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To be able to express relationships between two variables in different ways, using words, words and symbols, symbols, tables and graphs.
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| Resources |
Vocabulary |
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Notesheets Gardens 1 and 2 (one per pair)
Notesheet Gardens 3 (one per pair)
Paper
Large prepared tables and graphs for class sharing
Pencils, rubbers and rulers
Small toy people for the Left/Right Robots
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pattern, adding, doubling, symbol, multiplying, trebling, algebra, plot, steepness, slope, intercept, axis, axes |
| Organisation |
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Working in near ability pairs
Draw tree from Gardens 1 with twigs and branches but no leaves onto the board before the lesson
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| Whole Class Preparation, Group Work and Sharing: (about 15-20 mins) |
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Refer children to the drawing on the board. Add leaves to one of the branches.
What do you notice about the leaves, twigs and branches? Two leaves at the beginning of each branch, groups of three, and so on. Repeat for the next branch.
Give out Gardens 1 notesheet.
Children work on the rest of the Gardens 1 questions for five minutes.
Ensure pairs write a sentence to explain how to work out the number of leaves.
How could we write this in symbols? 3t + 2 = l Compare with the relationship expressed in words.
On the board, draw up a table of the results as a class.
Look at the adding 3 pattern. How does this compare with the 3t + 2 = l?
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| Paired Work: (about 10 mins) |
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Give out Gardens 2 notesheet and begin a whole-class discussion of the pattern, using the board.
Children then work in pairs to suggest further patterns.
Suggest the number of white tiles needed for 100, 17 and 333 black tiles.
Children work on describing the relationship between black and white tiles (questions 1-5 on the notesheet) and write down their thoughts.
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| Class Sharing: (about 10 mins) |
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Fill in the table together on the board (see Gardens 2).
As a class, discuss and record the final formulation for the relationship between the white and black tiles. w = 2b + 1.
What did you notice that was similar about the trees and the tiles? See question 6 on the notesheet. Record the responses on the board.
What did you notice that was different? Record the responses on the board
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| Paired and Group Work: (about 10 mins) |
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Give out Gardens 3 notesheet.
Children work in pairs to plot graphs and then discuss findings in groups.
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| Class Sharing: (about 15 mins) |
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Discuss and compare the two graphs. What is similar and what is different about the two patterns? Starting points, gradient, both straight lines. What would happen if you took intermediate points?
What are the advantages and disadvantages of each of the representations? The pictures, tables, verbal and symbolic representations of the relationships and the graphs.
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