7th Grade - Gateway 1
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Focus & Coherence
Gateway 1 - Partially Meets Expectations | 57% |
|---|---|
Criterion 1.1: Focus | 4 / 6 |
Criterion 1.2: Coherence | 4 / 8 |
The materials reviewed for Math Mammoth Grade 7, Light Blue Series, partially meet expectations for focus and coherence. For focus, the materials do assess grade-level content, but they partially provide all students with extensive work with grade-level problems to meet the full intent of grade-level standards. The materials do not meet expectations for coherence and consistency with the CCSSM, as they do not address the major clusters of the grade and do not have content from prior and future grades connected to grade-level work. The materials do have supporting content connected to major work and make connections between clusters and domains.
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 Mammoth Grade 7, Light Blue Series, partially meet expectations for focus as they do assess grade-level content but partially 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 Mammoth Grade 7, Light Blue Series, meet expectations for assessing grade-level content and, if applicable, content from earlier grades. The curriculum has a Grade 7 Tests and Cumulative Reviews section which includes an End-of-Chapter test for each chapter, a Cumulative Review for every chapter after Chapter 1 and one End-of-the-Year test. There are assessment items that are aligned to above grade level skills, but these materials can be removed or modified without impacting the structure of the materials.
Examples of assessment items that assess grade-level content include:
Tests and Cumulative Reviews, Chapter 2 Test, Question 9, “a. Write an expression for the distance between -2 and -18. b. Write an expression for the distance between x and 5. c. Evaluate the expression from (b) when x = -2.” (7.NS.1c and 7.EE.1)
Tests and Cumulative Reviews, Chapter 5 Test, Question 2, “Ethan purchased 24 cookies and a loaf of bread for a total of $$\$6.85$$. He didn’t pay attention to the cost of the cookies but he remembered that the bread cost $$\$3.25$$. Find the cost of one cookie by writing an equation and solving it.” (7.EE.4)
Tests and Cumulative Reviews, Chapter 10 Test, Question 4, “Logan and Alex tossed two coins 400 times. a. List all the possible outcomes when two coins are tossed just one time. b. Here are Logan’s and Alex’s results. Calculate and fill in the table with the experimental and the theoretical probabilities to the nearest tenth of a percent. c. Suggest a reason for the large discrepancy between the experimental and theoretical probabilities.” (7.SP.7 and 7.SP.8 )
Examples of mathematically reasonable assessment items that align to above-grade-level standards that could be removed or modified without impacting the structure or intent of the materials include, but are not limited to:
Tests and Cumulative Reviews, Chapter 4 Test, Question 9, “Write the numbers in scientific notation. a. 25,600,000 b. 7,810,000,000” (8.EE.3)
Tests and Cumulative Reviews, Chapter 8 Test, Question 6, “Draw two lines that are perpendicular to each other using only a compass and a straightedge.” (G-CO.12)
Tests and Cumulative Reviews, End of Year Test, Question 45, “*a. Find the volume of the cylindrical part of the juicer, if its bottom diameter is 12 cm and its height is 4.5 cm. b.* Convert the volume to milliliters and to liters, considering that 1 ml = 1 cm3.” (G-GMD.3)
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 Mammoth Grade 7, Light Blue Series, partially meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. The materials provide limited opportunities for all students to engage in extensive work with the grade-level-problems including but not limited to: 7.EE.3, 7.EE.4b and 7.G.5 . Some off-grade-level work negatively impacts students’ work with grade-level content.
The materials are divided into two Worktexts, 7-A and 7-B. Each Worktext is divided into chapters. Each chapter is divided into lessons that contain content instruction, mental math problems, puzzle corners, and practice problems, in addition to chapter reviews and a chapter test.
Examples of extensive work with grade-level problems to meet the full intent of some grade-level standards include:
Worktext 7-A, Chapter 1: The Language of Algebra, Growing Patterns 1, Question 1, “a. Draw the next steps. b. How do you see this pattern growing? (There is more than one way to look at it!) c. How many flowers will there be in step 39? d. What about step n?” Students are provided three steps, the first step has three flowers, the second step has six flowers, and the third step has nine flowers. In The Distributive Property, Question 13, “a. Sketch a rectangle with an area of 9x+15. b. Sketch a rectangle with an area of 9a +15b + 3.” In Chapter 5: Equations and Inequalities, Growing Patterns 2, Question 2, “a. How do you think this pattern is growing? b. How many snowflakes will there be in step 39? c. Write a formula for the number of snowflakes in step n. Check your answer with your teacher before going on to part (d). d. In which step will there be 301 snowflakes? Write an equation and solve it.” Students are provided three steps, the first step has five snowflakes, the second step has seven snowflakes, and the third step has nine snowflakes. In Worktext 7-B, Chapter 7: Percent, Percent Equations, Question 1, “Write an expression for the final price using a decimal for the percentage. c. Pizza sauce: price x, discounted by 17$$\%$$. New price = _____ d. Sunglasses: price s, price increased by 6$$\%$$. New price = _____” In Chapter 7 Review, Question 3, “A flashlight is discounted by 18$$\%$$, and now costs $$\$23.37$$. Let p be its price before the discount. Find the equation that matches the statement above and solve it.” Students choose from: p - 0.18 = $$\$23.37$$, p - 18 = $$\$23.37$$, 0.82p = $$\$23.37$$, and 0.18p = $$\$23.37$$ . Students engage in extensive work with grade-level problems to meet 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 are related.)
Worktext 7-A, Chapter 2: Integers, Addition and Subtraction on the Number Line, Question 3, “Write an addition or a subtraction. a. You are at -3. You jump 6 to the right. You end up at ____. b. You are at -3. You jump 6 to the left. You end up at ____. c. You are at 2. You jump 7 to the left. You end up at _____. ” Next to each problem is an empty box with the heading of Addition/subtraction for the student to write the corresponding equation. Question 4, “Write an addition or subtraction to match the number line jumps. a. ____ b. ____ c. ____” Students are given a number line with four number line jumps and they are tasked with writing four equations. Question 7, “Draw a number line jump for each sum and complete the addition sentence. a. 2+(-5) = _____ b. -2+(-5)= _____ c. -1+(-4)= _____” Students are provided four numbers lines running from -10 to 3. Students engage in extensive work with grade-level problems to meet the full intent of 7.NS.1(Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.)
Worktext 7-B, Chapter 10: Probability, Counting the Possibilities, Question 1, “a, How many outcomes are there for rolling the same number on both dice (such as (5, 5))? b. What is the probability of rolling the same number on both dice?” Question 4, “a. Complete the tree diagram to show the outcomes when you first roll a die, then toss a coin. The bottom row lists the outcomes using number-letter combinations, such as 1H and 1T. Now find these probabilities: b. P(even number, heads). c. P(not 6, heads)” Question 10, “In tossing two distinct coins, one of the possible outcomes is HT: first coin heads, second coin tails. a. List all the possible outcomes. b. Each of the possible outcomes is equally likely. Therefore, what is the theoretical probability of each outcome? c. Now toss two coins 200 times and compare the experimental probabilities to the theoretical ones. Before you do, predict about how many times you would expect to see each outcome: _____ times d. Check whether the observed frequencies are fairly close to those predicted by the theoretical probabilities. Let’s say they were not. What could be the reason?” Students engage in extensive work with grade-level problems to meet the full intent of 7.SP.7 (Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.)
The materials provide limited opportunities for all students to engage in extensive work with grade-level-problems for standards including, but not limited to:
Students do not have the opportunity to engage in extensive work with 7.EE.3 (Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies). In Worktext 7-A, Chapter 5: Equations and Inequalities, Word Problems, Question 1, “Which equation matches the problem? Once you find it, solve the equation. a. Mrs. Hendrickson bought herself a cup of coffee that cost $$\$3$$. She also bought ice cream cones that cost $$\$2.20$$ each for each of her preschoolers. She paid for all of it with $$\$25$$. How many ice cream cones did she buy?” A box with the following four equations is provided: n(3+2.20)=25 3+2.20n=25 3(n+2.20)=25 3n+2.20=25. “b. Mr. Sanchez spent about $$\$35$$ to treat some people in his bicycling club to a cup of coffee and an ice cream cone each. Each coffee cost $$\$3$$, and each ice cream cone cost $$\$2.83$$. How many people were treated to coffee and ice cream by Mr. Sanchez?” A box with with the following four equations is provided: n(3+2.83)=35 3+2.83n=35 3(n+2.83)=35 3n+2.83=35. Students are provided with limited opportunities to solve multi-step real-life and mathematical problems posed with negative decimals.
Students do not have the opportunity to engage in extensive work with 7.EE.4b (Solve word problems leading to inequalities of the form px+q>r or px+q
Students do not have the opportunity to engage in extensive work with 7.G.5 (Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure). In Worktext 7-B, Chapter 8: Geometry, Angle Relationships, Question 9, “a. Find a pair of vertical angles in the figure. b. Write an equation for \alpha, and solve it. Hint: Look for angles that form a straight line. c. What is the measure of ∠$$\gamma$$?” A diagram with 5 angles is shown. The angles are labeled \gamma, 43°, \alpha, 107°, and \beta. Students are provided with limited opportunities to write and solve equations for unknown angles in a figure using facts about those angles.
The materials include some off-grade-level content that negatively impacts students’ work with the grade-level standards. Examples include, but are not limited to:
Worktext 7-A, Chapter 5: Equations and Inequalities, Using the Distributive Property, Question 4, “a. 2(x+7)=3(x-6)… d. 3(w-\frac{1}{2}) = 6(w+\frac{1}{2})…”. Students are asked to engage in solving equation using the distributive property and collecting like terms, which does not align to a seventh grade standard.
Worktext 7-B, Chapter 8: Geometry, Angle Relationships, Question 11, “In this figure, lines k and m are parallel and line l intersects them both. a. Mark all the pairs of vertical angles in the figure. b. Measure or calculate all the eight angles. Mark them in the figure. What do you notice?” Students are given a picture of two parallel lines cut by a transversal. Students are asked to solve problems involving angles created when parallel lines are cut by a transversal, which does not align to a seventh grade standard.
Criterion 1.2: Coherence
Each grade’s materials are coherent and consistent with the Standards.
The materials reviewed for Math Mammoth Grade 7, Light Blue Series, do not meet expectations for coherence. The majority of the materials, when implemented as designed, do not address the major clusters of the grade. The materials do include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade and do have supporting content that enhances focus and coherence simultaneously by engaging students in the major work of the grade. The materials do not include content from future grades that is identified and related to grade-level work and do not relate grade-level concepts explicitly to prior knowledge from earlier grades.
Indicator 1c
When implemented as designed, the majority of the materials address the major clusters of each grade.
The materials reviewed for Math Mammoth Grade 7, Light Blue Series, do not meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. The materials do not devote at least 65$$\%$$ of instructional time to the major clusters of the grade:
The approximate number of chapters devoted to major work of the grade (including assessments and supporting work connected to the major work) is 6 out of 10, approximately 60$$\%$$.
The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 66 out of 112, approximately 59$$\%$$.
The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 96 out of 188, approximately 51$$\%$$.
A day-level analysis is most representative of the instructional materials as the lessons typically cover multiple days that focus on major work of the grade. As a result, approximately 51$$\%$$ of the instructional 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 Mammoth Grade 7, Light Blue Series, 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. The materials include a Common Core Alignment Document that does not provide guidance for connections between supporting and major work of the grade.
Examples of connections between supporting and major work include:
Worktext 7-A, Chapter 5: Equations and Inequalities, Some Problem Solving, connects the supporting work of 7.G.5 (Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure.) to the major work of 7.EE.1(Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.) For example, Question 8, “Four adjacent (side by side) angles form line l. a. Write an equation to solve for the unknown a. b. Find the measure of each of the four angles, rounded to the nearest 0.01 degree.” A diagram is provided of the four angles that form line l. Students use facts about supplementary angles and apply properties of operations in order to write and solve an equation for unknown angles.
Worktext 7-B, Chapter 8: Geometry, Angle Relationships, connects the supporting work of 7.G.5 (Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure.) to the major work of 7.EE.4 (Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.). For Example, Question 4, “Write an equation for each of the unknown angles. Then solve it. Do not measure any angles.” Given a diagram in part a. that shows a line with a ray extended from the center forming angle x on the left and a 78° angle on the right and a diagram for b that shows a right angle with a ray splitting it into two angles; the left angle is 76° and the right angle is labeled a. Students are asked to determine the equations and solutions, “a. Equation for x: _____ Solution: _____ b. Equation for a: _____ Solution: _____” Students use facts about supplementary and complementary angles to write equations using variables to represent quantities in a mathematical problem.
Worktext 7-B, Chapter 10: Probability, Experimental Probability, connects the supporting work of 7.SP.7 (Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.) to the major work of 7.RP.2 (Recognize and represent proportional relationships between quantities.). For example, Question 2, “Through the marvels of automation, you will now ‘roll’ a dice more times than in Exercise 1. You can use this online dice roller: https://www.mathmammoth.com/practice/dice-roller Or you can use a spreadsheet file (#1) from the list at https://www.mathmammoth.com/lessons/probability_simulations a. Predict about how many times you expect to get each of the six possible numbers if you roll a die 1,000 times: About _____ times b. Now roll one die 1,000 times. If you use the virtual roller, ... Record in the table the frequencies of each outcome and calculate experimental probabilities. Observe how close each experimental probability is to the theoretical probability of \frac{1}{6} = 16.67$$\%$$.“Students develop a probability model to make predictions and use proportional relationships between quantities to record observed frequencies.
Supporting work is not connected to the major work of the grade, but the separation is mathematically reasonable. For example:
7.G.3: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
A connection between supporting work and major work of the grade that is entirely absent from the materials is the following:
No connections are made between 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.) and the major work of 7.EE.1(Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.) In the lessons related to area, volume, and surface area, there are no questions that apply the properties of operations as strategies to determine the answers.
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 Mammoth Grade 7, Light Blue Series, 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. Included within the materials is a Common Core Alignment document, however, the document does not provide explicit guidance for connections between or among domains and clusters. .
There are connections from supporting work to supporting work and major work to major work throughout the grade-level materials, when appropriate. Examples include:
Worktext 7-A, Chapter 5: Equations and Inequalities, Two-Step Equations: Practice, connects the major work of 7.NS.1d (Apply properties of operations as strategies to add and subtract rational numbers.) to the major work of 7.EE.4 (Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.). For example, Question 1, “Write an equation to match the number line model and solve for the unknown.” For part a, students are given a labeled number line that goes from - 8 to 12, three segments of equal size are marked with x and one segment is labeled with a 5. Students solve mathematical problems by writing and solving equations using the properties of operations.
Worktext 7-B, Chapter 6: Ratios and Proportions, Floor Plans, 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.). For example, Question 6, “A floor plan is drawn using the scale 5 cm: 1 m. a. Calculate the dimensions in the plan for a kitchen that measures 4.5 m by 3.8 m in reality. b. The living room measures 26 cm by 22.5 cm on the plan. What are its dimensions in reality?” Students use their understanding of proportional relationships to compute the dimensions of figures.
Worktext 7-B, Chapter 8: Geometry, Conversions Between Metric Units of Area, connects 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.). For example, Question 8, “Jerry’s favorite lake to fish in is roughly a rectangle that measures 1.5 cm by 0.8 cm on a map with a scale of 1:20,000. What is its approximate area in reality, to the nearest thousand square meters? To the nearest tenth of a hectare?” Students use a scale to solve an area problem about a two-dimensional object.
Some connections are entirely absent from the materials. Examples include:
No connections are made between the major work of 7.EE.A (Use properties of operations to generate equivalent expressions.) to the major work of 7.EE.B (Solve real-life and mathematical problems using numerical and algebraic expressions and equations.).
Some clusters and domains are not connected, but the separation is mathematically reasonable. For example, the Geometry (7.G) and Statistics & Probability (7.SP) domains remain separate throughout the curriculum. This is mathematically reasonable, as their content does not typically overlap within the seventh grade content.
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 Mammoth Grade 7, Light Blue Series, do not 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. While some references to future or earlier grade work does occur in the introduction lesson, these references are limited, and are not always related to grade-level concepts or work. The materials include a Common Core Alignment Document that lists the grade-level standards addressed in each lesson, however, the document does not include information regarding the progression of the lesson standards between grade-level bands.
There are some examples of references to future grade content, however these references are not always identified and/or related to grade-level work. Examples include, but are not limited to:
Worktext 7-A, Foreword, states, “The curriculum meets and actually exceeds the Common Core Standards (CCS) for grade 7. The two main areas where it exceeds those standards are linear equations (chapter 5) and the Pythagorean Theorem (chapter 9). Linear equations are covered in more depth than the CCS requires, and the Pythagorean Theorem belongs to grade 8 in the CCS. You can access a document detailing the alignment information either on the Math Mammoth website or in the download of this curriculum.”
Worktext 7-B, Chapter 8: Geometry, Introduction, “We also briefly study the proof for the formula for the area of a circle. I feel it is important that students encounter justifications for mathematical formulas and procedures and even read some proofs before high school. We don’t want students to think that mathematics is only a bag of magic tricks or formulas to memorize that seemingly came out of nowhere. Proofs and logical thinking are foundations to mathematics and school mathematics should not be left without them.”
There are some examples of references to prior grade learning, however not all references relate grade-level concepts explicitly to prior knowledge from earlier grades. Examples include, but are not limited to:
Worktext 7-A, Chapter 4: Rational Numbers, Introduction, “Obviously, students already know a lot about rational numbers and how to calculate with them. Our focus in this chapter is to extend that knowledge to negative fractions and negative decimals.”
Worktext 7-B, Chapter 7: Percent, Introduction, “In this chapter we review the concept of percent as ‘per hundred’ or as hundredth parts and how to convert between fractions, decimals, and percents. The lesson Solving Basic Percentage Problems is intended for review of sixth grade topics, focusing on finding a known percentage of a number (such as 21$$\%$$ of 56) or finding a percentage when you know the part and the total.”
Indicator 1g
In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification.