Grade 6 Math Syllabus

Unit 1 Introduction

Problem solving is not the act of hunting for a keyword and attacking the nearest numbers. It is the work of deciding what a situation means, representing its structure, choosing a plan, and defending the conclusion.

This unit keeps most computations within whole numbers so the reasoning stays visible. You will identify missing and unnecessary information, uncover hidden questions, and interpret remainders according to context.

Many problems have more than one reasonable path. Some have no unique answer until an assumption is stated. The goal is not merely to arrive at a number. The goal is to build an argument that another person can inspect, question, and trust.

Unit 2 Introduction

Decimals are not a separate number system with a mysterious collection of point-moving tricks. They are ordinary place-value numbers written in units smaller than one. Every decimal operation in this unit grows from that idea.

You will predict before calculating, use models to explain algorithms, track units through word problems, and compare methods. The unit moves from computation to decision-making: first learn how the operations work, then decide which operation or sequence of operations a situation requires.

Accuracy matters, but advanced work asks for more. You should be able to explain why a decimal point belongs where it does, why a quotient terminates or repeats, why two division expressions are equivalent, and why an answer is reasonable before using a calculator.

Unit 3 Introduction

A fraction problem can look as though it is only about fractions, yet the quickest path often begins with whole numbers. To simplify $\frac{84}{126}$, we need common factors. To add $\frac{5}{12}+\frac{7}{18}$, we need a common multiple. To decide whether a large number is prime, we need divisibility and factor structure.

This unit develops those ideas as a connected system. You will search for patterns, test conjectures, compare methods, and explain why procedures work. You will calculate, decide which calculation is useful, prove that an answer must have a certain form, and find every possible answer. You will also decompose fractions into sums of distinct unit fractions, connecting equivalent fractions, subtraction, divisibility, and number structure through Egyptian fractions. The goal is to understand number structure, not memorize fraction tricks.

Unit 4 Introduction

Numbers do more than count objects. They can describe opposite directions, locations below a reference point, gains and losses, and points anywhere on a coordinate plane. Once zero becomes a reference point instead of a starting point, negative numbers become natural rather than strange.

This unit develops signed rational numbers through distance, symmetry, order, and location. You will place integers, fractions, and decimals on number lines; reason about opposites and absolute value; graph inequalities; and use coordinates to measure horizontal and vertical distance without relying on a distance formula.

The goal is not to memorize that “two negatives make a positive” or that “the larger-looking negative is smaller.” The goal is to see the geometry behind those statements so that the rules become unavoidable.

Unit 5 Introduction

Arithmetic asks for the value of a calculation. Algebra asks a broader question: what relationships make the calculation true? A letter can stand for a number that changes, a number not yet known, or an entire family of possible values. Expressions describe calculations, and equations describe equal quantities.

This unit begins by completing the arithmetic of signed integers. It then builds the language of variables, coefficients, terms, powers, and expressions before turning to equations. You will interpret and evaluate exponents, apply the order of operations to numerical expressions, substitute values carefully, simplify expressions, use the distributive property, solve equations from one step through several steps, work with variables on both sides, and decide when an equation has one solution, no solution, or infinitely many solutions.

The guiding principle is equality. We will not “move” terms mysteriously or change signs by ritual. Every equation step will follow from doing the same legal operation to equal quantities. Algebra is not a collection of tricks. It is careful arithmetic with structure.

Unit 6 Introduction

Ratios compare quantities. That sounds simple, but ratio reasoning connects pictures, fractions, tables, graphs, equations, similar figures, rates, speed, work, and unit conversions. A ratio is not merely two numbers separated by a colon. It records how two quantities change together.

This unit begins with concrete comparisons and builds toward proportional relationships. You will simplify ratios containing whole numbers, fractions, and decimals; find unknown quantities from part-to-part and part-to-whole information; represent equivalent ratios in tables and graphs; solve proportions whose solutions may be whole numbers, fractions, or decimals; analyze similar figures; work with multi-part ratios; and use unit rates, dimensional analysis, and multistep proportional reasoning.

The goal is to recognize one structure in many forms. A tape diagram, a ratio table, a graph through the origin, an equation $y=kx$, and a proportion can all describe the same multiplicative relationship. Once that connection is visible, proportional reasoning becomes a method instead of a collection of tricks.

Unit 7 Introduction

Percent is comparison to 100. It connects fractions, decimals, ratios, equations, estimation, and real-world change. A percent is a multiplier tied to a reference whole, not decoration attached to a number.

This unit develops conversions, percent-of calculations, mental strategies, equations, discounts, markups, tax, tips, increases, decreases, and successive changes. Three questions guide every problem: What is the reference whole? What multiplier represents the percent? What quantity is the part? Once those roles are clear, percent problems become connected reasoning rather than unrelated rules.

Unit 8 Introduction

Geometry asks us to measure space without losing sight of structure. A complicated figure is often only a familiar figure that has been cut, rearranged, folded, or stacked. The central habits of this unit are to decompose, rearrange, and track dimensions carefully.

You will derive area formulas rather than merely receive them, solve composite-area and cost problems, classify three-dimensional solids, investigate nets, and build surface-area and volume formulas from the faces and layers of a solid. The unit ends by comparing how length, area, and volume change under scaling and by using volume ratios to solve packing problems.

The goal is not to memorize a shelf of disconnected formulas. It is to see that a parallelogram can become a rectangle, a triangle can be doubled into a parallelogram, a net is a solid unfolded, and a prism is a stack of congruent bases. Once those connections are visible, the formulas stop behaving like mysterious paperwork.

Unit 9 Introduction

Statistics is the mathematics of learning from data. It begins with a question that expects variation rather than one fixed answer. We collect observations, organize them, display them, measure their center and spread, and then use the whole distribution to make a reasonable conclusion.

In this unit, you will distinguish statistical questions from nonstatistical questions, classify data, build frequency tables and graphs, and interpret line plots, histograms, and box plots. You will also study mean, median, mode, range, mean absolute deviation, quartiles, and interquartile range. Every formula will be translated into everyday language before it is used, because symbols should shorten an idea after the idea is understood, not replace the idea entirely.

The central habit is to look beyond a single number. A useful statistical description considers center, variability, shape, and context together. Statistics requires more than calculating an average: it also explains what the data say, how strongly they say it, and what they do not say.