Upper Primary Mathematics Fractions - Commonwealth of Learning

Equivalent Fraction Concepts
Pupils should have a sound knowledge of equivalent fractions before learning
the four operations on common fractions especially addition and subtraction.
Two fractions are equivalent if they are representations for the same amount.
To acquire the conceptual understanding of equivalent fractions pupils should
use models such as area, length, and sets to discover different names for
models of fractions.
Practice Activity 7: Area Models
Paper folding can be used to effectively model the concept of equivalent
fractions. Fold a sheet of paper into halves or thirds. Unfold and colour a
fraction of the paper. Write the fraction. Now refold and fold one more time
(Figure 1.7). Before opening, guess how many parts will be in the whole
sheet and how many will be coloured. Open the paper. What fraction names
can be given to the shaded region? Is the name still the same? Why? What
about the amount of the shaded part, is it still the same? Why? Record the
equivalent fractions you have generated.
Figure 1.7
Rectangle Slicing: Multiply-by-1-method
We would like you to develop an equivalent fraction algorithm using
rectangle slicing with your pupils.
Put pupils in cooperative learning groups. Give them papers. Have them draw
several equal squares whose sides are 8 cm. Have them shade the same
fraction in several different squares vertically subdividing lines. Next, pupils
slice each rectangle horizontally into different fractional parts, as shown in
Figure 1.8. Help pupils focus on the products involved by having them write
top and bottom numbers as a product in the fraction.
1
Start with each square showing
2
1
2
=
1 × 2
=
2 × 2
2
4
Figure 1.8: A model for the equivalent fractions
Continues on next page
1
2
=
1 × 6
=
6
2 × 6 12
Module 2: Unit 1 10
Common Fractions