Monday Maths: Vicki Robinson, Communications Officer

# A farm-filled #MondayMaths

Posted: 7/11/16

For this week’s agricultural-themed #MondayMaths, we’re asking puzzle-solvers to tackle the areas of two different sized fields and express them algebraically.

This puzzle ties in nicely to this term’s Year 9 mastery curriculum , where students are developing their understanding of factorising quadratic equations and manipulating expressions with squared terms. This learning will then be built upon in Year 10.

**A helping hand**

This might *seem* like quite a confusing and abstract question. Here are some tips to get your class started.

- Encourage students to write down what they know about the fields’ areas. Helen’s field has an area of
*h*^{2}*,*so what is the area of Ian’s field in terms of*h*? - Students can then link their expression for the area of Ian’s field to the quadratic form, a
*h*^{2}+ b*h*+ c. - This is a good opportunity to talk about what factorisation actually means and how it might bring them to a solution.
- Students can then check their answer by expanding out their brackets.
- To simplify the problem, consider the following: If the area of another field is 24m
^{2}, what could the side lengths be? This demonstrates the process of finding two factors that multiply together to equal 24m^{2}. - To support students and show them how this links back to the real life problem, you could say that
*h*is equal to 19, and then ask them to find the lengths of Ian’s field.

**Factorising further a-field**

In simple(ish) terms, factorisation is rewriting an expression as a product. In this case, the a*h*^{2} + b*h* + c expression can be factorised as an (*h* + _)(*h *+ _) expression – which are two linear expressions that multiply to the area of Ian’s field.

Can students spot that these must be the side lengths of Ian’s field?

Looking at rectangles is a great opportunity to explore quadratic factorisation visually and this type of question frequently features in exams.

Why not extend this puzzle with a task using algebra tiles? They’re a fantastic way to explore quadratic equations visually!

**The answer to this week’s puzzle will be revealed on Thursday – make sure you tune in to ****Twitter**** for the answer. **