Activity 5.3a: Fraction Addition Models

Math Activity: Modeling Addition and Subtraction

Purpose: Apply physical models for the addition or subtraction of fractions.

Materials: Color strips or color rods, pattern blocks, paper & colored pencils.

Considerations: For these models we view a fraction as an equal part of a whole, addition as combining and counting, and subtraction as a comparison where we identify the difference.

Part 1: Color strips (online toy Links to an external site.)

First, use color strips to show the sum as a part of the whole.
Then, draw and label a color strip for each fraction, and show them as a part of a whole.
Name the combined part of the whole. That is, what does the illustration show the sum to be?

1. Choosing the dark green color strip to be one whole, show 1/3 + 1/3.
   
   
   
2. Choosing the dark green color strip to be one whole, show 1/6 + 1/3.
   
   
3. Choosing the dark green color strip to be one whole, show 1/2 + 1/3.
   
   

Part 2: Pattern Blocks (online toy Links to an external site.)

First, use pattern blocks to show the sum as a part of the whole.
Then, draw and label a pattern block for each fraction, and show them as a part of a whole.
Name the combined part of the whole. That is, what does the illustration show the sum to be?

1. Choosing the yellow hexagon as one whole, show 1/3 + 1/3.
   1/3 + 1/3 = 2/3 of one whole.
   
   
   
2. Choosing the yellow hexagon as one whole, show 1/3 + 1/6.
   
   
3. Choosing the yellow hexagon as one whole, show 1/3 + 1/2.
   
   
4. Using two hexagons as one whole, show 2/3 + 1/12.
   
   

Part 3: Square Cakes

Draw and label a square for each fraction. The squares should be the same size whole, the first cut vertically and the second horizontally.
Cut each square like the other if necessary.
Name the combined part of the whole. That is, what does the illustration show the sum to be?

1. Show 1/2 + 1/3.
   
   Combine 1/3 with 1/2. Problem, they are different sizes.
   So cut each cake like the other.
   
   How many equal shaded pieces are there in both squares?
   How many equal pieces are there in one whole square?
   There are 5 shaded pieces out of 6 in the whole.
   So 1/3 + 1/2 = 5/6.
   
   
   
2. Show 1/3 + 2/5.
   
   
3. Show 2/5+3/4.
   
   
4. Show 3/2+2/3.
   
   
5. Show 1/6+1/2.