In the previous post, we talked about two common mistakes in drawing bar models – not aligning the starting points of the bars being compared and having disjoint bars for parts. Here we want to illustrate why it is important for us to draw bar models correctly from the beginning when we first use them for word problems.
Bar models are particularly useful for comparisons and before-and-after problems. Take the following example,
A full crate of apples weigh 230 pounds. After 4/5 of the apples were sold, the remaining apples and crate weigh 90 pounds. The weight of the crate when empty is _____ pounds.
The solution can be easily observed if we draw bar models correctly:
This is a typical “before and after” problem where an intervention caused a change in the bar model, e.g. in this case, removing 4/5 of the apples. If students learned to draw bar models correctly since 2nd and 3rd grade, he/she would naturally start drawing the before-after bar models properly aligned to the left and bars for the apple units without gaps in between, before knowing what the answer is. Then the answer becomes immediately apparent from the bar models.
Conversely, if he does not have the habit of drawing bar models correctly, e.g. representing the apple units as separate bars, it is not visually obvious that the difference in quantity before and after is exactly equal to 4 units. He might still get the correct answer assisted by abstract reasoning, but the power of the bar models is that we let the visuals tell us the answers.
For more related resources, please refer to our Bar Models page.