5 Tips for Middle School Math
The math homework dilemma – to give or not to give (IF you have the option in your district)? How much to give? To go over it all or only review some of it? What will be most helpful to your students?
Maybe your experiences have been similar to mine: I’ve adjusted my practices from year to year, sometimes spending a lot of time reviewing homework, but other times spending little; some years giving homework related to the lesson, other years giving homework that was basic skills practice; some years lots of problems, other years just a few. There seemed to be pros and cons to each.
Thinking about this topic yet again, I decided to look for some research to see how we can help students get the most out of the homework we assign.
Have I mentioned that I love Jo Boaler’s books and site, Youcubed.org? Well, I do! She shares so much fantastic research and so many wonderful ideas.
So, I was reading her book Mathematical Mindsets 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 classes last year during a little bit of down time, and they liked it. I hadn't really thought of using it 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.
To set up their game, students each outlined a 20 by 20 area on their own graph paper. They took turns rolling their dice and creating 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, while 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" was the student with the fewest number of boxes left (some did get to zero left). The students really had fun with this!
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!
The next 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 to 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 in your math classroom? If so, please share how!
Using the Date to Encourage
More Math Thinking
2) The other way I used the dates was to write the date so that students have to solve an expression for each number in the date.
It's been fun to see some students writing these in the corner of their notebooks during class! Others have asked to write their equations or expressions on the board during the last period of the day.
What I love about these ideas are that they are quick, can be done at any time (beginning of class, finished early time, closing of class, or in homeroom) and they help kids to expand their number sense and use some "out of the box" thinking. The "date as an expression" idea can also be expanded to challenge students: students can create their own expressions, students can solve the expressions (using the bar as a division sign - a student did this on his own one day!), and if you happen to make a "mistake," students can find it correct it!
I also look at the date-writing as a way to introduce notation my students haven't seen before, like the cube root, as well as reinforcing some concepts, like exponents. I don't know about your students, but mine often forget that 2 cubed means 2 x 2 x 2, not 2 x 3. Using the exponents in the date keeps bringing that concept back for review.
Update: I've started posting math dates at the beginning of every week on Instagram (always on Instagram) and Facebook (most weeks on FB), so if you'd like to use them, I hope you'll follow me on one of those platforms (if you aren't already).
Another update: I've created Math Dates resources for you to use throughout the year - these have been published by individual months and as a year-long resource.
Hi, I'm Ellie! I've been in education for 25 years, teaching all subject areas at both the elementary and middle school levels.