7th Grade - Gateway 2

The materials reviewed for Core Curriculum by MidSchoolMath Grade 7 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

Examples of problems and questions that develop conceptual understanding across the grade level include:

• In 7.RP.A.2a Hot Sauce!, students investigate heat ratings and discover that values must increase at the same rate, and ratios must be equivalent to each other in order to form a graph that is a straight line through the origin. 

• In 7.NS.A.1b Space Selfie, the Teacher Instruction includes, “What was the Trackometer reading right before the ship shut down?; In which direction were they headed when the ship shut down?; Should the distance from home be more or less than 50 parsecs?; What does the number 50 represent?; What does the number -32 represent?; What is 50 + -32?; How far are they from home?; How does a number line help you calculate this answer?”

• In 7.RP.A.2b Coffee Caravan, the Teacher Instruction includes, “Let’s take a deeper look at the constant of proportionality and how it is represented in various representations of proportional relationships. Let’s start with a verbal description of a proportional relationship. In a cookie recipe, for every 2 eggs there are 3 cups of flour. We could make a ratio table to show this relationship. We start with what we know, and then we can fill the rest in using the given proportion. For every 2 eggs, there are 3 cups of flour, which tells us, then, that for every 1 egg there will be $$1\frac{1}{2}$$ (or $$\frac{3}{2}$$) cups of flour.”

• In 7.EE.A.2a Taxing Problem, students rewrite equations and expressions in a variety of ways and decide between two sides of an argument. Students watch a video and try to determine, “Which dude is right?” about the cost of a bill. One dude argues, “It’s 0.085 times the bill, plus the bill” and the other says, “No dude, it’s 1.085 times the bill.” Teacher Instruction also provides other examples including calculating the cost of something at a discount.

Examples where students independently demonstrate conceptual understanding throughout the grade include:

• In 7.NS.A.2a Reverse Meditation, Practice Printable, Question 1 states, “Use a pattern to fill in each blank, and then explain the pattern.” In Part A, students create a table from 4 to -4, and multiply by 4. They should see that the products are decreasing by 4 each time, leading to the conclusion that a negative times a positive yields a negative product. In Part B, they do the same except multiply by -4 leading to a negative times a negative yields a positive product. 

• In 7.RP.A.2a Hot Sauce!, Practice Printable, Question 3 provides information about the cost of a gym membership at 2 gyms and students determine “For which company is the total cost proportional to the number of months? How do you know?”

• In 7.RP.A.2d Doggy Diet, Practice Printable, Question 3 states, “Plot and label the following points on the graph: a) $1.25 will buy 5 pencils.; b) 0 pencils cost $0.00.; c) The unit rate is $0.25 per pencil.; d) 8 pencils for $2.00.; Write three other points that could be on this graph if it were extended.” The graph shows the relationship between the number of pencils bought and the cost, in dollars, of the pencils.

• In 7.G.A.1 Build a Better Box, Practice Printable, Question 1 states, “Determine if each given scale factor would ENLARGE or REDUCE the size of the figure. a) 45%; b) $$\frac{6}{5}$$; c) 1.5; d) $$\frac{1}{3}$$; e) 110%; F) 0.8.”

The materials reviewed for Core Curriculum by MidSchoolMath Grade 7 meet expectations for attending to the standards that set an expectation of procedural skill and fluency.

The materials develop procedural skill and fluency throughout the grade level in the Math Simulator, examples in Teacher Instruction, Cluster Intensives, domain specific Test Trainer Pro and the Clicker Quiz. Examples include:

• In 7.NS.A.1d Bad Accounting, Teacher Instruction, the teacher prompt states, “Let’s rewrite the expression by replacing each subtraction with adding the additive inverse,” and “Now we can use the commutative property of addition to rearrange the terms by grouping positives and then negatives. We can then simplify.”

• In 7.EE.A.1 Mathmalian Logic, Teacher Instruction, the teacher prompt states, “Remember the order of operations when simplifying expressions.” The teacher works through three examples; the first example asks if two expressions are equivalent “$$3xy+4y-2x+8x-2xy-6y$$ and $$y(x+4)-6(y-x)$$”, the second involves simplifying an expression with fractional coefficients, and the third involves subtracting one expression from another. The Teacher’s Guide further prompts the teacher to discuss which properties might be used in each step, and walks though reordering, grouping, and combining like terms using the given example. In the Simulation Trainer, students are given an image of a large amount of land with the width being an integer, and the length divided into smaller lengths and labeled with variables. Students create two expressions that represent the total area.

• In 7.EE.B.4a Pen Perimeter, Teacher Instruction, the teacher discusses a real-world problem in which a jeweler makes a flat rate plus an additional $10 per sale. The teacher reasons through solving the problem.  Then he/she writes an equation and says, “We can solve the equation using inverse operations. We begin by subtracting the constant from both sides so we can isolate the variable.”

Examples of students independently demonstrating procedural skills and fluencies include:

• In 7.NS.A.1d Bad Accounting, the Practice Printable contains six expressions in Question 1, “Evaluate each expression. Indicate the properties of operations where appropriate, “ such as “1b.) $$22-8+(-3)+10$$” and “1d.) $$11.6-(-12.4)+15.3-9$$.”

• In 7.EE.A.1 Mathmalian Logic, Practice Printable, Question 1 states, “Simplify each expression. Combine all like terms when possible,” and contains a table of five complex expressions. Question 2, “For which value of $$m$$ would Expression 2 be equivalent to Expression 1?” A table with five pairs of expressions is provided. 

• In 7.EE.B.4a Pen Perimeter, Practice Printable, Question 7 states, “The sum of a number and 9 is multiplied by -2. The result is -8. What is the unknown number?”

The materials reviewed for Core Curriculum by MidSchoolMath Grade 7 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of mathematics. Engaging applications include single and multi-step problems, routine and non-routine problems, presented in a context in which mathematics is applied. 

Examples of students engaging in routine application of skills and knowledge include:

• In 7.NS.A.1b Space Selfie, Practice Printable, Question 1 states, “The temperature at 6 a.m. was $$38\degree$$F. Throughout the day until 10 p.m., the temperature rose $$26\degree$$F and then fell $$23\degree$$F. What was the temperature at 10 p.m.?”

• In 7.NS.A.3 Chocolate Certified, an example is “Mark and his three friends went to the movies, where each ticket cost $11.25. They decided to share two large popcorns, which cost $4.25 each, and they each got a small soda for $3.25 each. Tax was 7.5% of the total. What was the total amount that they spent?”

• In 7.EE.B.3 Hay Talk, Practice Printable, Question 1 states, “After receiving the given raise at work, who will make the most money per hour? Malala $9.90 per hour,  6% raise; Aaliyah $9.75 per hour,  7% raise;  Phan $10 per hour, 4% raise.”

Examples of students engaging in non-routine application of skills and knowledge include:

• In 7.EE.B.4b The Fur Trader, the lesson narrative states, “It is important to not only know how to solve an inequality, but to also interpret an appropriate solution for the given context. In The Fur Trader, Professor Picklebottom decides to trade furs so he can make enough to survive the winter. He has already agreed to sell a large fur for $50, but needs to determine how many small furs he needs to obtain and sell, for $3 each. The data provided is two images -- one of Professor Picklebottom, contemplating his need to earn at least $100 to survive the winter and the other, an image of a large fur and small fur, showing the Trader’s payout amounts for each size.”

• In 7.RP.A.2b Coffee Caravan, Practice Printable, the Introduction Problem states, “At what rate are they traveling? Misha and Sonia decide to go on another road trip. Traveling always makes them remember their dad, which is one reason why they like to drink coffee. He loved coffee. To honor their father, the sisters like to measure their rate of travel in miles per cup of coffee, so Sonia keeps track of their trip in her notebook.This time, though, Misha distracted her with karaoke, so she missed writing down a few cups. Look at Sonia’s notes carefully, and determine their rate of travel.” The data provided is a table with four data points for the number of cups of coffee and miles traveled.

• In 7.RP.A.2c Food Factor, Practice Printable, the Introduction Problem states, "What equation should Ariel give to the guides? Mountain guide Ariel created an equation that has helped her fellow guides calculate the amount of food necessary based on the number of people on a trip. Since that equation has worked out so well, she wants an equation that the guides can use to determine the amount of water necessary for an excursion. She asks her guides to send another postcard with their water usage and number of people in the group. Help Ariel analyze the postcards, and write an equation that will calculate the liters of water necessary (w) based on the number of people in the group (n).” The data provided are three postcards with the requested information. 

• In 7.EE.B.3 Hay Talk, Practice Printable, the Introduction Problem states, “How many bales should Ron and Carlie buy? Ron and Carlie recently rescued five more horses who were abandoned by their previous owners: Prius, Creed, Dalla, Chibi and Drago. They need to go to Howard’s Hay again and purchase more hay. Use the information in the vet report to calculate how many bales Ron and Carlie should buy.” The data provided is a note from the vet, “When ordering hay bales, it’s important to purchase quality straw with a high moisture content. In our area we recommend Howard’s Hay which sells 80-pound blaes. Don’t forget horses eat 2% of theis weight in hay each day! Below you will find the latest weights of your rescues from their most recent check-ups. Need to purchase for: Oct, Nov, Dec, Jan, Feb, Mar.”

The materials reviewed for Core Curriculum by MidSchoolMath Grade 7 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. 

Examples of the three aspects of rigor being present independently throughout the materials include:

• In 7.G.A.3 Doctor Dilim's Dimensions, students develop their conceptual understanding of two-dimensional plane sections by describing results from slicing three-dimensional figures. In the Practice Printable, Question 2 states, “Lloyd has two clay figures on a flat surface in front of him: a right square pyramid and a cube. He will make slices through each figure that are parallel and perpendicular to the flat surface. Determine which statements are true about the two-dimensional plane sections that could result from one of these slices. Place an ‘X’ in the appropriate column.” Students are given a chart with three statements for each of the shapes to identify if a cross-section could be triangular, square, or rectangular, but not square. 

• In 7.EE.A.2 A Taxing Problem, students develop procedural skill in determining if given expressions are equivalent. In the Practice Printable, Question 3, students, “Determine whether each pair of expressions is equivalent.” There are four sets of expressions to compare such as “$$3(a-4b) + 2a$$ and $$-12b + 5a$$.”

• In 7.G.B.6 Miracle Mural, students solve real-world problems involving area, surface area, and volume. In the Practice Printable, Question 2 states “Lauren’s grandma made her a birthday cake in the shape of an ‘L.’ She put frosting on all sides of the cake except for the bottom. a) How many square inches of cake did Grandma cover with frosting? b) How many cubic inches of space does Lauren’s cake take up?” 

Examples of multiple aspects of rigor being engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study include:

• In 7.SP.A.1 Poll Position, students apply their conceptual understanding of sampling to solve real-world problems. In the Practice Printable, Question 3 states, “Darlene wants to know if sweetened tea or unsweetened tea is more popular in the United States. She posts a poll on social media that asks which one people prefer. 75% prefer unsweetened tea, and 25% prefer sweetened tea. Is this an accurate representation of the U.S. population? Why or why not?”

• In 7.EE.B.4b The Fur Trader, students develop skill in solving inequalities, then use conceptual understanding to match the inequalities with number lines that show the solutions. In the Practice Printable, Questions 4-8 state “Match each inequality with the correct graph of solutions: $$6x - 32 > 50$$; $$2x - 14 ≤ -29$$; $$118+\frac{2}{3}t≥160$$; $$-0.5x + 6 < 10$$ with corresponding graphs.”

The materials reviewed for Core Curriculum by MidSchoolMath 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. 

Examples where MP1 (Make sense of problems and persevere in solving them) is connected to grade-level content include:

• In 7.G.B.4 Crop Circle, Lesson Plan Overview, “It can be challenging for students to make sense of the formula for area of circle. Crop Circle creates a meaningful context for students to use area of circle, but they may not know the formula. In Immersion, teachers prompt students to connect to their prior knowledge of area of rectangles, and to explore the difference between that and a circle. In the Resolution phase, students discuss the relationship between area of rectangles, a circle, and pi, which will help their conceptual understanding of the formula.” 

• In 7.G.B.5 Guarding the Great Gate, Lesson Plan Overview, “In Immersion and Data & Computation, students will use the diagrams and what they know about straight angles to make sense of the relationship between angles and to identify angle measures. Using the ‘Math Circles’ protocol, students make sense of the problem by discussing five questions about straight lines and angles that help them plan and determine how to solve the problem. This lesson offers extra practice of planning how to solve a problem and making a problem of your own.”

• In 7.NS.A.1a Ghost Tamers!, Detailed Lesson Plan states, “In Immersion and Data & Computation, students will connect the idea of “neutralizing a charge” to the concept of zero pairs made from a negative value and positive value. This lesson provides an opportunity for students to struggle to make sense of the problem and persevere to solve through applying different approaches.”

Examples where MP2 (Reason abstractly and quantitatively) is connected to grade-level content include:

• In 7.NS.A.2a Reverse Meditation, Lesson Plan Overview, “Reverse Meditation offers context for reasoning abstractly by visualizing the outcome to encourage brain communication as described by Jo Boaler in her tip for SMP2. In Data & Computation, students are asked to practice ‘decontextualizing’ and ‘contextualizing’ a situation using multiplication with signed numbers. In Resolution, students have an opportunity to visualize and create their own problem representing the math concept. In Clicker Quiz and Practice Printable, students will interpret problems in context and translate these problems from a situation to an equation. They work with real life examples in order to strengthen their knowledge and understanding of multiplication with signed numbers.”

• In 7.RP.A.2d Doggie Diet, Detailed Lesson Plan, “SMP2: During Data & Computation, students analyze the abstract graphical representation and contextualize the parts of the graph as they relate to Simba’s diet situation.”

• In 7.EE.B.3 Hay Talk, Detailed Lesson Plan, Applying Standards for Mathematical Practice, “Hay Talk provides students with an opportunity to solve a real-life situation by modeling with mathematics. In Immersion, the problem is unstructured, and students must make assumptions and approximations to simplify the situation. They must determine how certain quantities, such as the number of horses and number of days, affects how much hay will be needed. In Data & Computation, students will likely see a different approach in the Data Artifact (using the weight of the horse) than they had taken, prompting them to think about revising their model to include additional details and/or revising their model to be more accurate. In Resolution, the full intent of the practice is met as students present different ways of approaching the problem, and consider final revisions to make the model more accurate and complete.”

The materials reviewed for Core Curriculum by MidSchoolMath 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 include 10 protocols to support Mathematical Practices. Several of these protocols engage students in constructing arguments and analyzing the arguments of others. When they are included in a lesson, the materials provide directions or prompts for the teacher to support engaging students in MP3. These include: 

• “Lawyer Up! (12-17 min): When a task has the classroom divided between two answers or ideas, divide students into groups of four with two attorneys on each side. Tell each attorney team to prepare a defense for their ‘case’ (≈ 4 min). Instruct students to present their argument. Each attorney is given one minute to present their view, alternating sides (≈ 4 min). Together, the attorneys must decide which case is more defendable (≈ 1 min). Tally results of each group to determine which case wins (≈ 1-2 min). Complete the protocol with a ‘popcorn-style’ case summary (≈ 2-3 min).”

• “Math Circles (15-28 min): Prior to class, create 5 to 7 engaging questions at grade level, place on different table-tops. For example, Why does a circle have 360 degrees and a triangle 180 degrees? Assign groups to take turns at each table to discuss concepts (≈ 3-4 min each table).”

• “Quick Write (8-10 min): After showing an Immersion video, provide students with a unique prompt, such as: ‘I believe that the store owner should…’, or ‘The person on Mars should make the decision to…’ and include the prompt, ‘because…’ with blank space above and below. Quick writes are excellent for new concepts (≈ 8-10 min).”

• “Sketch It! (11-13 min): Tell students to draw a picture that includes both the story and math components that create a visual representation of the math concept (≈ 5-7 min). Choose two students with varying approaches to present their work (≈ 1 min each) to the class (via MidSchoolMath software platform or other method) and prepare the entire class to discuss the advantages of each model (≈ 5 min).” 

The materials include examples of prompting students to construct viable arguments and critique the arguments of others.

• In 7.RP.A.2a Hot Sauce!, Practice Printable, Introduction Problem, “Use Marty’s notes to determine if Mr. Davis’ perceived heat rating is proportional to the Scoville heat rating, and explain your reasoning.”

• In 7.SP.A.1 Poll Position, Practice Printable, Question 5, “In a poll of Mr. Grey’s English class at Harrington High, 66% percent of students say that English is their favorite subject. A school newspaper reporter in the class wants to write an article stating that English is the favored class among students at Harrington High. Explain why this population is not an accurate representation of the student body, and suggest a way to better gather data to determine which subject is favored by the entire student body.”

• In 7.NS.A.1d Bad Accounting, Practice Printable, Introduction Problem, “Cora Malone and her family have had issues with Mr. Skinner’s banking practices for as long as she can remember. She makes it a point to check Mr. Skinner’s calculations each time she goes to do business at the bank. He almost always has the incorrect balance. Determine if Mr. Skinner is swindling Miss Malone. If so, calculate Miss Malone’s actual account balance.”

• In 7.EE.A.1 Mathmalian Logic, Practice Printable, Introduction Problem, “Whose method is correct and why? Mathmalians Lumi and Dalek are working to purchase two lots on Earth. They have just decided on their lots and now wish to calculate the total cost of the lots. The price per yard is p dollars. As always, they each have a different idea on how to calculate the cost. Lumi wants to use the following method to determine total cost: $$70(x + y)p$$. Dalek wants to use the following method to determine total cost: $$70xp + 70yp$$. Determine whose method is correct and explain your reasoning.”

• In 7.EE.A.2 A Taxing Problem, Practice Printable, Introduction Problem, “The Giggle Barn has placed another order for Talking Giraffe 2, along with Singing Parrot. The quantities for each are equal, except the quantity is unknown. The dudes are again using different equations to determine the quantity. Dude #1: $$58x = 18,850$$; Dude #2: $$23x + 35x = 18,850.$$ Which dude is right? Explain your reasoning.” 

The materials provide guidance for teachers on how to engage students with MP3. In several lessons, the Detailed Lesson Plan identifies MP3 and provides prompts that support teachers in engaging students with MP3. Examples include:

• In 7.NS.A.1d Bad Accounting, “During the Immersion, students use the ‘Think-Pair-Share’ protocol to talk through what they need to know, with the teacher prompt (‘What are your ideas?’) provided. In Data & Computation, students are paired to use the ‘Lawyer Up!’ protocol to defend Ms. Malone’s or Mr. Skinner’s case. They are informed that one of them will be defending the ‘incorrect’ side but to try to make the strongest mathematical case possible. By arguing for a position that is incorrect, students learn to consider different perspectives and see how flawed arguments are formed. After a brief period, the student ‘attorneys’ must agree on which side they find most logical with best supporting evidence. This lesson encourages students to construct viable arguments and use reasoning while critiquing the arguments of others, including being able to see both strengths and weaknesses in arguments.”

• In 7.NS.A.3 Chocolate Certified, the materials include that this lesson “uses a role play protocol that provides an interesting way for teachers to engage students in critiquing the reasoning of other students. In Resolution, both the teacher and students engage in a feedback process that reinforces how their assumptions, variables, and visual representations support a constructive argument developed within a model and how they can be improved.”

The materials reviewed for Core Curriculum by MidSchoolMath Grade 7 meet expectations for supporting the intentional development of MP4 and MP5 for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Examples of the intentional development of MP4 to meet its full intent in connection to grade-level content include:

• In 7.EE.B.3 Hay Talk, the Detailed Lesson Plan states, “MP4: Model with mathematics. Hay Talk provides students with an opportunity to solve a real-life situation by modeling with mathematics. In Immersion, the problem is unstructured, and students must make assumptions and approximations to simplify the situation. They must determine how certain quantities, such as the number of horses and number of days, affects how much hay will be needed. In Data & Computation, students will likely see a different approach in the Data Artifact (using the weight of the horse) than they had taken, prompting them to think about revising their model to include additional details and/or revising their model to be more accurate. In Resolution, the full intent of the practice is met as students present different ways of approaching the problem, and consider final revisions to make the model more accurate and complete.”

• In 7.G.B.4 Crop Circle, Lesson Plan Overview, “MP4: Model with Mathematics. On Day 1, during the Data & Computation phase, students will use the formula for area of a circle to solve a real-world problem. During the Resolution phase, students will see the relationship between area of a circle and pi, which will help their conceptual understanding of the formula.”

• In 7.NS.A.3 Chocolate Certified, students calculate how much chocolate to bring on a group hike. The Detailed Lesson Plan states, “MP4: Model with mathematics. Chocolate Certified provides an opportunity for students to experience all aspects of Jo Boaler’s recommendations for this practice (open questions, make assumptions, create visuals, and revise work). This is a ‘deep’ modeling task with a role play protocol. Teachers are encouraged to spend additional time, in Immersion, to explore this multifaceted task and in debrief, during Resolution, to explore the process of modeling.”

Examples of the intentional development of MP5 to meet its full intent in connection to grade-level content include:

• In 7.G.A.2 Love Triangle, the Detailed Lesson Plan states, “MP5: Use appropriate tools strategically. During Data & Computation, students strategically choose what tools they will use to help the designer construct a triangle and meet the client’s specifications, indicating the precise measurements. The protocol, which immerses students into the context of working as interns for the design company, enhances their thinking to consider a wider array of tools than they might if they maintained a student-only role.”

• In 7.SP.C.7b Break Time, the Detailed Lesson Plan states, “MP5: Use appropriate tools strategically. In Resolution, students choose what tools to use in the development of a model that supports them in determining the likelihood of an outcome of an everyday life situation. Initial tools may include questionnaires or other observational tools. In Data & Computation, students may use spreadsheets, calculators, computational software, paper and pencil, rulers or other tools. In presentations, students may select a final medium, such as posters, animation software, slide decks, etc. Students are encouraged to choose tools that are appropriate and strategic to gather, calculate and communicate their data findings.”

The materials reviewed for Core Curriculum by MidSchoolMath Grade 7 meet expectations for supporting the intentional development of MP6: Attend to precision for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

The materials use precise and accurate terminology and definitions when describing mathematics, and the materials provide instruction in how to communicate mathematical thinking using words, diagrams, and symbols. Examples include:

• Each Detailed Lesson Plan provides teachers with a list of vocabulary words and definitions that correspond to the language of the standard that is attached to the lesson; usually specific to content, but sometimes more general. For example, 7.RP.2c states, “Represent proportional relationships by equations.” The vocabulary provided to the teacher in 7.RP.A.2c Food Factor is, “Constant of proportionality: The constant value of the ratio of two proportional quantities, typically x and y; often written as $$k=\frac{y}{x}$$; also known as the rate of change.”

• The vocabulary provided for the teacher is highlighted in red in the student materials on the Practice Printable.

• Each Detailed Lesson Plan prompts teachers to “Look for opportunities to clarify vocabulary” while students work on the Immersion problem which includes, “As students explain their reasoning to you and to classmates, look for opportunities to clarify their vocabulary. Allow students to ‘get their idea out’ using their own language but when possible, make clarifying statements using precise vocabulary to say the same thing. This allows students to hear the vocabulary in context, which is among the strongest methods for learning vocabulary.” 

• Each Detailed Lesson Plan includes this reminder, “Vocabulary Protocols: In your math classroom, make a Word Wall to hang and refer to vocabulary words throughout the lesson. As a whole-class exercise, create a visual representation and definition once students have had time to use their new words throughout a lesson. In the Practice Printable, remind students that key vocabulary words are highlighted. Definitions are available at the upper right in their student account. In the Student Reflection, the rubric lists the key vocabulary words for the lesson. Students are required to use these vocabulary words to explain, in narrative form, the math experienced in this lesson. During ‘Gallery Walks,’ vocabulary can be a focus of the ‘I Wonder..., I Notice…’ protocol.”

• Each lesson includes student reflection. Students are provided with a list of vocabulary words from the lesson to help them include appropriate math vocabulary in the reflection. The rubric for the reflection includes, “I clearly described how the math is used in the story and used appropriate math vocabulary.” 

• Vocabulary for students is provided in the Glossary in the student workbook. “This glossary contains terms and definitions used in MidSchoolMath Comprehensive Curriculum, including 5th to 8th grades.” 

• The Teacher Instruction portion of each detailed lesson plan begins with, “Here are examples of statements you might make to the class:” which often, though not always, includes the vocabulary used in context. For example, the vocabulary provided for 7.RP.A.3 Sport Stats is “Proportional Relationship” and “Percent/Percentage.” The sample statements provided are, “In Sport Stats, we had to help Dave and Shannon calculate the win percentage for each unicycle hockey team so they could broadcast it on air; They calculated the win percentage by making a ratio of the number of games won to the total number of games played, dividing to create a decimal, and multiplying by 100; This is one way of solving this problem, but there are others. I’m wondering how does this relate to proportional relationships we’ve been studying?”

The materials reviewed for Core Curriculum by MidSchoolMath Grade 7 meet expectations for supporting the intentional development of MP7 and MP8 for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Examples of the intentional development of MP7 to meet its full intent in connection to grade-level content include:

• In 7.G.B.6 Miracle Mural, the Detailed Lesson Plan states, “MP7: Look for and make use of structure. In Data & Computation, students have an opportunity to look for and use familiar structures (grids, 2-D figures within the mural) in the Data Artifact to determine the area. They are asked several prompting questions that help them look for and understand patterns and structures. In Practice Printable, students will make sense of structure by decomposing figures into simpler figures from which to calculate area and/or volume.”

• In 7.NS.A.1d Bad Accounting, the Detailed Lesson Plan states, “MP7: Look for and make use of structure. On Day 1, during both the Immersion and Data & Computation phases, students will recognize that they can use properties of operations to rewrite or rearrange expressions involving adding and subtracting rational numbers.”

• In 7.RP.A.2a Hot Sauce!, the Detailed Lesson Plan states, “MP7: Look for and make use of structure. In Data & Computation, students are asked to draw a visual representation that is connected to the data. As students look for patterns apparent in the visual, they begin to see the underlying structure (a graph) that helps them determine if the pattern is proportional (linear). In Resolution, students apply Jo Boaler’s tip for SMP7 as they share different ways they solved the problem. They are encouraged to look for structures that help illustrate proportional relationships.”

Examples of the intentional development of MP8 to meet its full intent in connection to grade-level content include:

• In 7.NS.A.1b Space Selfie, the Detailed Lesson Plan states, “MP8: Look for and express regularity in repeated reasoning. During Teacher Instruction, students experience repeated reasoning as they use the operation of addition with negative and positive numbers to solve each problem. This computation is further understood as repeated reasoning as they see the solution in a visual form on a number line. The full intent of the practice occurs as students are asked to generalize a rule in abstract form (using p and q as integers) through the prompts:  Explain when p + q is positive.;  Explain when p + q is negative.; Explain when p + q is neither positive nor negative.”

• In 7.RP.A.2c Food Factor, the Detailed Lesson Plan states, “MP8: Look for and express regularity in repeated reasoning. During Data & Computation, Practice Printable, and Clicker Quiz students have various opportunities to engage in MP8 as they look for the repeated reasoning within data provided either in a tabular format or in a verbal description. Students express regularity in the repeated reasoning shown in proportional relationships by writing an equation that relates the two variables in a general manner.”