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To develop understanding of fractions, ratio and proportion in a variety of familiar contexts.
To link language to meaning and make connections.
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| Resources |
Vocabulary |
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Notesheets Two jars, one about half full of coloured water (if demonstrating practically)
A3 copies of the notesheet – one between two
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full, empty, half full, half empty, half of a half, quarter, halving,dividing by 2, add, more of, lots of, times |
| Organisation |
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Near achievement pairs on mixed tables
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| Whole Class Preparation: (about 10 mins) |
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Refer I’ve got water in this jar and I pour half of it into another jar. Demonstrate with two jars or mime and ask children to imagine that you have a half-full jar.
What can you tell me about either of the jars? Half of a half... half take away a quarter... half divided by two... half empty... half full. Collect the suggestions in sentences, words, pictures and numbers or symbols. In other words, ‘If we take half of a half we get a quarter’ or ‘1/2 – 1/4 = 1⁄4’.
Are there any things on the board that you think mean the same thing?
Explore connections between the different descriptions.
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| Paired Work: (about 10 mins) |
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Give out a copy of the notesheet Halving and Thirding to each pair.
Here are pictures of a bar of chocolate.
You will need to quickly shade in the pictures to show what is happening.
Going across the page, you need to shade half, then half again. Point out that they can only shade where the lines are, just as you would break a bar of chocolate, and cannot make up lines of their own.
Going down you need to shade a third and then a third again.
Remind them about the recording that you did on the board for two jars. You should record what is happening in words and numbers or symbols, like we did before.
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| Class Sharing: (about 10 mins) |
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How did you decide where to shade? Some children will do this intuitively by spatial awareness and others will need to count squares.
Stick the notesheet on the board and collect feedback on one or two particular pictures where children have a lot to say.
How would you describe the top right picture? Start with contributions from the least able children.
The centre picture is described as 1/3 of a 1⁄2; has anyone else got a different description? 1/2 of a 1/3, 1/6, 6/36. In what ways are these the same? Explore difference between. When would you use each one? When would you say it one way or another way?
What about the bottom middle picture?
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| Paired Work: (about 15 mins) |
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Imagine that I have got two pots of paint in my hands. They are not full and they have the same amount of paint in each one. Mime actions.
The paint in one pot is blue and in the other it’s yellow.
I pour half of the blue paint into the yellow paint and stir it really well.
Then I pour half of the mixture back into the first tin and stir it really well.
Is the paint in the pots the same colour? Why or why not? Can you prove it?
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| Class Sharing: (about 10 mins)
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Collect feedback, asking children to demonstrate with diagrams, or number explanations on the board. Let the children discuss each other’s’ arguments.
How much darker is it? Accept general responses, such as ‘almost twice as dark’, leading to a ratio of 9 to 5 (see diagram).
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