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Describing the relationship across columns in different ways, including using letters as symbols.
Understanding ratio and the link to multiplication.
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| Resources |
Vocabulary |
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Scaffolding 1 and 2 notesheets – one per pair
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double, treble, vertical,
upright, slope, half, halve,
feet, factor, relationship
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| Organisation |
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Near ability pairs on mixed ability tables
Table prepared on board (for both first and second episode)
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| Whole class Preparation: (about 10 mins) |
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What Have large copy of Scaffolding 1 on a flipchart.
How could you describe Column A?
Write down their suggestions on the board.
Has anyone else got a different way of describing Column A?
Repeat this for the other columns. Allow pairs a few minutes to write ideas on the notesheet.
Focus only on the patterns going down separate columns, not on those linking one column to another yet.
Ensure that a variety of different descriptions are shared.
We have been looking at patterns going down. Now we are going to look at patterns going across.
Look at Columns A and B. (cover up C & D) What do you notice about the relationship between them? Now look at A & C (cover up B & D)
Write the suggestions down on the board.
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| Paired Work: (about 15-20 mins) |
Give pairs a copy of Notesheet 1. Agree with your partner on a
description of the relationship between the other columns.
Record your descriptions on the notesheet.
Move from pair to pair, accepting suggestions regarding
relationship between columns, moving towards and encouraging algebraic suggestions.
Identify particular pairs to give feedback to the whole class.
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| Class sharing : (about 10-15 mins)
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Share the descriptions of the relationships between columns given by the children.
Look for understanding of generalisation through questioning.
How can I convert a number from B to D? And back?
If I know B is 20 what would C be?
If B is 36, what is C? How can we find this out? How do we find half of 36?
If B is 200, or 202...?
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| Paired Work: (about 10 mins) |
Distribute Scaffolding 2 notesheet.
Explain why ‘feet’ is used as a measurement unit. We have changed the worksheet to metres. But feet are more
appropriate to the context. As we have this instruction to discuss the use of feet and maybe we should add – demonstrate foot length, let’s stick to feet.
Ask children for explanation of what scaffolding is (relate to building work).
On Scaffolding 2 diagram, draw the children’s attention to the lower slope (to 16 feet on vertical rod) and upper slope (to 20 feet on vertical rod).
Explain the need Class to strengthen Sharing: (about scaffolding 10 mins) with additional
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| Class sharing: (about 10 mins) |
Collect the results in a table format on the board, close to the previous table.
How did you work it out for 15 feet? For 40 feet?
How could we describe the relationship going across? The ground to upper slope is 1.25 times the height of ground to lower slope.
If you had to extend the scaffolding to include an upright at 40
feet, what would be the heights at the upper and lower slopes? 40 feet and 32 feet.
What would the upper slope be if the lower slope was 12 feet? 15 feet.
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