I visited Susan Carrusca’s grades 1 and 2 class at Byng Elementary to introduce some different ways to use ten frames to support visualization leading to working with mental mathematics strategies. Byng’s school goal is around developing computational fluency and greater student engagement in mathematics
Many of the tasks we did together were based upon ideas from a Math Solutions book – It Makes Sense! Using Ten Frames to Build Number Sense.
We came together on the carpet area and I used Trevor Calkin’s large Power of Ten cards to play Flash It with the students. I held up a ten frame card for a second and asked the students to call out what number they saw represented. We talked about not trying to count but to take a picture with your brain. We discussed what numbers were easier and why (9 was easy for them because the students said they saw one space empty so they knew one less than 10 was 9) and which ones were more difficult – 7 and 8. Using a large magnetic ten frame on the whiteboard I showed them the importance of “building on 5″ and seeing 7 and 8 as five and something (5 and 2, 5 and 3). We played Flash It again, and the students were more confident (and louder) at recognizing the numbers.
The students then moved back to their desks where they each had a ten frame mat and a basket of loose parts/counters. We played Show It, where I held up a ten frame card long enough for all students to have a look and then the students showed that number by building it on their ten frames.
Using the same ten frame mats and loose parts, the students played Roll it, Build It by rolling a regular dice. Simply, they rolled the dice and then built that number not their ten frames. After a few rolls we extended the task by asking the students to visualize using the ten frame “how many more to make 10?” for each roll and build.
We came back to the carpet to work on combining numbers and the strategy of Making 10. Using 8 + 5 below as an example, I build 8 in one ten frame and 5 in the other, writing the equation below. I asked the students how we could use the ten frames to help us “make 10″. A student suggested counting on and another suggesting combining the two 5s across the top (using doubles, but also making a 10!) and then adding the three. After recording those ideas, I asked the students then to connect to what we just did with the ten frames. If we had an 8, how many more would we need to make 10? They all called out 2 and I asked them where they could take a 2 from. The students began to see they could “decompose” the 5 and take a 2 from it to make the 8 into a 10, leaving us with 10 and 3 to make 13.
That may seem like a long way around to get the answer to 8+5. I should have mentioned that most of the students knew the answer was 13 before we started our discussion. Some counted on from 8 with their fingers or in their heads and others just “knew” the answer. Knowing basic facts is essential but knowing mental mathematics strategies is even more essential and powerful. By developing strong number sense and a repertoire of thinking strategies, students will be able to figure out questions like 28 + 5 and then 48 +35 in their heads because they can apply strategies like “making 10″ as we did here with 8 + 5. We want students to understand the mathematics they are doing and to become fluent and flexible in their thinking.
As a final practice task, the students played Race to 20 using a double ten frame mat, loose parts and a regular dice. For this game, they shared the dice with a partner, taking turns rolling. Each student build the number he or she rolled and built it on the ten frame. For this game, they didn’t clear their boards after each roll, their total accumulated with the goal of reaching 20. As students played, we asked them to visualize what their double ten frame mats would like, before they added the loose parts. They continued playing and the classroom teacher and I circulated amongst students, asking them to explain how many more they needed to roll to make 20 and how they knew that. The students that were able to record their equation string did so on their game mat. This time, we played that you didn’t have to roll the “exact” number to reach 20, going over was fine.
Throughout our afternoon together, we kept coming back to the idea of using the ten frame as a tool to help us think and to visualize.
A sweet end to the afternoon was having one of the young girls ask me quietly as we were tidying up the materials if she could take her ten frame mat home so she could play math at home. There was a lot of engagement and big thinking about mathematics all afternoon and it was great to hear that this student wanted to continue this “play” at home.