William asks the children in year two and year six if they walk to school. This graph shows the results. Altogether, how many children do not walk to school? And there’s a second question: how many more year six children than year two children walk to school?
Before we start answering the questions, let’s have a quick look at the graph to check that we understand it. We know that it shows information from two groups of children. And we can see these labelled on the 𝑥-axis: year two and also year six. And for each year group, the results are shown in two bars. And we know what these bars represent because there’s a key on the right-hand side.
The pink bars for each year group show the number of children that walk to school. And then, the orange bars in each year group represent the number of children that don’t walk to school. And on the vertical axis, the 𝑦-axis, we can see the number of children are marked.
The scale goes up in 20s: 20, 40, 60, and so on. But not every line is marked. There is a line in between each multiple of 20. So we know each line is worth 10. This will be important later. The first question asked us to calculate the number of children that do not walk to school. And it begins with the word “altogether,” which is important. It’s asking us to work out the total number of children over year two and year six who don’t walk to school.
If we want to find the number of children who do not walk to school, what colour bar should we be looking at? Well, we know from the key on the right that we need to be looking at the orange bars. Let’s start with year two. How many children in year two don’t walk to school? To find the answer, we can use a ruler and we can draw a line from the top of the bar across to the 𝑦-axis.
We can read the scale on the 𝑦-axis to see that the number of children in year two who don’t walk to school is halfway in between 100 and 120. So we know the number of children in year two who don’t walk to school is 110.
Let’s now think about year six. Remember we’re thinking about the orange bar. So again, we can we can use a ruler to read across from the top of the orange bar to the 𝑦-axis. This time, we can see that the number of children is halfway in between 80 and 100.
To find the number of children who don’t walk to school altogether, we need to add our two results: 110 plus 90. And so, we know the number of children who don’t walk to school altogether is 200.
In the second part of the problem, we’re asked how many more year six children than year two children walk to school. Because we’re thinking about children walking to school, we’re now looking at the pink bars.
Again, we can read across from the top of each bar to find out how many children there are. The number of children in year two that walk to school is halfway between 60 and 80. We must be careful with these halfway points. It’s easy sometimes to look at the 60 underneath and to think that halfway up must be 65 because we’re used to scales being marked in multiples of 10 — 60, 70, 80, and so on.
So always look at the number below and above and to think what halfway between those two numbers is. We’ve got 60 and 80 either side. And halfway between those numbers is 70. The year six result is slightly easier. It’s 120. So to find out how many more year six children than year two children walk to school, we need to find the answer to 120 take away 70. We know that 12 take away seven equals five. And so, we can use this fact to help us find the answer. 120 take away 70 equals 50 children.
A quick way to find the answer using the graph will be to start with year two and count up to year six: 10, 20, 30, 40, 50. Altogether, the number of children that do not walk to school is 200. And there are 50 more year six children than year two children that walk to school.