Square numbers

Square numbers

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
This task is about square numbers and name their square roots.
 
Forty-nine is a square number because we can write the equation:   7 × 7 = 49.
  
a) i) Which of these is also a square number? (Circle one)
    (A)
(B)
(C)
(D)
(E)
  		 11
17
22
25
31
  
  ii)

 
Write the equation which shows that the number you chose is a square number.
 
____________________
 
b) i) Which of these numbers is a square number? (Circle one)  
    (A)
(B)
(C)
(D)
(E)
  		 54
64
76
84
99
  
  ii)

 
Write the equation which shows that the number you chose is a square number.
 
____________________
 
c)
Name two other square numbers under 100, and write the equations that show these numbers are square.
 
   
  Square number Equation
i)

 

  
ii)

 

  
Task administration: 
This task is completed with pencil and paper only.
Level:
4
Curriculum info: 
Maths, Number and Algebra, Number Knowledge
Keywords: 
powers, square numbers, basic facts
Description of task: 
Students identify square numbers and write the equation showing the factors for each.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Using symbols and expressions to think mathematically, sets 4-5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
   

Y9 (06/1996)
a) i)
ii)		 D, and
5 × 5 = 25		 easy
b) i)
ii)		 B, and
8 × 8 = 64		 very easy
c) i), ii) Two square numbers and the factors for each.
One square number and its factors.
[Square numbers could be any of: 0, 1, 2, 9, 16, 36, 49, 81, 100 and the correct factors for each.]		 easy
very easy

NOTE: For all questions students must state the square number and the factors to obtain full marks.