Upper Primary Mathematics Fractions - Commonwealth of Learning
Upper Primary Mathematics Fractions - Commonwealth of Learning
Upper Primary Mathematics Fractions - Commonwealth of Learning
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3 1<br />
4 3<br />
÷<br />
2<br />
1<br />
2<br />
÷<br />
4<br />
1<br />
4<br />
Figure 3.7: Ratio Table<br />
These are all algorithms for division <strong>of</strong> common fractions. You can discover<br />
some more.<br />
Unit Activity 5<br />
2<br />
1. (a) Make a story problem involving 1<br />
3<br />
1<br />
÷<br />
2<br />
2<br />
(b) Model 1<br />
3<br />
1<br />
÷<br />
2<br />
using strips and counters.<br />
2. Why does the invert-and-multiply rule work?<br />
3. Prove that the common denominator algorithm is a valid algorithm.<br />
4. In the ratio table, write the operations carried out to move from one<br />
2<br />
column to the next in each <strong>of</strong> the workings for<br />
3<br />
3<br />
÷<br />
4<br />
8<br />
=<br />
9<br />
5. Sibeso has difficulty with division. What is the cause <strong>of</strong> her error? How<br />
3<br />
can you help her?<br />
4<br />
1<br />
÷<br />
2<br />
3 1<br />
= x ÷<br />
4 2<br />
3<br />
=<br />
8<br />
Reflection<br />
Which <strong>of</strong> these two algorithms is ‘best’—the common denominator algorithm<br />
or the invert-and-multiply algorithm. Why?<br />
Practice Activity 5<br />
3<br />
4<br />
1<br />
3<br />
2<br />
1<br />
2<br />
4<br />
1<br />
4<br />
9<br />
4<br />
1 1<br />
6<br />
4<br />
17<br />
4<br />
1. Have pupils model partitive division and measurement division.<br />
2. Help pupils generate common denominator algorithms and invert-andmultiply<br />
algorithms.<br />
Module 2: Unit 3 34 Multiplication and Division <strong>of</strong> Common <strong>Fractions</strong><br />
2<br />
1<br />
4<br />
10<br />
17<br />
10<br />
17<br />
1
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