Choosing the Just-Right Problem
When it comes to problem-solving, I find myself spending too much time searching for a particular problem that will work for all of my students. You know, a problem that my students can read and understand. One that has a familiar story or situation. And, I look for rich tasks that do not tell students how to solve, allowing for creative solution paths. Ideally, the problem connects a few mathematical concepts. Sound too good to be true?
What I am describing is possible. John Hattie refers to this as the “Goldilocks” challenge, meaning that learners need to participate in an appropriate problem that balances complexity and rigor. (Hattie, 2019) Choosing a problem that is “just right” is essential to providing engaging mathematical experiences for students.
The CueThink problem bank provides excellent “Goldilocks” examples. Below, you will find a few for grades 2 - 5 that I recommend as a starting point. Students will not only be able to solve these problems in more than one way, but they will also be better able to describe the “why” behind mathematical concepts.
Operations In Base Ten Problems
A Summer Garden - Grade 2
This problem provides enough information to draw a picture or create a model of the flowers planted in a garden. Students may solve using addition or subtraction strategies that will provide clarity to their level of understanding operations using base ten. *
Charlie’s Gumballs - Grade 3
The context provided in this problem is relatable to students as they have likely experienced sharing candy. Students must figure out how many gumballs Charlie started with after sharing with multiple people. This problem can be modeled with concrete objects or represented using a number line*
Assembly Seating - Grade 4 - Math Forum
Arranging chairs for a school assembly is a scene students can visualize. Students can choose to multiply or divide to solve and some may access this problem using repeated addition. An extra bonus challenges students to create a similar problem for a different number of seats.*
Geometry And Measurement
Recycling - Grade 2 - Math Forum
Students will create a graph to display data given in this problem. Deciding how to organize and represent data (pictograph or vertical/horizontal bar graph) in the plan phase of CueThink will allow for purposeful feedback. Classmates can write questions that can be answered using the graph to support writing and communication in mathematics.*
What’s in a Name? - Grade 4 - CueThink
This problem allows students to creatively showcase their understanding of geometric vocabulary including parallel and perpendicular, obtuse and acute. Students create and label examples of each by writing a word of their choice. Depending on the word chosen, students will have more or less of a challenge.
Cubic Changes - Grade 5 - Math Forum
This scenario problem allows students to critically think about the area and volume of a cube using friendly numbers. A bonus question is provided to challenge students to make a generalization based on the information gained from solving the problem.*
Fraction Problems
Art Class Clean Up - Grade 4
This problem provides great insight to student thinking and allows all ability levels to share success. Students are asked to predict and justify their choices for combining different amounts of paint. Access is available for a solution as simple as combining 2 jars both ½ full to as complex as combining ¼ and ⅔ .*
Sheila’s Shelves - Grade 4
Need a problem that combines fractions and functional text? Students will write instructions to Sheila telling her how to estimate the number of books the bookcase will hold. The exact answer is not necessary as the focus is on estimation and reasoning.*
A Jar of Coins - Grade 5
The context of this problem (counting coins in a jar) is relatable to students. There are many ways to solve from modeling with actual coins to creating a table to organize work. This problem also includes an extra challenge for students who seek to transfer learning.*
Works Cited
Almarode, John et al. Teaching Mathematics in the Visible Learning Classroom: Grades 3-5. Corwin Press, 2019.
