# Number Strings

### What are they?

A series of related math questions that build towards fluency in a particular strategy by exploring relationships between the questions and focusing on mental math strategies. (Fosnot)

### Why are they useful?

“Number strings help students to notice relationships among math facts and explore related fact strategies” Source

**Podcast**: The do’s and don’ts of “problem strings”

### Using a Number String in Class

**Time in Class:** 10-15 minutes

#### Prior to the lesson: Design the String

Be clear about the intention of the string. What strategy will you focus on? Be intentional and explicit.

Prepare a set of related math questions (could be represented as images, dot cards, ten frame cards, equations, etc.). The first question should be fairly easy to solve and lend itself to a particular strategy, though multiple strategies at this point are acceptable. The second question should connect to the first question, building upon a particular strategy. The following questions should continue to connect to the strategy, building in complexity.

#### Implementation:

Present the first question. Give students time to determine the answer. Students can share thinking with a partner. Intentionally select students whose strategy matches the focus strategy to share their thinking with the class while the teacher models their thinking on the board. Other strategies can be shared but this shouldn’t be turned into a Number Talk where all strategies are shared.

Present the second question. Gives students time to determine the answer and share with a partner. Students share their thinking while the teacher models their thinking on the board. The teacher, when appropriate, draws their attention to when a student has used the first question to help them solve the second question.

Repeat for all further questions.

### Examples of Number Strings

#### Example 1: “Give and Take Strategy”

7 + 9: Student takes one from the 7 and gives it to the 9, ending up with 6+10=16.

6 + 9

6 + 19

16 + 19

13 + 18

29 + 14

51 + 49

#### Example 2: “Near Doubles”

5 + 5

5 + 4

5 + 6

6 + 6

#### Example 3: “Decomposing”

10 x 15

2 x 15

12 x 15

20 x 15

22 x 15

19 x 15

#### Example 4: “Compensation”

9 – 5

10 – 5

19 – 5

20 – 5

20 – 7

30 – 7

119 – 2

120 – 2

299 – 13

300 – 13

#### Example 5

If 4x + 8 = 40, then

4x + 9 =

4x + 7 =

4x + 28 =

4x =

8x + 16 =

8x + 20 =

40 x + 5 =

#### Other Examples:

Number Strings to Encourage Addition Strategies: Part 1, Part 2 ARPDC

Number Strings to Encourage Multiplication Strategies: Part 1, Part 2 ARPDC

Source for Fosnot’s description above: VoicEd Radio: The Math Pod Episode 01 Minilessons and Representation with Cathy Fosnot, Melissa Peddie, Christina Chabot and Laurie Clayton