1. Copyright © Allyn and Bacon 2010
Big Ideas
For students to really understand fractions, they must experience fractions across many functions, including part of a whole, ratio, and division.
Three categories of models exist for working with fractions—area, length, and set or quantity.
Partitioning and iterating are ways for students to understand the meaning of fractions, especially numerator and denominator.
Students need many experiences estimating with fractions.
Understanding equivalent fractions is critical.
Copyright © Allyn and Bacon 2010

2. Building on Whole- Number Concepts
Misunderstandings of Fractions and Fraction Parts
Thinking of numerator and denominator as separate values
Not thinking of equal parts
Thinking that a fraction is smaller because it has a smaller denominator
Using the rules from whole numbers to compute
Only one size for the whole
Copyright © Allyn and Bacon 2010

3. Copyright © Allyn and Bacon 2010
Models for Fractions
Region or area models
Length models
Set models
Copyright © Allyn and Bacon 2010

4. Using Fraction Language and Symbols
Counting fraction parts: Iteration
Fraction notation
Fractions greater than 1
Assessing understanding
Copyright © Allyn and Bacon 2010

5. Estimating with Fractions
Benchmarks of zero, one-half, and one
Using number sense to compare
More of the same-size parts
Same number of parts of different sizes
More and less than one-half or one whole
Closeness to one-half or one whole
Including equivalent fractions
Copyright © Allyn and Bacon 2010

6. Equivalent-Fraction Concepts
Conceptual focus on equivalence
Equivalent-fraction models
Developing an equivalent-fraction algorithm
— a region model approach
— writing fractions in simplest terms
— multiplying by one
Copyright © Allyn and Bacon 2010

7. Teacher Considerations for Fraction Concepts
Focus on meaning
Develop a generalizable rule
Emphasize that fractions are numbers
Focus on fractions greater than one early
Provide a variety of models
Copyright © Allyn and Bacon 2010

8. More Teacher Considerations for Fraction Concepts
Link fractions to benchmarks
Give emphasis to fractions as division
Link fractions, decimals, and percents
Gain awareness of individual thinking
Look for examples and activities that engage
Copyright © Allyn and Bacon 2010

9. Fraction Review!

10. Just for fun…Which is your favorite fraction?
1/2
1/3
1/4
1/8
20 of 30

11. Which are true about fractions?
Part of a whole
A division problem
Equal parts
All of the above
22 of 30

12. Seconds
Remaining
Which is larger?
1/8
1/12 22 of 30

13. Here is a picture. Notice how the denominator shows how big or small the pieces are. 1/8 is larger because when there are fewer pieces, the pieces are larger!
1/8
1/12

14. Compare ½ and ¼. 20 30
½ > ¼
½ < ¼
½ = ¼
None of the above

15. Which fraction is greatest?
3/8
1/2
5/8
1/4
:00
19 of 30

16. Let’s look at it again! 3/8, 1/2, 5/8, 1/4
When we compare fractions we think about how much of the whole is represented. For example:
1/2 - The numerator is half of the denominator, so we know it is equal to one half.
5/8 – The numerator would need to be 4 to be half of 8 and 5 is more than 4, so it is greater than half!
3/8 – We know it is less than half because 3 is less than 4!

17. Which fraction is greatest
Which fraction is greatest? (Remember to compare the numerator with the denominator!)
1/10
2/4
4/5
3/5 21 of 30

18. Which fraction is the least?
3/4
7/8
1/2
12/16
17 of 30

19. When you looked at the last question (Which is least- 3/4, 7/8, 1/2, 12/16) did you compare the numerator with the denominator?
YES! NO
20 of 30

20. Which fraction is the greatest?
5/6
3/4 21 of 30
:00

21. Did you notice? …
3/4 and 5/6 are both just one piece away from being a whole!
So, which piece is smaller?
That’s right one sixth is a smaller piece than one fourth.
That means that although both fractions are only one piece away from being a whole, 5/6 is bigger because it needs a smaller piece added to become a whole!

22. Here is a picture!
5/6
3/4

23. Which fraction is least
Which fraction is least? (Remember to think about the size of the pieces!)
1/2
1/3
1/4
1/5 21 of 30

24. Which choice shows the fractions in order from least to greatest?
1/4, 3/5, 7/10
3/5, 1/4, 7/10
3/5, 7/10, 1/4
7/10, 1/4, 3/5
22 of 30

25. Which symbol will make this statement true? 9/12 5/8
<
> = ≤
:00
22 of 30

26. What is an equivalent fraction?
It is the same part of a whole, but is shown in a different way.
For example- 1/2 is the same as 2/4.
So, instead of 1 piece shaded out of two, you have two pieces shaded out of 4.
The relationship between the numerator and denominator is still the same! (1 is half of 2 and 2 is half of 4)

27. Which fraction is equivalent to 1/2?
4/8
3/4
1/3
2/5
20 of 30

28. Which fraction is equivalent to 2/8?
1/2
1/4
1/8
3/8
19 of 30

29. Fraction Riddles-Color Tiles
Riddle 1: A rectangle is red, green, blue, and the rest yellow. How much of the rectangle is yellow? Draw the rectangle on grid paper and record the fraction that tells which part is yellow.

30. Fraction Riddles- Color Tiles
Riddle 2: A rectangle is red. The rest is blue and yellow but not in equal amounts. What could the rectangle look like? Record.

31. Fraction Riddles- Color Tiles
Riddle 3: A rectangle is red and blue. Also, it has one green tile and one yellow tile. What could the rectangle look like? What fractional part is green? Yellow? Record

32. Fraction Riddles- Color Tiles
Now write your own!

33. 2005 Aims Education Foundation
Pattern Blocks
If the equilateral triangle is one, what whole number is represented by the rhombus?
If the triangle is one, what whole number is the hexagon?
If the rhombus is one, what whole number is represented by the hexagon?
If the trapezoid is one, what number is the hexagon?
2005 Aims Education Foundation

34. 2005 Aims Education Foundation
Pattern Blocks
If the hexagon is one, what fraction is represented by the trapezoid?
If the hexagon is one, what fraction is the rhombus?
If the rhombus is one, what fraction is represented by two triangles?
If the hexagon is one, what fraction is represented by a triangle and a trapezoid?
If the rhombus is one, what number is represented by the trapezoid?
2005 Aims Education Foundation

35. Fraction Riddles-Pattern Blocks
The area of all the blocks together is the same as the area of 24 green triangles.

36. Fraction Riddles-Pattern Blocks
The area of all the blocks together is the same as the area of 24 green triangles.
Three of the blocks together make up 75% of the total area.

37. Fraction Riddles-Pattern Blocks
The area of all the blocks together is the same as the area of 24 green triangles.
Three of the blocks together make up 75% of the total area.
The green blocks cover one-half as much area as the blue blocks.

38. Fraction Riddles-Pattern Blocks
There are 9 blocks.

39. Fraction Riddles-Pattern Blocks
There are 9 blocks.
The area covered by the yellow blocks is equal to the area covered by the blue blocks.

40. Fraction Riddles-Pattern Blocks
There are 9 blocks.
The area covered by the yellow blocks is equal to the area covered by the blue blocks.
The area covered by the red block is one-eighth the area covered by the yellow and blue blocks combined.

41. Fraction Riddles-Pattern Blocks
The blocks can be arranged to cover a yellow hexagon.
They can also be arranged to make a parallelogram.
There are only 2 colors of blocks.
There are no red blocks.

42. Fraction Riddles-Pattern Blocks
Now write your own!

43. Cuisenaire Rods
The yellow rod is half as long as the orange rod. Use the rods to demonstrate this. You can write this relationship in this way: ½ o=y
Find all the other pairs of halves you can with the rods and build them.
Find all the rods that show a relationship of thirds.

44. Cuisenaire Rods Find a blue rod.
What is the relationship of light green to blue?
Which rod would show 1/5 of blue?
What is the relationship of red to orange?
Find all possibilities comparing 1 rod to another.
How many different combinations can you make to show fractions? -Record.

45. Cuisenaire Rods Let the brown represent one whole.
How would you describe 1 purple + 1 white as a fraction?
What is the fractional name for light green?
What is the fractional name for black?
Find fractional names for all the other rods.

46. Wipe Out
You need: a partner, 1 set of pattern blocks, a cube with the faces marked: 1/2, 1/3, 1/3, 1/6, 1/6, 1/6, 1/6
The goal of the game is to be the first to discard your blocks. You each should start with the same number of hexagons (One, two, or three). Follow these rules:
Take turns rolling the cube. (You have three options on each turn):
Remove a block only if it’s the fractional part of the hexagon indicated by the fraction face-up on the cube.
Exchange any of your remaining blocks for equivalent blocks. OR…
Do nothing and pass the cube to your partner.
You may not remove a block and trade on the same turn. You can only do one or the other.