# Mathematics

## What Do Students Learn in 7th Grade Math?

In seventh grade, students extend and apply many of the concepts they've learned in sixth grade in order to discover new types of relationships, new and efficient ways to solve problems, and new ways to analyze and look at data and associations. Students will investigate proportional relationships and use this understanding to solve real-world problems involving discounts, interest, taxes, and scale drawings. Building off of their sixth-grade understanding of integers, seventh-grade students will apply the properties of operations to all rational numbers in order to efficiently and thoughtfully work with the number system, including how it applies to expressions and equations. Lastly, students will learn to question what it means to be a representative sample of a population and how to effectively compare different populations.

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## Units

Unit 1

18 Lessons

### Proportional Relationships

Students deepen their understanding of ratios to investigate proportional relationships, in order to solve multi-step, real-world ratio problems using new strategies that rely on proportional reasoning.

Unit 2

18 Lessons

### Operations with Rational Numbers

Students extend the operations of addition, subtraction, multiplication, and division to include positive and negative rational numbers, and build fluency with evaluating numerical expressions.

Unit 3

11 Lessons

### Numerical and Algebraic Expressions

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.

Unit 4

12 Lessons

### Equations and Inequalities

Students solve equations and inequalities with rational numbers, and encounter real-world situations that can be modeled and solved using equations and inequalities.

Unit 5

19 Lessons

### Percent and Scaling

Students expand on and apply their understanding of percentages by studying percent increase and decrease, percent applications such as tax and simple interest, and scaled geometric drawings.

Unit 6

21 Lessons

### Geometry

Students apply algebraic and proportional reasoning skills to investigate angle relationships, circle measurements, uniqueness of triangles, and solid figure application problems.

Unit 7

9 Lessons

### Statistics

Students investigate how to use sampling to make inferences about larger populations of interest, engaging in hands-on activities to select random samples and to compare samples of different sizes.

Unit 8

9 Lessons

### Probability

Students have their first encounter with probability, as they develop their understanding of probability through calculating theoretical probabilities and designing and running their own simulations.

## How Do Students Build 7th Grade Math Skills Across Units?

In Unit 1, Proportional Relationships, students begin the year by recalling familiar concepts of ratios and unit rates from sixth grade. They work with more complicated unit rates involving fractions and investigate the concept of proportionality. Using tables, equations, and graphs, students compare proportional relationships and nonproportional relationships and the contexts under which they arise.

In Unit 2, Operations with Rational Numbers, students learn that the properties of operations they use with whole numbers, fractions, and decimals apply to all rational numbers, including negative numbers. Developing a strong conceptual understanding and procedural ability to work with rational numbers is critical to students’ algebra progression in middle school. These standards are covered early in the year in order for students to continue to hone them and apply them throughout the year.

In Unit 3, Numerical and Algebraic Expressions, and Unit 4, Equations and Inequalities, students use their number sense skills learned in the previous unit to evaluate expressions, generate equivalent expressions, and efficiently solve equations and inequalities. Students become increasingly more adept at modeling situations, decontextualizing situations in order to represent them algebraically, and then recontextualizing to interpret their meaning.

Unit 5, Percent and Scaling, reengages students with the concept of proportionality from Unit 5, but this time they investigate and solve problems involving percent and scale drawings. This unit is placed later in the year, rather than immediately after Unit 1, in order for students to utilize and apply the skills they’ve learned in Units 2–4.

In Unit 6, Geometry, students further their study of measuring two-dimensional and three-dimensional figures by finding volume, surface area, and angle measures. They study triangles in depth and are introduced to constructions which they will revisit in high school geometry.

Lastly, students end the year with two units, Unit 7, Statistics, and Unit 8, Probability. In their Statistics unit, students find and use statistical measures to compare distributions and make inferences about populations. As students engage in probability concepts, they lean on their understandings of ratio and proportions learned earlier in the year.

Note that this course follows the 2017 Massachusetts Curriculum Frameworks, which include the Common Core Standards for Mathematics.

### What math skills do students learn in 7th grade?

In seventh grade, students extend their work with ratios to include varied types of proportional relationships, apply the properties of operations to all rational numbers, and deepen their understanding of equations and inequalities.

### What Common Core Math Standards do students focus on in 7th grade?

The major work of the course focuses on the following Common Core State Standards:

• 7.RP.A Analyze proportional relationships and use them to solve real-world and mathematical problems.
• 7.NS.A Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
• 7.EE.A Use properties of operations to generate equivalent expressions.
• 7.EE.B Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

### What are the fluency expectations and culminating standards for 7th grade math?

• 7.EE.4.a: Solve word problems leading to equations of the form px + q = r and p(x + q)= r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
• 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. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or$2.50, for a new salary of \$27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. (Culminating)
• 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. (Culminating)
• 7.NS.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. (Culminating)

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