Authentic Lessons for 21st Century Learning

3x - 2x Doesn't Equal 1?

Simplifying Algebraic Expressions

K20 Center, Judy Schwarz | Published: May 20th, 2022 by K20 Center

  • Grade Level Grade Level 7th, 8th, 9th, 10th
  • Subject Subject Mathematics
  • Course Course
  • Time Frame Time Frame 1-2 class period(s)
  • Duration More 100 minutes


Students will physically model the concept of simplifying algebraic expressions as a class then apply this knowledge to written expressions. This is a great lesson for both introducing the concept as well as remediating like terms, if needed.

Essential Question(s)

How can abstract concepts in math fit together?



Students will sort various objects into groups and explain their reasoning.


Using large variable cards, students will stand up and model expressions that the teacher has on the board. After the initial expression, students will regroup and combine similar variables.


Students will construct the 'rules' for simplifying based on what they did in the Explore activity.


In small groups, students will continue to model algebraic expressions with note cards, and then translate information to written form.


Students will "Create the Problem" using various answers written on the board.


  • Items to sort: tangram tiles, centimeter cubes, playing cards, fruit, etc. (Be creative and use what you have!)

  • Large group cards

  • Small group cards and group documentation sheet

  • Row accountability problems

  • Create the Problem format sheet


Divide students into groups and give them 10-15 items to sort. (Keep it at around 3-4 different groups of items) Ask students to write an explanation of how they decided to sort their items and, on a dry erase board, make a list of their items and how many of each type they have.

Combine two or three groups into one to form larger groups. Give the expanded groups a new board (or piece of paper) and a new color of marker. They should title the new board "RESULT." Ask the groups to come up with new item totals by counting items. Have them compare their RESULT board to their first brainstorm boards of their initial groups and reasons. Have each group present their combined findings.


Place the printed copies of the variable cards in stacks (X, -X, Y, and -Y) that are visible to students. Write a simple expression (or the first problem on the handout, 3x + 2y) on the board and ask students to come take one card each to model the expression.

Add another expression, (x + 5y), and have another set of students model this expression in another area, such that two expressions are being modeled at the same time.

Put a plus sign (+) on the board between the two expressions, and tell the students to figure out how to combine together correctly. Have students determine the final expression and write it on the board.

Continue with this format for a few more examples. After students seem to understand addition, do a few subtraction problems.


Have students look back on all of the examples and the answers. Students will write, either on paper or in their notebooks, a modified Justified List. That is, they will write what they think the 'math rules' are for the problems and what evidence they have from the examples to justify their 'rules.'

Next, have students group into pairs to compare their 'rules' and edit as needed. Continue the discussion using the Inverted Pyramid strategy by having the pairs form larger groups and then come back together as a whole class. Discuss until there is a class consensus of what the 'rules' are for simplifying expressions.


Match students in pairs and give them copies of the "Group Problem Worksheet" and "Group Work Small Variable Cards."

Have students take turns modeling each problem in their pairs. For each problem, the team member who did not model the expression should explain conceptually what is happening using the correct math terminology.

Toward the end of the class period, have students simplify some expressions without the cards. Also, consider simplifying some expressions without performing the actual grouping but by underlining the x terms and circling the y terms (assuming this is an acceptable form of regrouping in your classroom).


Do a Create the Problem activity where you give students the simplified expression (i.e. the answer) and they create a problem that would lead to that answer by following various guidelines (it needs two subtractions, it needs to use the distributive property, etc.). Use the "Create the Problem" attachment as a guide. Have students share some of their problems and emphasize correct use of symbols and vocabulary.