##
* *Reflection: Intervention and Extension
Distributive Property and Number Tricks - Section 3: Practice

While walking around, I noticed that many students were struggling to write two different expressions for Step 3 of magic trick #1. I also noticed that some students were not noticing the differences between magic trick 1 and 2. I stopped the group work and wrote these expressions on the board: 2(x + 3), 2x +3, 2x + 6 and 2(x+6). I asked students if any of these expressions matched the end of either of the magic tricks. Students participated in a **Think Pair Share. **

** **I called on students to share their ideas and I pushed them to use algebra tiles to prove their thinking. Students were able to explain that 2x + 6 and 2(x +6) were not equivalent, since if you double x + 6 you end up with 2 x blocks and 12 unit blocks, or 2x + 12. Students were also able to identify that 2(x + 3) and 2x + 3 were not equivalent.

In our discussion, one student asked whether the expression (x+3)^2 would be equivalent to 2(x + 3). I turned the question to the students and asked them what (x+3)^2 would represent. One student explained that since it was raised to the second power, it would represent (x+3) (x+3). I showed students how they will multiply expressions in later grades, and then I asked them to help me combine like terms. Students were able to see that (x+3)^2 and 2(x+3) were not equivalent.

*Intervention and Extension: Equivalent Expressions Discussion*

# 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

## Big Idea: What is the distributive property? Is 4(x +3) equivalent to 4x +12? How do you know? Students work to demonstrate the distributive property using algebra tiles and algebraic expressions.

*50 minutes*

#### Do Now

*7 min*

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.

*expand content*

**Notes:**

- 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.

*expand content*

#### Practice

*18 min*

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.

*expand content*

#### Closure and Ticket to Go

*10 min*

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**

*expand content*

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- UNIT 1: Intro to 6th Grade Math & Number Characteristics
- UNIT 2: The College Project - Working with Decimals
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Fraction Operations
- UNIT 5: Proportional Reasoning: Ratios and Rates
- UNIT 6: Expressions, Equations, & Inequalities
- UNIT 7: Geometry
- UNIT 8: Geometry
- UNIT 9: Statistics
- UNIT 10: Review Unit

- LESSON 1: Translating Algebraic Expressions and Equations
- LESSON 2: Working with Expressions and Equations Part 1
- LESSON 3: Working with Expressions and Equations Part 2
- LESSON 4: Working with Expressions and Equations Part 3
- LESSON 5: Introduction to Solving Equations
- LESSON 6: Writing and Solving Equations
- LESSON 7: Writing and Solving Equations Part 2
- LESSON 8: Equations, Tables, and Graphs Day 1
- LESSON 9: Equations, Tables, and Graphs Day 2
- LESSON 10: Finding Solutions to Equations
- LESSON 11: Working with Inequalities
- LESSON 12: Show What You Know about Expressions, Equations, & Inequalities
- LESSON 13: Area and Combining Like Terms
- LESSON 14: Perimeter, Area, and Combining Like Terms
- LESSON 15: Number Tricks
- LESSON 16: Distributive Property and Number Tricks
- LESSON 17: Area and the Distributive Property
- LESSON 18: Review Stations
- LESSON 19: Unit Closure
- LESSON 20: Unit Test