All bottled up
This is a level 3 number link activity from the Figure It Out series. It is focused on finding a fraction of a whole number. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers' notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
- Find a fraction of a whole number.
All bottled up
Achievement objectives
NA4-3: Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
Required materials
- Figure It Out, Link, Number, Book One, "All bottled up", page 23
See Materials that come with this resource to download:
- All bottled up activity (.pdf)
Activity
The capacity context of this activity allows students to explore the concept of the fraction of a set more fully. Use the first diagram in each pair shown in question 1 to help the students to appreciate the capacity of the whole container as an equivalent fraction for 1. Have the students record these fractions for 1 for each part of the question. They could record these fractions in a table.
Question |
1a |
1b |
1c |
1d |
1e |
1f |
|---|---|---|---|---|---|---|
Whole container as cups |
6/6 |
10/10 |
8/8 |
7/7 |
24/24 |
100/100 |
Question 1e will trap the unwary if they do not read the caption carefully. Question 1e also focuses the students on the complementary relationship between full and empty. After the students have answered question 1e, you could make this relationship quite explicit for each part of question 1 to reinforce the equivalent fractions for 1. Another table could be useful:
Question |
1a |
1b |
1c |
1d |
1e |
1f |
|---|---|---|---|---|---|---|
Fraction shown |
1/3 |
2/5 |
3/4 |
1/2 |
3/8 |
4/10 |
Fraction needed to make the whole |
2/3 |
3/5 |
1/4 |
1/2 |
5/8 |
6/10 |
This is a good activity to introduce the double number line as a tool for visualising the relationship between the fraction and the set. For question 1a, the number line could look like this:
Question 2 shows the effect of halving again and again. A ratio table would show this very powerfully:
Number of cups left |
16 |
8 |
4 |
2 |
1 |
|---|---|---|---|---|---|
Fraction left |
1 |
1/2 |
1/4 |
1/8 |
1/16 |
(The shaded part shows what happens if you continue halving.)
1.
a. two cups
b. four cups
c. six cups
d. three and a half (31/2) cups
e. 15 cups
f. 40 cups
2.
four cups
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