Three in a row
Purpose:
The purpose of this multi-level task is to engage students in using operations on integers to solve a
problem.
Achievement Objectives:
NA5-3: Understand operations on fractions, decimals, percentages, and integers.
NA5-7: Form and solve linear and simple quadratic equations.
Description of mathematics:
The background knowledge presumed for this task is outlined in the diagram below:
The task can be presented with graded expectations to provide appropriate challenge for individual
learning needs.
Activity:
Task: Find three consecutive integers, a, b and c, that give the same value for:
a+(bc)
and
a(b+c)
The arithmetic approach
The student is able to find a solution set by exhaustive calculation of all the integers in the range
given.
A prompt from the teacher could be:
One solution set is 2, 3, and 4. Find all the solutions between -5 and 5.
The procedural algebraic approach
The student is able to find a solution set by exhaustive calculation of all the integers in the range
given. The student shows understanding that the task is asking for the equation a+(bc)=a(b+c).
A prompt from the teacher could be:
Find all the solution sets between -5 and 5.
The conceptual algebraic approach
The student shows understanding that the task is asking for the equation a+(bc)=a(b+c) and can use
this knowledge to form and solve appropriate equations to solve the problem.
Prompts from the teacher could be:
1. Since these three numbers are consecutive, they could be written in terms of just one of the
numbers.
2. Find all the possible solutions.