Length, area and algebra

Length, area and algebra

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about using algebraic expressions to find length and area of a shape.
diagram of shape with side lengths marked
[Not drawn to scale]

Question 2Change answer

a)  Write an expression, in its simplest form, for the length of
side M: 
side N: 

Question 2Change answer

b)
i)  If the value of x was 11 cm what would be the length of the longest side?
     Longest side =  cm
 
 ii) Write an expression to find the area of the shaded rectangle.
 
 iii) Calculate the area of the shaded rectangle if the value of x was 5 cm.
       Area of shaded rectangle =  cm2

Question 2Change answer

c)  If the length of the longest side was 63 cm, solve an equation to find the value of x. 
     Show all your working in your calculation.
x =  cm
Task administration: 
This task is completed with pencil and paper or online.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Equations and expressions
Keywords: 
algebraic expressions, equations, simplify, substitution, area
Description of task: 
Students write the simplest algebraic expressions for the lengths and area of parts of a composite shape, then solve these expressions using substitution. They then solve an equation that relates an algebraic expression to a given side length.
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 (08/2001)
a)
i)
ii)
 2x

3x + 3 or 3(x + 1)
moderate
difficult
b)
i)
ii)
iii)
58
3x × 2x or 6x2
150 [Accept correct calculation using answer given in b ii).]
easy
moderate
moderate
c)  
12, e.g., working
5x = 63 - 3
5x = 60
x = 60 / 5
 
Correct substitution with error in calculation, e.g.,
5x + 3 = 63
5x = 66
x = 66 / 5
x = 13.2
[Accept correct calculation using answer given in a) ii).]
2 correct - moderate
 
1 correct - moderate
Diagnostic and formative information: 
 

Common error

Likely reason
a) i)
    ii)

3x - x
5x + 3 - 2x

Expressions not simplified.
b) ii)
    iii)

3x + 2x + 3x + 2x
25

Confusing area with perimeter.