1. Fractions with Pattern Blocks

2. You will need . . .
Students will need to have many pattern blocks of each shape available to them for this lesson.

3. Investigation
How many green triangles does it take to cover each pattern block piece below?
Begin by having students decide how many green triangles cover each of the other pattern blocks they have.
This information will be recorded on their recording sheet. In addition to writing these values, have students also draw the images as they are using the manipulatives.

4. Discovery
How many green triangles does it take to cover each pattern block piece below? 6 3 2

5. 1 ? ? Investigation If the yellow hexagon represents 1 whole.=
Place the red trapezoids on the hexagon to find the answer.
What does the red trapezoid represent? ? =
Have students discuss this with their partner or group, then ask a few students to share out what they think with the rest of the class.
What does the blue rhombus represent?
Place the blue rhombi on the hexagon to find the answer. ? =

6. Discovery 1 = 1 2 1 3

7. Compare: <, >, = 1 2 1 3 ? 1 2 1 6 ?
Before using the pattern blocks, ask students which fraction they think is greater.
Have the students represent these values with their pattern blocks.
Were their answers different when they used the blocks? What did they notice about the greater fraction? 1 6 1 3 ?

8. Findings: <, >, = 1 2 1 3
> 1 2 1 6
> 1 6 1 3
<

9. Investigation 1 2 ? 6 ? 6 1 = =
In this investigation, students are representing and adding fractions with their pattern blocks.
Ask: If one yellow hexagon represents one whole, which pattern block represents sixths?
Ask: One yellow hexagon is equal to how many sixths? Have students show this with their blocks. (6/6)
Ask: One red trapezoid is equal to how many sixths? Have students show this with their blocks. (3/6)
Ask: One blue rhombus is equal to how many sixths? Have students show this with their blocks. (2/6)
Ask: If we add 1/6 to 1/3, how can we represent this with the pattern blocks? (a blue rhombus and a green triangle)
Ask: When we put a blue rhombus and green triangle together, what pattern block does it represent? Prove it! (a red trapezoid, it covers the blue rhombus and green triangle perfectly) ? 6 ? 6 1 3 1 6 1 3 + = =

10. Discovery 1 2 3 6 6 1 = = 3 6 2 6 1 3 1 6 1 3 + = =

11. Investigation ? 6 ? 6 1 3 1 6 1 2 1 3 = + = +
We just completed 1/3 + 1/6, let’s try the next one.
Ask: What pattern blocks can we use to represent ½ and 1/3? (A blue rhombus and red trapezoid)
Ask: What do you think ½ + 1/3 equals?
(If students struggle, have students place the green triangles over both the rhombus and the trapezoid. Some students may instantly see that one sixth is missing, and know the answer, but continue have them use the green triangles on top of both the rhombus and trapezoid)
Ask: What pattern blocks can we use to represent ½ and 1/6? (A red trapezoid and a green triangle)
Ask: What pattern blocks can we use to cover the trapezoid and triangle? (We could use 4 green triangles. This is not in simplest form, so we could also use 2 blue rhombi)
Ask: What answer did you get?
Follow up questions could be:
Are 4/6 and 2/3 the same?
How do you know?
Which answer is in simplest form?
Ask: What pattern block can we use to represent 1/3? (a blue rhombus)
Ask: What can we do to add these together?
Ask: Is there another way we could add them together?
Ask: Are the answers the same? Explain! ? 6 ? 6 1 2 1 6 1 3 1 3 = = + +

12. Discovery 5 6 3 6 1 3 1 6 1 2 1 3 = + = + 4 6 4 6 1 2 1 6 = 1 3 1 3 = + +

13. Investigation 1 1 3 = ? ? = =
Ask: If we have a yellow hexagon and a blue rhombus, what number does this represent?
Ask: If we have two yellow hexagons, a blue rhombus and a green triangle, what number does this represent?
Ask: If we have three yellow hexagons, a red trapezoid, and a blue rhombus, what number does this represent?
Note: Some students may need to use the green triangles to cover some of the blocks to figure out the fractional part. Keep encouraging students to play with the blocks, covering them with other blocks to come up with the answer.

14. Discovery 1 1 3 = 3 5 6 2 1 2 = =

15. Addition/Subtraction Practice
Try the following addition and subtraction problems with your pattern blocks.
Have students practice adding these fractional parts together using their pattern blocks.
Students can draw a CRA table in their composition books (concrete=pattern blocks, representational=drawing the problems with shapes, and abstract=showing how to add the fractions together using the algorithm—some students may not be able to do the abstract part yet and that is ok)
As you lesson comes to a close, here are other questions to consider:
What is the relationship between the green triangle and the blue rhombus? (answers may vary…the triangle is half of the rhombus. Or one sixth is half of one third)
What is the relationship between the triangle and the trapezoid? (the triangle is one third of the trapezoid. Or, one sixth is one third of one half)
Ask more questions like this to facilitate student thinking and discovery!

16. Pattern Blocks Riddle 1: I have red and blue tiles.
½ the items are blue.
3 are red.
Find my tiles.
What number do they represent?

17. Pattern Blocks Fraction Puzzle 1:
Build a triangle that is 1/3 green and 2/3 red.
What number is this?

18. Pattern Blocks Fraction Puzzle 1:
Build a triangle that is 1/3 green and 2/3 red.
Are there other solutions?
Don’t show this triangle until students have had some time to try this for themselves.

19. Pattern Blocks Fraction Puzzle 2:
Build a parallelogram that is that is 3/4 blue and 1/4 green.

20. Pattern Blocks Fraction Puzzle 2:
Build a parallelogram that is that is 3/4 blue and 1/4 green.
Are there other solutions?