Want to try our new problem strings?

Pam’s promised to release problem strings and they are finally ready for you.  We welcome feedback in the comments section about what went well and what needs some tweaking.

  • What worked well?
  • What was unnecessary?
  • What more is needed?

Be sure to leave some context of what class you used it for and where it fit in with your overall lesson development sequence.

Problem Strings


String at a Glance


Proportional Reasoning with Ratio Tables 1

The goal of this string is help students construct the ratio table as a generalizable model for reasoning about equivalent ratios.

Factor Pairs

The goal of this problem string is to help students develop the “factor pair” strategy and the “factoring using the zero product property” strategy when solving quadratic equations.

Solving Equations 1: Beginning to Build the Number Line 

The goal of this string is to begin to build the double open number line as a tool for solving equations.


Function or Not?

The goal of this string is to sharpen students’ notion of the definition of a function, using ordered pairs to raise and work out common misconceptions.


 (2, 5)
(4, 3)
(-2, 5)
(-1, 3)
(2, -5)
(4, 1)

Missing Terms (Geometric)

The goal of this string is to help students continue to build understanding of the multiplicative, exponential nature of geometric sequences by finding the multiplier when consecutive terms are missing.

1, 64

1, ___, 64

1, ___, ___, 64

5, ___, ___, 40

-2, ___, ___, -250

1, ___, ___, ___, 81

Division as Ratio: Geometric Sequence

This one can be done in algebra 1 or 2, before or after geometric sequences.  You might want to use it early on as a priming mini-lesson, or after as a solidifying activity.


Difference or Ratio?

This string can help students solidify the differences between arithmetic and geometric sequences by using the first two terms to create both kinds of sequences.

4, 2, ___

1, 5, ___

3.2, 6.4, ___

0.1, 0.01, ___