Purpose
The purpose of this activity is to support students understanding that fractions can represent quantities greater than one. For example, 8/4 = 2 represents eight quarters, which is equal to two ones.
Achievement Objectives
NA3-1: Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.
NA3-5: Know fractions and percentages in everyday use.
Required Resource Materials
- Strips of paper and Fraction Strips
Activity
- Use iterations of unit fractions (from fraction strips) and a number line to explore making different fractions that equal one.
How many parts will we need of this fraction to make one? How do you know? (Look for students to recognise the meaning of the denominator)
What numbers will we get if we add one more part to each fraction?
For example, adding 1/4 to 4/4 gives the improper fraction 5/4.
How else might we write each improper fraction?
3/2 = 1 ½, 4/3 = 1 ⅓, 5/4 = 1 ¼, etc.
Emphasise that mixed numbers are a combination of whole numbers and fractions. - You might introduce releavant te reo Māori kupu, such as hautau nui ake i te kotahi
(improper fraction).
- Ask students to make specific improper fractions (e.g. 5/3) and rename them as mixed numbers (i.e. as 1 2/3). You might use fractions strips and number lines as a supportive strategy. Good examples are:
- Increase the size of the numerators to encourage students developing a standard method for working out a mixed number from a given improper fraction.
Imagine I have 13 halves. How do I write that number as a fraction? (13/2)
How do I write 13 halves as a mixed number? (6½)
The most important aspect for students to consider is that two halves make one (2/2)
Dividing the numerator by two tells how many ones can be made. The remainder give the fraction of the mixed number. 13 ÷ 2 = 6 remainder 1. The division by two can easily be modelled by laying out 13 half strips and pairing them up to form ones.
- Provide other conversion examples, such as:
- Imagine I have 11 thirds. How do I write that number as a fraction? (11/3)
How do I write 11 thirds as a mixed number? (3 ⅔) - Imagine I have 17 quarters. How do I write that number as a fraction? (17/4)
How do I write 17 quarters as a mixed number? (4 ¼) - Imagine I have 24 fifths. How do I write that number as a fraction? (24/5)
How do I write 24 fifths as a mixed number? (4 ⅘)
- Imagine I have 11 thirds. How do I write that number as a fraction? (11/3)
Next steps
- Increase the level of abstraction by progressing from using fraction strips, to diagrams, and then to symbols only.
- Ask students to rename an increasing array of improper fractions to mixed numbers, e.g. 15/4 = 3 ¾, and rename mixed numbers to improper fractions, e.g. 6 ⅗ = 33/5.
- Explore equivalence with improper fractions. For example, 14/4 = 7/2.
Add to plan
Level Three