I’m not sure what her point is here because I’m sure they’ll all be stumped.
After a couple of minutes of silent “think time” she calls on someone and they have a number. A couple of other kids have the same number. A knot is forming in my stomach.
How has a class of inner city 5th graders mentally solved a division problem that I would need a calculator or at least pencil and paper to solve?
I sat in awe and soaked up the strategies students offered. They had more than one way to solve the problem and they were accurate. It became obvious that somewhere along the line, I had missed some kid of important math boat and I would be fervently working to climb aboard over the next few weeks.
This teacher had gradually built up her students’ number sense every day with a short routine called a number talk. Over the years I have found number talks to be a quick and effective technique for building number sense in both younger and older elementary students.
The Steps of a Number Talk
- The teacher presents a problem – Can be shown with dot cards, unifix cubes, ten frames, as a word problem, or as an equation.
- Students silently find the answer – When they have the answer, they signal with a “thumbs up” in their lap. This lets the teacher know they are ready without distracting other students who are still thinking.
- Students share answers – The teacher calls on 3 to 5 students to share just their answer and records the answers on the board. Even if an incorrect answer is given, record it.
- Students share their thinking – If you have time, have students share their strategy with a neighbor first so everyone gets a chance to share their thinking. Then have 3-4 students share their thinking with the class and record their thinking with pictures, symbols, and words.
- The class agrees on the real answer – The answers given in step 3 are seen as conjectures. If incorrect answers were given, help students see where they went wrong or what step was left out. This step is about confirmation and clarity rather than about testing who is right or wrong. This is a great opportunity to build a classroom culture where mistakes are seen as learning opportunities rather than something to ridicule.
- The steps are repeated for other problems – This routine should only take 5 – 15 minutes so keep that in mind when you are deciding whether or not to go on to other problems.
Watch a Number Talk in Action:
Notice how this teacher starts with an easy problem, something everyone can solve. Then she uses that problem as a scaffold to help kids solve something a little harder. Also notice the hand signals she has taught her class to show that they have solved the problem, have more than one strategy, or that they agree with the solution just given.
If you search “number talk” on YouTube you can find lots of great videos across a wide range of grades and topics. Many of them differ slightly from the steps given above but they all focus on building number sense.
Number Talk Examples
First and second graders learn about strategies for solving single digit math facts. Here’s a number talk that could facilitate the process. Present the students with a doubles fact that they already know. They should quickly get the answer. Then prompt them by saying, “Use what you know about 4+4 to help you solve this next problem.” Present them with the problem 4+5. Hopefully they will see that 4+5 is just one more than 4+4 so the answer has to be just one more as well. Name the strategy, “You just used a double you knew and added one more, that’s called doubles plus 1.” Then see if they can use the strategy again with a new problem. Put up 6+7. Prompt them. “See if the doubles +1 strategy can help you with this problem. Students may need to do similar number talks several times to get comfortable with using the strategy.
Here’s a number talk for students who are beginning to build fluency with adding and subtracting 2-digit numbers. The first problem is designed to be easy for students. Now, prompt them to compare the first problem to the second, “See if the first problem can help you solve this second problem.” Students will probably see that 29 is just one less than 30. So their answer should be one less than the first problem. Allow students to share their thinking but also summarize the strategy for them: “So if we have a number that’s really close to a friendly number, we could solve the problem with the friendly number and then add or subtract a little to get the actual answer.” Give them the third problem and say, “See if using a friendly number can help you solve this problem.”
Number sense involves understanding that number can be taken apart. In this example, students are being led to the idea of decomposing numbers to help with multiplication. The first two problems serve as a scaffold and should be easy. Prompt your students to see if the first two problems can help them with the next problem. Hopefully someone will see that 13 can be broken apart into 10 and 3. Then it’s easier to solve 10×7 and 3×7, and add the two parts together to get a final answer. The last problem challenges them to apply this decomposition strategy again. It is easier to break apart the 15 into 10 and 5. Then they can solve 10×5 and 5×5, and put the two answers together.
Give number talks a try in your classroom!
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Math Perspectives (2007). Number Talks. Retrieved from http://www.mathperspectives.com/pdf_docs/number_talks.pdf
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