Five pages on breaking fractions apart and putting them back together, with thirds, fourths, fifths, sixths, eighths and tenths. Page 1 shows a bar with some parts shaded, such as 3 of 4: students write 3/4 as 1/4 + 1/4 + 1/4, with a worked example first. On page 2 each fraction has two bars, each with its parts in two colors (gray and dots in black and white), and students write both ways, like 5/6 = 2/6 + 3/6 and 5/6 = 1/6 + 4/6. Page 3 turns it around: shade a bar to show 2/8 + 3/8 and write the sum, then add six short sums of unit fractions. Page 4 breaks fractions greater than 1 into a whole and the rest, like 7/4 = 4/4 + 3/4 = 1 + 3/4, then finds the missing part in six other ways to break them apart. Page 5 asks for every way to break 4/5 into two parts, and ends with three short stories about a ribbon, a pizza and cups of water.
Fraction strips or paper strips folded into equal parts make this concrete: give each student 5 sixths and ask them to split the pieces into two piles in as many ways as they can, writing an equation for each. For page 4, line up 7 fourth pieces under a 1 whole strip so students see 4 fourths make 1 and 3 fourths are left. Page 5 makes a good partner check: one student colors a way, the other writes it.
Cut a sandwich or a paper strip into fourths or sixths and share the pieces between two plates in different ways: "2 sixths on this plate and 3 sixths on that one is 5 sixths in all." Measuring cups work too: three 1/4 cups of water fill a 3/4 cup.
This pack supports the following Common Core State Standards for Mathematics:
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A 5-page pack for 3rd grade on breaking fractions apart and putting them back together. Write a fraction as a sum of unit fractions, like 3/4 = 1/4 + 1/4 + 1/4, read bar models that break a fraction apart two different ways, like 5/6 = 2/6 + 3/6 = 1/6 + 4/6, put two parts together and add unit fractions, break fractions greater than 1 into a whole and the rest, like 7/4 = 4/4 + 3/4 = 1 + 3/4, find every two-part way to make 4/5 and solve three short stories. Every page comes in color and in black and white. Answer keys included.
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