Prime Climb Continues!
A Challenge for Older Students
If you do not remember what Prime Climb is or you are a new subscriber or viewer then please go back and read the blogs:
- Prime Climb Round 1: here
- Prime Climb Round 2: here
- Prime Climb Round 3: here
- Prime Climb Round 4: here
These are lessons inspired by Dan Finkel - Math for Love
I was first introduced to Dan Finkel and Prime Climb at a staff meeting one year ago through the video Five Principles of Extraordinary Math Teaching:
I was very curious what my grade three students could tell me about the color circles because through our daily math routine we learn skip counting, factors, multiples and divisibility connected to our school day number.
Here are the colored circles I put up for my Grade 3 students to explore.
My students engaged in this activity about 6 times within a 6 month period and I wrote 4 blogs to share the learning connected to the exploration time. If you haven’t read my blogs, see the links at the top of this post.
Many of my students found the first round quite challenging. There was definitely a productive struggle, but NOBODY was frustrated! When I put up the colored circles for round 2 many cheered and commented how much fun they were having. Our goal was to color in numbers up to 50 by the end of June, however, time ran out. I can tell you they were very disappointed!
The intent of this blog post is to share the learning of Grade 4, 5 and 6 students who I’ve engaged in Prime Climb through recent subbing experiences. I am fortunate that teachers who I sub for give me the freedom to plan the math.
Prior to subbing in a Grade 4 classroom I was told the focus of their learning was multiplication and division so without hesitation, I chose Prime Climb. For students to be efficient with these operations they need to have a conceptual understanding of factors, multiples and divisibility of numbers.
I put the colored circles up 1 to 20 and asked the students to look carefully at the circles, numbers and colors.
Here is what the students shared:
- All even numbers are orange
- Some circles are fractions-half, thirds
I did ask why certain circles were shared as fractions but they weren’t able to explain and that is okay. This would be something they would need to make the connections to through further exploration.
- 7 and 14 are purple cause you can count by 7 to get to 14 and 14 is also orange because it is even
- 5 is blue and 15 is ½ blue and ½ green because 3 x 5 = 15
- 3, 6, 9, 12, 15, 18 all have green because you are counting by 3
- Numbers you can count by 5 have blue
- If you double each number 2 to 9 those numbers have the same colors. Eg. double 2 is 4 so the circle with 4 also has orange, if you double 6 it is 12 so 12 has green, etc
- 11, 13, 15, 17 are red because there are not any numbers (2, 3, 4, 5, 6, 7, 8 or 9) you can count by to get to them
- Numbers you can count by 6 to are also green because you can count by 3
I didn’t ask but I should have asked if all numbers divisible by 6 can be counted to by 3? This would have been a great opportunity to see if a conjecture could have been formulated.
I asked why 1 would be gray and nobody was able to explain this to me.
After this discussion, I provided each student with the new blank color circle chart that Dan Finkel has provided which is awesome!
I left the sheets and an explanation of the activity for the teacher hoping she will learn more about Prime Climb for the benefit of students to move into a ‘deep’ phase learning.
Further opportunity for exploration would enhance their learning and understanding of multiplication and division as well as benefit the understanding of fractions.
A few days later, I taught in a Gr. 5 / 6 class as well as a Grade 5 class. Here is their thinking:
- The colors are based on multiples. Multiples of 2 are orange, multiples of 3 are green, multiples of 5 are blue, multiples of 7 are purple
- 12 is both orange and green because 2 x 6 = 12, 12 is also green because it is divisible by 3
- 12 is shared into thirds because 4 has two orange parts and 3 is one whole green and 3 x 4 = 12
- 7 is full purple but 14 is half purple and half orange because 2 x 7 = 14
- Multiples of 10 have blue and orange because they are divisible by 2 and 5
- 5 x 3 = 15 so 15 is both blue and green
- 1 is clear (white, gray) and all circles have some white because you can count by 1 to all numbers
- 2 is full orange, double 2 is 4 so circle has two parts, double 4 is 8 and 8 has 3 parts and double 8 is 16 and 16 has 4 parts. So as you double the number the circle has one more part. It goes whole, ½, ⅓, ¼.
- Red are prime numbers
- 10 has two parts cause 5 and 2 are factors and 20 has 3 parts (2 orange and 1 blue) because the two orange represent 4 and the one blue represents 5 and 5 x 4 = 20
Some very interesting thinking was happening. A productive struggle was going on which I think is critical and awesome. A few of the Grade 5 students were asking for ‘answers’ but my reply was, “with further exploration time you will come up with the answers (and conjectures) yourself.”
The educational assistant in the classroom asked the students if there was any pattern or reason for how the circle was colored. For example, if the top half was orange and the bottom half blue could these colors be reversed? Something to ponder.
The teachers of the two classes are going to continue this exploration and purchase the game so I am excited to hear (and hopefully get to see) how the learning grows.
Below you will find a few pictures of the students’ work. I found it interesting how many of the upper elementary students chose to color the numbers out of sequence whereas my Grade 3 students worked in sequence.
The pictures demonstrate the students' recognition of patterns (eg. all even numbers needed orange, all numbers divisible by 5 needed blue). As students were coloring I was moving around the class asking questions to see if any conjectures were being formulated. I didn’t hear any, but deep thinking was happening and I believe if these students are provided further opportunity to explore and continue to color in the chart conjectures will come.
One of the grade 6 boys said to his partner, "Let’s color all numbers divisible by 11 red because 11 is red."
I was thrilled to hear the response of his partner, “No, we can’t do that because 22, 44, 66, 88 are even numbers and 55 is divisible by 5."
Through my classroom experiences, Prime Climb engages students and allows them the opportunity to explore. The learning that emerges is deep, meaningful and rich which is of benefit to understanding number. In turn, this deeper understanding of number will strengthen their conceptual understanding of skip counting, multiples, factors, divisibility, and the operations of whole numbers as well as fractional numbers.
I recommend that you purchase this game for your class or for home, to play as a family. If you can’t find it at a Chapters near you then you can purchase it using this link:
If you have purchased this game, or choose to purchase this game, and/or engage your students just using the circles you can retrieve here (link), please comment to this blog and share with us what learning is happening.
I would love to hear from you and I most definitely know Dan Finkel himself would love to hear any feedback!