Multiples

Yesterday the grade 6's did a problem using multiples, although they didn't really know that at first. Here was the question:

On Thursday morning, the local radio station held a call-in contest. 

• every third caller won a t-shirt
• every seventh caller won a baseball cap

In 50 calls, which callers won a T-shirt? A baseball cap? Both prizes?

Students worked in pairs to try and solve the problem. It was interesting that students used a variety of strategies to come to the same conclusion. Here, a pair of students used multiples to help them find their answer:

Here, you can see that the students found the multiples of 7 and the multiples of 3, and then circled the COMMON multiples. This term, common multiple, is a new one for us, so we discussed that for a little bit. After looking at  a few samples of student work, we discussed the idea of multiples as well. Students should understand that multiples are the same as counting by 3's or 7's, etc. 

Here is another way a pair of students figured out the problem: 

 This is a similar strategy, but the students used a table, which is a little more organized and may help find common multiples a little easier. Both ways work! 

What is important, and that we try to stress, is that there are almost always more than one way to solve a problem. The important thing that we want to see students trying to do is to show all of their thinking, as they have done here. I also encourage them to show their thinking in Numbers, Pictures and Words, if possible. 

Here is another interesting way of finding the solution to this problem. This student wrote all the numbers from 1 -50 in a list, and then placed letters (t- for tshirt, b- for baseball cap) next to the appropriate multiple. I thought this was an excellent, different way to find the solution for the problem. 

We will be continuing to examine multiples today, and then moving on to Prime and Composite numbers, which students generally find fairly easy.