# GRADE 7 MATH

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**A. Number theory**

1 Prime or composite

2 Prime factorization

3 Multiplicative inverses

4 Divisibility rules

5 Greatest common factor

6 Least common multiple

7 GCF and LCM: word problems

8 Classify numbers**B. Integers**

1 Understanding integers

2 Integers on number lines

3 Graph integers on horizontal and vertical number lines

4 Understanding opposite integers

5 Understanding absolute value

6 Absolute value

7 Absolute value and integers: word problems

8 Integer inequalities with absolute values

9 Compare and order integers**C. Operations with integers**

1 Integer addition rules

2 Add integers using counters

3 Add integers using number lines

4 Add integers

5 Add three or more integers

6 Integer subtraction rules

7 Subtract integers using counters

8 Subtract integers using number lines

9 Subtract integers

10 Integer addition and subtraction rules

11 Add and subtract integers using counters

12 Add and subtract integers

13 Complete addition and subtraction sentences with integers

14 Add and subtract integers: word problems

15 Understand multiplying by a negative integer using a number line

16 Integer multiplication rules

17 Multiply integers

18 Integer division rules

19 Equal quotients of integers

20 Divide integers

21 Integer multiplication and division rules

22 Multiply and divide integers

23 Complete multiplication and division sentences with integers

24 Add, subtract, multiply, and divide integers

25 Evaluate numerical expressions involving integers**D. Decimals**

1 Decimal numbers review

2 Compare and order decimals

3 Decimal number lines

4 Round decimals**E. Operations with decimals**

1 Add and subtract decimals

2 Add and subtract decimals: word problems

3 Multiply a decimal by a multi-digit whole number

4 Multiply decimals and whole numbers: word problems

5 Multiply decimals

6 Divide decimals by whole numbers

7 Divide decimals by whole numbers: word problems

8 Divide decimals

9 Estimate sums, differences and products of decimals

10 Add, subtract, multiply and divide decimals: word problems

11 Multi-step inequalities with decimals

12 Maps with decimal distances

13 Evaluate numerical expressions involving decimals**F. Fractions and mixed numbers**

1 Understanding fractions: word problems

2 Equivalent fractions

3 Write fractions in lowest terms

4 Fractions: word problems with graphs and tables

5 Least common denominator

6 Compare and order fractions

7 Compare fractions using benchmarks

8 Compare fractions: word problems

9 Convert between mixed numbers and improper fractions

10 Compare mixed numbers and improper fractions

11 Round mixed numbers

12 Put a mix of decimals, fractions and mixed numbers in order**G. Add and subtract fractions**

1 Add and subtract fractions with like denominators

2 Add and subtract fractions with like denominators: word problems

3 Add fractions with unlike denominators using models

4 Add fractions with unlike denominators

5 Subtract fractions with unlike denominators using models

6 Subtract fractions with unlike denominators

7 Estimate sums and differences of fractions using benchmarks

8 Add and subtract fractions with unlike denominators

9 Add and subtract fractions with unlike denominators: word problems

10 Add 3 or more fractions with unlike denominators

11 Complete addition and subtraction sentences with fractions

12 Estimate sums and differences of mixed numbers

13 Add and subtract mixed numbers

14 Add and subtract mixed numbers: word problems

15 Inequalities with addition and subtraction of fractions and mixed numbers**H. Multiply fractions**

1 Multiply unit fractions by whole numbers using number lines

2 Multiply unit fractions by whole numbers using models

3 Multiply fractions by whole numbers using number lines

4 Multiplying fractions by whole numbers: choose the model

5 Multiply fractions and whole numbers

6 Multiply fractions and whole numbers: word problems

7 Multiply two fractions using models

8 Multiply fractions

9 Multiply fractions: word problems

10 Complete the fraction multiplication sentence

11 Multiply three or more fractions and whole numbers

12 Multiply mixed numbers and whole numbers

13 Multiply mixed numbers

14 Multiply mixed numbers: word problems**I. Divide fractions**

1 Divide whole numbers by unit fractions using models

2 Reciprocals

3 Divide whole numbers and unit fractions

4 Divide whole numbers by fractions

5 Divide fractions

6 Divide fractions: word problems

7 Estimate quotients when dividing mixed numbers

8 Divide fractions and mixed numbers

9 Divide fractions and mixed numbers: word problems

**J. Rational numbers**

1 Identify rational numbers

2 Convert between decimals and fractions or mixed numbers

3 Absolute value of rational numbers

4 Compare rational numbers

5 Put rational numbers in order

6 Add and subtract fractions and decimals

7 Multiply and divide fractions and decimals

8 Estimate products and quotients of fractions and mixed numbers

9 Add, subtract, multiply and divide fractions and mixed numbers: word problems

10 Evaluate numerical expressions involving fractions

11 Apply addition and subtraction rules

12 Add and subtract positive and negative decimals

13 Apply multiplication and division rules

14 Multiply and divide positive and negative decimals**K. Exponents and square roots**

1 Understanding exponents

2 Evaluate exponents

3 Solve equations with variable exponents

4 Exponents with negative bases

5 Exponents with decimal and fractional bases

6 Evaluate numerical expressions involving exponents

7 Square roots of perfect squares

8 Estimate square roots**L. Ratios, rates and proportions**

1 Understanding ratios

2 Identify equivalent ratios

3 Write an equivalent ratio

4 Equivalent ratios: word problems

5 Unit rates

6 Equivalent rates

7 Compare ratios: word problems

8 Compare rates: word problems

9 Ratios and rates: word problems

10 Do the ratios form a proportion?

11 Do the ratios form a proportion: word problems

12 Solve proportions

13 Solve proportions: word problems

14 Estimate population size using proportions

15 Rate of change: tables

16 Rate of change: graphs

17 Constant rate of change

18 Scale drawings: word problems**M. Proportional relationships**

1 Find the constant of proportionality from a table

2 Write equations for proportional relationships from tables

3 Identify proportional relationships by graphing

4 Find the constant of proportionality from a graph

5 Write equations for proportional relationships from graphs

6 Identify proportional relationships

7 Complete a table and graph a proportional relationship

8 Interpret graphs of proportional relationships

9 Write and solve equations for proportional relationships**N. Percents**

1 What percentage is illustrated?

2 Convert between percents, fractions and decimals

3 Compare percents to fractions and decimals

4 Estimate percents of numbers

5 Percents of numbers and money amounts

6 Percents of numbers: word problems

7 Solve percent equations

8 Solve percent equations: word problems**O. Consumer math**

1 Add, subtract, multiply and divide money amounts: word problems

2 Price lists

3 Unit prices

4 Unit prices: find the total price

5 Percent of a number: tax, discount and more

6 Find the percent: tax, discount and more

7 Sale prices: find the original price

8 Multi-step problems with percents

9 Estimate tips

10 Simple interest**P. Problem solving and estimation**

1 Estimate to solve word problems

2 Multi-step word problems

3 Guess-and-check word problems

4 Use Venn diagrams to solve problems

5 Find the number of each type of coin

6 Elapsed time word problems**Q. Units of measurement**

1 Estimate metric measurements

2 Compare and convert metric units

3 Metric mixed units

4 Convert square and cubic units of length

5 Convert between cubic centimeters and milliliters

6 Precision**R. Coordinate plane**

1 Coordinate plane review

2 Quadrants and axes

3 Follow directions on a coordinate plane

4 Distance between two points**S. Number sequences**

1 Identify arithmetic and geometric sequences

2 Arithmetic sequences

3 Geometric sequences

4 Number sequences: mixed review

5 Number sequences: word problems

6 Evaluate variable expressions for number sequences

7 Write variable expressions for arithmetic sequences**T. Expressions and properties**

1 Write variable expressions

2 Write variable expressions: word problems

3 Evaluate linear expressions

4 Evaluate multi-variable expressions

5 Evaluate absolute value expressions

6 Evaluate nonlinear expressions

7 Identify terms and coefficients

8 Sort factors of expressions

9 Properties of addition and multiplication

10 Multiply using the distributive property: area models

11 Multiply using the distributive property

12 Solve equations using properties

13 Write equivalent expressions using properties

14 Add and subtract like terms

15 Add and subtract like terms with exponents

16 Simplify linear expressions

17 Factor linear expressions: area models

18 Factors of linear expressions

19 Identify equivalent linear expressions using algebra tiles

20 Identify equivalent linear expressions

21 Identify equivalent linear expressions: word problems**U. One-variable equations**

1 Which x satisfies an equation?

2 Write an equation from words

3 Model and solve equations using algebra tiles

4 Write and solve equations that represent diagrams

5 Solve one-step equations

6 Solve two-step equations

7 Solve one- and two-step equations: word problems

8 Solve equations involving like terms

9 Solve equations: complete the solution

10 Solve equations with variables on both sides

11 Rearrange multi-variable equations

**V. One-variable inequalities**

1 Solutions to inequalities

2 Graph inequalities on number lines

3 Write inequalities from number lines

4 Solve one-step inequalities

5 Graph solutions to one-step inequalities

6 One-step inequalities: word problems

7 Solve two-step inequalities

8 Graph solutions to two-step inequalities**W. Two-variable equations**

1 Does (x, y) satisfy the equation?

2 Identify independent and dependent variables

3 Solve word problems involving two-variable equations

4 Complete a table for a two-variable relationship

5 Write a two-variable equation

6 Identify the graph of an equation

7 Graph a two-variable equation

8 Interpret a graph: word problems

9 Write an equation from a graph using a table**X. Two-dimensional figures**

1 Identify and classify polygons

2 Name, measure and classify angles

3 Classify triangles

4 Identify trapezoids

5 Classify quadrilaterals

6 Graph triangles and quadrilaterals

7 Find missing angles in triangles

8 Interior angles of polygons

9 Lines, line segments and rays

10 Parallel, perpendicular and intersecting lines

11 Identify complementary, supplementary, vertical, adjacent and congruent angles

12 Find measures of complementary, supplementary, vertical and adjacent angles

13 Transversals of parallel lines: name angle pairs

14 Transversals of parallel lines: find angle measures

15 Find lengths and measures of bisected line segments and angles

16 Parts of a circle

17 Central angles of circles**Y. Transformations**

1 Symmetry

2 Identify reflections, rotations and translations

3 Translations: graph the image

4 Translations: find the coordinates

5 Reflections: graph the image

6 Reflections: find the coordinates

7 Rotations: graph the image

8 Rotations: find the coordinates

9 Identify congruent figures

10 Congruence statements and corresponding parts

11 Side lengths and angle measures of congruent figures

12 Combinations of reflections, rotations, and translations

13 Compositions of congruence transformations: graph the image

14 Identify similar figures

15 Dilations: graph the image

16 Dilations: find the coordinates

17 Dilations: scale factor and classification

18 Side lengths and angle measures of similar figures

19 Similar figures and indirect measurement**Z. Constructions**

1 Construct the midpoint or perpendicular bisector of a segment

2 Construct an angle bisector

3 Construct a congruent angle

4 Construct a perpendicular line

5 Construct parallel lines

6 Construct an equilateral triangle or regular hexagon**AA. Three-dimensional figures**

1 Bases of three-dimensional figures

2 Nets of three-dimensional figures

3 Front, side and top view**BB. Geometric measurement**

1 Perimeter

2 Area of rectangles and parallelograms

3 Area of triangles

4 Area of trapezoids

5 Area with mixed numbers

6 Area and perimeter: word problems

7 Circumference of circles

8 Area of circles

9 Circles: word problems

10 Semicircles: calculate area, perimeter, radius and diameter

11 Quarter circles: calculate area, perimeter and radius

12 Area of sectors

13 Area of compound figures with triangles, semicircles and quarter circles

14 Area between two shapes

15 Arc length

16 Relationship between volume and the area of the base: word problems

17 Volume of prisms and cylinders

18 Surface area of prisms

19 Surface area of pyramids

20 Surface area of cylinders

21 Perimeter, area and volume: changes in scale**CC. Data and graphs**

1 Interpret tables

2 Interpret line plots

3 Create line plots

4 Interpret stem-and-leaf plots

5 Create stem-and-leaf plots

6 Interpret bar graphs

7 Create bar graphs

8 Interpret histograms

9 Create histograms

10 Create frequency charts

11 Interpret circle graphs

12 Circle graphs and central angles

13 Interpret line graphs

14 Create line graphs

15 Choose the best type of graph**DD. Statistics**

1 Calculate mean and range

2 Calculate mean, median, mode and range

3 Interpret charts to find mean and range

4 Interpret charts to find mean, median, mode and range

5 Mean and range: find the missing number

6 Mean, median, mode and range: find the missing number

7 Changes in mean and range

8 Changes in mean, median, mode and range

9 Identify an outlier and describe the effect of removing it

10 Identify representative, random and biased samples**EE. Probability**

1 Probability of simple events

2 Probability of simple events – word problems

3 Probability of opposite, mutually exclusive and overlapping events

4 Experimental probability

5 Make predictions

6 Compound events: find the number of outcomes

7 Counting principle

8 Identify independent and dependent events

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