Distributive Property and Number Tricks

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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.

Do Now

7 minutes

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.  

Distributive Property and Algebra

15 minutes

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. 

Practice

18 minutes

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

10 minutes

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