Daily Practice Leads to Deep Understanding
Trial and Error Leads to Deep Understanding
Skip Counting and Factorization are Important
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These are lessons inspired by Dan Finkel - Math for Love:
I have to say this fourth round of Prime Climb has been interesting and exciting because of the students continued growth in the understanding of factors and divisibility.
As mentioned in previous blogs my Grade 3 students have been working with skip counting, factors and divisibility based on the number of school days they have been at school.
It is important you keep in mind this learning began on Day 1 of school and we have not missed a day. It starts with understanding of what number patterns we can count by to that number beginning at 0. For example, when we started at 1 we could count by 1. One group of 1 is 1. Then for 2 we could count by 1 and by 2. There are 2 groups of 1 in 2 and 1 group of 2 in 2.
This learning continued every day and from the start we had to do the skip counting one number at a time with the support of a 100’s chart and/or number line to determine the factors and sometimes it was trial and error. When I say trial and error students may provide numbers in sequence as factor. For example, at Day 20 students may say we can count by 1, by 2, by 3, by 4, by 5, by 6. We would skip count to verify and this is surface level learning.
Then the deep learning began and by the time we got to 30 many students realized that in 10 there are 2 fives so in 30 there are 6 fives and in 10 there are 5 twos so in 30 there are 15 twos. They also knew that 3 tens are 30 so then 10 threes are 30. They began to connect that factors come in pairs and are opposite one another in the amount of groups. This of course, lends itself to the commutative property. If 10 x 3 = 30 , then 3 x 10 = 30.
It has been an incredible learning journey for my students and it was wonderful watching students’ surface level understanding of factors and divisibility move into deep and transfer learning.
You may ask what benefits does skip counting and factorization have to students’ success in mathematics?
- Skip counting is the pre-learning to multiplication and division.
- Factorization allows flexibility with teen digit and multi-digit multiplication and division.
- Both skip counting and factorization is of benefit to working with fractions which is connected to decimals.
I ask you to take a look at your curriculum, whether it is Kindergarten or Grade 6 and ask yourself where and how this learning is important to start and how it progresses and connects to other concepts/strands.
Now let’s get back to the work of my students. I have included pictures and some short video clips. Remember there are students who are still grappling with this, but it is productive struggle. You will specifically hear this productive struggle in a short video where a young boy is trying to explain why he colored 27 in the way he did, based on fractions. He knew how to color 27 based on the factorization and patterns of the Prime Climb circles, however, he wasn’t quite certain about the addition of his fractions. But again, think of the learning that is taking place. I didn’t correct him because I do plan for this learning to continue as we move into May and June.
Here are the pictures as well as the videos. I hope they are of value to your learning. If you haven’t yet tried Prime Climb, give it a try with your students and let us know what happens by adding a comment to the Blog. I would absolutely love to hear about the learning in your classrooms.
Prime Climb is a game created by Dan Finkel (Math4love) and it can now be purchased in Canada.