Using the Properties of Multiplication

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Objective

SWBAT multiply rational numbers by using the commutative property and associative property.

Big Idea

Students work in homogenous groups to use properties of multiplication to evaluate multiplication problems with rational numbers

Do Now

10 minutes

Students enter silently and find another “sprint” on their desks. This assessment includes 25 questions to be completed in 1.5 minutes. The first 10 questions are fraction/decimal conversions and the remaining 15 questions are multiplication facts using positive and negative integers. Students who raise their hand to indicate they’re finished will have their paper stamped and collected for grading. Students who answer all problems correctly earn two achievement points. All answers are reviewed as a class and displayed on the power point. As an incentive, a student actively engaged in checking may be given the opportunity to click the next answer on the power point remote.

At the end of the Do Now students will be given a sheet of paper with the hierarchy of consequences for the class as well as a list of prizes students can obtain by redeeming achievement points. Behavior at this point in the year starts to lag, so I am using this as an opportunity to reignite motivation as we continue to move through operations with rational numbers.

Check Homework

10 minutes

Homework was checked for completion during the Sprint in the earlier section of class. Next, we use the powerpoint to display the answers to the homework assignment.

I display slide 8 and ask three different students to read those sentences out loud, stating what should go on the blank.

In the next slide there is a box which students are instructed to read in partner groups, making sure to jot down any questions that might come up. We share out and answer those questions together.

Next, I ask students to check their answers silently to the remaining operation problems (multiplying signed fraction). A timer goes up on the board to show that they only have 2 minutes to check their answers alone. If they have any questions about solutions, they must hold off until these 2 minutes are up.

Finally, I set a 5 minute timer to be used for questions. Those students who got every answer correct and showed appropriate work will become chelpers. They will be floating around the room, like I will, answering individual student questions.

The main ideas I and my chelpers will be reinforcing include:

  • when multiplying signed fractions, ignore the +/- signs at first and multiply the same way you would with positive fractions
    • convert mixed numbers to improper fractions
    • reduce where possible (vertically and diagonally only!)
    • multiply straight across
  • after multiplying, you can consider the signs and remember,
    same good, different bad, ugh! (8th Grade Master Teacher, Jeff Li does an excellent job in this lesson of explaining this strategy used by multiple KIPP teachers in our network)

Task - Cornell Notes

15 minutes

Students are asked to find their answers to the survey on the opposite page of the “Sprint” and stand behind their chair. A couple of minutes are set aside for students who did not get an opportunity to answer these questions during the Do Now.

Next, students are asked to rearrange the room using the image in one of the ppt slides:

Students are then asked to move to one of the 3 different areas of the room (labeled ABC) based on the answer to the first question. The 13th slide indicates where students ought to sit based on the answers to both questions. The idea behind this activity is to have students separate themselves into homogenous groups. This will make it easier for me to know where I should prioritize my time during the task section. It is important to note that some students may not be aware (or want to be aware) of their struggles with a topic, OR they may elect to just go with their friend. I make it clear that I trust them to select the correct area of the room and that if I ask them to move, it is only to help. 

Students work together to review the notes and ask each other and me questions about the operations. I will have different students put the examples up on the chalk board.

Most of my time will be spent helping students review rational number addition/subtraction. This includes the use of white boards to give small groups of students practice problems before attacking the last three examples in the notes sheet. I expect that some will be intimidated by those problems. To arm them with confidence, I might begin by giving them pairs of integers to multiply, steadily increasing difficulty until we are able to successfully multiply three integers. Then, we will share out strategies and apply them to the examples at the end of the notes. About half of the students in each of my 7th grade classes has mastered these operations and the other half need more practice. Thus, it will be important to have jobs for those students should they finish the notes early. I can have them help other teammates, writing problems on the board, or I could give them additional problems to solve on white board. 

Once we have 10 minutes left in class and if students finish Cornell notes early, they are given the homework to start for the night.

Closing

10 minutes

Students respond to a journal entry question. They receive a small sheet of paper to tape into their journals and must then use the lines to explain further.

This journal entry will ask students to justify the steps for evaluating a multiplication expression using the properties explored in today’s lesson. After identifying the properties, students will explain how these properties made the product easier to find. 

Homework will be distributed while students work.