A school plans to collect 200 pounds between January and May. This chart shows how much they collected by the end of April. And then we’re shown a chart to help us. Write the name of each month where they collected more than 50 pounds. There’s a second part to the problem. How much money did they collect in February and March altogether?
So in this problem, we’ve got a school who want to raise an amount of money between January and May. The first sentence tells us that their target is 200 pounds. And we can also see this on the right-hand side of the chart. They haven’t reached their target yet. The chart shows four bars, one for each month that’s gone by so far. It’s almost as if the children have been colouring in the bars with each amount of money they’ve raised. This is the bar that shows how much they raised in January, then February, March, and finally April. So with still May to go, they’re reached this point here, which is over 160 pounds.
In the first part of our problem, we’re asked to write the name of each month where the school collected more than 50 pounds. To work out the amount of money that they collected each month, we need to look at the start amount and the end amount for each month and then calculate how much it was.
At the start of January, they were starting from a point of zero pounds. But we can see from the chart that, by the end of January, they collected 20 pounds. At the start of February then, they began with 20 pounds. And they ended February somewhere between 60 and 80 pounds. But we don’t know exactly how much. So how can we narrow it down and work out how much was collected during February?
Well, we know that halfway between 60 and 80 is 70 pounds. And we can mark this on the scale. We can see that, by the end of February, the school had collected between 70 and 80 pounds. To jump from 20 pounds to 70 pounds is a jump of 50 pounds. But if the school collected a little bit more than 70 pounds, that means they collected more than 50 pounds. So although we don’t know the exact amount, we can say that, during February, the school did collect more than 50 pounds.
Now let’s think about March. We can see that the school ended March, having collected 100 pounds. If they’d have started on 80 and ended on 100, that would mean that they collected 20 pounds. But they started on less than 80. So this means they must’ve collected more than 20 pounds. If the jump had been from 70 pounds to 100 pounds, that would’ve meant they’d collected 30 pounds. But we can see that the starting point was a little bit more than 70 pounds. So in March, the school collected somewhere between 20 and 30 pounds. Of course, this is not more than 50 pounds. So this isn’t one of the months that we need to write down in answer to this part of the problem.
Finally, if we look at the bar for the month of April, we can see that the school started with 100 pounds and ended April somewhere between 160 and 170 pounds. Again, we don’t know the exact amount. But we know that it was more than 60 pounds that they raised during April. And so the two months where the school collected more than 50 pounds were February and April.
On to the second part of the problem, how much money did they collect in February and March altogether?
Well, we’ve already gone along the chart and tried to work out how much money they collected each month. We know that, during February, the school collected more than 50 pounds. But we don’t know how much. And in March, they collected somewhere between 20 and 30 pounds. But again, we don’t know how much. How can we work out the amount they collected in February and March?
Well, the clue to solving this problem is to look at the end of March. The end of March we know for definite the school had collected 100 pounds. So we know that January plus February plus March equals 100 pounds. We could sketch a little bar model to show this. The value of January plus February plus March equals 100 pounds. What else can we write on the bar model?
Well, we already know exactly how much was collected during January. So we can now say that 20 pounds plus February plus March equals 100 pounds. And in a way, it doesn’t matter whether the school raised 52 pounds in February or 23 pounds in March. What we’re looking for is the total of February and March together.
And now we can see on the bar model how to find the answer. It’s the difference between 100 pounds and 20 pounds. 100 take away 20 equals 80. And so the total amount of money that the school collected in February and March was 80 pounds.
This is an interesting question because when we first look at the chart, it almost seems impossible. How can we find the total of these different amounts when they’re not marked next to exact numbers on the chart? But that’s why to solve the problem, we need to use reasoning. We use what we do know to help us to find out what we don’t.
The two months where the school collected more than 50 pounds were February and April. And the amount of money that the school collected in February and March altogether was 80 pounds.