Bar Models!

This past week, we have been working with bar models to help us think about addition and subtraction problems. Bar models aren't a method of doing addition or subtraction. We will still be using the methods for addition and subtraction - using place value drawings and number-based strategies - that we learned in the fall. Instead, bar models are a great way to think about how story problems work using the beginnings of algebraic thinking.

These pictures show the product of a game we played to introduce the concept of bar models. Students pulled two cards out of a deck, then used two colors of cubes to show the two quantities. Then, they drew a bar model to show the additive process, with an addition and a subtraction sentence that match. The game is also a thinly-veiled excuse to practice basic math facts, and to explore the reciprocal nature of addition and subtraction.

Bar models can model addition problems, which we call "part, part, whole" problems, or subtraction problems, "whole, part, part". If you know both parts and you are trying to determine an unknown whole, it is an addition problem. If you know the whole and one of the parts, then it can be solved with subtraction. The model above can show both of these story problems. Can you figure out which is "part, part, whole" and which is "whole, part, part"? (they are a little sneaky, so read carefully!)

Kate went shopping with her robot two days last week. On Monday, she bought 7 cans of oil. She bought some more on Thursday. At the end of the week, she had 23 cans of oil. How much did she buy on Thursday?

Pete picked 7 pumpkins in the school garden. Maya picked 16 more pumpkins than Pete did. How many pumpkins did Maya pick?

You can do the same thing with larger numbers:

Alex ate 437 pizza slices on Monday. He ate 516 cucumber slices on Tuesday. How many slices of food did he eat on those two days?

Since with this story problem we know both parts, and the whole is unknown, we draw a bar model with the whole as the unknown, shown with a question mark, like this:

If it was a "whole, part, part" story problem instead, the question mark would go in the box of the unknown part instead of under the bracket.

When students get older, bar models can be a visual representation of an algebraic equation, with letters representing the unknown parts or wholes. Students will also use bar models for problems that require multiple steps to solve, as well as problems with more than two "parts" that make up the "whole". Bar models are a very useful tool, and a crucial part of the Math in Focus curriculum.