A short instructional video (presenter Rebecca plus a co-presenter) demonstrating ‘greater depth’ algebra tasks for teachers/pupils. It shows how to find positive whole-number solutions to 3m = 4n (examples: m=4,n=3 and scaled solutions like m=8,n=6) and explores multiple operation sequences that map input 4 to output 7 (add 3; add 2 then add1; ×2 then −1; ×3 then −5), with guidance on questioning pupils to reveal deeper conceptual understanding.
Chapters
Hi, my name is Rebecca. And in this film we're going to be looking at some greater depth problems to show understanding of the key concepts of algebra. Now, for pupils to be working at greater depth in algebra, one of the things they need to be able to do is to find all the possible combinations for two or more variables. So let's have a look at a problem.
Here we have 3. M equals 4n, where m and n.
Are positive whole numbers.
What could the values of m and M be?
What combinations can you find?
Is there a pattern and can you.
Explain why this pattern occurs? To begin with, you would need your pupils to have a look at the relationship between the two variables.
They should be able to see that three times a number is the same.
As four times a number. So the total of on either side of the calculation would need to be a multiple of three and a multiple of four. Let's test that out and see if that works.
We could reason that m is 4. So if we did 3 times 4, that would give us 12. We could then say that n is 3. If we did 4 times 3, that would give us 12. So we know that m could be.
4 and n could be 3. Then we would need to challenge our pupils to look for some other combinations. We could use a doubling approach to do this. If we doubled four and made it into eight, we could see if that works well.
Three times eight gives us 24. We could double three to make it six. Four times six gives us 24.
So in that way we can also.
See that m could be 8 and.
N could be 6. Let's have a look at another problem. Pupils working at greater depth should also be able to work out all the possible operations that could happen in order to achieve a given number.
Here we have a function machine with the input 4 and the output 7.
And the question says, what are the possible rules that the function machine could be using? How many could you find? Now, pupils are likely to straight away see that the first function could be.
Could be add 3, 4, add 3 is 7.
But you can challenge them to say, well, what if there were multiple additions? What could it be then?
The solution to that could be add.
Two and then add one. To take this even further, you could say, well, what if it was a multiplication and a subtraction?
Pupils could times four by two to.
Give them eight and then subtract one.
To give them seven.
Keep challenging them the whole time. What about if you multiplied it by 3?
4 times 3 would give you 12.
So you would need to do a subtraction of 5 to get it back to the 7. So there you go. There's just a few ways that you can challenge your greater depth pupils to show their true understanding of algebra.
