Examples for

Common Core Math: Grade 7

In seventh grade, students gain fluency in manipulating expressions and solving equations, including those with negative numbers and numbers expressed as fractions or decimals. Students compute with percentages and ratios and describe proportional relationships using numerical, graphical, algebraic and verbal representations. Students analyze and compare data from random samples and generalize to make inferences about populations. Students also work with probability, performing probability experiments and computing probabilities with probability models. Students compute areas, volumes and surface areas of regular and irregular shapes and solve problems involving angles, including drawing shapes to match given geometric conditions and classifying types of triangles.

Number System

Perform arithmetic with integers, fractions and decimals, including with multiple operations in one expression.

Add and subtract rational numbers (CCSS.Math.Content.7.NS.A.1):

-4 + 9/2
-5/8 - 1/4

Recognize patterns in multiplication and division (CCSS.Math.Content.7.NS.A.2):

negative number * positive number

Perform multiple operations with rational numbers (CCSS.Math.Content.7.NS.A.2c):

(-5)(-2) - (4)(-3)
(-1/2 + 3/8 + 1/4 + -3/2) / 2

Convert a rational number to a decimal (CCSS.Math.Content.7.NS.A.2d):

5/8 as a decimal
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Ratios & Proportions

Compute with ratios and percents in various contexts.

Determine the unit rate associated with a ratio (CCSS.Math.Content.7.RP.A.1):

0.75 feet per 0.25 hour
5 miles per 1/8 of a gallon

Represent changes in quantities with percents (CCSS.Math.Content.7.RP.A.3):

5 increased by 300%

Determine prices and tips using percentages (CCSS.Math.Content.7.RP.A.3):

20% tip on $38.40
$80 with 30% markdown
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Expressions & Equations

Manipulate expressions and solve equations and inequalities, including those with negative numbers.

Simplify expressions (CCSS.Math.Content.7.EE.A.1):

expanded form 3.2 (x - 5) - 8x + 4 (2.7 + x)
combine like terms 1/2x + 2 - 3/4x + 3/2

Factor expressions (CCSS.Math.Content.7.EE.A.1):

factor 6x + 18

Solve an equation (CCSS.Math.Content.7.EE.B.4a):

solve 0.5 (x + 3) = -15
solve 46.4 = 4x + 11.2

Solve an inequality (CCSS.Math.Content.7.EE.B.4b):

solve 8 - x > 2.2
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Statistics & Probability

Analyze and compare datasets, including those from probability experiments.

Compare the centers of two datasets (CCSS.Math.Content.7.SP.B.4):

mean {2, 1, 4, 8, 2, 1} vs mean {7, 8, 6, 8, 9, 4}
median {187, 202, 112, 198, 155} vs median {34, 78, 61, 42, 89}

Compare the variability of two datasets (CCSS.Math.Content.7.SP.B.4):

IQR {2, 4, 8, 2, 1} vs IQR {7, 8, 6, 9, 9}

Perform probability experiments (CCSS.Math.Content.7.SP.C.6):

20 coin tosses
probability of rolling 7 on two 6-sided dice
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RELATED EXAMPLES

  • Algebra
  • Common Core Math: Grade 6
  • Common Core Math: Grade 8
  • Elementary Math
    • Geometry

    Draw shapes and compute geometric measurements.

    Draw a triangle with given side lengths, if possible (CCSS.Math.Content.7.G.A.2):

    triangle with side lengths 2, 6, and 7

    Draw shapes with given conditions (CCSS.Math.Content.7.G.A.2):

    parallelogram with all right angles

    Solve for measurements of circles (CCSS.Math.Content.7.G.B.4):

    area of circle with radius = 2

    Solve for measurements of three-dimensional solids (CCSS.Math.Content.7.G.B.6):

    volume of a cylinder with radius = 2 and height = 5
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