Key Stage 3: age 13 - 14
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
One-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 sequence where the rule is quadratic.
Resources required
Squared paper.
Learning activity
George works for a dairy that uses square milk crates. These can be divided
up to contain a square number of bottles fitting the crates with dividers.
Using two dividers George can fit four bottles into a crate. Using four
dividers he can fit 9 bottles into another sized crate. See the diagram.
How many bottles
can be fitted into a square crate if 30 dividers are used?
How many dividers would be needed for a square crate that could hold 100
milk bottles?
Start with the simple examples.
|
Crate
|
Number
of dividers
d |
Number
of milk bottles
m |
|
1
|
2
|
4
|
|
2
|
4
|
9
|
|
3
|
6
|
16
|
The pupils might notice
the following.
Square numbers are involved and because the dividers are used in pairs
then the number of them is always a multiple of two.
On each side of the crate there is one more spaces then the number of
dividers.
A general rule for the number of milk bottles can be generated:m = (½d + 1)²
Extension
Investigate rectangular
milk crates.
