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2. How to Use Visual Models to Find Equivalent Fractions
Dawn Galente, Arlington CSD 2012
This is a self-paced tutorial. Click the screen each time you want to see the next step.
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3. Standard 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models….use this principle to recognize and generate equivalent fractions. 1 3 =
Start with a simple fraction like 1/3.
Picture what this model would look like if we broke each part into 2 equal pieces. What fraction would this new model represent?
This model represents 2/6 because 2 out of 6 pieces are now shaded. 2 6 =

4. I can find any number of equivalent fractions by simply breaking each piece in the model into smaller pieces.
Start with 1/3…
break each piece into 4 equal pieces…
to get 4/12. x4
I have four times as many shaded pieces now; 1 x 4= 4. 1 3 4 12 = x4
I have four times as many total pieces now…
3 x 4 = 12.

5. 3 4 9 12 Here’s another example. Start with ¾.
What happens if we break each piece into 3 equal pieces?
We get 9/12. x3
Now I have three times as many shaded pieces:
3 x 3 = 9 shaded. 3 4 = 9 12 x3
Now I have three times as many total pieces:
4 x 3 = 12 total.

6. What if I want to find a specific equivalent fraction?3 ? =
Start with a model of the first fraction. 5 10
Think: I have 5 total pieces now. I need 10 total pieces.
How can I break 5 pieces into smaller pieces so that I have 10?
Break them into 2 pieces each!
How many shaded pieces do I have?
3 x 2 = 6. 6 x2 3 5 10 = x2

7. 2 6 3 ? 2 3 6 9 What if I want to find a specific equivalent fraction?=
Start with a model of the first fraction. 3 ?
Think: I have 2 shaded pieces now. I need 6 shaded pieces.
How can I break 2 pieces into smaller pieces so that I have 6?
Break them into 3 pieces each!
Now how many total pieces do I have?
3 x 3 = 9. x3 = 2 3 6 9 x3

8. a/b is equivalent to (n × a)/(n × b) means…..3 4 = a b x3 3 4 a b
x n 9 12 =

9. The End