Truth Tiles

Task 30 ... Years 2 - 8

Summary

Three equations have to be made true simultaneously using the digits 1 to 9 to fill the empty spaces.

Can you find a solution?
Can you find a different solution?

Materials

9 numbered tiles

Content

basic arithmetic skills
problem solving strategies
number patterns
connection between addition and subtraction
symmetry and combination theory properties
fundamental laws of arithmetic - identity, commutative, inverse operations

Iceberg

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

Finding one solution is not too difficult, either by using a guess and check strategy, or by realising that it the multiplication:

can't be 1 x (something) because that would require a repeated digit
must only be 2 x 3 or 2 x 4, otherwise the product would have two digits

Then comes a discussion about what makes a different solution. For example, if you have a solution using 2 x 3, is it different if everything else is the same but you make the multiplication 3 x 2? In effect, it doesn't matter, as long as you describe/define what you mean as different.

However, most agree that a different solution occurs when there is some change in the arrangement of digits in the other two equations. Two possible solutions are:

5 + 4 = 9
8 - 7 = 1
2 x 3 = 6 7 + 1 = 8
9 - 5 = 4
2 x 3 = 6

The iceberg is driven by the mathematician's questions:

How many solutions are there?
How do I know when I have found them all?

Convincing someone else of the number of solutions requires application of problem solving strategies and fundamental laws of arithmetic.

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 turn this task into a whole class investigation you could make a class set of number tiles. These would have many other uses. However, you could also ask students to rip up scrap paper so that they made nine pieces between each pair.
Start the problem in a central place using a large set of nine digits you prepared earlier. Gather the students in a central place (tables or floor space) and hand out the cards. Then place the +, -, x, and 3 = cards you also prepared earlier on the space (as in the picture above) and explain the problem. Students with cards try to solve the problem, as others advise. As appropriate offer students the opportunity to find a solution for themselves using their number tiles.
Visit Truth Tiles on Maths300:
Guest ... Member

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 task is an integral part of:

MWA Number & Computation Years 3 & 4

The Truth Tiles lesson is an integral part of:

MWA Number & Computation Years 3 & 4

MWA Number & Computation Years 7 & 8

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

Follow this link to Task Centre Home page.