You may also like

problem icon

Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

problem icon

I'm Eight

Find a great variety of ways of asking questions which make 8.

problem icon

Dice and Spinner Numbers

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

Trebling

Stage: 2 Challenge Level: Challenge Level:1

sum: 1abcde multiplied by 3 equals abcde1.
sum: 2fghij multiplied by 3 equals fghij2


Can you replace the letters with numbers?
Is there only one solution in each case?

Once you've had a chance to think about it, click below to see how two different pupils began working on the task.
 

Here is Abdullah's work:

"For each problem I first looked to find a number that would make the units column accurate, then I substituted the number for the answer in the tens column and then continued the process until the calculation was complete."


 

Joshua wrote:

"I wrote out single digit multiples of three up to 9 because each letter was one digit. I noticed that the numbers 1 to 9 only appeared once in the units column of the answers. I looked at the question and realised that 3 x e had to be 21 because it was the only answer ending in 1. This meant that e had to be 7.

I carried the 2 and took it from 7 (the other e) and got 5. So d x 3 had to end in 5 which meant d had to be 5 because 5 x 3 = 15. I then repeated the process."


 

Can you take each of these starting ideas and develop it into a solution?