Saturday, June 20, 2015

3rd Grade Math - The Distributive Property

Here's a post I started a few months ago, but never finished...

My step-daughter, Brianna is currently student teaching 3rd grade.  The other day she was expressing her frustration with teaching the distributive property to her students.  She felt that it was overwhelming due to the fact that many of them don't know their times tables, therefore they have difficulty finding the area of a rectangle, and ultimately struggle with the Distributive property.

I remember when my son, who is now in 4th grade, was struggling with this very topic last year.  He is a B student when it comes to math (go figure) and this was probably the most difficult math topic for him in 3rd grade.

She asked for my opinion on some activities that she could do with her students to help them understand.  Here is what she came up with:

Each group of students is going to receive these rectangles: 5 x 1, 5 x 2, 5 x 3, 5 x 5, 5 x 6, and 5 x 7.  She cut these out and highlighted the edge of the rectangle to make them easier to identify.  For example, she highlighted all the 5 x 3 rectangles in orange.  Hopefully she took more pictures than I did.  This is all I have.

Then she will give each group of students a paper with a 5 x 8 rectangle on it.  The students need to use the rectangles they have place two at a time without overlapping to create the 5x8 rectangle.  Very tactile, very hands on, excellent.

The students will be able to use the rectangles 5 x 1 and 5 x 7 to complete the activity, also 5 x 2 and 5 x 6, or 5 x 3 with 5 x 5.

One word of caution from Bri: She didn't create the rectangles 5 x 4 for the students.  She found that when she was trying to talk to the students about two congruent rectangles, the student were confused as to which one she was referring.

That's her lesson for today and she will build on this foundation, but I can't help but keep thinking about this 3rd grade topic.  My son struggled with it, her students are struggling with it, I remember a frustrated Facebook post about this from a friend of mine, and I'm sure there are many others who struggle with this.

What do you do when a math topic is proving difficult for students?  Why you create a game of course.

I'm not all that familiar with a group of 3rd graders, please keep that in mind.

I like the idea where Bri gave her students different rectangles to manipulate, so I think that should be a component of the game.  There are 15 different rectangles 1 x 1  up to 5 x 5.  And I like that she gave her students a target 5 x 8, so for the game I see the target changing.

Each team of students is given 15 random rectangles.  Some will be repeats and that's okay.  The teacher displays the target and the students try to create as many as they can with the rectangles they have.  It is possible that the students won't be able to create the target since the rectangles given are random.

Here are all the different rectangles.  The teachers will need to create as many sets as there are students plus at least one extra set. 23 students means 24 of each rectangle below.

1x1  1x2  1x3  1x4  1x5

2x2  2x3  2x4  2x5

3x3  3x4  3x5

4x4 4x5

5x5

Here are all the different targets that can be created with any 2 of the rectangles.  The teacher will need to create just one of each target.

1x2    2x2

1x3    2x3    3x3

1x4    2x4    3x4    4x4

1x5    2x5    3x5    4x5    5x5

1x6    2x6    3x6    4x6    5x6

1x7    2x7    3x7    4x7    5x7

1x8    2x8    3x8    4x8    5x8

1x9    2x9    3x9    4x9    5x9

1x10  2x10  3x10  4x10  5x10

For each pair or rectangles that a team successfully creates the target, they get 2 points.
If a team can use 3 rectangles to create the target, then they receive 3 points.  And so on.
After that round is over, the students hand in the rectangles they just used and replace them with new random ones.

The team with the most points after a certain amount of time (teacher's choice), is the winner.

Students are given still given the 15 random rectangles (is 15 too many?), but this time 36 of the 39 targets are written on the board in a 6x6 array randomly.

Teams take turns using at least 2 rectangles to make a target.  That target is circled in that team's color.  The team then hands in the rectangles they just used and are replaced with random rectangles.

The first team to get 4 (maybe 3?) in a row wins.

If the 6 x 6 board is too small, some targets could be written more than once.

Again, sorry about the lack of photos.  I was so excited to create this game, that when I did I proceeded to give the 'game pieces' to Bri immediately and forgot to take a picture.  Sorry :(

1 comment:

1. This is very nice!

In thinking about games, I find it helpful to consider two, in particular: Mastermind and Battleship.

In Mastermind, there is some initial answer, and one person (or team) guesses in a way that the other person (or team) can give feedback. The game ends when the guesser finds the correct answer. (The set-up requires a bit of trickiness by the non-guesser, after which the game is collaborative.)

In Battleship, each of two people (or teams) has an initial answer, and both play the role of guesser/responder. The game ends when the person (or team) correctly guesses the answer of the other person (or team). (The set-up for each requires a bit of trickiness, after which the game is competitive.)

And so the open-ended question to think about here is: Are there Mastermind and/or Battleship games that one can create using the sort of materials described in your post?

MQ