Saturday, February 11, 2012

Commutative Property

Day 1: I Have, Who Has?

Introduce the commutative property. Write several number sentences on the board that illustrate it, such as 3 + 2 = 2 + 3, 8 + 11 = 11 + 8, etc. Explain these, then write a few more and ask the students to tell you what goes on the other side of the equals sign.

Does the commutative property work for subtraction? Why not? (Rather than introducing negative numbers at this point, I vote we just say something along the lines of, "If I only have 3 pieces of candy, you can't take 4 away from me!")

Play "I Have...Who Has..." Play it the regular way first so they get the hang of it, then tell students to use the commutative property and reverse the addends on the card. (So instead of "who has 3 + 4", they would ask "who has 4 + 3") If the commutative property really works, the game should still work! If there's time, have students switch cards and/or time them and see if they can beat their record.

How to play the game:
Distribute the cards randomly to your students.
Some students may get more than one card, but ALL CARDS NEED TO BE IN PLAY.
Select a student to begin by reading their card aloud.
(example: I have 14. Who has who has 3+4?)
The student who has the card with the correct answer to the previous student’s
“Who Has...” question reads their card aloud.
(example: I have 7. Who has 10+5?) And so on.
Students must listen for their turn and try not to break the chain.
When the chain is circles around to the first student, the game is over.

Day 2: Triangle Arrays

Draw the array of triangles from the triangle worksheet on the board. Review the commutative property and demonstrate how you can divide the triangles lots of different ways, but they will always still add up to 32 (even if you divide them into more than two groups). Give each student a copy of the triangle worksheet. Have the students divide the triangles in the first array any way they want, then (simultaneously) pass the worksheet to the next person, who has to write the commutative number sentence (e.g. 30 + 2 = 2 + 30) below it, then divide the next triangle array. Keep dividing, passing, and solving until all six spots on the sheet have been completed, then tell students to turn the page over and draw their own commutative property picture using any object they want (footballs, birthday cakes, stars, guitars, whatever!) Tell them to take the picture home and see if their parents know about the commutative property and can solve the problem.

Day 3: MATH-terpieces

Have students solve the puzzles in a few more pages of MATH-terpieces by Greg Tang. (Bring a laptop or iPad with the powerpoint in addition to the book so everybody can get a good look at the paintings and the groups of objects.) Students should write each addition sentence on their own sheet. Emphasize that we're using the commutative property here- 4 + 6 peaches is the same as 6 + 4 peaches, so that only counts as one solution.

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