Math

I chose a number greater than 5 to encourage the use of composition (e.g. 5+1). I believed that this was the type of problem every child could be successful in solving with the hope of building confidence in their mathematical abilities. In addition, I aimed for students to share strategies that the group might try to use in subsequent problems.

Building on the compositions I was looking for in the single ten frame, I chose a double ten frame that would sum to ten. My goal was for students to see ten partners in this problem.

This final clip uses double ten frames that sum to a number greater than 10. This is the grade level fluency standard for first grade and was the ultimate goal of the entire Number Talk. As you can see in the video, there were three different answers presented by students. Each answer was honored and recorded. After several solutions were given that supported the correct answer, I purposefully used questions to engage the students who gave incorrect answers in critiquing their solutions.

Dot Image

The goal of this Number Talk was to help students find the total without having to count them all. It was expected that many of the students would use the count all strategy, but having students share their thinking aloud encourages those with less efficient strategies to reconsider the best way to find the total.

At the end of the video, I chose to ask what connections the students could find between two strategies for two reasons. First, I believed it would engage students in thinking about the similarities between strategies. Secondly, it promoted the focus on and consideration of more strategies than just their own.

Note: When using dot images, having printed copies to use when recording thinking is very helpful because it allows students to see in a concrete way what their classmates are thinking. 

Number String

This number string was a great follow up activity to the dot image for these third graders because it pushed their thinking beyond dots. One important thing to remember when conducting a Number Talk is to 
record student thinking as accurately as possible. This will require that you ask plenty of questions about their solutions and strategies in order to promote their ability to engage in Standards for Mathematical 
Practice #3 (Construct viable arguments and critique the reasoning of others). This number string was designed for students to see a pattern as the expressions progressed. The final expression was 7 x 7.

It was expected that students would see that the sum of 3 x 7 and 4 x 7 would be the same as 7 x 7. During this lesson, students did not make this connection. In order to help students see this important mathematical pattern (SMP 7: Look for and make use of structure), I would facilitate another Number Talk that included different expressions with the same pattern the following day. Through questioning strategies and the use of an area model to display thinking, I would help students see the structure of the number string. I would then reference the number string from the previous day to strengthen the students' understanding of the mathematical concept.