Teaching Number Sense by Gillis Kallem

At Hamlin, we develop number sense through a series of mini lessons called Number Talks or Problem Strings. These lessons last no more than 15 minutes and can be taught as a whole class or in small groups. During a number talk, a “string” of number problems are presented one at a time. A string is a collection of related problems designed to guide students to construct big ideas about numbers and devise their own strategies. The number string gives students a chance to notice patterns and practice mental computation strategies. Over time, number talks help to elicit efficient and reliable strategies.

During a number talk, girls are asked to solve a problem using mental math. When they have an answer, they place a thumbs up on their chest so as not to disturb others who might still be working. While a quick student is waiting with her thumb up, she is encouraged to solve the problem in a different way. For each additional way she finds, she can raise another finger. When enough thumbs are up, the teacher calls on a student to share her answer. The teacher will call on other students to collect different answers.  All answers are accepted and written on the board regardless of accuracy.

Next, the teacher asks for a student to defend an answer by sharing her strategy. While the student shares, the teacher represents the student’s strategies on the whiteboard using open number lines, arrays, ratio tables or pure numbers. The teacher facilitates a conversation about the meaning the girls are generating from the problem.After several different strategies have been recorded, the teacher will present the next problem and repeat the process. At some point in the number talk, a student will share a highly efficient strategy. Through the facilitated discussion, other students will take note of it and with teacher encouragement, the whole class will be asked to give this strategy a try for the next problem in the string.

Number talks while short offer clear and direct instruction for developing computational fluency that reach far beyond the use of standard algorithms. They make use of breaking numbers apart, making friendly numbers, adjusting numbers, and doubling and halving to name a few strategies.  They work to develop deep understanding of numbers, cultivate relational thinking and support creative yet highly efficient pathways for solving problems mentally.

Examples of number strings

First Grade – Making Tens

7 + 3 =

7 + 5 + 3=

3 + 6 + 7 =

Second Grade – Doubles and Near Doubles

30 + 30 =

29 + 29 =

29 + 31 =

Third Grade – Making Landmark or Friendly Numbers

37 + 69 =

79 + 26 =

89 +28 =

99 + 19 =

Fourth Grade– Doubling and Halving

35 x 8 =

70 x 4 =

140 x 2 =

Fifth Grade – Doubling and Halving to remove the fraction

2 ½ x 28 =

5 x 14 =

10 x 7 =