Substituting Values into Expressions with Variables

How to start substituting values into expressions

Now that your students have been introduced to the terms variables, coefficients, and expressions it is time to start substituting values into the expressions. We can continue working with our picture tiles before going directly to calculations using symbolic representations to further develop their understanding of variables and expressions.

Again, they will be able to use real-world problems with some physical representations to manipulate and combine variables. I start small and build up the number of terms so that students can take small steps toward the end goal. I like to pretend we are going shopping. We build a cart with the picture tiles. Then, we create an algebraic expression. Finally, the values of the items are revealed, and we can figure out the cost of each cart.  Click here to access a freebie with the examples below.

One Variable Expressions

Start with just one item to keep the expression at only one term. For example, “Javier bought 6 bananas at the grocery store.” Have your students model the amount of the item by selecting enough picture tiles to represent the item in the word problem. In this scenario, they would select 6 banana tiles. Then, they ask them to write an expression using the variable, b, for banana. This should all be familiar from the previous lesson. Now, we are adding the substitution of values for the banana so that we can figure out how much 6 bananas would cost. At the first store, bananas might cost $0.25 each. Students would multiply 6 x $0.25 to find the cost of 6 bananas. They can compute the cost of bananas at a few different stores with different costs. You can also have students research the cost of bananas at a store in their neighborhood to figure out what the cost might be.

Two Variable Expressions

Move on to two items to create expressions with two terms. For example, “Javier bought 6 bananas and 1 bunch of grapes at the grocery store.” Have your students model the amount of the items by selecting enough picture tiles to represent the items in the word problem. In this scenario, they would select 6 banana tiles and 1 grape tile. Then, they ask them to write an expression using the variable, b, for banana and the variable, g, for grape. This should still be familiar from the previous lesson. The two terms will be added together because we are calculating the cost of all of the items purchased. Once the expression is written, students can begin substituting values. Bananas might cost $0.25 each while grapes cost $2.50 a bunch. Students find the sum of the cost of the bananas and the cost of grapes. They can compute the cost of the purchase at different stores with different coasts. Again, you can extend the lesson by having students research the cost of bananas and grapes at a store in their neighborhood to figure out what the costs might be.

Three Variable Expressions

Lastly, add one additional item to create expression with three terms and repeat the process. The more terms, the longer the calculations might take. If students are having trouble substituting in decimal values, switch to whole number costs like $1.00, $2.00, etc.

Extension ideas

You can fill envelopes with different combinations of picture tiles and have students write the expressions to match what is in the envelope. Make a price sheet to show the cost of each item and have students substitute in the values to find the cost of the items in the envelope.

Of course, you can do this activity with items other than picture tiles. If your students are food motivated, give them each a snack size bag of M&Ms or Skittles. Have them sort by colors and write an expression to represent all the items in a bag. Then, assign values to each color and have your students find the sum of the bag. Most importantly, make it fun!

Do your students need a complete unit (including guided notes) on variables, terms, and expressions? Click here to get our guided notes product.