Exploring the Distributive Property

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SWBAT use the distributive property to write expressions featuring area diagrams.

Big Idea

Area models and expressions will help build a solid foundation of how the distributive property works.


20 minutes

The students will be completing an activity adapted from NCTM’s illuminations.  The activity uses rectangles and line segments to write equivalent expressions.  Additionally, the students will be using the area diagrams to write the expression using the distributive property. 

I chose this problem because it sets them up for the learning for today.  This is a straight forward worksheet , with examples, that will help students see how to write the expressions.  If this is a challenge for some students, they can partner up to discuss strategies and solutions.

I’m anticipating that question 4 will give them a hard time.  Students will want to answer it 2x instead of x². Remind students that when we find area we are multiplying l times w.  What happens when I multiply x • x? (SMP 2)

In questions 5 – 7, the students will need to find the area of each pair.  Again, a reminder of the area formula couldn’t hurt.  For the pairs that are missing a side length, ask the students if there is any other information there that could help them find that side length? (SMP 1).

For questions 8 – 10, remind students that are finding the total length.  Ask them, when finding the total length of a line segment, what operations should be used?

For questions 11 – 13, the students are finding the area as a product and as a sum.  There is an example for them to use.  Let students try these on their own. 

After working through these problems, go over as a whole group to check for understanding. 

Matching Activity

25 minutes

Materials: Poster paper, glue, area cards, expression cards, marker.

The students will be using the area and expression cards from the MAP activity.  The object here is to match 2 expression cards with one area card.(SMP 5 and 7)  The students will be working in pairs and both partners have to agree that it is a match.  Once they find the match, they must clearly explain why the feel the diagram and expression match.  If both partners agree, the cards get placed off to the side to be used later. Partners should take turns finding and explaining the matches. When they have all cards matched, they will place them on their poster paper.  DO NOT glue at this time.

For students that are struggling, remove any cards that have fractions and let them work with the whole number expressions.

Questions to ask students as you are walking around:

Why did you choose this expression?

Show me a different expression from your partner’s that checks their match?

Explain why your partner chose that as a match?

Sharing Work

10 minutes

Materials: Post-it notes

Allow students time to look over the work from other classmates.  If they have concerns, have them write them down on their post-it notes and place them by the appropriate cards.  (SMP 3)

Creating a Poster

20 minutes

When students return to their desks, they should look at the post-it notes concerns and take into consideration what is written on them.  If students don’t agree with the suggestion, they can leave it alone.  If they agree, then they should make the appropriate changes.  Once they have completed any changes, the students should glue down their matches (2 expressions and 1 area).  Each match needs a written explanation as to why they feel it is the solution.

Save this poster as evidence of student learning. 

Closure + Homework

10 minutes

Give students back their original area and expression assessment with their feedback on it. They can use this as a resource for their homework.

Students will be revisiting the area and expressions assessment.  At this time, my expectation is that students should be very familiar with making the equivalent expressions and this should no longer be an issue.  Have students start working on this at the end of class. They can take home any remaining problems or explanations for homework.