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Middle school · Grade 7

Math 7

13 chapters89 lessons
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1

Adding and subtracting integers

4 lessons

Adding signed numbers on the number line, subtraction as adding the opposite, and distance as the absolute value of a difference.

Review first: Opposites and zero pairs Absolute value
1.1Adding integers
1.2Subtracting integers
1.3Distance on a number line
1.4Temperatures below zero and temperature change
2

Operations with rational numbers

7 lessons

The sign rules for products and quotients, all four operations on rational numbers, and decimals that terminate or repeat.

2.1What makes a number rational
2.2Multiplying and dividing integers
2.3Operations with rational numbers
2.4Multiplying and dividing rational numbers
2.5Order of operations with negative numbers
2.6Terminating and repeating decimals
2.7Rational numbers in real situations
3

Proportional relationships

9 lessons

A proportional relationship has a constant ratio; recognize it in tables, graphs and equations, and solve proportions.

Review first: Rates and unit rates Ratio tables
3.1Unit rates when the amounts are fractions
3.2What a proportion says
3.3The constant of proportionality and proportional tables
3.4Recognizing a proportional relationship in a graph
3.5Recognizing a proportional relationship in an equation
3.6Solving a proportion
3.7Setting up proportions from word problems
3.8Currency exchange
3.9Flow rate
4

Percent applications and percent change

12 lessons

The three percent questions, percent increase and decrease with a multiplier, and money problems from discounts to simple interest.

Review first: Finding a percent of a quantity
4.1Finding what percent one number is of another
4.2Finding the whole from a part and a percent
4.3Solving percent problems with an equation or a proportion
4.4Percents above 100 and below 1
4.5Percent increase and decrease
4.6The multiplier for a percent change
4.7Two percent changes one after the other
4.8Discounts, sales tax, tips and commission
4.9Markup and margin
4.10Simple interest
4.11Measurement error
4.12Percent error
5

Equivalent expressions

5 lessons

Rewrite linear expressions with rational coefficients by combining like terms, distributing and factoring.

Review first: Terms, coefficients and constants
5.1Combining like terms
5.2The distributive property with variables
5.3Distribute, then combine
5.4Factoring out the greatest common factor
5.5Rewriting an expression to show what it means
6

Two-step equations and inequalities

6 lessons

Solve two-step equations and inequalities with rational numbers, including why the inequality sign flips, and use them to solve problems.

Review first: One-step equations Inequalities on the number line
6.1Two-step equations
6.2Equations of the form p(x + q) = r, from words
6.3Equations from proportions and percents
6.4Converting between Celsius and Fahrenheit
6.5One-step inequalities and the sign flip
6.6Two-step inequalities
7

Scale drawings

4 lessons

A scale factor multiplies every length; read and make scale drawings, maps and plans, and see what scaling does to area.

7.1Scale factor
7.2Scale factor multiplies every length
7.3Using a scale on maps, plans and models
7.4Scale factor, area and volume
8

Angles, triangles and constructions

8 lessons

Complementary, supplementary, vertical and adjacent angles, and when three lengths make a triangle.

8.1Congruent angles, angle addition and bisectors
8.2Complementary and supplementary angles
8.3Adjacent angles and linear pairs
8.4Vertical angles
8.5Finding unknown angle measures
8.6Parts of a triangle
8.7Triangle inequality
8.8Drawing triangles from given sides and angles: one, many or none
9

Circles: circumference and area

4 lessons

Pi links the diameter of a circle to its circumference, and cutting a circle into slices shows why its area is pi r squared.

9.1Radius and diameter
9.2Circumference
9.3Area of a circle
9.4Why the circle area formula works
10

Area, surface area and volume of prisms

5 lessons

Area of composite figures, slices of solids, and the surface area and volume of right prisms and cylinders.

Review first: Nets of solids Surface area, and how it compares with volume
10.1Area of composite figures and shaded regions
10.2Converting square and cubic units
10.3Cross sections of solids
10.4Surface area of prisms and cylinders
10.5Volume of prisms and cylinders
11

Probability

9 lessons

Probability measures chance on a 0 to 1 scale; build probability models and compare them with relative frequencies from experiments.

11.1What randomness means
11.2Chance in words and the 0 to 1 scale
11.3Sample spaces, outcomes and events
11.4Listing a sample space: lists and tables
11.5Probability of an event
11.6Complements and probabilities that add to one
11.7Probability models: equally likely or not
11.8Experimental probability and relative frequency
11.9Geometric probability
12

Compound events and simulation

7 lessons

Find probabilities of compound events with tree diagrams and the counting principle, and estimate them by simulation.

12.1The fundamental counting principle
12.2Tree diagrams and organized lists
12.3Independent events and the multiplication rule
12.4Dependent events and drawing without replacement
12.5Designing a simulation
12.6The law of large numbers and the gambler's fallacy
12.7Running a simulation and estimating a probability
13

Sampling and comparing populations

9 lessons

Random samples support inferences about a population, samples vary, and two populations are compared by center and spread.

Review first: Mean absolute deviation Making and reading box plots Describing a distribution
13.1Populations, samples and census
13.2Convenience and voluntary response samples
13.3Response bias and question wording
13.4Simple random samples and the sampling frame
13.5Parameters and statistics
13.6Sampling variability and simulating it
13.7Comparing box plots
13.8Comparing two distributions
13.9Comparing two populations: the gap between means in MADs