Addition and Multiplication boxes

Addition and Multiplication boxes

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
This task is about completing addition and multiplication equations using numbers 1-10
 

Complete each equation by filling in the boxes. 

Use only the numbers above. Each number can be used more than once.

 

a) 9 + + = 18
               
b) + + 5 = 22
               
c) + 8 + = 27
               
d) 2 × × = 32
               
e) × 3 × = 36
               
f) × × 7 = 49
Task administration: 
This task is completed with pencil and paper only.
Level:
3
Curriculum info: 
Maths, Number and Algebra, Equations and expressions
Keywords: 
addition, multiplication, linear equations
Description of task: 
Students complete addition and multiplication linear equations by selecting from a range of numbers.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Using symbols and expressions to think mathematically, set 4
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  Y7 (03/2005)
a) 1,8 or 2,7 or 3,6 or 4,5 very easy
b) 7,10 or 9,8 very easy
c) 9,10 very easy
d) 2,8 or 4,4 moderate
e) 2,6 or 3,4 difficult
f) 1,7 difficult
Results are based on a representative sample of 220 students.

NOTE: The order of the numbers in the equation can be reversed for all questions

Diagnostic and formative information: 
  Common error Likely calculation Likely misconception
d) 10,12 2 × 10 + 12 Ignores given operators.
d)
e)
f)		 4,8 or 8,4
6,6
7,7

4 × 8
6 × 6
7 × 7

 Ignores the number and operator already displayed in the equation.
d)
e)

10,6
10,2

2 × (10 + 6) = 32
(10 + 2) × 3 = 36

 Ignores given operators and order of operation.
e) 6,3 or 3,6 or 9,2 18 × 3 = 36 Uses 2 × instead of 3 ×.
f) 0,7 0 × 7 × 7 = 49 Applies the attributes of the additive identity to a multiplicative equation.  Also uses a number outside of the given range.
Next steps: 
Seeing an equation in a structural way is an important algebraic skill.  To assist students in developing this skill, encourage them to generalise a way of finding the missing numbers in an equation rather than just depending on trial and error or utilizing basic facts.

Many of the incorrect responses also indicated a lack of knowledge of the correct order of operations for addition and multiplication.  Students could explore the effects of changing the order in which operations are performed on the result of equations, and develop a general rule to explain the process to use.