Multiplying and Dividing Signed Numbers

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Objective

SWBAT review multiplication and division of positive and negative numbers

Big Idea

Students revisit multiplying and dividing signed numbers analyzing patters and participating in a Relay Race

Launch

15 minutes

As students enter the room I hand each a Launch Start up Card. Today I have pre-cut and shuffled the cards. I ask students to read the problem and to write their answer on the back of the card.

I give the class a couple of minutes to work and then I ask them to discuss their question with their elbow partner. The three problems are distributed among the whole class, so it is likely that most partners have different questions.

Next, I will call on students to go to the board and not only write their responses, but explain their reasoning about the problem. I encourage classmates to ask questions or add to the explanation of the problem, if they have something to add on.

If a student presenter did not use a product or a quotient involving signed numbers in their explanation, I make sure I ask how the situation could be modeled using one of these operations with signed numbers.

The 3 situations should be exemplified as follows

  1. A temperature drop of 2 degrees is -2, so -2 x 12 or -24
  2. The burning of 3 calories is represented by -3,so -3 x 60 min or -180 (burned 180 calories)
  3. A debt of $675 is represented by -675. If 3 people share the debt, then this means -675 divided by 3, or -225. Each member owes  $225 or -225


New Info

25 minutes

I start the new info segment by projecting three slides, one at a time on the smart board.

Students should read the instructions and discuss the slide with their partners before answering. The purpose of these slides is so students could see that there is a reason behind the multiplication and division rules for integers. (Most of my students have tried to memorize these in the past, but they struggle to explain the meaning of the rules.) It is important that students discuss the problems among each other first, then share any explanations and questions with the entire class. I want them to explain these rules in their own words, rather than simply memorize a mathematical definition. (See my Class Discussions reflection).

For the discussion I call on volunteers. I ask each volunteer to explain the patterns and give us the missing steps. Here are the expected answers to the Slides:

 


Relay Race (Application)

15 minutes

Before I pass out Relay Race, I ask  the students if they have any questions or doubts about the multiplication and division rules. Once any lingering questions are answered, I tell the students that each column of desks is a team. Then, I hand a worksheet, face down, to the first student in each column. (If there is a column with too small an amount of students, or with more than 5 students, I adjust the tables appropriately)

I explain to the class that the first student will compute the first problem when I say, "Go." Then, he/she will pass the sheet to the student behind them. The second person will insert the previous answer into the blank space of the next problem and then, compute that problem (see Relay_Race_Demo). This same procedure continues until all five problems have been answered. If a team has only 4 students, then that last student will have to answer two problems. 

Once the last person in the column is done, they raise their sheets, and I collect these in the order they are raised. The first team to answer their five problems correctly is the winner. After a team has won, I go over each question with the entire class. 

Homework

The Homework for this evening continues to emphasize fluent and efficient calculation.