Two days a week in my resource classroom, we use a computer program that works with students at an individual level to help fill in their math gaps. Recently, I had a student have a melt down over using the program. It wasn’t the program itself, but the glaring fact that the student cannot learn his multiplication facts. The program will not move to another concept until a student completes a section with 80% mastery. As you can only imagine, a 7th grader who keeps getting multiplication problems over and over and over and over was bound to have a melt down…. SOOOOO, yesterday, instead of working on the computer program, he and I played a little game.
I printed out a square piece of grid paper on the internet, grabbed a pair of dice, and two color pencils. I told him the rules were simply: fill in the largest most coordinate squares with his colored pencil. To do that, we rolled the dice and multiplied them together.
A 4 and a 6 meant that we made a 4×6 or a 6×4 array, colored it in, counted the squares, and wrote 24 in the middle. I didn’t tell the student how to figure out the number of squares. Sometimes he counted them all, sometimes he skip counted, sometimes he multiplied – he used many strategies. My favorite strategy was 4 x 5. He said that he knew 8 x 5 was 40 and that 4 was half of 8, so 4 x 5 must be 20 because half of 40 is 20.
(even though he can’t memorize… he does a heck of a job with figuring out relationships)
What was really interesting about playing this game with him was watching his spatial reasoning skills. He pretty quickly picked up on the idea that placing arrays all over the grid would lead to disaster later. He also started finding side lengths to help him place a new array without having to count. For example, placing a 4×6 on the side of a 2×6. He already knew it was 6 long so he could quickly draw to rows upwards and move on.
Another interesting fact is that this student has a hard time differentiating between a 5 and a 6 on a rolled die. There were a few times when he rolled a 6×4 and would only fill in a 5×4 array. It wasn’t because he was miscounting, or even trying to cheat… he truly couldn’t differentiate between the 5 and the 6 without physically counting the number of pips on the side.
This immediately reminded me of another blog post I read from Donna Boucher at Math Coach’s Corner
(I can’t currently find the post I’m looking for… but when I do, I’ll post it!)
After playing our game for 30 minutes, and as class was winding down, I asked my student to relate the game back to three different math concepts that he used in the game. His answer is below:
1) figure out the amount of space inside (when probed for the correct vocabulary term, he eventually came up with area)
2) finding where each piece fits nicely (I told him we call this spatial reasoning)
3) that he could multiply to find the area
4) he had to keep a running score so that we didn’t have to count up the boxes individually at the end.
I was REALLY excited that he not only came up with FOUR ways instead of just three, but also didn’t complain that he didn’t know how it related to math.
Here is what we ended up with after 30 minutes of playing. I didn’t realize at the time that the squares were soooo little.
Today, we finished up our game from yesterday and upped the ante a little bit! Today, instead of using 2 green die, we used 1 red and 1 green. The difference (other than the obvious color)… the green die stood for how many rows the array should have and the red stood for how many columns. My student really enjoyed the game today – you could see him thinking more carefully about where he placed his arrays and the counting strategies became more fluent.
I’m really excited that the last two days have been less stressful for him. He’s smiling again and we had some really nice conversation about math during our game.
Check back tomorrow on my Facebook page… There may be a FREEBIE posted for you 😀