# Decimal Fractions of a Set

Teacher’s Notes

### Number Framework domain and stage:

Fractions ratios and proportions, addition and subtraction stage 6, advanced additive

### Curriculum Reference:

Number, level 6

### Numeracy Project book reference

These activities can be used to follow the teaching episodes based on, Book 7, page 11 (Hungry Birds) and are for those students who are able to use the associated number properties.

### Figure it out References

These activities can be used to follow Number Book 1, Level 2 pages 17 (Flipping Fractions), 19 (Dazzler Digs On) and Number Book 2, Level 2 page 24 (Finding the Fractions) with the emphasis on decimal fractions.

### Prior knowledge. Students should be able to:

- Explain why 10/10 is another name for one whole
- Identify mixed numbers and explain how they relate to improper fractions
- Find fractions of a quantity

### During these activities students will meet:

- Adding and subtracting fractions with the same denominator
- Converting fractions (tenths) to decimals
- Finding fractions of a quantity

### Background

Exercise 1: Adding tenths

With the exception of the last 2 problems, in this exercise the answers are less than one, and as the questions require students to convert their answers to decimals, simplification of the fractions is not required, but could be discussed as another way of ‘tidying up’ the numbers.

Exercise 2: Adding tenths

In this exercise, all of the answers are greater than one. Question 7 and beyond represent a slight change in the pattern. Here each rooster is eating more than one worm, so the answers can be sorted by ‘adding like to like’, that is adding the whole numbers and the fractional parts separately.

Exercise 3: Adding and subtracting tenths. Finding “tenths of …”

In this exercise students are combining the skills of adding fractions to one whole and finding the fraction of an amount. In the last problem, Tim and Ted are equally sharing nine tenths, meaning they get four and a half tenths each. Discussing how to write such fractions should be covered either before the exercise is sat, or afterwards as a debrief, where the students are asked to explain how they met this challenge. Going back to materials (decimats are a good resource here) to display (4/2)/10 and sorting out *why* it equals 9/20 is useful.

Exercise 4: Finding tenths of coins/working with money.

In this exercise students not only work out fractions of an amount, but also work out how much money that have with this number of coins

### Practice exercises with answers:

### Related activity

Flipping Decimal Fractions - Memory game based on “Flipping Fractions” (Figure it Out Number Book 1, Level 2 page 17):
PDF (74KB) or Word (67KB)

Domino activity: PDF (91KB) or Word (110KB)