# PowerPoint Presentation by 65AKdK

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The Garden Path Problem
An approach to problem solving
This is an example of a problem or starting point that
enables pupils to explore and investigate new mathematics.
It enables them to solve increasingly demanding problems
and evaluate solutions; explore connections in mathematics
across a range of contexts; generate fuller solutions

Represent problems and synthesise information in algebraic,
geometric or graphical form; move from one form to
another to gain a different perspective on the problem

8.1
Using and applying mathematics
Objectives addressed in ‘Garden path’

 Suggest extensions to problems, conjecture
and generalise; identify exceptional cases or
counter-examples, explaining why; justify
generalisations, arguments or solutions;
pose extra constraints and investigate
whether particular cases can be generalised
further

8.2b
The Garden Path problem

7m

5m

5m    3m

A metre wide path surrounds a garden.The area of the path is ?
What do you notice about the dimensions and the area?
Will this always be true?How can you prove this?
Teachers guide

Students should get the answer 20cm2 and see that this is
equivalent to 3+5+5+7.

They can then try this for other numerical solutions but should
then move into algebra as per next slide
The Garden Path problem

?m

Am

?m Bm

What will be the lengths represented by the question marks?
A+2

A

B
B+2

Can you now prove your numerical generalisation?
PROOF

AREA = (A+2)(B+2) – AB

= AB+2A+2B+4-AB

= 2A +2B + 4

ADDING SIDES GIVES A+B+A+2+B+2

= 2A+ 2B + 4

THEREFORE ADDING SIDES WILL ALWAYS GIVE THE AREA

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