What two ...?
56 406 is the product of two consecutive numbers. What are these two numbers?
Age
7 to 11
Challenge level
Problem
$462$ is the product of two consecutive numbers. These numbers are $21$ and $22$, because $21 \times 22 = 462$.
Now try this.
$56 406$ is also the product of two consecutive numbers. What are these two numbers?
Getting Started
Perhaps you could try two consecutive numbers and see how close you are?
Do you have sense of how big the numbers will be?
Student Solutions
Louise of Headington Junior School gives the answer of 237 and 238.
"I worked this out by finding the square root of 56,406 and then wrote down the whole number (237) and rounded it up to 238".
Class 7P from Loretto Junior, Musselburgh apporached this problem using trial and improvement which is a very useful strategy:
Kitty said let's try 600 x 600 = 360000 and that is too big!
Angus said let's try 100 x 100 = 10000 and that is too small.
Ashleigh thought 200 x 200 was 40000 which was a little too small.
Graeme knew that 250 x 250 was 62,500 - close!
Sophie offered 230 x 230 which is 52,900 - getting there.
Gair now tried 240 x 240 and got 57,600.
Tom provided the masterstroke and said our number 56406 should be in the high 230s , so we looked at 236x 237 but the last digit is a 2 because 6x7 = 42.
Finally Caitlin shouted in excitement 'try 237x 238 as the last digit will be a 6'. The answer therefore is 237 x 238.
Teachers' Resources
Why do this problem?
This problem is a short challenge that may introduce pupils to the idea of square numbers and square roots. It can also be opened up in all sorts of ways (see the 'Possible extension' section below).
Possible approach
You may want to give learners this challenge as you are taking the register, for example, as it does not need much explanation.
Sharing ways of approaching the solution will be valuable, however, as children are likely to have done different things. Some might have used trial and improvement, some may have used a calculator to find the square root.
Key questions
Perhaps you could try two consecutive numbers and see how close you are?
Do you have sense of how big the numbers will be?
Possible extension
This problem can be extended in all sorts of ways by asking 'what if ...?' questions. This sheet gives you some suggestions.
Possible support
A calculator is likely to be useful.