6th Grade Math

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Course Summary

What is 6th grade math all about?

In sixth grade, students learn key concepts along the progression toward middle school algebra. Ratios and proportions emerges as a new domain of study, where students explore and reason with ratios and rates in order to solve problems. Sixth graders will also investigate negative numbers for the first time and round out their study of the rational number system before operating with all rational numbers in seventh grade. Work with numerical expressions extends to algebraic expressions, which sets students up to solve one-step equations and inequalities. Students will also continue their study of area and volume of geometric shapes, and will learn how statistics can be used to better understand data about our world.

How did we order the units?

Sixth-grade students start their year with a unit on ratios. In Unit 1, Understanding & 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 & 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 & 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 & Algebraic Expressions, and Unit 6, Equations & 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.

Course Map

Unit 1 18 Lessons

Understanding and Representing Ratios

Unit 2 14 Lessons

Unit Rates and Percent

Unit 3 17 Lessons

Multi-Digit and Fraction Computation

Unit 4 13 Lessons

Rational Numbers

Unit 5 Coming 1/18

Numerical and Algebraic Expressions

Unit 6 Coming 2/18

Equations and Inequalities

Unit 7 Coming 3/18


Unit 8 Coming 4/18


How to Use This Course


Mathematics at Match

The goals of Match Education’s math program are intrinsically tied to our school’s mission of providing our students with the skills and knowledge they will need to succeed in college and beyond. At Match, we seek to inspire our scholars to pursue advanced math courses, and we provide them with the foundations they will need to be successful in these courses.

Our math curriculum is designed around several core beliefs about how to best achieve our ambitious goals. These beliefs drive the decisions we make about what to teach and how to teach it.

  1. Content-rich Tasks: We believe that students learn best when asked to solve problems that spark their curiosity, require them to make novel connections between concepts, and may offer more than one avenue to the solution.
  2. Practice and Feedback: We believe that practice and feedback are essential to developing students’ conceptual understanding and fluency.
  3. Productive Struggle: We believe that students develop essential strategies for tackling complex problems, and build non-cognitive skills such as grit and resilience, through productive struggle.
  4. Procedural Fluency Combined with Conceptual Understanding: We believe that knowing “how” to solve a problem is not enough; students must also know “why” mathematical procedures and concepts exist.
  5. Communicating Mathematical Understanding: We believe that the process of communicating their mathematical thinking helps students solidify their learning and helps teachers assess student understanding.

For more information, view our full Mathematics Program Overview.