7th Grade - Gateway 1

The materials reviewed for Fishtank Plus Math Grade 7 meet expectations for assessing grade-level content and, if applicable, content from earlier grades. The curriculum is divided into eight units and each unit contains a Pre-Unit Assessment, Mid-Unit Assessment, and Post-Unit Assessment. Pre-Unit assessments may be used “before the start of a unit, either as part of class or for homework.” Mid-Unit assessments are “designed to assess students on content covered in approximately the first half of the unit” and may also be used as homework. Post-Unit assessments “are designed to assess students’ full range of understanding of content covered throughout the whole unit.” Examples of Post-Unit Assessments include: 

• In Unit 1, Post-Unit Assessment, Proportional Relationships, Problem 2 states, “A vehicle uses 1\frac{1}{8} gallons of gasoline to travel 13\frac{1}{2} miles. At this rate, how many miles can the vehicle travel per gallon of gasoline? a. \frac{16}{243}, b. \frac{4}{3}, c. 12, d. 13.” (7.RP.1)

• In Unit 2, Post-Unit Assessment, Operations With Rational Numbers, Problem 3 states, “Which expression is equivalent to 4 − (−7)? a. 7 + 4  b. 4 − 7 c. −7 − 4 d. −4 + 7.” (7.NS.1c) 

• In Unit 4, Post-Unit Assessment, Equations and Inequalities, Problem 14 states, “Mr. Kim has 550 take-out boxes at his restaurant. He estimates that he will use 80 boxes per week. Mr. Kim wants to re-order more boxes when he has fewer than 100 left. After how many weeks should Mr. Kim re-order more take-out boxes? Write and solve an inequality.” (7.EE.4b)

• In Unit 6, Post-Unit Assessment, Geometry, Problem 7 states, “Kiyo used wire fencing to form a border around a circular region in his backyard. If the radius of the circular region was 5 yards, what was the total length of the border, rounded to the nearest tenth of a yard? a. 15.7 b. 31.4 c. 78.5 d. 157.1.” (7.G.4)

The instructional materials reviewed for Fishtank Plus Math Grade 7 meet expectations for the materials giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The instructional materials provide extensive work in Grade 7 by including Anchor Problems, Problem Sets, and Target Tasks for all students in each lesson. Within Grade 7, students engage with all CCSS standards. Examples of problems include:

• In Unit 1, Proportional Relationships, Lesson 17 engages all students with extensive work with 7.RP.3 (Use proportional relationships to solve multistep ratio and percent problems). In the Target Task, Problem 1, students use proportional reasoning to solve a multi-step problem. It states, “A furniture store offers a deal to new customers. On your first purchase, you can use a \frac{1}{4} discount on the price of any table. Brian is a new customer at the store and wants to buy a table that originally cost $96. What discounted price would Brian pay for the table?”

• In Unit 2, Operations with Rational Numbers, Lessons 15 and 17 engage all students with extensive work with 7.NS.2c (Apply properties of operations as strategies to multiply and divide rational numbers). In Lesson 15, Problem Set, Problem 4, students apply properties of operations as strategies to multiply and divide rational numbers. It states, “The temperature dropped 15\frac{1}{3} degrees in 5\frac{1}{2} hours. On average, what was the change in temperature in degrees per hour?” In Lesson 17, Target Task, students apply properties of operations as strategies to multiply and divide rational numbers. It states, “Use the properties of operations to evaluate the expression below. -\frac{5}{6}×24×(-9)÷(-\frac{3}{2})÷\frac{25}{12}”

• In Unit 8, Probability, Lesson 1 engages all students with extensive work with 7.SP.5 (Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. In Anchor Problem, Problem 3, students understand that the probability of an event happening is a number between 0 and 1. It states, “For each event below, design a spinner or a bag of cubes that would have the probabilities described. a. The probability of selecting a red cube is 0.5. b. The probability of spinning an even number is unlikely. c. The probability of spinning a number greater than 3 is certain. d. The probability of selecting a yellow cube is very likely. e. The probability of spinning the color blue is 0.”  

The instructional materials provide opportunities for all students to engage with the full intent of Grade 7 standards through a consistent lesson structure, including Anchor Problems, Problem Sets, and Target Tasks. Anchor Problems include a connection to prior knowledge, multiple entry points to new learning, and guided instruction support. Problem Set Problems engage all students in practice that connects to the objective of each lesson. Target Task Problems can be used as formative assessment. Examples of meeting the full intent include:

• In Unit 3, Numerical and Algebraic Expressions, Lesson 9 engages students with the full intent of 7.EE.2 (Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related). In Problem Set, Problems 2 and 3, students write and interpret expressions in different ways. Problem 2 states, “Ms. French needs some number of tiles to cover her kitchen floor. She already has 60 tiles. Tiles come in packages of 4. She writes the following expressions to represent the number of tiles she will need to cover the floor:  60 + 4x; 4(15 + x) A. Explain what 4x represents in the first expression in the context of the situation. B. Explain what 15 represents in the second expression in the context of the situation.” Problem 3 states, “Mr. Gerard always likes to have more pencils than pens to lend to students since they tend to prefer writing in pencil. He likes to have 20 more pencils than pens. A. Write an expression that gives the number of pens and pencils Mr. Gerard has in his class. Let c be the number of pencils he has. B. Write a different but equivalent expression to represent the total number of pens and pencils. C. Devin thinks the expression 2c + 20 represents the total number of pens and pencils. What mistake did Devin likely make? Explain.”

• In Unit 6, Geometry, Lessons 12 and 15 engage students with the full intent of 7.G.2 (Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions). In Lesson 12, Anchor Problem 2, students draw geometric shapes using a ruler, protractor and compass. It states, “Draw a rectangle with dimensions 3 inches x 5 inches. Can you draw a different quadrilateral with side lengths 3 in., 3 in., 5 in., and 5 in.? If so, draw the shape and name it.“ In Lesson 15, Anchor Problem 2, students determine if a unique triangle can be made from given conditions. It states, “Two triangles are described below. Determine if each description results in one unique triangle, more than one triangle, or no triangle. Explain your reasoning or draw images to support your conclusion. Triangle EFG is an isosceles triangle with two angles measuring 35°. Sinde length EG measures 10 cm. Triangle PQR is an isosceles triangle with ∠P and ∠Q measuring 22°. Side length PQ measures 8 cm.”

• In Unit 7, Statistics, Lesson 2 engages students with the full intent of 7.SP.1 (Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences). In the Target Task, students examine a sample to determine whether it is valid. It states, “A teacher wants to treat his homeroom class for having perfect attendance the last three months. He is deciding between offering a pancake breakfast in the morning or a pizza lunch in the afternoon. To help him decide, he takes a poll of the first 10 students to arrive at school in the morning. Do you agree with the teacher’s choice of sampling method? Explain why you think this method will be representative of the class, or describe a different method the teacher should use to get a representative sample.”

The materials reviewed for Fishtank Plus Math Grade 7 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of the grade. The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade: 

• The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 5 out of 8, approximately 63%.

• The number of lessons devoted to major work of the grade (including supporting work connected to the major work) is 89 out of 125, approximately 71%. The total number of lessons include: 117 lessons plus 8 assessments for a total of 125 lessons.

• The number of days devoted to major work (including assessments, flex days, and supporting work connected to the major work) is 105 out of 143, approximately 73%. There are a total of 18 flex days and 16 of those days are included within units focused on major work. By adding 16 flex days focused on major work to the 89 lessons devoted to major work, there is a total of 105 days devoted to major work.

• The number of days devoted to major work (excluding flex days, while including assessments and supporting work connected to the major work) is 89 out of 125, approximately 71%. While it is recommended that flex days be used to support major work of the grade within the program, there is no specific guidance for the use of these days.

A lesson-level analysis is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each unit. As a result, approximately 71% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Fishtank Plus Math Grade 7 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Materials are designed so supporting standards/clusters are connected to the major standards/clusters of the grade. These connections are sometimes listed for teachers as “Foundational Standards'' on the lesson page. Examples of connections include:

• In Unit 5, Percent and Scaling, Lesson 14, Anchor Problem 2 connects the supporting work of 7.G.1 (solve problems involving scale drawings of geometric figures) to the major work of 7.RP.2 (recognize and represent proportional relationships between quantities). In Anchor Problem 2, students use proportional reasoning as they reason about scale factor. It states, “A projector is connected to your computer and projects onto a large wall. The projector enlarges what is on your computer screen by a scale factor of 325 percent. An image on your computer is $$8\frac{1}{2}$$ inches long. What is the length of the projected image on your wall?”

• In Unit 6, Geometry, Lesson 6, Target Task 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) to the major work of 7.RP.2 (recognize and represent proportional relationships between quantities). In Problems 1 and 2, students use the ratio of circumference to diameter to approximate $$\pi$$ and apply the formula for circumference to find the diameter. Problem 1 states, “Describe the relationship between the circumference of a circle and its diameter.” Problem 2 states, “The top of a can of tuna is in the shape of a circle. If the distance around the top is approximately 251.2 mm, what is the diameter of the top of the can of tuna? What is the radius of the top of the can of tuna?” 

• In Unit 7, Statistics, Lesson 7, Problem Set, Problem 5 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.2d (convert a rational number to a decimal using long division) and 7.RP.2c (represent proportional relationships by equations). Students estimate population proportions using sample data. The problem states, “Lucy belongs to a youth group at a community center in her city. She volunteers to plan an activity for an upcoming festival. To determine what people would be most interested in, she asks a random sample of 30 members of the youth group if they would prefer arts and crafts or kickball. She counts 18 people who prefer kickball. a. What is the sample proportion of people who prefer kickball? b. If there are 85 people in Lucy’s youth group, about how many people could Lucy predict would choose kickball?”

• In Unit 8, Probability, Lesson 2, Problem Set, Problem 1 connects the supporting work of 7.SP.6 (approximate the probability of a chance event) and7.SP.7 (develop a probability model and use it to find probabilities of events) to the major work of 7.RP.2 (recognize and represent proportional relationships between quantities). Students represent the probability of an event as a fraction and equivalent percentage, and estimate the probability of a chance event. The problem states, “One student from your music class will be randomly selected to perform at the upcoming concert. There are 6 students in your music class. Your teacher assigns each student a number 1-6, and then rolls a fair number cube. a. What is the probability that you will be selected to perform at the concert? b. If there are 3 girls in the music class, what is the probability that a girl will be selected to perform at the concert? c. Describe the likelihood that a girl is selected to perform compared to the likelihood a boy is selected.”

The instructional materials for Fishtank Plus Math Grade 7 meet expectations that materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. Materials are coherent and consistent with the Standards. Examples of connections include:

• In Unit 1, Proportional Relationships, Lesson 7, Anchor Problem 1 connects the major work of 7.RP.A (analyze proportional relationships and use them to solve real-world and mathematical problems) to the major work of 7.NS.A (apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers). In Anchor Problem 1, students solve real-world ratio problems involving operations with rational numbers. It states, “In a video game, for every 3 coins you collect, you earn 4 points. a. Create a table of values to represent the relationship. b. Graph the relationship. c. Determine the equation that represents the relationship.” 

• In Unit 3, Numerical and Algebraic Expressions, Lesson 2, Target Task, Problem 2 connects the major work of 7.EE.A (use properties of operations to generate equivalent expressions) to the major work of 7.NS.A (apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers). In the Target Task, students “write and evaluate expressions for mathematical and contextual situations” and “Evaluative $$2x^3-4(x+4\frac{1}{2})$$ for x= -2.”

• In Unit 4, Equations and Inequalities, Lesson 5, Anchor Problem 2 connects the major work of 7.NS.A (apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers) to the major work of 7.EE.B (solve real-life and mathematical problems using numerical and algebraic expressions and equations). In Anchor Problem 2, students solve a word problem by applying their understanding of operations. It states, “The taxi fare in Gotham City is $2.40 for the first $$\frac{1}{2}$$ mile and additional mileage is charged at the rate of $0.20 for each additional 0.1 mile. You plan to give the driver a $2 tip. How many miles can you ride for $10? What are two different ways you can solve this problem?”

• In Unit 6, Geometry, Lesson 12, Problem Set, Problems 4 and 7 connect the supporting work of 7.G.A (draw, construct, and describe geometrical figures and describe the 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). In Problems 4 and 7, students “Draw two-dimensional geometric shapes using rulers, protractors, and compasses.” Problem Set, Problem 4 states, “Draw a pair of supplementary angles where one angle is 105°.” Problem Set, Problem 7 states, “Draw two different quadrilaterals that have the same area, but different perimeters. Label the side lengths of your quadrilaterals.”

The materials reviewed for Fishtank Plus Math 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.  

Content from future grades is identified within materials and related to grade-level work. These references are consistently included within the Unit Summary. Examples include:

• In Unit 2, Operations with Rational Numbers, Unit Summary connects 7.NS.A (Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers) to work in eighth grade. Unit Summary states, “By the time students enter eighth grade, students should have a strong grasp on operating with rational numbers, which will be an underlying skill in many algebraic concepts. In eighth grade, students are introduced to irrational numbers, rounding out their understanding of the real number system before learning about complex numbers in high school.” (8.NS.A)

• In Unit 4, Equations and Inequalities, Unit Summary connects 7.EE.B (Solve real-life and mathematical problems using numerical and algebraic expressions and equations) to the work of eighth grade. Unit Summary states, “students explore complex multi-step equations; however, they will discover that these multi-step equations can be simplified into forms that are familiar to what they’ve seen in seventh grade. Eighth-grade students will also investigate situations that result in solutions such as 5=5 or 5=8, and they will extend their understanding of solution to include no solution and infinite solutions.” (8.EE.7)

• In Unit 5, Percent and Scaling, Unit Summary connects 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) to the work of eighth grade. Unit Summary states, “In eighth grade, students will refine their understanding of scale and scale drawings when they study dilations in their transformations unit. They will define similar figures and use dilations and other transformations to prove that two images are similar or scale drawings of one another.” (8.G.4)

• In Unit 8, Probability, Unit Summary connects 7.SP.C (Investigate chance processes and develop, use, and evaluate probability models) to the work of high school. Unit Summary states, “In high school, students will further explore probability, distinguishing between independent events and conditional events and developing rules to calculate probabilities of these compound events.” (HSS-CP.A, HSS-CP.B)

Materials relate grade-level concepts from Grade 7 explicitly to prior knowledge from earlier grades. These references can be found within materials in the Unit Summary or within Lesson Tips for Teachers. Examples include:

• In Unit 3, Numerical and Algebraic Expressions, Unit Summary connects 7.EE.A (Use properties of operations to generate equivalent expressions) to the work from 6th grade (6.EE.A). It states, “In sixth grade, students learned how the same rules that govern arithmetic also apply to algebraic expressions. They learned to expand and factor expressions using the distributive property, and they combined terms where variables are the same.” In this unit, “Students manipulate expressions into different equivalent forms as they expand, factor, add, and subtract numerical and algebraic expressions and face authentic real-world, multi-step problems.”

• In Unit 5, Percent and Scaling, Lesson 3, Tips for Teachers connects 7.RP.3 (Use proportional relationships to solve multistep ratio and percent problems) to work from 6th grade (6.RP.3c). It states, “This lesson focuses on finding the part of a number when given the percent and the whole. Students recall strategies from sixth grade, such as tables, double number lines, and equations, while also using proportions, a new strategy learned in Unit 1 of seventh grade.”

• In Unit 6, Geometry, Unit Summary connects 7.G.A (Draw, construct, and describe geometrical figures and describe the relationships between them) and 7.G.B, (Solve real-life and mathematical problems involving angle measure, area, surface area, and volume) to the work from fourth grade (4MD.C), fifth grade (5.MD.C), and sixth grade (6.G.A). It states, “The foundational skills for the standards in this unit stem from fourth through sixth grades. In fourth grade, students studied the concepts of angle measurement and understood angle measure to be additive. In fifth grade, students developed an understanding of three- dimensional volume, which they further built on in sixth grade. Sixth-grade students also began to distinguish between the three-dimensional space an object takes up and the surface area that covers it.” In this unit, “Students apply algebraic and proportional reasoning skills to investigate angle relationships, circle measurements, uniqueness of triangles, and solid figure application problems.”

• In Unit 7, Statistics, Lesson 1, Tips for Teachers connects 7.SP.1 (Understand that statistics can be used to gain information about a population by examining a sample of the population) to the work from sixth grade (6.SP.A). It states, “In sixth grade, students studied statistical questions, understanding that statistical questions anticipate variety in the data.” In this lesson, students “Understand and identify populations and sample populations for statistical questions.”