A short instructional video (Rob Langman, uploaded 2024-04-04) demonstrating two deeper problems for teaching percentages. Problem 1 shows how fractions larger than one produce percentages over 100% (examples: 1.5 → 150%, 1.25 → 125%). Problem 2 is a multi-year profit example: a company makes £25,000 in year 1 and grows 10% each year, illustrating compound growth (year 2: £27,500; year 3: £30,250). The presenters prompt pupil discussion and show common student misconceptions (treating the 10% increment as a fixed £2,500 each year).
Questions this video answers
2024-04-04
£25,000
£2,500
£27,500
£30,250
Chapters
Hi, I'm Hannah, and in this video.
We'Re going to look at some greater depth problems which will allow you to.
Assess your pupil's understanding of percentages.
This first problem requires reasoning.
It says we cannot have more than 100%.
Is this statement true or false? Prove it. It's a good idea to give your.
Pupils some time to discuss the problem.
Do they agree or disagree and can they explain their reasoning?
So if we have a look here we have 1, 2, and that is.
The same as 0.5.
If we multiply that by 100, we get 50%. Here we have a whole that is.
The same as one.
If we multiply it by 100, we get 100%. But what happens if we continue with.
This pattern and add 0.5 again?
Well, here we have one and a half.
One and a half is the same as 1.5.
If we multiply that by 100, we get 150%. So, yes, we can have a percentage greater than 100%.
Another example might be one and a quarter.
That would be the same as 1.25 or 125%.
This next problem, again requires your pupils to reason.
The question says, a company in the first year makes £25,000 profit.
It's a good idea to get your.
Pupils to explain how they're going to answer the problem.
So, for example, they might say they're.
Going to take 100% of last year's profits and add it to 10% of last year's profits to find out this year's profits. So then they would be taking £25,000 and adding it to 10% of that. We can work out 10% by dividing it by 10.
So we've got £2,500.
That means that in year two, they have made £27,500 profit.
Your pupils now might think that they're going to keep adding £2,500.
So they might think that in year.
Three, they're going to make £30,000.
However, these. This would be them making a crucial mistake. They haven't realized that the amount of profit that is being made is changing.
Each year and as such, the 10%.
Is going to change in value.
We're now going to have to take.
10% of this value here, 27,500.
So to work out year three, we'll.
Have to do 27,500, add 2,750.
Which equals £30,250. So now we can see that we're never going to make exactly £30,000.
And this is because we've now exceeded £30,000, and each year the profit is.
Just going to grow.
So that is how your pupils could approach a problem like this.
So now you've seen two different problems.
Which will help your pupils work at percentages, at greater depth.
