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In the Common Core, comparing two fractions with the same denominator or the same numerator is grade 3 work, with halves, thirds, fourths, sixths and eighths; the fraction bars sheet is the place to start. Comparing fractions with different numerators and different denominators is grade 4, with fifths, tenths and twelfths as well. Ordering three or four fractions is the harder sheet.

The same denominator or the same numerator

When the bottom numbers are the same, the parts are the same size, so the larger top number is the larger fraction: 5/8 > 3/8. When the top numbers are the same, the fraction cut into more parts is the smaller one, because each part is smaller: 3/4 > 3/8. Children often get this one backwards, reading the 8 as bigger than the 4.

Different tops and bottoms

Write both fractions over the same denominator, then compare the top numbers: for 2/3 and 3/4 the common denominator is 12, 2/3 = 8/12 and 3/4 = 9/12, so 2/3 < 3/4. When one fraction is less than a half and the other more, 1/2 decides it at once: 2/5 < 1/2 < 4/7, so 2/5 < 4/7. Two fractions can be equal though they look different: 2/3 = 4/6.

Ordering fractions

Give every fraction the same denominator, then order the top numbers: 3/4, 1/3 and 3/8 over 24 are 18/24, 8/24 and 9/24, so from least to greatest they are 1/3, 3/8, 3/4. The key shows the fractions over their common denominator.

Related printables 12

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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