Cognitive Cardio Math
  • Cognitive Cardio Math
  • Math Blog
    • Math Blog Table of Contents
  • Math Resource Center Info
  • Free Math Resource Center
  • Shop
  • Math Games
  • Privacy Policy

Focus & Fun with the Array Game, Using Polyhedral Dice

4/22/2016

1 Comment

 
Pin it
playing the array game
Have you used the array game with your math students?

I was reading the book Mathematical Mindsets by Jo Boaler (so much fantastic research and so many wonderful ideas in her books!) this week, and read about the “array game” (called How Close to 100), which I’ve seen all over Pinterest and thought was very cool.

​I tried it with my 6th grade math classes last year during a little bit of down time, and they liked it. I hadn't really thought of using it in 6th grade again this year, but last week I noticed the baggie of polyhedral dice that I've had for a looooong time and thought it would be cool to use the dodecahedron dice for the array game. With these dice, the students could use numbers up to 12, rather than 6.

Setting up and Playing the Array Game:

Looking for a fun, challenging way to practice area concepts? Try Looking for a fun and challenging way to practice area concepts? Try the array game using polyhedral dice!
To set up their array games, all students needed to do was outline a 20 by 20 area on their own graph paper.

To play the array game, students paired up and then took turns rolling their dice and drawing arrays to represent the multiplication problem they had rolled.

It was very interesting to observe the way students arranged their arrays:
  • Some started in the corner and worked their way out.
  • Others started on one side and worked their way across.
  • Some made the arrays touch, if possible, while others left a row between each one.
  • Some just drew their first few arrays anywhere and then discovered that they didn't have a lot of room to fit additional ones.

The "winner" of the array game was the student with the fewest number of boxes left (some did get to zero left). The students really had fun with this!

student drawing a shape during array game
examples of student sheets during array game
examples of student sheets during array game

Array Game Extensions:

Of course, some finished their games earlier than others. In these cases, I asked students to create arrays that used different numbers than the numbers they rolled, but represented the same area.
  • For example, if they rolled 12 and 5, their arrays could be 10 by 6, 15 by 4, or 20 by 3 (not 30 by 2, we discussed, because the grid is only 20 by 20).
  • If they rolled a number that couldn't be represented by a whole-number array, they could then use an irregular shape, or a triangle - anything they could find the area of. It was interesting to see how some students got stumped when they tried to draw an irregular shape to represent a number like 81.
Most students enjoyed this twist (we continued it the next day so they all got to play this version), but a few complained that it made their heads hurt! That's ok...I know they were really thinking and growing mathematically!

A second extension for early finishers (only a few) was to use the icosahedron (20-sided) dice, and have students create area models to cover their grids and find the answer to the multiplication problems.
  • This required a larger grid, so I had them tape 2 pieces of graph paper together and create 20 by 40 grids.
  • Using the icosahedron dice gave a mix of 1-digit by 1-digit, 1 by 2-digit, and 2 by 2-digit problems to model and solve.
Most students didn't get very far with this before we ran out of time, but I think this is a great way for them to visualize what multiplying by a two-digit number means. I'd like to revisit this one!

I'm so glad I thought about using those polyhedral dice! 

​Have you used polyhedral dice or played the array game in your math classroom? If so, please share!​
Picture
Pin it

To Read Next:

1 Comment
    Picture

    Author

    Hey there! I'm Ellie - here to share math fun, best practices, and engaging, challenging, easy-prep activities ideas!
    Looking for a particular topic or activity? Check out the Blog Table of Contents or use the Search feature below.

    Five days of free math lessons for middle school math
    Select to receive 5 days of free lessons!
    Pixel art create your own color by answer
    math color by number activities for grades 5 to 7
    note taking graphic organizers for 6th grade math

    Archives

    March 2021
    January 2021
    December 2020
    November 2020
    October 2020
    September 2020
    August 2020
    July 2020
    March 2020
    February 2020
    January 2020
    September 2019
    August 2019
    July 2019
    May 2019
    April 2019
    March 2019
    February 2019
    January 2019
    December 2018
    November 2018
    October 2018
    June 2018
    May 2018
    March 2018
    January 2018
    December 2017
    November 2017
    October 2017
    September 2017
    August 2017
    May 2017
    April 2017
    March 2017
    February 2017
    September 2016
    July 2016
    April 2016
    February 2016
    November 2015
    September 2015
    May 2015
    March 2015
    February 2015
    January 2015
    November 2014
    October 2014
    August 2014
    March 2014
    October 2013
    September 2013
    July 2013
    May 2013
    January 2013

Back to Free Page
  • Cognitive Cardio Math
  • Math Blog
    • Math Blog Table of Contents
  • Math Resource Center Info
  • Free Math Resource Center
  • Shop
  • Math Games
  • Privacy Policy