Fraction Division (With Models)
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4Fraction Division (with Models)
Consider a typical whole-number division problem like 41 ÷ 3. People
often solve it by thinking about how many 3s are in 41. The same thought
process applies to the division of fractions, and when used in combination
with fraction models, it helps students gain meaningful understanding of
dividing fractions.
Build Understanding
Have students use graph paper or templates to draw fraction models. As
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a review, ask students to represent fractions like
,
,
, and
. Encourage
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students to use a variety of shapes, such as squares, circles, hexagons, and
triangles. Ask students how they would represent a whole number, such as 5.
Using page 79, explain that students will use models to show the division. In
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Example 1, thinking about pizzas can help students visualize how many
s
3
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are in 5. If you have 5 pizzas, and divide each pizza into
s, then you have
3
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15 portions. In Example 2, if you have
of a pizza and want portions in
s,
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you divide the whole pizza into portions, each one the size of
of a pizza.
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You end up with 3 portions. Use questions like the following to guide students
through the examples:
• How do you represent the dividend? (Draw the number of shapes
needed — whole shapes for whole numbers and a part of a shape
for any fraction less than 1.)
• How would you divide each unit? (Divide each unit into the number
of equal pieces identified by the divisor.)
• How do you find the quotient? (Count the total number of pieces.)
Error Alert
Watch for students with inaccurate drawings, especially when
both the dividend and the divisor are fractions. Remind students that they
need to divide each whole unit shape into the number of equal pieces identified
by the divisor.
Page 79
Check Understanding
Answer Key
Have students work in pairs, and instruct partners to take turns drawing
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models. Circulate around the room checking drawings. Then work through a
couple of additional examples if necessary. When you are reasonably certain
that most of your students understand the algorithm, assign the “Check Your
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Understanding” exercises at the bottom of page 79. (See answers in margin.)
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Teacher Notes
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