Bar Model
Calculation · Year 1–Year 6
Quantities as lengths. Cover a number to turn the picture into a question.
About the bar model
Two bars, drawn to scale, so the numbers have a size you can see. It is the picture behind most of the word problems in the mastery schemes, and the one children are asked to draw for themselves from Year 2 onwards.
Length is value, always, and both rows are measured with the same ruler. A bar of 8 is exactly twice as long as a bar of 4, and a bar of 1 beside a bar of 100 is a sliver, because it should be. The label moves outside the bar when it will not fit, rather than the bar growing to fit the label.
Parts of a whole puts the whole on top and its parts below. The whole is the sum, and there is no way to make it anything else, so the picture cannot show parts that overrun the bar above them. Compare two bars puts them one under the other and draws the gap between them as a dashed box, which is where difference stops being a subtraction fact and starts being a thing on the board.
The question is posed by covering rather than by leaving a box blank. Set 24 and 10, tap the gap, and the board asks how many more. Cover the whole instead and the same picture is an addition.
How to use it on your whiteboard
- 1Use the plus and minus buttons to set each bar. The whole adds itself up.
- 2Tap any box to cover its number. Tap it again, or Show all, to reveal.
- 3Model switches between parts of a whole and comparing two bars.
- 4Steps of sets the buttons to move in 1s, 10s or 100s.
- 5Tap Fullscreen so the bars fill the board.
Questions
- What is the difference between this and the part-whole model?
- The same arithmetic, drawn so you can see the sizes. A part-whole diagram tells you 24 is 14 and 10. A bar model also shows you that 14 is a bit more than half of it, which is what makes it work for word problems and for comparing.
- Why can I not set the whole directly?
- Because then it could disagree with the parts. The whole is the sum of the bars below it and the tool keeps it that way, so what is on the board is always true. Change the last bar and the whole follows.
- Why is one of my bars almost invisible?
- Because it is small compared to the other one. Every bar on the board is drawn at the same scale, so 5 next to 500 really is a sliver. Giving small bars a minimum width would make the picture say the two numbers are close, which is the one thing a bar model must never do.
- How do I show a difference?
- Switch Model to Compare. The shorter bar is followed by a dashed box reaching the end of the longer one, and that box is the difference. Tap it to cover it and the board asks how many more.