8th grade math worksheets

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Pythagorean theorem

Grade 8

Find an unknown side of a right triangle using the Pythagorean theorem

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What to practice this year

The Pythagorean theorem is the year's centerpiece, and the direction matters. Finding the hypotenuse is an addition and a square root; finding a leg is a subtraction and a square root, and a child who has only practiced the first will add when they should take away. Both directions get their own sheets here for that reason, and every triangle is built from a whole-number triple so the arithmetic never obscures the method.

Why these skills come next

Whole-number answers are what make the practice about the theorem. Built from any two legs, a right triangle almost never has a whole hypotenuse, and a sheet full of surds tests notation rather than method. Every triangle here comes from a Pythagorean triple, which is what a textbook does and for the same reason.

Step 1 of 12

The Pythagorean theorem

Both directions on a triangle, then the same theorem on a coordinate grid.

Step 2 of 12

Roots, powers, and what kind of number

Undoing a square, sizing up the roots that never come out, and writing a number too big to write out.

Step 3 of 12

Angles and round solids

Two angle facts the year turns on, and the two solids a circle makes.

Step 4 of 12

Working with powers and letters

The three exponent rules, solving with x on both sides — and knowing when there is no answer at all.

Step 5 of 12

Moves on the grid

Sliding, flipping and turning a point — and what each move does to its coordinates.

Step 6 of 12

What a function is

Every input gets one output — and then whether the rule draws a straight line. Both have one catch each.

Step 7 of 12

Lines, and where two of them cross

The two numbers a line carries — and the pair that satisfies two lines at once.

Step 8 of 12

Moves on the grid, one at a time

The three transformations separately, before they are asked for mixed.

Step 9 of 12

Equations, all the way

Two steps, then a letter on both sides, then how many solutions there are.

Step 10 of 12

Angles and circles carried on

The parallel-line pair split out, and a slice of a circle measured.

Step 11 of 12

Roots on their own

Square and cube roots separately, which is how they are asked for.

Step 12 of 12

Two variables at once

A table, a cloud of points, and what either says about the pair.