Garden perimeter and area

Garden perimeter and area

Pencil and paper
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This task is about writing algebraic expressions for the perimeter and area of a garden.

[Not drawn to scale]

 

The diagram above shows Tamanui's garden measured in metres.
 
a)
i)
 
 
 
 
ii)
Complete this equation to find the length of a fence around the perimeter (P) of 
the garden. Write each section of the perimeter as a separate term.
 
P = ________________________________________
 
Simplify the equation you have written above.
 
P = ________________________________________
 

b)

Complete this equation to find the area (A) of the garden.

 

A = _________________________________________

 

Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Equations and expressions
Keywords: 
algebraic expressions, simplify, perimeter, area, linear equations
Description of task: 
Students use measurements to write algebraic expressions for the perimeter and area of a garden.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Using symbols and expressions to think mathematically, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y10 (10/1999)

a)

i)

ii)

x + x + 2x + 5 + 3x + x + 5
[Accept in any order]
8x + 10 or 10 + 8x
[Accept a simplification that is consistent with a) i).]

very difficult

moderate
b)  

Any 1 of:

•   x2 + 15x
•   3x(x + 5) - 2x2
•   x(x + 5) + 10x
or algebraically equivalent expressions

 very difficult
Diagnostic and formative information: 
   Common error Likely reason

a) i)

x + x + 2x + 5 + 3x
x + x + 2x + 5 + 3x + 6
x + x + 2x + 5 + 3x + 6x

Ignores unmarked dimension.
Assumes missing dimension is 6.
Assumes missing dimension is 6x.