What Is A Number Talk?
Number Talks is a phenomenon that is spreading across the mathematics education world in which students are asked to solve problems in multiple ways and share their thinking orally. Teaching students to talk about math is a powerful tool in supporting the Common Core State Standards. In addition, Number Talks help students see math as more than just memorization of facts and drill and kill worksheets. In the words of a 6th grade student after his first Number Talk experience, "It's like math, but better!"
What Is The Purpose Of These Videos?
The purpose of these videos is to demonstrate how Number Talks might look the first time you share it with your students. With practice and routine, a Number Talk will take 10-15 minutes. When you begin, however, allowing more time for students to learn and practice the routines and practice sharing their mathematical thoughts is necessary. Be patient with them and with yourself. Each math talk will be better than the last and before you know it, your students will be thinking, sharing, and comparing mathematical thoughts that would never have been possible with a standard worksheet.
How Do I Get Started?
Beginning Number Talks with a dot image (either random or within a five or ten frame) is a great way to ensure that each student in your class will have some level of success with the task. In the beginning, many
students will simply count them all. This is a great first step! However, dot images also provide an opportunity for students to begin to find more efficient ways of finding the total. This provides an opportunity
for all students to feel engaged and successful in the task with an appropriate amount of challenge for their needs.
The goal of this Number Talk is to help students add numbers with a sum greater than 10. Each of the next three videos builds up to that objective by increasing the difficulty of each problem.
Single Ten Frame
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.
Double Ten Frame
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.
Double Ten Frame #2
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.
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.
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.
Remember that Number Talks is a year long (and life long) journey. Do not expect perfection your first time or even your hundredth time. Do expect that students progress in their ability to think about math in a flexible way and communicate their thinking with others.
Jamie Garner is a math consultant with the Stanislaus County Office of Education. Previously, she taught in an elementary school setting for 12 years.
During her tenure as a teacher, she was the recipient of both the Stanislaus County Teacher of the Year award and the Presidential Award for Excellence in Math and Science Teaching.