Truth Tiles 1Task 30 ... Years 2  8SummaryThree equations have to be made true simultaneously using the digits 1 to 9 to fill the empty spaces.

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IcebergA 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:
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:
The iceberg is driven by the mathematician's questions:

Whole Class InvestigationTasks 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. For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 30, Truth Tiles, which is extended by companion software. Also, the PhillipStevenHarley Challenge in Calculating Changes was developed by these students during a whole class investigation of Truth Tiles 1. 
Is it in Maths With Attitude?Maths With Attitude is a set of handson learning kits available from Years 310 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:
The Truth Tiles lesson is an integral part of:

Lake Cargelligo Central SchoolDoug WilliamsConsultant 
I had the opportunity to work with a Stage 1 class (5/6 year olds) for a short while using this task in a whole class sense. Their teacher suggested the multiplication could be a problem. I took my lead from the companion Maths300 lesson and began a True/False game based on characteristics of myself, kids and things in the classroom. The children were sitting in a 'circle' around me on the mat. Then, we continued, using only one set of digits from 1 to 9... 
Okay, I can see you are good at the true/false game. Now let's try it with these signs. Firstly, tell me what they mean. 
True or false? 
True or false?

I introduced the subtraction sign and we tried a few more.
True or false?

How about this? Something take away 1 equals something.


Now I am getting really tricky. Can you make these both true at the same time using only the number cards 1  9? 
It's marvellous to see a smile of recognition when a student tries and gets to a position such as this.
Uh oh! Nearly there, but you say it can't work.

Their teacher then realised that after a couple of days exploring that question and building a display of solutions, she could try introducing the multiplication part, along with exploring the x button on their calculator.