Truth Tiles 2

Task 17 ... Years 2 - 10

Summary

You have five consecutive numbers from 3 to 7. The problem is to use just these to make the following equation true.

This cameo has a From The Classroom section in the form of a video of two students explaining their solutions and showing their journal work at the end of their first ever lesson using tasks.

Materials

5 number tiles

Content

basic number skills
addition and subtraction
combination theory
problem solving strategies, such as:
- break the problem into smaller parts
- try every possible case

Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

One part of the iceberg is clearly:

How many solutions are there?
How do you know when you have found them all?
In fact, there are either 12 solutions, or 24, depending on the definition of 'different'. If students feel that 3 + 6 - 5 = 4 and 6 + 3 - 5 = 4 are different, then this doubles the number of solutions. The 12 basic solutions are:

3 + 6 - 4 = 5
3 + 6 - 5 = 4
4 + 5 - 3 = 6
4 + 5 - 6 = 3
3 + 7 - 4 = 6
3 + 7 - 6 = 4 4 + 6 - 3 = 7
4 + 6 - 7 = 3
4 + 7 - 5 = 6
4 + 7 - 6 = 5
5 + 6 - 4 = 7
5 + 6 - 7 = 4

Several strategies can be used to find these and often students start with a simple idea such as testing every possible combination, and then adapt as they notice patterns.
Blair and Alexander, Year 5, Ashburton Primary School, in the first lesson the class used tasks, show a perceptive approach to Truth Tiles 2 in this Cube Tube Video.

Additional iceberg challenges are:

The tiles are consecutive starting at 3. What happens if you use five consecutive numbers beginning with a different number? Will there be the same number of solutions?
Suppose the problem was:

x ÷ =
and the numbers were 8, 16, 32, 64, 128. Investigate possible solutions.

Note: This investigation has been included in Maths At Home. In this form it has fresh context and purpose and, in some cases, additional resources. Maths At Home activity plans encourage independent investigation through guided 'homework', or, for the teacher, can be an outline of a class investigation.

Visit the Home Page for more Background.

For this specific activity click the Learners link and on that page use Ctrl F (Cmd F on Mac) to search the task name.

Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.

To convert this task into a whole class lesson each pair of students needs to tear a piece of paper into eight parts. Digits 3 to 7 are written on 5 of them and the +, - and = are written on the others.

I like the task because it is so open-ended. All my students can find some solutions and achieve a level of success, but the option of finding all the solutions, or adding tiles 8, 9, 10..., increases the depth of the task significantly and can challenge my very capable students.

For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 168, Truth Tiles 2, which includes an Investigation Guide and software.

Is it in Maths With Attitude?
Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.
The Truth Tiles 2 task is an integral part of:

MWA Number & Computation Years 3 & 4

MWA Number & Computation Years 9 & 10

This task is also included in the Task Centre Kit for Aboriginal Students and the Secondary Library Kit. Solutions for tasks in the latter kit can be found here.

Follow this link to Task Centre Home page.