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.
In Unit 5, Percent and Scaling, students reengage with the concept of proportionality from Unit 1, 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, so that students can 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.