Sixth-grade students start their year with a unit on ratios. In Unit 1, Understanding and Representing Ratios, students have the opportunity to study a concept that is brand new to them, while leaning on reasoning skills around multiplicative comparisons learned in prior grade levels. Students learn both concrete and abstract representations, including double number lines and tables, which they will be able to use throughout the year.
In Unit 2, Unit Rates and Percent, students continue their study of ratios by extending the concept to rates and percentages. Students use the representations they learned in Unit 1 to reason through more complex ratio, rate, and percent problems. Later in Unit 6, students will revisit solving percent problems when they study solving equations.
In Unit 3, Multi-Digit and Fraction Computation, and Unit 4, Rational Numbers, students focus on the number system, honing skills they’ve been developing in previous grades with fluency, applying understandings to new computations with fractions, and expanding their understanding of the world of numbers to include negatives. Including these units at this point in the year offers opportunity to remediate any related previous grade-level skills and concepts early on while also allowing time for spiraling and integration of these skills into future units.
Unit 5, Numerical and Algebraic Expressions, and Unit 6, Equations and Inequalities, prepare students for future work with more complicated equations in seventh and eighth grades. Students lean on their work with the number system from Unit 3 to support their work with numerical expressions and solving equations. In Unit 6, students revisit ratio concepts from the first two units by representing relationships in the coordinate plane and with equations. Students also apply their equation skills to percent problems as another method to solve problems.
In Unit 7, Geometry, students learn how composing and decomposing unfamiliar shapes into familiar ones can extend their ability to find area and volume. Students draw on knowledge and skills from major work of the grade covered in previous units of the year in order to determine measurements, understand formulas, and represent 2-dimensional shapes in the coordinate plane. In Unit 8, Statistics, the last unit of the year, students are introduced to the study of statistics. They learn how to represent sets of data and how using different measurements about the data set can be used to analyze the information and answer the statistical question. By studying numbers in statistical contexts, students are able to expand and solidify their understanding of the number system.
Note that this course follows the 2017 Massachusetts Curriculum Frameworks, which include the Common Core Standards for Mathematics.