Begin this lesson by reading the book, Two of Everything. This is a Chinese folktale about a hardworking, modest couple, Mr. and Mrs. Haktak, who discover a magical pot. When something is put into the pot, it is automatically doubled. This book creates a common experience about the concept of “doubling” to which the entire class can relate. After the book is complete initiate a conversation about the book with the class by asking some of the following questions:
- What was special about the pot that Mr.Haktak found?
[Everything he put into the pot was doubled.]
- What happened when Mr. Haktak fell into the pot?
[Two Mr. Haktaks came out of the pot.]
- What happened when Mr. and Mrs. Haktak put 5 coins in the pot?
[Ten coins came out.]
After the students have confirmed an understanding of the book, write equations to show what happened to Mr. Haktak and the coins Write 1+1=2 to represent Mr. Haktak being doubled, and write 5+5=10 to represent the coins being doubled.
To begin the main activity, sit in a circle with the students. Explain that you have a very special “doubling machine” (mirror) that is going to show them how different things are doubled. Hold up the “doubling machine” next to a student and ask the class to explain what happened. [The student was doubled and now you can see two students. Now ask how they could write that as an equation. [1+1=2.] Repeat this with different objects around the room.
Have the students remain in a circle, and ask them if they would like to use their own “doubling machine.” Explain that they are going to play a game and use the “doubling machines” to help them. Create a larger version of the Seeing Double activity sheet and model how to play the game as you sit at the head of the circle and the students watch.
- roll one number cube
- place the number rolled in the square on the Enlarged Seeing Double Activity Sheet
- select that number of plastic chips and place them on the desk
- have your partner hold up the doubling machine behind the chips so that you can see the reflection
- count all of the chips (the real ones, plus the reflected ones)
- write an equation
For instance, let’s say you roll a 4. Then place 4 chips on the desk. With students watching, place the mirror behind the chips so that the reflection of all 4 chips is visible. Then count all 8 chips. Finally, write an equation that represents this situation: 4 + 4 = 8.
Have students follow these same six steps, and then switch roles with their partner.
Divide the students into pairs and give each pair a number cube, plastic chips, and a handheld mirror. In addition, give each student in the pair a Seeing Double activity sheet. Let the students play this game until they have written four equations. If students finish early they may turn their paper over and continue rolling the number cube and recording equations.
Closure
When the class is finished, have them clean up their game and again sit in a circle. In the circle, ask students to imagine that they have a doubling pot. What would they put inside? Record any ideas that they may have on chart paper. Explain that they are going to be authors of their own book called Our Class Doubling Pot. Instruct the students to choose something they would like to put in their pot--it can be from the class generated list or one of their own ideas. Then have each student select one of the four equations from their Seeing Double activity sheet and circle it. They will use that equation as a basis for what they are going to write on their page of the book. Give each student a Doubling Pot activity sheet to create their page for the class book. They will write their equation and create an illustration to represent it. Print a copy of the Our Class Doubling Book cover sheet for the class book, and write all students’ names on the cover. To compile the class book, place all of the student’s pages underneath the cover and bind the book by stapling along the left side, or by punching three holes down the left side and securing it with ribbon or yarn.
Student examples:
