Monday Maths: Vicki Robinson, Communications Officer
A farm-filled #MondayMaths
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 h2, 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, ah2 + bh + 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 24m2, what could the side lengths be? This demonstrates the process of finding two factors that multiply together to equal 24m2.
- 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 ah2 + bh + 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.