Grade 6 math

Binary Numbers (Base 2)

Convert between binary (base 2) and ordinary decimal numbers using place values 1, 2, 4, 8, 16 and up.

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Squares of Numbers

Find the square of a number (the second power) only: 3² to 9² first, then up to 20², round numbers like 40², negatives like (-7)², decimals like 0.3² and fractions like (2/3)².

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Multi-Digit Operations (Mixed Review)

Add, subtract, multiply, and divide large whole numbers.

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LCM & GCF (Mixed Review)

Find the least common multiple and greatest common factor.

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GCF of Two Numbers

Find the greatest common factor (GCF) of two numbers, from pairs like 8 and 12 up to pairs like 84 and 126.

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LCM of Two Numbers

Find the least common multiple (LCM) of two numbers, from pairs like 4 and 6 up to pairs like 24 and 36.

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Prime Factorization

Use factor trees to break numbers into prime factors, and write prime factorizations with exponents, such as 72 = 2³ × 3².

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Fraction Operations (Mixed Review)

Add and subtract fractions, simplifying your answer.

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Decimals, Fractions & Percents (Mixed Review)

Convert between decimals, fractions, and percents.

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Multiplying & Dividing Fractions (Mixed Review)

Multiply and divide fractions, including mixed numbers.

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Dividing Fractions by Fractions

Division of fractions: whole numbers ÷ unit fractions, fractions ÷ whole numbers, like denominators, unit fractions, proper fractions, simplifying and mixed numbers.

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Converting Fractions to Percents

Conversion of fractions to percents only: 37/100 and 3/4 first, then 7/20, 3/8, improper fractions, fractions not in lowest terms and mixed numbers.

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Converting Percents to Fractions

Conversion of percents to fractions in simplest form only: 30% = 3/10 and 25% = 1/4 first, then 35%, 36%, 125% as a mixed number, 12.5% and 0.5%.

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Percent Basics

Find a percent of a number using common percents.

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Multiplying & Dividing Decimals (Mixed Review)

Multiply and divide decimals with larger numbers.

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Converting Decimals to Percents

Conversion of decimals to percents only: 0.4 = 40% and 0.35 = 35% first, then 0.05, 1.25, 0.125 and 0.005.

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Dividing Decimals by Decimals

Division of a decimal by a decimal: ÷ 0.1 and 0.01, tenths ÷ tenths, hundredths ÷ tenths and hundredths, 2-digit decimal divisors, annexing zeros, whole numbers ÷ decimals and larger dividends.

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Finding the Whole from a Percent

Find the whole when a part and its percent are known, only: "6 is 10% of what number?" first, then 25%, 5% steps, 1% steps, percents over 100% and 12.5%.

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Finding What Percent One Number Is of Another

Find the percent, only: "What percent of 40 is 10?" with answers like 10%, 50% and 25% first, then 5% steps, 1% steps, answers over 100% and 12.5%.

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Long Division of Decimals by 2-Digit Whole Numbers

Division of decimals by 2-digit whole numbers with long division: tenths and hundredths, quotients less than 1, zeros in the quotient, annexing zeros and whole-number dividends with decimal quotients.

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Multiplying Decimals: 2 Decimal Places × 2 Decimal Places

Multiplication of decimals: hundredths × hundredths, from 4.25 × 0.36 up to 15.48 × 12.75. Answers have 4 decimal places.

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Multiplying Decimals: 2 Decimal Places × 1 Decimal Place

Multiplication of decimals: hundredths × tenths, from 3.45 × 0.6 up to 24.75 × 13.2. Answers have 3 decimal places.

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Multiplying Decimals by Decimals (Mixed Practice)

Multiplication of decimals with 1, 2 or 3 decimal places in any mix, including answers that need extra zeros, and word problems.

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Percent of a Number

Find a percent of a number only: 10% and 50% first, then 25% and 75%, 5% steps, 1% steps, percents over 100%, 12.5% and finally numbers like 18% of 46.

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Finding the Whole & the Percent (Mixed Review)

Find the whole when you know a part and its percent, find what percent a part is, and solve percent word problems.

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Converting Percents to Decimals

Conversion of percents to decimals only: 40% = 0.4 and 35% = 0.35 first, then 5%, 125%, 12.5% and 0.5%.

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Rounding Decimals, Then Dividing

Round decimals to the nearest tenth, hundredth or thousandth, then divide the rounded numbers. Easy rounds to tenths, Medium to hundredths, Hard to thousandths, with whole-number and decimal divisors.

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Rounding Decimals, Then Multiplying

Round decimals to the nearest tenth, hundredth or thousandth, then multiply the rounded numbers. Easy rounds to tenths, Medium to hundredths, Hard to thousandths.

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Measurement & Rates

Solve rate word problems involving speed and unit price.

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Ratios

Simplify ratios to their lowest terms.

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Ratio Tables & Equivalent Ratios

Complete ratio tables and find equivalent ratios, including ratio word problems.

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Solving Proportions

Solve proportions such as 3/4 = x/20 with equivalent ratios and cross-multiplication, then set up and solve proportion word problems.

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Unit Rates & Unit Prices

Find unit rates and unit prices, decide which is the better buy, compare two rates, and use a unit rate to find a new amount.

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Integer Operations (Mixed Review)

Add, subtract, and multiply positive and negative integers.

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Absolute Value

Find absolute values as distances from zero, compare them, and use them in real-world situations.

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Adding Integers

Addition of positive and negative integers only: 7 + (-3) and (-4) + (-5) first, then opposite signs, numbers up to 100, three addends and zero pairs.

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Comparing & Ordering Rational Numbers

Compare and order positive and negative integers, decimals and fractions.

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Integers, Opposites & the Number Line

Use integers for real-world situations, find opposites, and read and locate integers on a number line.

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Subtracting Integers

Subtraction of integers only: 3 - 8, then (-4) - 6, 5 - (-2) and (-7) - (-3), building up to numbers as large as 100.

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Order of Operations

Evaluate expressions using the correct order of operations.

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Exponents (Mixed Review)

Evaluate expressions with exponents.

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Dependent & Independent Variables

Identify dependent and independent variables and relate them with tables and equations.

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Equivalent Expressions

Write equivalent expressions using the distributive property, combining like terms and factoring out the GCF.

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Evaluating Expressions with Variables

Substitute values for variables and evaluate expressions and formulas using the order of operations.

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GCF & the Distributive Property

Use the greatest common factor and the distributive property to rewrite sums like 36 + 8 as 4(9 + 2).

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One-Step Equations

Solve one-step equations using addition, subtraction, multiplication and division, including decimals and fractions.

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Writing Expressions from Words

Translate word phrases and real-world situations into algebraic expressions with a variable.

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Writing & Graphing Inequalities

Write inequalities from words and graphs, graph them on a number line, and test solutions.

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Classifying Quadrilaterals

Classify quadrilaterals by their sides, angles and parallel sides.

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Area of Triangles, Parallelograms & Trapezoids

Use area formulas to find the area of triangles, parallelograms and trapezoids, and to find a missing base or height.

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Area of Composite Figures

Find the area of figures made of rectangles and triangles by splitting them into simpler shapes or subtracting a cut-out.

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Coordinate Plane: Four Quadrants

Read and name points in all four quadrants, reflect points across the axes, and find distances between points that share a coordinate.

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Cubes of Numbers

Find the cube of a number (the third power) only: 2³ to 7³ first, then up to 12³, round numbers like 30³, negatives like (-4)³, decimals like 0.2³ and fractions like (2/3)³.

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Nets & Surface Area

Use nets to find the surface area of cubes, rectangular prisms, triangular prisms and square pyramids.

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Polygons on the Coordinate Plane

Draw polygons from their vertices and use coordinates to find side lengths, perimeter, area and missing vertices.

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Surface Area of Shapes Made of Cubes

Surface area from pictures of solids built from unit cubes: a row of cubes, flat slabs and boxes, then steps and staircase shapes. Count every outside face, including the bottom and the back.

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Surface Area of Cubes

Surface area of cubes only: 6 × edge², from small whole-number edges to decimal edges, finding the edge from the surface area, and word problems.

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Surface Area of Rectangular Prisms

Surface area of rectangular prisms (boxes) only: SA = 2lw + 2lh + 2wh, from small whole numbers to decimal edges and word problems.

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Volume with Fractional Edge Lengths

Find the volume of rectangular prisms with fractional edge lengths using V = lwh and V = Bh, and by packing unit cubes.

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Mean, Median, Mode & Range

Find the mean, median, mode, and range of a data set.

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Box Plots & Interquartile Range

Read box plots and find the five-number summary and interquartile range of a data set.

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Dot Plots & Histograms

Read dot plots and histograms to count data, find the mode, median and range, and compare intervals.

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Range & Mean Absolute Deviation

Measure how spread out a data set is with the range and the mean absolute deviation (MAD).

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Venn Diagrams: Counting with Two Sets

Use a two-circle Venn diagram to find how many are in both groups, only one group, or neither.

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Word Problems

Percent word problems.

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Decimal Word Problems

Multi-step decimal stories: unit prices and best buys, dividing by decimals, shopping with change, averages, and rounding money to the nearest cent.

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Dividing Fractions Word Problems

Solve real-world problems by dividing whole numbers, fractions and mixed numbers.

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