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Middle school · Grade 8

Math 8

13 chapters89 lessons
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1

Exponents and scientific notation

8 lessons

The laws of exponents, including zero and negative exponents, and scientific notation for very large and very small numbers.

Review first: Base, exponent and the value of a power
1.1Multiplying and dividing powers with the same base
1.2Powers of powers, products and quotients
1.3Zero and negative exponents
1.4Monomials and the exponent rules
1.5Writing and reading scientific notation
1.6Comparing numbers in scientific notation
1.7Calculating in scientific notation
1.8Significant figures
2

Roots, irrational numbers and the real numbers

9 lessons

Square and cube roots, numbers that are not rational, approximating them, and the real number line that holds them all.

Review first: Perfect squares and perfect cubes
2.1Which fractions give terminating decimals
2.2Turning a repeating decimal into a fraction
2.3Square roots
2.4Cube roots and higher roots
2.5Irrational numbers
2.6Approximating irrational numbers
2.7The real number line
2.8Sorting a number into its sets
2.9Terminating and repeating decimalsretaught
3

Linear equations in one variable

4 lessons

Solve multi-step linear equations, with variables on both sides, decide how many solutions there are, and solve a formula for one variable.

Review first: Two-step equations The distributive property with variables
3.1Multi-step equations
3.2Equations with variables on both sides
3.3No solution, one solution, or every number
3.4Literal equations: solving for one variable
4

Proportional relationships and slope

7 lessons

Rate of change and slope from graphs, tables and two points, with proportional relationships as lines through the origin.

Review first: The constant of proportionality and proportional tables
4.1Rate of change
4.2Slope from a graph or a table
4.3The slope formula and the four kinds of slope
4.4Slope triangles: why a line has one slope everywhere
4.5Direct variation
4.6Inversely proportional relationships
4.7Recognizing a proportional relationship in a graphretaught
5

Linear relationships

7 lessons

Lines as y = mx + b, graphed from tables and equations, written from points and slopes, and used to model situations.

5.1Graphing a line from a table of values
5.2Slope-intercept form
5.3Graphing a line from its equation
5.4Point-slope form and the line through two points
5.5Standard form of a line
5.6Parallel and perpendicular lines
5.7Modeling with linear relationships
6

Functions

11 lessons

A function assigns each input exactly one output; read functions from tables, graphs and stories, and compare linear functions.

Review first: Functions as input-output rules Independent and dependent variables
6.1Relations and functions
6.2Domain and range from pairs and tables
6.3Graphing a function from a table
6.4Testing graphs and equations for functions
6.5Evaluating a function at a number
6.6Reading values off a graph
6.7Constant rate of change and linear tables
6.8Reading a linear function from its graph
6.9Linear and nonlinear functions
6.10Comparing linear functions given different ways
6.11Graphs that tell a story
7

Systems of linear equations

4 lessons

The solution of a system is where two lines meet; solve by graphing, substitution and elimination, and apply to word problems.

7.1Solving systems by graphing
7.2Solving systems by substitution
7.3Solving systems by elimination
7.4Systems in word problems
8

Rigid motions and congruence

9 lessons

Translations, reflections and rotations keep lengths and angles, and two figures are congruent when rigid motions carry one onto the other.

8.1Segment length, addition and congruence
8.2Midpoints and segment bisectors
8.3Perpendicular bisector of a segment
8.4Translations
8.5Reflections
8.6Rotations
8.7What rigid motions preserve
8.8Composing transformations
8.9Rigid motions and congruence
9

Dilations and similarity

4 lessons

A dilation scales every length from a center, and similar figures are related by rigid motions and dilations.

Review first: Scale factor
9.1Similar figures
9.2Dilations
9.3Similarity transformations
9.4Scale factor, area and volumeretaught
10

Parallel lines, transversals and the triangle sum

5 lessons

Angles formed by a transversal, why the angles of a triangle sum to 180 degrees, and the angle-angle test for similar triangles.

Review first: Vertical angles Adjacent angles and linear pairs
10.1Corresponding angles
10.2Alternate and same side angles
10.3Triangle angle sum
10.4AA similarity
10.5Proportions in similar triangles
11

The Pythagorean theorem and distance

7 lessons

Why the Pythagorean theorem and its converse hold, and using them to find lengths and distances on the coordinate plane.

Review first: Distance on a number line Approximating irrational numbers
11.1The Pythagorean theorem
11.2Proving the Pythagorean theorem by rearrangement
11.3Converse of the Pythagorean theorem
11.4Using the Pythagorean theorem
11.5The Pythagorean theorem in three dimensions
11.6Pythagorean triples
11.7The distance formula
12

Volume of cylinders, cones and spheres

6 lessons

Volume formulas for cones and spheres built from the cylinder, and volumes of composite solids.

Review first: Cylinders and cones
12.1Volume of a cylinder
12.2Volume of pyramids and cones
12.3Spheres
12.4Volume of a sphere
12.5Composite solids and density
12.6Volume of prisms and cylindersretaught
13

Scatter plots and two-way tables

8 lessons

Patterns of association in bivariate data, from scatter plots and lines of fit to relative frequencies in two-way tables.

13.1Plotting paired data: explanatory and response variables
13.2Describing a scatter plot
13.3Line of best fit
13.4Interpreting the slope and intercept
13.5Relative frequency tables
13.6Joint and marginal frequencies
13.7Conditional relative frequencies
13.8Association in a two way table and segmented bar graphs