Problem String Studio
Choose a grade
61 problem strings across five grade bands, each grouped by the level of reasoning it builds. Pick a string, play it one problem at a time, and record what students say.
Grade 5
15 problem strings
additivemultiplicative
Powers of ten · Decimal products from a whole-number anchor · Smart Partial Products …
Grade 6
13 problem strings
additivemultiplicativeproportional
Scaling a ratio up and down · Finding and using a unit rate · Percentages from 10% and 1% …
Grade 7
12 problem strings
additivemultiplicativeproportional
Adding and subtracting signed numbers · Signs in multiplication and division · Percent increase as a single multiplier …
Grade 8
10 problem strings
multiplicativeproportionalfunctional
Exponents that multiply and divide · Zero and negative exponents · Scientific notation …
Algebra 1
11 problem strings
multiplicativefunctional
Multiplying binomials · Factoring by reading the signs · Difference of squares, on numbers first …
Reasoning levels and strategy names follow Pamela Weber Harris, Developing Mathematical Reasoning: Avoiding the Trap of Algorithms (Corwin, 2025). Unit sequence follows Illustrative Mathematics, CC BY 4.0; problems original.