Adding and subtracting fractions

Prior knowledge.

• Identify that the denominator in a fraction tells us how many equal sized parts are in a whole, and the numerator tells us how many of the pieces we are interested in
• Students can coordinate the numerator and the denominator in a fraction to create and explain meaning for fractions

Background

Before this activity is commenced, students should have learnt that fractions can be smaller than one, can equal one, and be greater than one, and can relate drawings to numeric fractions. It is also useful if they can convert improper fractions to mixed numbers, though as the students are at stage 5 this is likely to be using additive methods rather than multiplicative ones.

Comments on the Exercises

Exercise 1
Asks students to solve addition problems with fraction with the support of diagrams.  Exercise 1 is an exploration that hopes to build on students’ existing knowledge about fractions to help students establish/invent a strategy for adding simple fractions. The first problems have both a word story and a set of drawings to represent the story mathematically. Some students may need to be introduced to the idea that both of these representations show the same thing. The next problems rely simply on the drawings. Once students have developed a strategy for adding such fractions, they are then invited to use this on some numeric fractions

Exercise 2: Parts in a whole
Asks students to revisit the idea that n/n = 1

Exercise 3
Asks students to solve problems involve addition of fractions with like denominators. Many have answers that are greater than one. Students who have learned to convert improper fractions to mixed numbers should be challenged to make this conversion, even though the answers do not provide this format. Likewise, answers are not simplified as students at this stage cannot be expected to understand multiplicative processes.

Investigation
Asks students to think about subtraction of fractions with like denominators, again starting with story problems and drawings that show these. Some students may find it challenging to make up the word problems required, or how this could be represented with drawings. This investigation can form part of a teaching session which covers the same concepts.

Exercise 4
Asks students to solve basic subtraction problems with like denominators