Key Stage 3: age 11-13
Links to the National
Curriculum and Numeracy Strategy
- Represent problems and solutions in algebraic or graphical forms.
- Describe the general term of a simple sequence in words, then using symbols.
Duration
Two hours
Learning Objectives
Pupils will:
- select appropriate stategies to use for a numerical and algebraic problem.
- represent problems and solutions in algebraic form.
- find and describe in symbols the next term or nth term of a sequencewhere the rule is linear.
Resources required
Squared paper and/or access to Tile Archimedes'
Bathroom
Learning activity
Growing tile patterns.
Draw the following tile patterns on squared paper and continue the pattern.
How many blue tiles would be needed with 20 yellow tiles?......100 yellow tiles?
A table of results can be drawn
|
Number
of yellow tiles
y |
Number
of blue tiles
b |
|
1
|
5
|
|
2
|
8
|
|
3
|
11
|
|
4
|
14
|
The pupils might notice
the following.
Three more blue tiles are needed for each yellow tile. This sequence is
generated 5, 8, 11, 14.......
Each yellow tile needs three more blue tiles except the first tile which
needs an extra two at the side.
A general rule for the number of matchsticks can be generated:b = y x 3 + 2 or b = 3y + 2
Therefore 20 yellow
tiles will need 20 x 3 + 2 = 62 blue tiles.
Therefore 100 yellow
tiles will need 100 x 3 + 2 = 302 blue tiles.
Inverse functions
Use function machines to generate the inverse function:
t = (m-2)/3
Extension
Investigate other growing
tile patterns:
|
Number
of yellow tiles
y |
Number
of blue tiles
b |
|
1
|
8
|
|
2
|
13
|
|
3
|
18
|
|
4
|
23
|
The pupils might notice
the following.
Five more blue tiles are needed for each yellow tile. This sequence is
generated 8, 13, 18, 23,.......
Each yellow tile needs five more blue tiles except the first tile which
needs an extra three at the side.
A general rule for the number of matchsticks can be generated:b = y x 5 + 3 or b = 5y + 3
Therefore 20 yellow
tiles will need 20 x 5 + 3 = 103 blue tiles.
Therefore 100 yellow
tiles will need 100 x 5 + 3 = 503 blue tiles.
Inverse functions
Use function machines to generate the inverse function:
t = (m-3)/5
Move on to children
creating their own growing tile patterns.