Example-based Problem Sets for Grades 4 & 5

Getting Started

Quick Facts:

  • MathByExample is specially designed to target common misconceptions and errors in mathematics through worked examples and prompts in which students are asked to explain a fictitious student’s work.
  • MathByExample is made up of 60+ assignments each for grades 4 and 5, with two sets of problems in each assignment.
  • Each problem set targets common math mistakes through a worked example (marked as either correct or incorrect) and a practice problem.
  • All assignments are aligned to the Common Core State Standards for Mathematics.
  • The assignments went through numerous rounds of revisions based on feedback from teachers, coaches, and math experts.

Various Uses:

  • Warm-up / do now
  • Exit ticket
  • Homework
  • During centers
  • Formative assessment
  • Review before a unit test (or standardized testing)

Students can work on the assignments:

  • Independently
  • With partners
  • In groups


1. Familiarize yourself with the materials.

  • Assignments are grouped by topic, but individual assignments can be used in any order that you find appropriate.
  • Teachers usually determine in advance how MathByExample assignments align with their district math curriculum for grades 4 and 5.

2. Plan how to orient your students to the materials.

  • Your students may not immediately understand how to complete the exercises. Make sure they know that they will be looking at both correct and incorrect examples of work done by "other students" and will be answering questions about that work.

3. Consider how to allot time.

  • Assignments are generally designed to take approximately 15-20 minutes. But you may decide to use an assignment over two days or to use two assignments in one day. There may be weeks where none of the assignments align to what you're teaching and other weeks when many of the assignments will fit well. MathByExample is designed to fit flexibly into your classroom without changes in the central content you teach.

Frequently Asked Questions

  • When should I use the assignments?
  • You can use the assignments whenever makes the most sense for you. Although intended for math class, you can use the assignments at any time throughout the day, such as homeroom or during a workshop period.
  • How often?
  • There’s no set frequency that we recommend — just whenever the assignments align to the content you’re teaching. You may decide to use an assignment over two days or to use two assignments in one day. There may be weeks where none of the assignments align to what you’re teaching, but other weeks when many of the assignments will fit well. On average, completing 2-3 assignments per week throughout the year would allow you to use all of the assignments with your students.
  • How long do the assignments take?
  • On average, assignments are designed to take about 15-20 minutes to complete.
  • Can I let my students work on the assignments together?
  • Absolutely. Many teachers have let us know that they find the assignments most beneficial when students work on the assignments together, since students start discussing the mathematics.
  • Do students have to answer the questions?
  • Research shows that at least attempting to answer the questions improves learning, so we suggest encouraging students to at least try to answer each question.
  • Do I have to use all of the assignments?
  • MathByExample was designed to be flexible — use as many or as few assignments as you like! However, past research has shown that the more students are exposed to worked examples the better! Also, note that you don’t have to use them all when first teaching the content — you can use them at any time throughout the year, such as a refresher when reviewing for spring standardized tests.
  • What if I don’t teach the content that some of the assignments cover?
  • We did our best to align the content of the assignments to the Common Core State Standards for each grade, but if you don’t teach some of the content, don’t feel obligated to use the assignments. We expect the scope and sequences to be different across each district and even within each district.
  • Does any research support this approach?
  • Yes! Preliminary analyses demonstrate statistically significant results for students using the MathByExample materials. We found that explaining correct and incorrect examples can be effective for students in upper elementary school. A previous study (AlgebraByExample) tested the effect of worked examples in Algebra assignments, too. Results of a randomized trial indicated significant impacts, the largest of which was for low achieving students. Learn more on the MathByExample website.
  • Any other questions?
  • Ask us! Email info@serpinstitute.org if you have any additional questions, comments, or recommendations!

The MathByExample Teacher Edition serves as a guide to each assignment.

The “Target” summarizes the targeted mathematical concept.

The “Targeted Error” notes a specific error, if applicable.

Sample response(s) are actually samples! Students will respond in various ways, so it will be up to you to judge whether a student understands the concept.

An image from each Student Workbook page is embedded within the Teacher Edition.

More math materials from SERP:

Development of MathByExample was led by Julie Booth (Temple University) through a SERP collaboration with several school districts. Major contributors to program development include: Kelly McGinn and Laura Young (Temple University), Allie Huyghe, Matthew Ellinger, Emily Schwartz, Avery Jones, and David Dudley (SERP). Special thanks! to the teachers, administrators, and students in our partner districts—Baltimore City Schools, Public Schools of Beloit, Public Schools of Brookline, Fort Madison Community School District, Oak Park Elementary District 97, and Penns Valley Area School District—who were essential to the project’s success, providing feedback at critical points and inviting us into their classrooms along the way!

The collaboration has been supported to conduct this work by the Institute of Education Sciences, U.S. Department of Education, through Grant R305A150456 to Strategic Education Research Partnership Institute. The information provided does not represent views of the funders.

Strategic Education Research Partnership  •  1100 Connecticut Ave NW, Suite 1310  •  Washington, DC  20036

(202) 223-8555  •  info@serpinstitute.org