Summary
Students will use manipulatives to solve algebraic equations.
Essential Question(s)
How can you use manipluatives to solve algebraic equations?
Snapshot
Engage
Students use a Think-Pair-Share strategy to discuss the value of triangles having the same value.
Explore
Students use a balance and pieces to solve for the unknown.
Explain
Students use a Pass the Problem strategy to create and solve another student's problem.
Extend
Students solve story problems by drawing or using their manipulative pieces.
Evaluate
Students use a Windows Notes strategy to solve a story problem.
Materials
Balance scale and pieces handouts (attached)
Teacher presentation slides (attached)
Window Notes handout (attached)
Pass the Problem handout (attached)
Think-Pair-Share handout (attached)
Dry erase markers (optional)
Colored pencils or crayons
Engage
Begin by presenting the attached slide presentation and introducing the lesson. Pause on the title slide and take a few minutes to lead a whole-class discussion on the question, "What is the purpose of a scale/balance?"
Slides three through six contain questions for whole-class discussion. Transition through these slides and solicit responses from students.
Transition to slide seven, and Introduce a Think-Pair-Share strategy. Distribute the attached Think-Pair-Share handout and ask students to partner and answer the question about the value of the two triangles on the right side of the balance. Allow students time to discuss the problem with their partner and collaborate on an answer, then solicit responses. Students should be able to describe how they determined the value of the triangles and explain their reasoning.
Students will likely say the value of each triangle is 5 since 5 + 5 = 10. Ask the class, "Could the values of the triangles be 4 and 6 since 4 + 6 = 10 also? Why or why not?"
Explore
Distribute the balance scale and pieces handouts to students. Students will use their pieces and balance scale to solve problems on slides 8–12. Students should model each slide using their scale and piece, then solve for the value of the black triangle and blanks representing the balance of each side of the scale.
On slide 11, students will discover that they do not have two 7s among their pieces. They will need to think about another way to model this, for example using a 10 and 4.
Explain
Transition to slide 13 and introduce the Pass the Problem strategy and pass out the attached student handout. During this activity, have the students create an equation for another student to solve. Have students model a problem using their scale and pieces before adding it to the Pass the Problem student handout.
Circulate around the class while students are creating their problems and check their work, offering assistance as needed. Once the students have created their problem, they will illustrate the problem on the Pass the Problem sheet using a colored pencil or crayon.
Have students sit in a circle and pass their problem to the left. Give students time to solve the problem they receive and write out an explanation of their solution. Next, have students pass the problem back to the student who created the problem. At this time, the students will look at their problem and its solution explanation. If the student who created the problem is not satisfied with the solution given by their peer, or if no explanation was written, have the two students discuss and re-evaluate the problem. Some students may need to re-write their response and others may need to re-write their problem, based on their discussion with their partner.
Below are some examples of actual student's Pass the Problem handouts and their peer's solutions:
Extend
Transition to slide 14 and read the story problem shown. Ask students to draw an equation to solve this problem. Have them explain how they know their answer is correct. Some students may want to use their balance and balance pieces.
Transition through similar story problems on slides 14, 16, and 18. Give students time to solve each of these problems using their balance sheet and pieces or by whatever method they find comfortable.
Evaluate
Introduce the Window Notes strategy and distribute the attached related handout. Have students read the story problem, which is similar to the ones they have practiced on the previous slides. The four "windows" should be completed with the following information about the story problem:
The Facts: Students list the facts from the story problem.
The Questions: Students identify the question from the story problem that needs to be answered.
My Process: Students write out how they think they could solve the question.
The Model: Students illustrate how to solve the question.
The completed Windows Notes handout will be used as an Exit Ticket to check for student understanding.
Below are some examples of actual student's Window Notes, along with explanations of each student's understanding of the lesson concept:
Resources
Free Image on Pixabay - Balance, Swing, Equality. (n.d.). Retrieved from https://pixabay.com/illustrations/balance-swing-equality-measurement-2108022/
K20 Center. (n.d.). Pass the problem. Strategies. Retrieved from https://learn.k20center.ou.edu/strategy/d9908066f654727934df7bf4f506c28b
K20 Center. (n.d.). Think-pair-share. Strategies. Retrieved from https://learn.k20center.ou.edu/strategy/d9908066f654727934df7bf4f5064b49
K20 Center. (n.d.). Window Notes. Strategies. Retrieved from https://learn.k20center.ou.edu/strategy/fc74060730ea745c8c4f356aa2015ac0