Last week I visited six classrooms in three schools to engage students in number talks and model this practice for teachers.
At Byng, in the two grades 4&5 classes we focused on multiplication strings beginning with the fact, 8 X 7. Most students were able to call out the answer (56) and then we focused on ways to fluently work with the numbers to help us understand multiplication. If you didn’t “know” the answer to 8 X 7, how could you figure it out? What do you know that could help you? A student shared that he could half the 8 and that he knew 4×7 was 28 and then he could just add 28 and 28 as that would be 8 7s. Another student said she would decompose 7 into 3 and 4 and do 3 7s and then 4 7s and then add them together. Since no students suggested it, I modelled decomposing the 7 into a 5 and 2 and asked if 5s and 2s were “easy” for their brains to work with and the students agreed that would be an efficient way to figure this question out. Students who are able to work fluently with multiplication like this demonstrate that they understand multiplication and have strong number sense which will help them out as they move to working with fractions, polynomials and higher level mathematics and making sense of numbers in their world.
In the grades 2&3 class at Byng, we focused on subtraction, building from two-digit subtracting one-digit numbers to two-digit subtracting two-digit number questions. The students demonstrated their fluency with the strategies of decomposing, counting back using a friendly number as a benchmark, using double and using known addition facts. The classroom teacher asked me to focus on the concept of adding up to subtract which requires an understanding of “difference” between two numbers. I find the open number line is the most accessible visual tool to support students’ understanding with this. As we proceeded with our number talks, I sensed the students’ growing understanding of this strategy and tool and for our last question, I called students up to the whiteboard to demonstrate their strategies themselves. The students added up by using tens and adding up to a benchmark/friendly number.
In the grades 1&2 class at Grauer, the students are beginning to use ten frames as a visual tool. We did a number talk using the ten frames, looking at decomposing numbers as they could see them visually in the ten frame. We played “flash it” and then “show it” where I flashed a ten frame card and then had to build and show it on their own ten frame. We then played “roll, build and see ten” to develop their understanding of complementary numbers to make ten. The students rolled one die, built their number on a ten frame and then visualized how many more to make 10 and had to say that number out loud. The game was extended for some students using a double ten frame mat to make 20. We then focused on the making 10 strategy as we did a number talk together not the board to figure out addition questions such as 8 + 5 and 9 + 6.
At Blair, in the grade 1 and the grades 1&2 classes, we did short number talks with ten frames, played some ten frame games like at Grauer and then did an addition number talk to focus on the strategies of counting on, making 10 and using doubles, having the magnetic ten frames available to students to use as a visual tool.