2, Lesson 9, 2.9.6 Practice Problems, Question 1, students determine whether a scenario represents a proportional relationship and explain their reasoning. “For each situation, explain whether you think the relationship is proportional or not. Explain your reasoning. a. The weight of a stack of standard 8.5×11 copier paper vs. number of sheets of paper. b. The weight of a stack of different-sized books vs. the number of books in the stack.” This activity attends to the full intent of MP6 and the specialized language of mathematics as students have to explain their choice in the context of proportionality.
Unit 2, End-of-Unit Assessment (A), Problem 7, students write an equation for a situation representing a proportional relationship and explain the context of a point based on the situation. “A recipe for salad dressing calls for 3 tablespoons of oil for every 2 tablespoons of vinegar. The line represents the relationship between the amount of oil and the amount of vinegar needed to make salad dressing according to this recipe. The point (1, 1.5) is on the line. 1. Label the axes appropriately. 2. Write an equation that represents the proportional relationship between oil and vinegar. Indicate the meaning of each variable. 3. Explain the meaning of the point (1, 1.5) in terms of the situation.” This activity attends to the full intent of MP6 and the specialized language of mathematics as students formulate clear explanations, label graphs appropriately, and specify units of measure.
Unit 7, Lesson 3, 7.3.6 Practice Problems, Question 3, students use what they know about supplementary and complementary angles to see if a given angle pair relationship is possible. “If two angles are both vertical and supplementary, can we determine the angles? Is it possible to be both vertical and complementary? If so, can you determine the angles? Explain how you know.” This activity attends to the full intent of MP6 and the specialized language of mathematics as students are required to use definitions accurately and mathematical language to explain their answers.
Indicator 2I
Materials support the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for Math Nation Grade 7 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards. Mathematical practices are identified in the Teacher Edition, Lesson Narrative and Teacher Edition, Activities Narrative. Explanations are provided in terms of how the mathematical practices “come into play” within the lesson and activity narratives (Grade 7, Course Guide).
There is intentional development of MP7 to meet its full intent in connection to grade-level content. Materials provide opportunities for students to look for patterns or structures to make generalizations and solve problems, look for and explain the structure of mathematical representations, and look at and decompose “complicated” into “simpler.” Examples include:
Unit 3, Lesson 3, 3.3.2 Exploration Activity, students measure the diameter and circumference of circular objects, plot these values, and identify a relationship between the two. “ Your teacher will give you several circular objects. 1. Explore the applet to find the diameter and the circumference of three circular objects to the nearest tenth of a unit. Record your measurements in the table. 2. Plot the diameter and circumference values from the table on the coordinate plane. What do you notice? 3. Plot the points from two other groups on the same coordinate plane. Do you see the same pattern that you noticed earlier?” This activity attends to the full intent of MP7 as students make use of the structure of the graph to look for patterns in order to answer the question.
Unit 5, Lesson 5, 5.5.3 Exploration Activity, students match expressions and number line diagrams and then add and subtract numbers to see that subtracting a number is the same as adding the opposite. “1. Match each diagram to one of these expressions: , , , . (Students are given four number line diagrams to match.) 2. Which expressions in the first question have the same value? What do you notice? 3. Complete each of these tables. (Students find the value corresponding to each of the following expressions for one of the tables: , , , , , .) What do you notice?” This activity attends to the full intent of MP7 as students look for structures to make some general claims of add and subtracting numbers with opposites.
Unit 6, Lesson 19, 6.19.1 Warm-Up, students use the distributive property to decompose and compose different expressions in order to evaluate. “Find the value of each expression mentally. , , , .” This warm-up attends to the full intent of MP7 as students make use of the structure of the layout of the expressions in order to solve them mentally.
There is intentional development of MP8 to meet its full intent in connection to grade-level content.
Materials provide opportunities for students to notice repeated calculations to understand algorithms and make generalizations or create shortcuts, evaluate the reasonableness of their answers and their thinking, and create, describe, or explain a general method/formula/process/algorithm. Examples include:
Unit 3, Lesson 8, 3.8.7 Practice Problems, Question 1, students examine a circle and its rearranged parts to explain the area formula for a circle. “The picture shows a circle divided into 8 equal wedges which are rearranged. The radius of the circle is r and its circumference is 2πr. How does the picture help to explain why the area of the circle is 𝜋𝑟2?”This activity attends to the full intent of MP8, look for and express regularity in repeated reasoning as students repeatedly use the information given about the radius and circumference to explain how the formula for area of a circle works.
Unit 4, Lesson 8, 4.8.1 Warm-Up, students explain a process for applying a percent increase or decrease. “How do you get from one number to the next using multiplication or division? From 100 to 106? From 100 to 90? From 90 to 100? From 106 to 100?” This activity attends to the full intent of MP8, look for and express regularity in repeated reasoning as students use repeated calculations of multiplication and division to generalize how percent increase and decrease works.
Unit 8, Lesson 4, 8.4.3 Exploration Activity, students consider the reasonableness of certain outcomes in simulation scenarios. “1. For each situation, do you think the result is surprising or not? Is it possible? Be prepared to explain your reasoning. a. You flip the coin once, and it lands heads up. b. You flip the coin twice, and it lands heads up both times. c. You flip the coin 100 times, and it lands heads up all 100 times. 2. If you flip the coin 100 times, how many times would you expect the coin to land heads up? Explain your reasoning. 3. If you flip the coin 100 times, what are some other results that would not be surprising? 4. You’ve flipped the coin 3 times, and it has come up heads once. The cumulative fraction of heads is currently . If you flip the coin one more time, will it land heads up to make the cumulative fraction ?” This activity attends to the full intent of MP8, look for and express regularity in repeated reasoning, as students think about the repeated coin flips and what would be surprising and not surprising if they were to flip it 100 times.
Overview of Gateway 3
Usability
The materials reviewed for Math Nation Grade 7 meet expectations for Usability. The materials meet expectations for Criterion 1, Teacher Supports, Criterion 2, Assessment, and Criterion 3, Student Supports.
Gateway 3
v1.5
Criterion 3.1: Teacher Supports
The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.
The materials reviewed for Math Nation Grade 7 meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the materials, include standards correlation information that explains the role of the standards in the context of the overall series, provide explanations of the instructional approaches of the program and identification of the research-based strategies, and provide a comprehensive list of supplies needed to support instructional activities. The materials partially contain adult-level explanations and examples of concepts beyond the current course so that teachers can improve their own knowledge of the subject.
Indicator 3A
Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.
The materials reviewed for Math Nation Grade 7 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students to guide their mathematical development.
Examples of where and how the materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials include:
Course Overview: A Course Overview (Unit 0) is found at the beginning of each course. Within each Course Overview there is a Course Narrative, which contains a summary of the mathematical content contained in each course, and a Course Guide. The Course Guide contains the following sections: Introduction, About These Materials, How to Use These Materials, Assessment Overview, Scope and Sequence, Required Resources, Corrections, and Cool-Down Guidance. Each of these sections contains specific guidance for teachers on implementing lesson instruction. For example, in the About These Materials section, teachers can find an outline of and detailed information about the components of a typical lesson, including Warm-Up, Classroom Activities, Lesson Synthesis, and Cool-Down. The How to Use These Materials section contains guidance about the three phases of classroom activities (Launch-Work-Synthesize) and utilizing instructional routines. In the Scope and Sequence section, teachers will find a Pacing Guide which contains time estimates for coverage of each of the units.
Teacher Edition: There is a Teacher Edition section for each unit that contains a unit introduction, unit assessments, and unit-level downloads. The Unit Introduction contains a summary of the mathematical content to be found in the unit. The Assessment component contains downloads for multiple types of assessments (Check Your Readiness, Mid-Unit, and End-of-Unit Assessment). Unit Level Downloads include: Student Task Statements Cool-downs, Practice Problems, Blackline Masters, and My Reflections all of which provide support for teacher planning. Each lesson has a Teacher Edition component that contains guidance for Lesson Preparation, Cool-down Guidance, and a Lesson Narrative. The Lesson Preparation component includes a Teacher Prep Video, Learning Goal(s), Required Material(s), and Full Lesson Plan downloads. Cool-down Guidance provides teachers with guidance on what to look for or emphasize over the next several lessons to support students in advancing their current understanding. The Lesson Narrative provides specific guidance about how students can work with the lesson activities.
Full Lesson Plan: Within each Teacher Edition lesson component, teachers can find a Full Lesson Plan that contains lesson learning goals and targets, a lesson narrative, and specific guidance for implementing each of the lesson activities. The Lesson Narrative contains the purpose of the lesson, standards and mathematical practices alignments, specific instructional routines, and required materials related to the lesson. Teachers are given guidance for implementing these routines as a way of introducing students to the learning targets. There is also teacher guidance for launching lesson activities, such as suggestions for grouping students, working with a partner, or whole group discussion. The planning section identifies possible student errors and misconceptions that could occur. There is also guidance on how to support English Language Learners and Students with Disabilities.
Materials include sufficient and useful annotations and suggestions that are presented within the context of specific learning objectives. Preparation and lesson narratives within the Course Guide, Lesson Plans, Lesson Narratives, Overviews, and Warm-up provide useful annotations. Examples include:
Course Guide, Assessments Overview, “Pre-Unit Diagnostic Assessments At the start of each unit is a pre-unit diagnostic assessment. These assessments vary in length. Most of the problems in the pre-unit diagnostic assessment address prerequisite concepts and skills for the unit. Teachers can use these problems to identify students with particular below-grade needs, or topics to carefully address during the unit. Teachers are encouraged to address below-grade skills while continuing to work through the on-grade tasks and concepts of each unit, instead of abandoning the current work in favor of material that only addresses below-grade skills…What if a large number of students can’t do the same pre-unit assessment problem? Look for opportunities within the upcoming unit where the target skill could be addressed in context…What if all students do really well on the pre-unit diagnostic assessment? Great! That means they are ready for the work ahead, and special attention likely doesn’t need to be paid to below-grade skills.”
Unit 1, Lesson 2, Full Lesson Plan, 1.2.3 Exploration Activity, “Anticipated Misconceptions Students may think that Triangle F is a scaled copy because just like the 3-4-5 triangle, the slides are also three consecutive whole numbers. Point out that corresponding angles are not equal.”
Unit 2, Lesson 7, Cool-down Guidance, “If students struggle with variable placement in the cool-down, plan to focus on how to use the equation y = kx when opportunities arise over the next several lessons. For example, in activity 1 of Lesson 9, have students share their thinking about using the equation to show a proportional relationship.”
Indicator 3B
Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.
The materials reviewed for Math Nation Grade 7 partially meet expectations for containing adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current courses that teachers can improve their own knowledge of the subject. The materials do not contain adult-level explanations and examples of concepts beyond the current grade so that teachers can improve their own knowledge of the subject.
Each lesson includes a Teacher Prep Video and a Full Lesson Plan resource that contains adult-level explanations and examples of the more complex grade-level concepts. Examples include:
A 5-10 minute Teacher Prep Video that provides an overview of the lesson, including content and pedagogy tips is provided for each lesson. During the video a Math Nation Instructor goes through the lesson, highlighting grade-level concepts and showing examples, while also giving suggestions that teachers can use during the lesson to support students.
Unit 2, Lesson 6, Full Lesson Plan, Lesson Narrative, “In the previous two lessons students learned to represent proportional relationships with equations of the form 𝑦 = 𝑘𝑥. In this lesson they continue to write equations, and they begin to see situations where using the equation is a more efficient way of solving problems than other methods they have been using, such as tables and equivalent ratios. The activities introduce new contexts and, for the first time, do not provide tables; students who still need tables should be given a chance to realize that and create tables for themselves. The activities are intended to motivate the usefulness of representing proportional relationships with equations, while at the same time providing some scaffolding for finding the equations.”
Unit 8, Lesson 8, Full Lesson Plan, 8.8.2 Exploration Activity, Classroom Activity, “In this activity, students learn 3 different methods for writing the sample spaces of multi-step experiments and explore their use in a few different situations. Since the calculated probability of an event depends on the number of outcomes in the sample space, it is important to be able to find this value in an efficient way…”
Indicator 3C
Materials include standards correlation information that explains the role of the standards in the context of the overall series.
The materials reviewed for Math Nation Grade 7 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.
The Course Guide, About These Materials sections, states the following note about standards alignment, “There are three kinds of alignments to standards in these materials: building on, addressing, and building towards. Oftentimes a particular standard requires weeks, months, or years to achieve, in many cases building on work in prior grade-levels. When an activity reflects the work of prior grades but is being used to bridge to a grade-level standard, alignments are indicated as ‘building on.’ When an activity is laying the foundation for a grade-level standard but has not yet reached the level of the standard, the alignment is indicated as ‘building towards.’ When a task is focused on the grade-level work, the alignment is indicated as ‘addressing.’” All lessons in the materials have this correlation information. An example:
Unit 7, Lesson 1, Full Lesson Plan, Lesson Standards Alignment, Building on 4.MD.6, 4.MD.7; Addressing 7.G.A, 7.G.B; Building Towards 7.G.B, 7.G.5.
Explanations of the role of the specific grade-level mathematics in the context of the series can be found throughout the materials including but not limited to the Course Guide, Scope and Sequence section, the Course Overview, Unit Introduction, Lesson Narrative, and Full Lesson Plan. Examples include:
Course Guide, Scope and Sequence, Unit 1: Scale Drawing, “Work with scale drawings in grade 7 draws on earlier work with geometry and geometric measurement. Students began to learn about two- and three-dimensional shapes in kindergarten, and continued this work in grades 1 and 2, composing, decomposing, and identifying shapes. Students' work with geometric measurement began with length and continued with area. Students learned to "structure two-dimensional space," that is, to see a rectangle with whole-number side lengths as an array of unit squares, or rows or columns of unit squares…This provides geometric preparation for grade 7 work on proportional relationships as well as grade 8 work on dilations and similarity. Students begin by looking at copies of a picture, some of which are to scale, and some of which are not. They use their own words to describe what differentiates scaled and non-scaled copies of a picture…In grade 8, students will extend their knowledge of scaled copies when they study translations, rotations, reflections, and dilations.”
Course Guide, Scope and Sequence, Unit 2: Introducing Proportional Relationships, “In this unit, students develop the idea of a proportional relationship out of the grade 6 idea of equivalent ratios. Proportional relationships prepare the way for the study of linear functions in grade 8…In grades 6-8, students write rates without abbreviated units, for example as ‘3 miles per hour’ or ‘3 miles in every 1 hour.’ Use of notation for derived units such as mi/hr waits for high school-except for the special cases of area and volume. Students have worked with area since grade 3 and volume since grade 5...”
Indicator 3D
Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.
The materials reviewed for Math Nation Grade 7 provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.
Unit Overview videos, available through the Math Nation website, and unit lesson summary videos, links to Vimeo and YouTube, outline the mathematics that students will be learning in that unit. Family Support materials are available for each unit (available digitally and can be printed; available in English and Spanish). These provide a brief overview of some of the main concepts taught within each unit followed by tasks, with worked solutions, for parents/caregivers to work on with their student. Examples include:
Student Edition, Unit 1, Family Support: Scale Drawings, “Here are the video lesson summaries for Grade 7, Unit 1 Scale Drawings. Each video highlights key concepts and vocabulary that students learn across one or more lessons in the unit. The content of these video lesson summaries is based on the written Lesson Summaries found at the end of lessons in the curriculum. The goal of these videos is to support students in reviewing and checking their understanding of important concepts and vocabulary. Here are some possible ways families can use these videos:
Keep informed on concepts and vocabulary students are learning about in class.
Watch with their student and pause at key points to predict what comes next or think up other examples of vocabulary terms (the bolded words).
Consider following the Connecting to Other Units links to review the math concepts that led up to this unit or to preview where the concepts in this unit lead to in future units.”
Four videos are provided (via Vimeo or Youtube) that take families through the lessons in the unit.
Student Edition, Unit 4, Family Support: Proportional Relationships and Percentages, Percent Increase and Decrease, “This week, your student is learning to describe increases and decreases as a percentage of the starting amount. For example, two different school clubs can gain the same number of students, but have different percent increases…”
Unit 6, Family Materials, Representing Situations of the Form px+q=r and px+q=r, Lessons 1-6, “In this unit, your student will be representing situations with diagrams and equations. There are two main categories of situations with associated diagrams and equations… Here is a task to try with your student: 1. Draw a diagram to represent the equation 3x+6=39. 2. Draw a diagram to represent the equation 39=3(y+6). 3. Decide which story goes with which equation-diagram pair: Three friends went cherry picking and each picked the same amount of cherries, in pounds. Before they left the cherry farm, someone gave them an additional 6 pounds of cherries. Altogether, they had 39 pounds of cherries. One of the friends made three cherry tarts. She put the same number of cherries in each tart, and then added 6 more cherries to each tart. Altogether, the three tarts contained 39 cherries.” Solutions with explanations are provided for families.
Indicator 3E
Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.
The materials reviewed for Math Nation Grade 7 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies. Instructional approaches of the program and identification of the research-based strategies can be found throughout the materials, but particularly in the Course Guide, About These Materials, and How to Use These Materials sections.
The About These Materials section states the following about the instructional approach of the program, “What is a Problem Based Curriculum? In a problem-based curriculum, students work on carefully crafted and sequenced mathematics problems during most of the instructional time. Teachers help students understand the problems and guide discussions to ensure the mathematical takeaways are clear to all. Some concepts and procedures follow from definitions and prior knowledge so students can, with appropriately constructed problems, see this for themselves. In the process, they explain their ideas and reasoning and learn to communicate mathematical ideas. The goal is to give students just enough background and tools to solve initial problems successfully, and then set them to increasingly sophisticated problems as their expertise increases. However, not all mathematical knowledge can be discovered, so direct instruction is sometimes appropriate. A problem-based approach may require a significant realignment of the way math class is understood by all stakeholders in a student's education. Families, students, teachers, and administrators may need support making this shift. The materials are designed with these supports in mind. Family materials are included for each unit and assist with the big mathematical ideas within the unit. Lesson and activity narratives, Anticipated Misconceptions, and instructional supports provide professional learning opportunities for teachers and leaders. The value of a problem-based approach is that students spend most of their time in math class doing mathematics: making sense of problems, estimating, trying different approaches, selecting and using appropriate tools, evaluating the reasonableness of their answers, interpreting the significance of their answers, noticing patterns and making generalizations, explaining their reasoning verbally and in writing, listening to the reasoning of others, and building their understanding. Mathematics is not a spectator sport.”
Examples of materials including and referencing research-based strategies include:
“The Five Practices Selected activities are structured using Five Practices for Orchestrating Productive Mathematical Discussions (Smith & Stein, 2011), also described in Principles to Actions: Ensuring Mathematical Success for All (NCTM, 2014), and Intentional Talk: How to Structure and Lead Productive Mathematical Discussions (Kazemi & Hintz, 2014). These activities include a presentation of a task or problem (may be print or other media) where student approaches are anticipated ahead of time. Students first engage in independent think-time followed by partner or small-group work on the problem…”
“Supporting English Language Learners This curriculum builds on foundational principles for supporting language development for all students. This section aims to provide guidance to help teachers recognize and support students' language development in the context of mathematical sense-making. Embedded within the curriculum are instructional supports and practices to help teachers address the specialized academic language demands in math when planning and delivering lessons, including the demands of reading, writing, speaking, listening, conversing, and representing in math (Aguirre & Bunch, 2012).”
“Instructional Routines … Some of the instructional routines, known as Mathematical Language Routines (MLR), were developed by the Stanford University UL/SCALE team…”
Within the Course Guide, How to Use These Materials, a Reference section is included.
Indicator 3F
Materials provide a comprehensive list of supplies needed to support instructional activities.
The materials reviewed for Math Nation Grade 7 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. Comprehensive lists of supplies needed to support the instructional activities can be found in Course Guides (Required Resources), Teacher Editions, for each lesson, under Lesson Preparation (Required Material(s)), and in Teacher Guides for specific lessons. Examples include:
Unit 1, Lesson 7, Lesson Preparation, Required Materials: “Blackline master for Activity 7.2, Cool-down, copies of blackline master, geometry toolkits (tracing paper, graph paper, colored pencils, scissors, and an index card)”
Unit 3, Lesson 3, Lesson Preparation, Required Materials: “Cool-down, cylindrical household items, empty toilet paper roll, measuring tapes”
Unit 8, Lesson 6, Lesson Preparation, Required Materials: “Blackline master for Activity 6.2, Cool-down, number cubes, paper bags, paper clips, pre-printed slips, cut from copies of the blackline master”
Indicator 3G
This is not an assessed indicator in Mathematics.
Indicator 3H
This is not an assessed indicator in Mathematics.
Criterion 3.2: Assessment
The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.
The materials reviewed for Math Nation Grade 7 meet expectations for Assessment. The materials include an assessment system that provides multiple opportunities throughout the courses to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up and provide assessments that include opportunities for students to demonstrate the full intent of course-level standards and practices. The materials partially include assessment information that indicates which standards and practices are assessed.
Indicator 3I
Assessment information is included in the materials to indicate which standards are assessed.
The materials reviewed for Math Nation Grade 7 partially meet expectations for having assessment information included in the materials to indicate which standards are assessed.
The materials consistently identify the standards assessed for each of the problems in each of the following formal assessments: Mid-Unit Assessment, End-of-Unit Assessment, and Cool-Downs. All assessments are available as Word or PDF downloads in English or Spanish versions. Materials do not identify the practices assessed for any of the formal assessments.
Examples of how the materials consistently identify the standards for assessment include:
Unit 3, End-of-Unit Assessment (A), Question 1, “A circle has radius 50 cm. Which of these is closest to its area? A. 157 cm B. 314 cm C. 7,854 cm D. 15,708 cm” Aligned Standard: 7.G.4.
Unit 6, Mid-Unit Assessment (B), Question 6, “A church is packing Thanksgiving baskets. Each basket weighs 30 pounds. Here are two situations. For each situation, write an equation to represent the situation. If you get stuck, consider drawing a diagram. 1. Each basket contains 3 identical bags of stuffing and a 6-pound bag of rice. 2. Each basket contains 3 boxes. Each box contains a 6-pound bag of rice and a bag of stuffing. The bags of stuffing are all identical.” Aligned Standard: 7.EE.4a.
Unit 7, Lesson 11, Cool-down, “Here is a pyramid with a base that is a pentagon with all sides the same length. 1. Describe the cross section that will result if the pyramid is sliced: a. horizontally (parallel to the base). b. vertically through the top vertex (perpendicular to the base). 2. Describe another way you could slice the pyramid that would result in a different cross-section.” The Full Lesson Plan identifies the standard alignment as 7.G.3.
Indicator 3J
Assessment system provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
The materials reviewed for Math Nation Grade 7 meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students’ learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
Student sample responses are provided for all assessments. Rubrics are provided for scoring restricted constructed response and extended response questions on the Mid-Unit Assessments and End-of-Unit Assessments. Mid-Unit Assessments and End-of-Unit Assessments include notes that provide guidance for teachers to interpret student understanding and make sense of students’ correct/incorrect responses.
Suggestions to teachers for following up with students are provided throughout the materials via the Mid-Unit, and End-of-Unit Teacher Guides, and each lesson provides a Cool-down Guidance that details how to support student learning.
Examples of the assessment system providing multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance include:
Course Guide, Assessments Overview states the following: “Rubrics for Evaluating Students Answers Restricted constructed response and extended response items have rubrics that can be used to evaluate the level of student responses.
Restricted Constructed Response
Tier 1 response: Work is complete and correct.
Tier 2 response: Work shows General conceptual understanding and mastery, with some errors.
Tier 3 response: Significant errors in work demonstrate lack of conceptual understanding or mastery. Two or more error types from Tier 2 response can be given as the reason for a Tier 3 response instead of listing combinations.
Extended Response
Tier 1 response: Work is complete and correct, with complete explanation or justification.
Tier 2 response: Work shows good conceptual understanding and mastery, with either minor errors or correct work with insufficient explanation or justification.
Tier 3 response: Work shows a developing but incomplete conceptual understanding, with significant errors.
Tier 4 response: Work includes major errors or omissions that demonstrate a lack of conceptual understanding and mastery.”
Unit 6, Mid-Unit Assessment (A), Question 6, “A food pantry is making packages. Each package weighs 64 pounds. Here are two situations. For each situation, write an equation to represent the situation. If you get stuck, consider drawing a diagram. 1. Each package contains 4 boxes. Each box contains a 7-pound bag of beans and a bag of rice. The bags of rice are all identical. 2. Each package contains 4 identical bags of rice and a 7-pound bag of beans. Solution Sample response: 1. 4(x +7) = 64 (diagram shows 4 equal parts of x+7 with a total of 64) 2. 4x+7 = 64 (diagram shows 4 equal boxes labeled x and one box labeled 7, with a total of 64) Minimal Tier 1 response: Work is complete and correct. Sample: 1. 4(x +7) = 64 (diagram shows 4 equal parts of x+7 with a total of 64) 2. 4x+7 = 64 (diagram shows 4 equal boxes labeled x and one box labeled 7, with a total of 64) Tier 2 response: Work shows general conceptual understanding and mastery, with some errors. Sample errors: one of the equations has been written correctly with errors in the other, diagram for one situation is drawn correctly but the other has errors. Tier 3 response: Significant errors in work demonstrate lack of conceptual understanding or mastery. Sample errors: both equations have been written incorrectly or both diagrams have been drawn incorrectly, both responses are flawed in some way.”
Examples of the assessment system providing multiple opportunities to determine students' learning and suggestions to teachers for following up with students include:
Course Guide, Cool-Down Guidance states the following: “Each cool-down is placed into one of three support levels: 1. More chances. This is often associated with lessons that are exploring or playing with a new concept. Unfinished learning for these cool-downs is expected and no modifications need to be made for upcoming lessons. 2. Points to emphasize. For cool-downs on this level of support, no major accommodations should be made, but it will help to emphasize related content in upcoming lessons. Monitor the student who have unfinished learning throughout the next few lessons and work with them to become more familiar with parts of the lesson associated with this cool-down. Perhaps add a few minutes to the following class to address related practice problems, directly discuss the cool-down in the launch or synthesis of the warm-up of the next lesson, or strategically select students to share their thinking about related topics in the upcoming lessons. 3. Press pause. This advises a small pause before continuing movement through the curriculum to make sure the base is strong. Often, upcoming lessons rely on student understanding of the ideas from this cool-down, so some time should be used to address any unfinished learning before moving on to the next lesson.”
Unit 3, Lesson 6, Cool-down Guidance, “Support Level 2. Points to emphasize. Notes If students struggle with estimating the area of irregular shapes in the cool-down, plan to focus on this skill when opportunities arise over the next several lessons. For example, in Activity 1 of Lesson 7, make sure to invite multiple students to share their thinking about how they estimated the areas of the shapes.”
Unit 7, End-of-Unit Assessment (B), Question 1, “Students failing to select A, or students selecting E, may need more work on approximate angle measures and calculating their sums. Students failing to select C, or students selecting B, need a review of the triangle inequality: 6, 12, and 13 is fine, but 11 cm is too long to be the third side of a triangle containing side lengths of 3 cm and 7 cm. Students failing to select D may have said so because they aren’t given the specific locations of the sides and angles, but this is a reason for more than one triangle to exist with the given conditions.”
Indicator 3K
Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.
The materials reviewed for Math Nation Grade 7 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of the course-level standards and practices across the series.
All assessments regularly demonstrate the full intent of grade-level content and practice standards through a variety of item types such as multiple choice, short answer, extended response prompts, graphing, mistake analysis, and constructed response items. Assessments are to be downloaded as Word documents or PDFs and designed to be printed and administered in-classroom. Examples Include:
Unit 2, Lesson 2, Cool-down, demonstrates the full intent of 7RP.2 and MP2. “When you mix two colors of paint in equivalent ratios, the resulting color is always the same. Complete the table as you answer the questions. (Table is provided) 1. How many cups of yellow paint should you mix with 1 cup of blue paint to make the same shade of green? Explain or show your reasoning. 2. Make up a new pair of numbers that would make the same shade of green. Explain how you know they would make the same shade of green. 3. What is the proportional relationship represented by this table? 4. What is the constant of proportionality? What does it represent?”
Unit 3, End-of-Unit Assessment (A), Question 5, demonstrates the full intent of 7.G.4 and MP1. “For each quantity, decide whether circumference or area would be needed to calculate it. Explain or show your reasoning. 1. The distance around a circular track. 2. The total number of equally-sized tiles on a circular floor. 3. The amount of oil it takes to cover the bottom of a frying pan. 4. The distance your car will go with one turn of the wheels”
Unit 4, End-of-Unit Assessment (B), Question 7, demonstrates the full intent of 7.RP.3 and 7.EE.3. “Jada’s sister works in a furniture store. 1. Jada’s sister earns $15 per hour. The store offers her a raise—a 9% increase per hour. After the raise, how much will Jada’s sister make per hour? 2. The store bought a table for $200, and sold it for $350. What percentage was the markup? 3. Jada’s sister earns a commission. She makes 3.5% of the amount she sells. Last week, she sold $7,000 worth of furniture. How much was her commission?”
Indicator 3L
Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.
The materials reviewed for Math Nation Grade 7 do not provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.
Assessments are available in English and Spanish and are designed to be downloaded as Word documents or PDFs and administered in class. There is no modification or guidance given to teachers within the materials on how to administer the assessment with accommodations.
Criterion 3.3: Student Supports
The program includes materials designed for each student’s regular and active participation in grade-level/grade-band/series content.
The materials reviewed for Math Nation Grade 7 meet expectations for Student Supports. The materials provide: strategies and supports for students in special populations and for students who read, write, and/or speak in a language other than English to support their regular and active participation in learning grade-level mathematics; multiple extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity; and manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
Indicator 3M
Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.
The materials reviewed for Math Nation Grade 7 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.
Course Guide, How to Use These Materials, Supporting Students with Disabilities sections states the following: “The philosophical stance that guided the creation of these materials is the belief that with proper structures, accommodations, and supports, all children can learn mathematics. Lessons are designed to maximize access for all students, and include additional suggested supports to meet the varying needs of individual students. While the suggested supports are designed for students with disabilities, they are also appropriate for many children who struggle to access rigorous, grade-level content. Teachers should use their professional judgment about which supports to use and when, based on their knowledge of the individual needs of students in their classroom.” Suggested supports are identified for teachers in the Full Lesson Plan to support learners of all levels. Lesson and activity-level supports, identified as “Support for Students with Disabilities,” are aligned to an area of cognitive functioning and are paired with a suggested strategy aimed to increase access and eliminate barriers. Supports are classified under the following categories: eliminate barriers, processing time, peer tutors, assistive technology, visual aids, graphic organizers, and brain breaks. Examples include:
Assistive Technology: “Assistive technology can be a vital tool for students with learning disabilities, visual spatial needs, sensory integration, and students with autism. Assistive technology supports suggested in the materials are designed to either enhance or support learning, or to bypass unnecessary barriers. Physical manipulatives help students make connections between concrete ideas and abstract representations. Often, students with disabilities benefit from hands-on activities, which allow them to make sense of the problem at hand and communicate their own mathematical ideas and solutions.” Unit 1, Lesson 9, Full Lesson Plan, 1.9.2 Exploration Activity, “Support for Students with Disabilities…Fine Motor Skills: Assistive Technology. Provide access to the digital version of this activity…”
Eliminate Barriers: “Eliminate any barriers that students may encounter that prevent them from engaging with the important mathematical work of a lesson. This requires flexibility and attention to areas such as the physical environment of the classroom, access to tools, organization of lesson activities, and means of communication.” Unit 4, Lesson 13, Full Lesson Plan, 4.13.2 Exploration Activity, “Support for Students with Disabilities…Conceptual Processing: Eliminate Barriers. Allow students to use calculators to ensure inclusive participation in the activity”.
Processing Time: “Increased time engaged in thinking and learning leads to mastery of grade level content for all students, including students with disabilities. Frequent switching between topics creates confusion and does not allow for content to deeply embed in the mind of the learner. Mathematical ideas and representations are carefully introduced in the materials in a gradual, purposeful way to establish a base of conceptual understanding. Some students may need additional time, which should be provided as required.” Unit 2, Lesson 7, Full Lesson Plan, 2.7.3 Exploration Activity, “Support for Students with Disabilities Conceptual Processing: Processing Time. Check in with individual students, as needed, to assess for comprehension of the concept of ‘constant pace.’”
There are several accessibility options (accessed via the wrench icon in the lower left-hand corner of the screen) available to help students navigate the materials. Examples include:
Tools Menu allow students to change the language, and access a Demos Scientific and Graphing Calculator.
Accessibility Menu allows students to change the language, page zoom, font style, background and font color, and enable/disable the following features: text highlighter, notes, screen reader support.
UserWay, allows students to adjust the following: Change contrast (4 settings), Highlight links, Enlarge text (5 settings), Adjust text spacing (4 settings), Hide images, Dyslexia Friendly, Enlarge the cursor, show a reading mask, show a reading line, Adjust line height (4 settings), Text align (5 settings), Saturation (4 settings).
Additionally, differentiated videos explaining course content - varying from review to in-depth levels of explanation - are resources available for each lesson to support students.
Indicator 3N
Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.
The materials reviewed for Math Nation Grade 7 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.
Course Guide, How to Use These Materials, Are You Ready For More? section states the following: “Select classroom activities include an opportunity for differentiation for students ready for more of a challenge. Every extension problem is made available to all students with the heading ‘Are You Ready for More?’ These problems go deeper into grade-level mathematics and often make connections between the topic at hand and other concepts at grade level or that are outside of the standard K-12 curriculum. They are not routine or procedural, and intended to be used on an opt-in basis by students if they finish the main class activity early or want to do more mathematics on their own. It is not expected that an entire class engages in Are You Ready for More? problems and it is not expected that any student works on all of them. Are You Ready for More? problems may also be good fodder for a Problem of the Week or similar structure.” If individual students would complete these optional activities, then they might be doing more assignments than their classmates.
Examples of opportunities for advanced students to investigate grade-level mathematics content at a higher level of complexity include:
Unit 3, Lesson 8, 3.8.5 Exploration Extension: Are you Ready for More?, “A box contains 20 square tiles that are 2 inches on each side. How many boxes of tiles will Elena need to tile the table?” This is a direct extension of the 3.8.4 Exploration Activity in which students calculate the area of a circular table with a given diameter.
Unit 5, Lesson 12, 5.12.4 Exploration Extension: Are you Ready for More?, “During which part of either trip was a Piccard changing vertical position the fastest? Explain your reasoning. 1. Jacques's descent; 2. Jacques’s ascent; 3. Auguste’s descent; 4. Auguste’s ascent“ This is a direct extension of the 5.12.3 Exploration Activity in which students use different operations with signed numbers to represent real-world situations.
Unit 7, Lesson 10, 7.10.4 Exploration Extension: Are you Ready for More?, “Using only a compass and the edge of a blank index card, draw a perfectly equilateral triangle. (Note! The tools are part of the challenge! You may not use a protractor! You may not use a ruler!)”
Indicator 3O
Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.
The materials reviewed for Math Nation Grade 7 provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.
The Course Guide, About These Materials, Design Principles section states the following: “Developing Conceptual Understanding and Procedural Fluency Each unit begins with a pre-assessment that helps teachers ascertain what students know about both prerequisite and upcoming concepts and skills, so that teachers can gauge where students are and make adjustments accordingly. The initial lesson in a unit is designed to activate prior knowledge and provide an easy entry to point to new concepts, so that students at different levels of both mathematical and English language proficiency can engage productively in the work. As the unit progresses, students are systematically introduced to representations, contexts, concepts, language and notation. As their learning progresses, they make connections between different representations and strategies, consolidating their conceptual understanding, and see and understand more efficient methods of solving problems, supporting the shift towards procedural fluency. Distributed practice problems give students ongoing practice, which also supports developing procedural proficiency.”
Examples of where materials provide varied approaches to learning tasks over time and variety of how students are expected to demonstrate their learning include:
Unit 4, Lesson 5, 4.5.1 Warm-Up, students are given decimal expansions of fractions and write down what they notice and wonder before sharing out. Students are able to revise their thinking during/after whole group discussion. “A calculator gives the following decimal representations for some unit fractions: ; ; ; ; ; ; ; ; ; . What do you notice? What do you wonder?” Full Lesson Plan, Activity Synthesis: “Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the image. After each response, ask the class if they agree or disagree and to explain alternative ways of thinking, referring back to the images each time. If rounding does not come up during the conversation, ask students to discuss this idea.”
Unit 5, Lesson 15, 5.15.1 Warm-Up, Students engage in a number talk as they mentally solve equations. “The variables a through h all represent different numbers. Mentally find numbers that make each equation true. ⋅ ; ; ; ; ; ”
Unit 7, Lesson 10, 7.10.2 Exploration Activity, students use an applet to draw as many triangles as they can given certain parameters and determine whether any of the triangles are unique. “Use the applet to draw triangles. 1. Draw as many different triangles as you can with each of these sets of measurements: 1. One angle measures , one side measures 4 cm and one side measures 5 cm. 2. Two sides measure 6 cm and one angle measures . 2. Did either of these sets of measurements determine one unique triangle? How do you know?”
Students can monitor their learning in the following ways: The “Check Your Understanding” provides three questions at the end of each lesson that covers the standards from the lesson and is auto-scored. Students are able to get feedback about the correct solution(s). The “Test Yourself! practice tool” provides ten questions (of different item types) taken at the end of the unit and is composed of the entire unit standards. It is also auto-scored, students can see what they got correct and incorrect, and a solution video for any question they choose.
Indicator 3P
Materials provide opportunities for teachers to use a variety of grouping strategies.
The materials reviewed for Math Nation Grade 7 provide opportunities for teachers to use a variety of grouping strategies.
The Course Guide, How to Use These Materials, states the following about groups: “Group Presentations Some activities instruct students to work in small groups to solve a problem with mathematical modeling, invent a new problem, design something, or organize and display data, and then create a visual display of their work. Teachers need to help groups organize their work so that others can follow it, and then facilitate different groups' presentation of work to the class.” Additionally, “the launch for an activity frequently includes suggestions for grouping students. This gives students the opportunity to work individually, with a partner, or in small groups.” However, the guidance is general and is not targeted based on the needs of individual students. Examples include:
Unit 4, Lesson 10, Full Lesson Plan, 4.10.1 Exploration Activity, “Launch Arrange students in groups of 2. Tell students to think of at least one thing they notice or wonder. Display the problem for all to see and give 1 minute of quiet think time. Ask students to give a signal when they have at least one thing they noticed or wondered.”
Unit 7, Lesson 14, Full Lesson Plan, 7.14.1 Exploration Activity, “Launch Arrange students in groups of 2. Display the prism assembled from the blackline master for all to see. Give students 1 minute of quiet think time followed by time to discuss their ideas with a partner. Follow with a whole-class discussion.”
Unit 8, Lesson 16, Full Lesson Plan, 8.16.2 Exploration Activity, “Launch Arrange students in groups of 2. Distribute bags of slips cut from the blackline master…Allow students 10 minutes of partner work time followed by a whole-class discussion.”
Indicator 3Q
Materials provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.
The materials reviewed for Math Nation Grade 7 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.
The Course Guide, How to Use These Materials section states the following: “The framework for supporting English language learners (ELLs) in this curriculum includes four design principles for promoting mathematical language use and development in curriculum and instruction. The design principles and related routines work to make language development an integral part of planning and delivering instruction while guiding teachers to amplify the most important language that students are expected to bring to bear on the central mathematical ideas of each unit.” The four design principles are, support sense-making, optimize output, cultivate conversation, and maximize meta-awareness. Each design principle has an explanation that goes into more detail about how teachers can use it to support students. The routines are the Mathematical Language Routines (MLRs), the materials state, “The mathematical language routines (MLRs) were selected because they are effective and practical for simultaneously learning mathematical practices, content, and language. A mathematical language routine is a structured but adaptable format for amplifying, assessing, and developing students' language. The routines emphasize uses of language that is meaningful and purposeful, rather than about just getting answers. These routines can be adapted and incorporated across lessons in each unit to fit the mathematical work wherever there are productive opportunities to support students in using and improving their English and disciplinary language use. Each MLR facilitates attention to student language in ways that support in-the-moment teacher-, peer-, and self-assessment for all learners. The feedback enabled by these routines will help students revise and refine not only the way they organize and communicate their own ideas, but also ask questions to clarify their understandings of others' ideas.” These design principles and routines are referenced under Instructional Routines, in the Full Lesson Plan for lesson, to assist teachers with lesson planning. The “Supports for English Language Learners” section within the Full Lesson Plan contains explanations of how to implement the MLRs.
Examples where the materials provide strategies and supports for students who read, write, and/or speak in a language other than English include:
Unit 4, Lesson 11, Full Lesson Plan, 4.11.2 Exploration Activity, “Support for English Language Learners Reading, Writing: MLR 6 Three Reads. Use this routine to support reading comprehension of this word problem, without solving it for students. In the first read, students read the problem with the goal of comprehending the situation (e.g., A car dealership bought a car. The dealership wants to make a profit. They need to decide what price the car should be.). If needed, discuss the meaning of unfamiliar terms at this time (e.g., profit, wholesale, retail price, commission, etc.). Use the second read to identify the important quantities by asking students what can be counted or measured (e.g., wholesale price, profit or markup, and retail price). In the third read, ask students to brainstorm possible mathematical solution strategies to complete the task. This will help students connect the language in the word problem and the reasoning needed to solve the problem while keeping the intended level of cognitive demand in the task. Design Principle(s): Support sense-making”
Unit 6, Lesson 17, Full Lesson Plan, 6.17.3 Exploration Activity, “Support for English Language Learners Conversing: MLR 4 Information Gap. This activity uses MLR 4 Information Gap to give students a purpose for discussing information necessary for solving problems involving inequalities. Design Principle(s): Cultivate conversation”
Unit 8, Lesson 3, Full Lesson Plan, 8.3.2 Exploration Activity, “Support for English Language Learners Speaking: MLR 1 Stronger and Clearer Each Time. After students decide whether it will be more likely to spin the current day of the week or the pull out the paper with the current month, ask students to write a brief explanation of their reasoning. Invite students to meet with 2–3 other partners in a row for feedback. Encourage students to ask questions such as: ‘How many days are there in a week?’, ‘How many months are there in a year?’, and ‘How did you determine the likelihood of spinning the current day of the week?’ Students can borrow ideas and language from each partner to refine and clarify their original explanation. This will help students revise and refine both their reasoning and their verbal and written output. Design Principle(s): Optimize output (for explanation)”
Indicator 3R
Materials provide a balance of images or information about people, representing various demographic and physical characteristics.
The materials reviewed for Math Nation Grade 7 provide a balance of images or information about people, representing various demographic and physical characteristics.
Materials provide a balance of images or information about people, representing various demographic and physical characteristics. Instructional videos are taught by a diverse group of teachers. Materials include problems depicting students of different genders, races, ethnicities, and other physical characteristics additionally all videos of the content have a diverse group of teachers. Examples include:
Unit 2, Lesson 3, 2.3.6 Practice Problems, Question 3, “Jada and Lin are comparing inches and feet. Jada says that the constant of proportionality is 12. Lin says it is 112. Do you agree with either of them? Explain your reasoning.”
Unit 6, Lesson 6, 6.6.3 Exploration Activity, “Story 1: Lin had 90 flyers to hang up around the school. She gave 12 flyers to each of three volunteers. Then she took the remaining flyers and divided them up equally between the three volunteers. Story 2: Lin had 90 flyers to hang up around the school. After giving the same number of flyers to each of three volunteers, she had 12 left to hang up by herself. 1. Which diagram goes with which story? Be prepared to explain your reasoning.”
Unit 8, Lesson 2, 8.2.7 Practice Problems, Question 1, “The likelihood that Han makes a free throw in basketball is 60%. The likelihood that he makes a 3-point shot is 0.345. Which event is more likely, Han making a free throw or making a 3-point shot? Explain your reasoning.”
Indicator 3S
Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.
The materials reviewed for Math Nation Grade 7 partially provide guidance to encourage teachers to draw upon student home language to facilitate learning.
Materials can be accessed in different languages by clicking on the wrench icon in the lower left-hand corner of the Teacher and Student Edition web pages. The web page content is then displayed in the selected language (135 options available). All Unit-level downloadable files (For example: Assessments and Unit Level Downloads) are available in English and Spanish. All Lesson-level downloadable files are only available in English. The lesson videos for students can be viewed in English and Spanish.
Additionally, the first time glossary terms are introduced in the materials they have a video attached to them, the video is available in five languages: English, Spanish, Haitian Creole, Portuguese, and American Sign Language. Students have access to all the glossary terms and videos in the Glossary section under Student Resources.
The materials do not provide guidance to encourage teachers to draw upon student home language to facilitate learning.
Indicator 3T
Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.
The materials reviewed for Math Nation Grade 7 do not provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning. Although, throughout the materials, references are made to other cultures and different social backgrounds, no guidance is provided to teachers to draw upon students’ cultural and social backgrounds to facilitate learning.
Indicator 3U
Materials provide supports for different reading levels to ensure accessibility for students.
The materials reviewed for Math Nation Grade 7 provide supports for different reading levels to ensure accessibility for students.
In the Full Lesson Plan, some of the supports identified as “Supports for Students with Disabilities,” could assist students who struggle with reading to access the mathematics of the lesson. The videos embedded within each lesson narrate the problem and may help struggling readers in accessing the mathematics of the exploration activity or practice problems. The materials provide Math Language Routines (MLRs) that are specifically geared directly to different reading levels to ensure accessibility for students. Detailed explanations of how to use these routines are included in the Full Lesson Plan in the “Supports for English Language Learners” section. However, none of these supports directly address different student reading levels. Examples include:
Unit 2, Lesson 2, Full Lesson Plan, 2.2.3 Exploration Activity, “Support for English Language Learners Representing, Reading: MLR 6 Three Reads. This is the first time Math Language Routine 6 is suggested as a support in this course. In this routine, students are supported in reading a mathematical text, situation, or word problem three times, each with a particular focus. During the first read, students focus on comprehending the situation; during the second read, students identify quantities; during the third read, students brainstorm possible strategies to answer the question. The question to be answered does not become a focus until the third read so that students can make sense of the whole context before rushing to a solution. The purpose of this routine is to support students’ reading comprehension as they make sense of mathematical situations and information through conversation with a partner. Design Principle(s): Support sense-making”
Unit 4, Lesson 5, Full Lesson Plan, 4.5.3 Exploration Activity, “Support for English Language Learners Representing, Writing: MLR 3 Clarify, Critique, Correct. Present an incorrect diagram to represent one of the unused equations that reflects a possible misunderstanding from the class. For example, for the equation , draw a diagram where y is greater than x. Prompt students to identify the error, and then write a correct diagram to represent the equation. This will support students to understand the relationship between equations and diagrams. Design Principle(s): Maximize meta-awareness ”
Unit 6, Lesson 2, Full Lesson Plan, 6.2.3 Exploration Activity, “Support for Students with Disabilities Receptive Language: Processing Time. Read all statements aloud. Students who both listen to and read the information will benefit from the extra processing time.”
Indicator 3V
Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
The materials reviewed for Math Nation Grade 7 meet expectations for providing manipulatives, both virtual and physical, that are representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
Virtual and physical manipulatives support student understanding throughout the materials. Examples include:
Unit 1, Lesson 3, 1.3.2 Exploration Activity, students use an applet to draw scale copies of selected figures. “1. Draw a scaled copy of either Figure A or B using a scale factor of 3. 2. Draw a scaled copy of either Figure C or D using a scale factor of .” A GeoGebra applet is available for students to increase or decrease the figure depending on the scale factor.
Unit 5, Lesson 7, 5.7.5 Exploration Activity, students plot points to create a shape and and find the side length of that shape. “Plot these points on the coordinate grid: , , , 1. What shape is made if you connect the dots in order? 2. What are the side lengths of figure ABCD? 3. What is the difference between the x-coordinates of B and C? 4. What is the difference between the x-coordinates of C and B? 5. How do the differences of the coordinates relate to the distances between the points?” A GeoGebra applet is available for students to use to plot the points.
Unit 7, Lesson 6, 7.6.2 Exploration Activity, students learn about what shapes are possible under certain constraints by using an applet to construct various polygons. “1. Use the segments in the applet to build several polygons, including at least one triangle and one quadrilateral. 2. After you finish building several polygons, select one triangle and one quadrilateral that you have made. a. Measure all the angles in the two shapes you selected. Note: select points in order counterclockwise, like a protractor. b. Using these measurements along with the side lengths as marked, draw your triangle and quadrilateral as accurately as possible on separate paper.” A GeoGebra applet is available with several lines of various lengths for students to build polygons with.
Criterion 3.4: Intentional Design
The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.
The materials reviewed for Math Nation Grade 7 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards; and have a visual design that supports students in engaging thoughtfully with the subject that is neither distracting nor chaotic. The materials do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, and do not provide teacher guidance for the use of embedded technology to support and enhance student learning.
Indicator 3W
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.
The materials reviewed for Math Nation Grade 7 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, when applicable.
All lessons have a Desmos Calculator and Desmos Graphing Calculator for students to use as they wish. Additionally, lessons contain multiple interactive activities embedded throughout the series to support students' engagement in mathematics. Examples include:
Unit 1, Lesson 2, 1.2.2 Exploration Activity, Question 1, students compare an original figure to two copies and then use a tool provided on applet to measure corresponding angles to uncover that corresponding angles are congruent in scaled copies. “One road sign for railroad crossings is a circle with a large X in the middle and two R’s—with one on each side. Here is a picture with some points labeled and two copies of the picture. Drag and turn the moveable angle tool to compare the angles in the copies with the angles in the original. 1. Complete this table to show corresponding parts in the three figures.”
Unit 3, Lesson 2, 3.2.5 Exploration Activity, Questions 1 and 2, students use a compass and a ruler on an applet to construct circles with specified diameter or radius. “Spend some time familiarizing yourself with the tools that are available in this applet. 1. Circle A, with a diameter of 6 cm 2. Circle B, with a radius of 5 cm. Pause here so your teacher can review your work.”
Unit 8, Lesson 4, 8.4.2 Exploration Activity, Questions 4 and 5, students use technology to roll a dice and determine the probability of particular outcomes. The applet graphs the probabilities automatically for students to analyze and interpret. “4. Begin by dragging the gray bar below the toolbar down the screen until you see the table in the top window and the graph in the bottom window. This applet displays a random number from 1 to 6, like a number cube. Mai won with the numbers 1 and 2, but you can choose any two numbers from 1 to 6. Record them in the boxes in the center of the applet. With your group, follow these instructions 10 times to create the graph. Click the Roll button for 10 rolls and answer the questions. 5. What appears to be happening with the points on the graph?”
Indicator 3X
Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.
The materials reviewed for Math Nation Grade 7 partially include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.
In the Teacher Edition, Lesson Preparation, Community Created Resource section, teachers are able to leave their names and comments on a Google Sheet that provides teachers access to resources created by other teachers as well as their comments and/or questions. There is no opportunity for students to collaborate with teachers or other students using digital technology
Indicator 3Y
The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.
The materials reviewed for Math Nation Grade 7 have a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.
There is a consistent design within units and lessons that support student understanding of mathematics. Examples include:
Each unit contains the following components: Unit Introduction, Assessments (In English or Spanish), and Unit Level Downloads (In English or Spanish). All assessments and unit-level downloads are available as either PDFs or Word documents.
Lessons begin with the Learning Target(s) which let students know the objective(s) of the lesson. Each lesson uses a consistent format with the following components: Warm-Up, followed by Exploration and Extension Activities, a Lesson Summary, Practice Problems, and Check Your Understanding (2-3 problems that review lesson concepts).
Teacher and student edition: Lesson outlines are always on the left and lesson content is always on the right of the screen. Tab to jump to the top when needed. Videos are highlighted in blue ovals labeled “Videos.” When students need to respond to questions it is either a blue rectangle that says “free response”, a blue oval that says “show your work”, or a pencil icon in a blue box.
Indicator 3Z
Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.
The materials reviewed for Math Nation Grade 7 partially provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.
In the Lesson Preparation, Full Lesson Plans are available for download either as Word documents or PDFs. Some lesson plans provide guidance for using embedded technology to support and enhance student learning. Examples include:
Unit 2, Lesson 12, Full Lesson Plan, 2.12.2 Exploration Activity, Launch, “The digital version has an applet with options to change line colors and hide points. You may want to demonstrate the applet before students use it, perhaps graphing Tyler's data from the previous activity together. Note: the applet can graph lines, rays, or segments. Your class can decide how to represent the data.”
Unit 3, Lesson 7, Full Lesson Plan, 3.7.2 Exploration Activity, Required Materials, “For classes using the digital version, students can record the class data in the spreadsheet and graph points directly on the grid using the Point tool. Note: you have to click on the graph side of the applet for the point tool to appear.”
Unit 7, Lesson 6, Full Lesson Plan, 7.6.2 Exploration Activity, Launch, “For classes using the digital materials, there is an applet for students to use to build polygons with the given side lengths. If necessary, demonstrate how to create a vertex by overlapping the endpoints of two segments. It may work best for positioning each segment to put the green endpoint in place first and then adjust the yellow endpoint as desired.”