## MTH212 Foundations of Elementary Math 2

### Fun with Fractions.

Notes on Fractions
Winter 2020

### Chapter 5: Integers and Fractions

#### § 5.3 Introduction to Fractions

Topics

Models:

Algorithms:
3/4+2/5= =23/20
• Fraction subtraction
Algorithms:
3/4-2/5= =7/20
• Fraction multiplication
Models:
Let two hexagons be one whole. Then this is 1/3 of 3/4.
• Fraction division
Models: 1/2 -: 1/6
How many groups of 1/6 are in 1/2?
##### 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

First, use color strips to show the sum as a part of the whole.
Then, draw and label a color srtip 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

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.

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.
2. Show 1/3+2/5.
3. Show 2/5+3/4.
4. Show 3/2+2/3.
5. Show 1/6+1/2.