Multiplication worksheets
Practice products of two whole numbers from the range you choose. The answer key lists each product.
Pythagorean theorem worksheets
Ten right triangles a page, each drawn to its own shape and turned a different way, with two sides given and x on the side to find: the hypotenuse, a leg, or either. Or answers to the nearest tenth, three lengths to test for a right triangle, or word problems. The answer key works each one through a² + b² = c². New triangles each time.
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Find the missing side · LetterFind the missing side · A4Find the hypotenuse · LetterFind the hypotenuse · A4Find a missing leg · LetterFind a missing leg · A4Answers to the nearest tenth · LetterAnswers to the nearest tenth · A4Is it a right triangle? From three side lengths · LetterIs it a right triangle? From three side lengths · A4Word problems · LetterWord problems · A4
Which sheet to choose
In the Common Core, using the Pythagorean theorem to find a missing side of a right triangle is grade 8 work, and so is its converse, telling from three lengths whether a triangle has a right angle. Start with the hypotenuse, then a missing leg, then the two mixed; move to the nearest tenth once the squares and square roots come easily, and finish with the word problems.
Finding the hypotenuse
In a right triangle a² + b² = c², where a and b are the legs, the two sides that make the square corner, and c is the hypotenuse, the side across from it and always the longest. For legs of 6 and 8: 6² + 8² = 36 + 64 = 100, and √100 = 10, so the hypotenuse is 10.
Finding a leg
To find a leg, take away instead of adding: with a hypotenuse of 13 and a leg of 5, x² = 13² − 5² = 169 − 25 = 144, so x = 12. Adding by mistake gives √194, about 13.9, longer than the hypotenuse, which cannot be right: a leg is always shorter than the hypotenuse. That is why some triangles on these sheets lie on their longest side.
Is it a right triangle?
Square the two shorter sides and add, then compare with the longest side squared. For 9, 12 and 15: 81 + 144 = 225, and 15² = 225, so it is a right triangle. For 6, 8 and 11: 36 + 64 = 100, but 11² = 121, so it is not. The longest side is c even when it is not written last.
Answers to the nearest tenth
Most square roots are not whole numbers. For legs of 4 and 7: 16 + 49 = 65, and √65 is about 8.06, which is 8.1 to the nearest tenth. A calculator gives the square root; the key shows the number under the root, so a wrong sum is easy to spot.
Related printables 12
Addition worksheets
Add pairs of whole numbers from your chosen range. Write each sum in the blank and check it against the answer key.
Subtraction worksheets
Subtract the smaller whole number from the larger one. Answers are zero or positive, with a separate key for checking.
Division worksheets
Divide a whole-number product by one of its factors. Every question has a whole-number answer; these sheets do not use remainders.
Fractions worksheets
Add two fractions with the same denominator. The answer key reduces each result by its greatest common divisor.
Telling time worksheets
Read an analogue clock and write its time. Questions use five-minute intervals, with the hour and minute in the answer key.
Counting money worksheets
Count the coins and write the total in cents: pennies, nickels, dimes and quarters drawn at their real size, six groups a page, totals under a dollar, with the answers on the key. Leave out the quarters for an easier sheet. New coins each time.
Number bonds worksheets
Number bonds to 10: the whole in the top circle, its two parts below, and one of the three left empty to fill in. Choose the largest whole, up to 100, and how many bonds; the answer key is on the last page.
Place value worksheets
Place value practice with numbers of 2 to 5 digits: half the questions ask what one digit is worth, as the 4 in 3,482 is worth 400, and half ask for the number in expanded form, as 3,000 + 400 + 80 + 2. The answer key is on the last page.
Measuring length worksheets
Six lines drawn at their true length, to measure with a ruler from the left end and write down to the nearest half inch, then two lines to draw at a given length, with a ruler to cut out at the foot of the page and the answers on page 2. Choose whole, half, quarter or eighth inches, or whole or half centimetres.
Measuring angles worksheets
Six angles a page, drawn at their true size from 10 to 170 degrees in steps of 5, to measure with a protractor and circle as acute, right or obtuse, with the answers on the key. One arm lies flat to start, pointing left or right; on the harder sheet both arms turn. New angles each time.
2D shapes worksheets
Eight flat shapes a page to name, and to count the sides and corners of: triangle, square, rectangle, rhombus, trapezoid, pentagon, hexagon, octagon, circle and oval, with the answers on the key. On the harder sheet each shape is turned and the triangles and rectangles change shape, so the name rests on the sides. New shapes each time.
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