Algebra multiplication squares

Algebra multiplication squares

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about what happens to indices when algebraic expressions are multiplied.
a)
The squares in the box below can be filled in so that each row and column equals x3y4 when the expressions in it are multiplied together.
 
   
Fill in the boxes in the order they are numbered. 
 
 
b) Fill in the squares in the box below so that each row and column equals x6y3 when the expressions in that row or column are multiplied together. 
 
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, multiplication, indices, arrays
Description of task: 
Students write algebraic expressions with indices which make equations true.
Curriculum Links: 
Key competencies
This resource involves identifying and implementing strategies to solve a multistep problem. This relates to the Key Competency: Thinking.
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)

Part 1 correct – moderate

Part 2 correct – moderate

Part 3 correct – moderate

Parts 4 and 5 correct – moderate
b) all correct – difficult

2-4 correct – moderate

NOTE: The order of x and y may be reversed, e.g., xy3 = y3x, [Accept xyyy = xy3, x1 = x etc.].