Jae needs to cut wood for a craft project. The instructions provide the size relationships, and Jae gets to decide the actual size. Her first piece of wood will be 𝒙 centimeters long. The middle part has to be 3 times as long as the first. The final part is 11 cm longer than the middle part.

a) Express the length of the final part in terms of 𝒙.

b) If the first piece of wood is 25 cm long, how long will the final part be?

A problem like this would likely be found in Primary 6 or US sixth grade math. Students are encouraged to make the connection between bar modeling and variables.

A unit in a bar model is pretty much just like a variable; it is another way to represent an unknown. Students who have experienced bar models and part-whole thinking are more likely to succeed when it comes to solving for variables.

If students struggle with representing the situations, they can start by bar modeling the problem. One sample solution could be like this. After the model is created, just place the 𝒙 in the appropriate bars.

For students who need support making a connection, ask questions like these:

- How many times do you see 𝒙?
- How do we write it when we have 3 times something?
- Imagine is a pencil. How could you write it with pencils instead of 𝒙?

A student who finds abstract thinking easier to access might come up with the following solutions immediately:

a) 3𝒙 + 11, or 3•𝒙+ 11, or 3(𝒙) + 11

b) 3(25) + 11 = 86

The final part is 86 cm long.

Did you or a student of your solve it a different way? Share the strategy with us!