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Problem Strings

BNVCTM 2025

A powerful routine for building students’ computational

and reasoning tool kits through high-dosage patterning

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Presenter:

Melanie Bagshaw

Title I Math Specialist

Prince William Co Schools

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Learn what problem strings are,

Learn where to find PS resources

Experience some problem strings

By the end of this session...

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Math Reasoning Progression

How should student thinking grow?

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What does reasoning progression look like?

Problem strings can help push students from comfortable counting strategies (count all) to additive reasoning strategies (count on, count groups.)

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Problem strings can help push students from comfortable additive strategies (skip counting) to multiplicative thinking (composing / decomposing in groups.

What does reasoning progression look like?

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a series of related problems
purposefully chosen
meant to develop reasoning relational thinking skills
focused on major (and efficient) computational strategies
about making student thinking visible by the teacher
about making connections and using what students know
a safe zone for practicing strategies at all levels

Are

based on memorization
about the answers (but about the thinking!)
a way to break down steps to solve one specific problem
a handout / worksheet
just to be done mentally - students CAN write their thinking!

Problem Strings....

Are Not

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Problem Strings vs. Number Talks

Use them together!!!

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Let’s Give Some a Try!

Practice

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Let’s see what a problem string feels like:

(Equivalent Ratios)

18 ÷ 2

36 ÷ 4

72 ÷ 8

144 ÷ 16

112 ÷ 8

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Count on from 5

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Near Doubles

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Resources

Minilessons for.... by Cathy Fosnot & Willem Uittenbogaard
Search Amazon for “Cathy Fosnot Minilessons”
Pam Harris Math Is Figureoutable Website
Pam Harris’ Problem Strings for every grade level books
Math Framework Website

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Questions or

Comments?