Factorising with Multilink
Why do this problem?
When students first meet factorisation, they often don't make the connection between factorising an algebraic expression and breaking a number into factor pairs. This problem introduces factorisation using a visual representation that allows students to make that connection and discover for themselves the properties necessary for a quadratic expression to factorise.
This problem is a nice example of a Low Threshold High Ceiling task, as students can use the representation to factorise more and more complicated examples. You can read more about Low Threshold High Ceiling tasks in this article.
Possible approach
Take a look at the second video to see how Becky and Charlie resolve their different rectangles into one that works for both of them.
Key question
What is the connection between the number of sticks you need, the number of units you need, and the dimensions of the rectangle?
Possible support
Start students off on families of examples such as:
$x^2 + 3x + 2$
$x^2 + 4x + 3$
$x^2 + 5x + 4$
...
Possible extension
Think about the rectangles it's possible to make if you use 2, 3, 4... squares, some sticks and some units.
Finding Factors consolidates the ideas met here and has factorisations which require negative terms.
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