Summary
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, as well as remediating, the concept of combining like terms.
Essential Question(s)
How can we simplify algebraic expressions?
Snapshot
Engage
Students recall how to model algebraic expressions.
Explore
Students use their models of algebraic expressions to add and subtract algebraic expressions.
Explain
Students formalize their understanding of subtracting algebraic expressions.
Extend
Students apply what they have learned to simplify algebraic expressions.
Evaluate
Students create their own adding and subtracting expressions problems given simplified expressions.
Materials
Lesson Slides (attached)
Variable Signs (attached; 8 sets; print one-sided)
Simplifying Algebraic Expressions handout (attached; one per student; print one-sided)
Create the Problem handout (attached; one per student; print one-sided)
Fruit Signs (optional; attached)
Student Variable Cards (optional; attached)
Pencils
Paper
Algebra Tiles (optional)
Student devices with internet access (optional)
Preparation
During the Engage phase of the lesson, students will model algebraic expressions using the attached Variable Signs, which are essentially algebra tiles containing: x, –x, y, and –y. The document contains four pages. Print at least eight copies of each page, and consider printing each page on a different colored paper. Then, create four stacks of signs, one stack for each page. For example, you might have eight blue pages with x in one stack, eight red pages with –x in another stack, etc. See the Optional Differentiating note at the end of Engage to determine if you also need to prepare the attached Fruit Signs in the same way.
Additionally, if you plan to reuse these signs, consider printing them onto cardstock paper.
During the Extend phase of the lesson, students will practice simplifying algebraic expressions. A digital option for algebra tiles is provided, but if your students need the support of algebra tiles, print and cut the attached Student Variables Cards. See the Optional Resources note at the beginning of Extend for more details.
Engage
10 Minute(s)
Introduce the lesson using the attached Lesson Slides. Slide 3 displays the lesson’s essential question. Slide 4 identifies the lesson’s learning objectives. Review each of these with your class to the extent you feel necessary.
Place the printed pages of the attached Variable Signs in stacks (x, –x, y, and –y) that are visible and accessible to students. Show slide 5 and ask volunteers to each take one sign to represent the expression on the slide (3x + 2y).
Have those volunteers return their signs to their stacks and return to their seats. Transition to slide 6. Again, ask for volunteers to model the expression on the slide (–2x + y).
Have those volunteers keep their signs and potentially step to the side (but not return to their seats) because another group is going to join them.
Display slide 7 and ask for another set of volunteers to model the expression on the slide (x + 3y). Direct students to stand such that the two groups holding signs are clearly both being modeled at the same time.
Explore
20 Minute(s)
Show slide 8, which has a plus sign (+) between the two expressions. Facilitate a class discussion on how to combine the expressions together correctly. Use this time to ask guiding questions, but do not tell students how to combine like terms. Have students determine the final expression (–x + 4y) and write it on the board.
Have those volunteers return to their seats then transition to slide 9. Ask for volunteers to model the two expressions: (4x + 2y) and (3x + y). Then, facilitate a class discussion on how to subtract the second expression from the first: (4x + 2y) – (3x + y). Again, this is the time to ask more questions than you give answers.
Repeat this once more using slide 10 for the expression: (2x – 3y) – (x – 2y).
After students seem to understand the basics of adding and subtracting expressions, have students find a partner or assign partners. Display slide 11 and before asking for volunteers to model the expression, have students discuss with their partner how they would simplify the expression on the slide: (–3x + 3y) – (–2x + 4y). Give students approximately 3 minutes for discussion. It is okay and expected even that most students will not have a completely simplified expression during this time.
Explain
20 Minute(s)
After pairs have discussed, ask for volunteers to model the expression, as before. Then, facilitate a class discussion on how to simplify the expression from slide 11: (–3x + 3y) – (–2x + 4y).
Display slide 15 to show students how to algebraically simplify the addition of '–x' and '–y' (the two signs) to –x – y.
This task of having students model this process should feel “like too much work.” So when you hear students express this, challenge them to the idea that there must be a better way.
While still showing slide 15, ask students to think critically about that last step, changing the addition of a negative term to the subtraction of a positive term. Move to slide 16 and ask students how they could use that same thinking to the expression they just simplified: (–3x + 3y) – (–2x + 4y). If students struggle to see the connection, go ahead and directly tell them that instead of subtracting, they can add a negative expression. In other words, that minus symbol can be replaced with a plus sign and a -1 in front of the second expression: (–3x + 3y) + (–1)(–2x + 4y). Display slide 17 to show students this.
Now, have students use the distributive property to simplify the expression. Point out to students how much easier this is than the modeling (from earlier in the lesson).
Extend
15 Minute(s)
Show slide 18 and give each student a copy of the attached Simplifying Algebraic Expressions handout. Encourage students to independently try each question. Tell them that once they finish (or get stuck) to check their work and discuss with their partner. If students are using modeling, consider having one student model, while the other practices using academic language to describe what the other is modeling; have students take turns.
If students are using modeling to simplify their expressions, encourage them to challenge themselves to “try the next problem” without the algebra tiles. This will help them be better prepared for the last questions on their handout that do not use x’s or y’s.
After most students have simplified the third expression, transition to slide 20 and bring the class together for a group discussion. Use this slide to show how to simplify an expression without writing the actual regrouping but by underlining the x terms and circling the y terms (assuming this is an acceptable form of regrouping in your classroom).
Evaluate
15 Minute(s)
Show slide 21 and give each student a half-page of the attached Create the Problem handout. Preview the activity with students by explaining that they are given five simplified expressions and need to fill in the blanks to create an equivalent unsimplified expression. Students are to select three of the five expressions, create those equivalent expressions, trade papers with a peer, and then check their peer’s work. Let students know that one of their three expressions needs to be question #4 or #5 because they need to write at least one expression that involves the distributive property.
Give students approximately five minutes to independently work on their three expressions.
Once students are done, display slide 22 and have students trade papers and check each other’s work. Have students discuss any corrections that might be needed with their partners.
If time allows, consider having volunteers for those who selected question #3, for example, to write their equivalent expression on the board. Emphasize to students that the list of expressions are all equivalent and all simplify to the same expression. Use this time to emphasize the correct use of symbols and vocabulary.
Resources
K20 Center. (n.d.). Create the problem. Strategies. https://learn.k20center.ou.edu/strategy/149
K20 Center. (n.d.). Polypad. Tech Tools. https://learn.k20center.ou.edu/tech-tool/4556
