Distributive Property and Number Tricks
Lesson 16 of 20
Objective: SWBAT: • Represent number tricks using words, algebra tiles, and algebraic expressions • Define and apply the distributive property • Identify equivalent expressions
See my Do Now in my Strategy folder that explains my beginning of class routines.
Often, I create do nows that have problems that connect to the task that students will be working on that day. Today I want students to review the distributive property. They have worked with the distributive property with whole numbers, but not with variables. I call on students to share out their answers. With each answer I ask students to explain why their match is correct.
- Each student needs a set of Algebra Tiles.
- The set I use has blue x squared tiles, green x tiles and yellow unit tiles.
- If you do not have Algebra Tiles, you can have students cut out a set of Paper Algebra Tiles for homework the previous night.
- Before this lesson, I use the data from the previous lesson’s ticket to go to Create Homogeneous Groups.
- I use a Group Work Rubric with each group to give students feedback on their cooperation and behavior.
- I Post a Key so groups can check their work as the complete problems.
I explain to students that we are going to connect the distributive property to algebraic expressions. I pass out the Algebra Tiles.
We work on these problems 1 and 2 together. Students are engaging in MP5: Use appropriate tools strategically and MP7: Look for and make use of structure.
I call on students to explain how we can use the word description to create a model using the Algebra Tiles. Then we work on creating an algebraic expression that is equivalent to our tiles. When we “double it” we can represent this as 2(4 + x) or 8 + 2x. I ask students if 2(x + 4) would also work. I want them to realize that 8 + 2x and 2x + 8 are equivalent. I ask whether 8 + x is an equivalent algebraic expression. A common mistake for students is to only multiply the factor by the first value inside the parentheses and leave the second value. I want students to use their algebra tiles to demonstrate that 8 + x is not an equivalent algebraic expression.
Students complete problem 3 independently. We come together to share their ideas.
I have students move into their groups. I explain that they will work on problems 4-7 with their group members. When they have completed these problems they will raise their hand and check in with me. If they are on track, I tell them to move onto the next section.
If students are struggling with problems 4-7, we come together and work on them together. I want students to have a solid understanding of how the distributive property works in algebra before moving on. I ask students to share ideas about problem 7. I want students to realize that both (b) and (c) are equivalent to 16 + 24x. I want students to be able to explain why 2(8x +12) does not work.
Students work in groups on these questions. I walk around and monitor student progress and behavior. Students are engaging in MP5: Use appropriate tools strategically and MP7: Look for and make use of structure.
If students are struggling, I ask them one or more of the following questions:
- What do you know?
- What are you trying to figure out?
- How can you represent this step with Algebra Tiles?
- How can you represent this step with an algebraic expression?
- How can you represent this expression in a different way? How do you know this expression is equivalent?
When a group completes a problem they raise their hands. I quickly scan their work. If they are on track, I allow them to check their work with the key. If they are struggling, I ask them questions and have them revise their work. If students successfully complete the problems they can move on to the challenge question.
Closure and Ticket to Go
I ask students to share out their work for practice problem 1. Students are engaging in MP3: Construct viable arguments and critique the reasoning of others and MP6: Attend to precision. I call students up to the front to show their work under the document camera and explain their thinking. I call on other students to share whether they agree with their classmates and why. I declare that magic trick 1 and 2 are the same because they both involve multiplying by 2 and adding 3. I want students to be able to explain with specific language that the tricks involve the same steps, but the different order results in different ending expressions.
I pass out the Ticket to Go and the Homework