Lately, we are experimenting with math warmups in elementary school classes. Today, I tried one on a fourth grade class. I think someone else tried the same warmup in a fifth grade class, so I will have to ask them how it went.
Math warmups take just 5 to 10 minutes at the start of math class. For maximum effect, they are done every day or almost every day. With math warmups, it is possible to teach specific skills related to number sense. Lots of math gurus talk about these, including Sandi Stanhope and Bob Laird from the Vermont Mathematics Initiative, Marilyn Burns, Cathy Fosnot, etc. etc.
Here’s the one from today:
4 x 8 =
8 x 4 =
8 x 3 =
4 x 6 =
2 x 6 =
1 x 6 =
½ x 6 =
¼ x 6 =
I asked the students to solve these mentally and write the answers. I didn’t want anyone to struggle, so, if they didn’t know it, I just told them or had another student tell them the answer. I encouraged students to use what they knew from the previous equations to help them find answers without the usual calculation.
When asked what they noticed, students were able to share that they saw the commutative property in action (without using that vocabulary word) and could see halving and doubling relationships.
For example, 8 x 3 and 4 x 6 both equal 24, and that 4 is half of 8 but 6 is double 3. When you double something then halve it, you are back to where you started.
Getting down to the series of _ x 6 was interesting. Students noticed the pattern of the 6 staying the same while the other factor kept getting reduced by half. By the time they got down to the fractions, they were able to use their knowledge of the properties of multiplication to help them through a potentially difficult task. These students haven’t yet studied much about multiplication of fractions, but were able to do it easily.
I am thinking in the future it might be fun to try a number times ¼ and let students work back up to one through doubling if necessary to assist them in solving the equation without an algorithm.
