Divide thousands using Expanded Notation and Pizza

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SWBAT to review multi-digit multiplication and practice dividing with four digit dividends and one digit divisors in a fast paced coloring game.

Big Idea

Students are able to use their division and multiplication skills in a fun game.

Warm Up

15 minutes

For this warm up, I give students a three digit dividend division problem to solve. I encourage students to use the expanded notation method presented yesterday, but do allow them to use any division strategy if necessary.

Then I spend the next ten minutes modeling the expanded notation method using a four digit dividend and one digit divisor.  My modeling looks very similar to the video below.




Concept development

40 minutes

For this lesson, students will play a game called Pizza Picasso in order to practice the expanded notation method for division and review multiplication. Students have spent several previous lesson exploring division methods. This lesson is important because it allows students an opportunity to be comfortable with a numeric based division method. As students move away from the place value chart method and pictorial strategies, it is imperative that they have an alternative effective division strategy.  While the place value method helped build a conceptual understanding for division with my students, it is not always the most efficient method.  I want my student to have an efficient method to divide upon the completion of this division unit. I chose this game because I like that students must use multiplication to check their division which reinforces the relationship between the two operations.  I also like that the game uses pizza, a food that many fourth graders love and eat a lot of!

Materials to Play the Game
• Pizza Picasso Coloring Sheet (one per player)PizzaPicassoACommonCoreFastPacedLongDivisionGameforththGrade.pdf
• Pencils
• Scrap Paper
•one set of regular playing cards (student's won't play with 10, Jacks, Queens, or Kings)
• Crayons

The object of the game is to complete division problems and be the first player to completely color in the Pizza Picasso coloring sheet thereby winning the game

How to play the game:

1. This game can be played in pairs or trios. ( my students played in trios because we do a lot of partner work on a regular basis. Working in trios adds a level of engagement simply because it's not the norm in my class, whereas working in partners is more the norm.)

2. Each player receives a Pizza Picasso coloring sheet, crayons, a pencil and a piece of scrap paper. Each pair or trio needs cards Ace through 9. Place the remaining Ace through 9 cards face down in a pile in the middle of the group.This pile will be the divisor pile.  (When playing with trios, it is very easy to have students quickly sort the cards by suit, and put the left over suit in the middle of the group as the divisor pile)

3. Each player then places their ace through nine cards in a separate face down pile as their dividend cards.

4. Each student draws a card from the divisor card pile to determine who goes first. The child who draws the highest number goes first. Return the cards to the digit pile and shuffle them before starting play.

5. PLAYER 1 selects four cards from their dividend pile. Using these four digits, they create the number of their choosing (if they draw 4, 3, 6, and 5 for example, they could create 4356, 6543, 5436, etc.) This number becomes the dividend.

6. PLAYER 1 then selects a card from the divisor pile. This number represents the divisor. So, for example, if PLAYER 1 decided to create the number 5364 from the numbers they selected from the digit pile, and then draws a 4 from the divisor pile, the division problem they are solving is 5364 ÷ 4.

7. As they are solving their division problem, PLAYER 2 starts drawing cards to create their problem in the same manner. They will begin solving their problem as PLAYER 1 is solving their work. This game is designed to be a fast paced game, where all students are working quickly and simultaneously. Students can tend to get loud. I remind my students that since they are only drawing cards and solving division problems, there shouldn't be a lot of noise in the classroom. 

8. When a player completes a division problem, they call “MATH CHECK!” and their opponents use the inverse operation of multiplication to check their work. If it is decided that their work is accurate, they can determine if they can play one of the digits in their quotient.

9. On the pizza, there are digits. Once the division has been completed and checked, a player can look at the digits in their quotient (in this case, 5364 ÷ 4 = 1341). PLAYER ONE could choose to color in a 1, a 3, or a 4 on their Pizza Picasso board. Any digit in the quotient or the remainder can be played (colored), but ONLY ONE digit can be used per turn. If the quotient or remainder is not on the pizza, the player quickly creates another problem, and play continues.

10. As players complete problems, the cards are shuffled face down into the pile.

11. Ultimately, the first player to completely color in their Pizza Picasso board is the winner of the game.

In this photo, you can see students sprawled out engaged in the game.


 In the following video you can watch a trio as one student calls for a "math check." The students get different answers when they check the quotient, but you can see how this group (similar to many other groups in the room) reasons and communicate with each other to figure out the correct answer.





Note:  Students will spend the next lesson finishing this game.  The 40 minutes of play they got today is NOT ENOUGH to finish the game.  I also had two groups playing in which I limited their play.  One group made 2 digit dividends, and the other group made three digit dividends. These students have been struggling with multiplication and have not yet mastered the are model method or dividing hundreds using expanded notation.