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Experiment 4 v7
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Exploring fractions with 120 counters
What fractions can you make out of 120 counters?
Purpose
This experiment gives children an opportunity to visualise fractions as whole numbers of counters and to practise counting.
The child will learn that adding two fractions is easy when they are rewritten to have the same denominator.
You need to know
- how to work with simple fractions
You will need
Steps
- Put all your counters in a big pile.
- Take one counter and put it in a new pile.
- Take another counter and put it in another new pile.
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Keep taking counters from your big pile and moving them to your new piles, adding to each in turn, until you have used up all the counters.
You should end up with two piles with the same number of counters in each.
- Count the number of counters in one of your piles.
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Draw this table and enter the number of counters you just counted in the 1/2 row.
Piles Fraction Counters out of 120 2 1/2 3 1/3 4 1/4 5 1/5 6 1/6 8 1/8 10 1/10 12 1/12 - Now bring the counters back together, then separate them into three piles.
- Count the counters in one of the piles and write this in the 1/3 row.
- Repeat this for the other rows in the table, to find the number of counters in 1/4, 1/5, 1/6, 1/8, 1/10 and 1/12.
Questions
- What is the equivalent fraction of 1/3 in 120ths?
- What is 2/3 in 120ths?
- Simplify the fraction 48/120 just using your table.
- What is 1/4 + 1/12 in 120ths? Simplify this fraction.
- What is 1/2 - 1/5 in 120ths? Simplify this fraction.
Expected answers
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1/3 is 40/120. This is the row with 40 counters in the table.
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2/3 is 80/120. This is double the previous answer.
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Using the table, 24/120 is 1/5, so 48/120 is 2/5.
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1/4 + 1/12 = 30/120 + 10/120 = 40/120. This is 1/3.
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1/2 - 1/5 = 60/120 - 24/120 = 36/120. This is 3 × 12/120 or 3/10.
The completed table should look like this:
| Piles | Fraction | Counters out of 120 |
|---|---|---|
| 2 | 1/2 | 60 |
| 3 | 1/3 | 40 |
| 4 | 1/4 | 30 |
| 5 | 1/5 | 24 |
| 6 | 1/6 | 20 |
| 8 | 1/8 | 15 |
| 10 | 1/10 | 12 |
| 12 | 1/12 | 10 |
Explore further (optional)
- Why do you think this experiment uses 120 counters instead of some other number?
- What is the smallest number that can be divided by 2, 3, 4 and 5?
Tips for further exploration
- 120 is divisible by lots of other numbers, so you can split the counters into piles with the same number in each pile. If this experiment used, say, 100 counters instead then you couldn't divide them equally into six, eight or ten piles.
- Any number divisible by 4 is also divisible by 2, so this is equivalent to finding the smallest number divisible by 3, 4 and 5. The simple way to get an answer (not necessarily the smallest) is to multiply them together. 3 × 4 × 5 = 60. In this case, that is the lowest answer.
