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Algebra for All! Preparing Students for Success

March 12, 2018

SRI International
   Kerry Friedman, REL Appalachia

Algebra I is often referred to as a gateway course because it predicts on-time high school graduation and opens doors for future postsecondary and workforce success.1, 2 In order for students to be prepared for and successful in algebra I, educators must be equipped with the tools to support all learners with mastery of algebra knowledge and skills. In January 2018 REL AP staff facilitated a bridge event in partnership with Virginia school division leaders to help elementary and middle grade educators learn about and understand evidence-based strategies to help ensure all students are prepared to succeed in algebra I. This bridge event brought together math educators from five Virginia school divisions—Charlottesville, Harrisonburg, Staunton, Waynesboro, and Winchester. The educators worked together to dig into strategies that support struggling learners and English learner students in developing essential proportionality skills to set them up for success in algebra I and beyond. Educators in other Virginia schools and beyond can easily use these materials and activities.

Opening doors for every student

Research shows that mastering proportional thinking and reasoning (think measurement, ratios, fractions, rates, and so on) in upper elementary and middle grades is a key part of algebra preparedness.1

Educators often make for challenging students. So, what better way to support educators in understanding teaching strategies than to have them engage in activities as students? Throughout the event, facilitators focused on evidence-based mathematics instructional strategies that support the needs of linguistically and socioeconomically diverse learners. They then modelled a variety of strategies to support proportional thinking and reasoning by engaging in mathematical tasks. The first task involved sharing jelly beans. Participants received the following problem:

Participants portraying Hector, Susan, and Pepita

Participants portraying Hector, Susan, and Pepita share some jelly beans to promote understanding of the math problem.

    Hector had a bag of jelly beans.
    He gave 1/4 of the jelly beans to Susan.
    Then Hector gave 1/6 of the jelly beans he had left to Pepita.
    After giving jelly beans to Susan and Pepita,
    Hector had 20 jelly beans left in his bag.
    How many jelly beans did Hector have at the beginning?

Before the participants could rush to their calculators to whiz through the problem, a facilitator pulled out a bag of jelly beans and asked for volunteers to play the roles of Hector, Susan, and Pepita. As Hector poured his jelly beans into Susan's cup, the participants realized the utility of acting out the problem to make the context and mathematics embedded within the task more accessible to students. Next, the facilitator had the participants read the problem again (and again and again) using a “three reads” strategy. On each read, the participants had a different prompt to complete:

  1. Context: The problem is about ...
  2. Purpose: I need to ...
  3. Information: The important information is ...

Facilitator Pam Buffington

Facilitator Pam Buffington shares the importance of using appropriate mathematical visual representations.

After each read, the participants shared out their responses to the prompt and the facilitator also asked participants for words in the problem that needed clarification and posted them on a flip chart. For example, a participant identified the word “left” as being challenging for some students because of its multiple meanings and the need to understand that word to solve the problem correctly.

The facilitator then introduced visual representations as a critical tool to broaden access to mathematics content for all students. Visual representations play a very important role in the success of all learners in pre-algebra and algebra topics. According to the Improving mathematical problem-solving in grades 4 through 8 Practice Guide, “both general education students and students with learning disabilities performed better when taught to use visual representations such as identifying and mapping relevant information onto schematic diagrams.”3

Participants share visual representations via a document camera

Participants shared their different visual representations via a document camera.

This is also applicable for English learner students and students with below grade reading skills because the visual representations provide an intermediate step between the text and symbols revealing the mathematical structure of a problem. The event facilitators challenged participants to create multiple diagrams to use as visual tools to help them solve the problem. The group shared eight different visuals they used to answer the sharing jelly beans problem.

Students steer math learning

The sharing jelly beans problem and other activities allowed the educators to use their own learning experiences to underscore some critical instructional strategies. The key takeaway from the day was that educators need to provide students with an arsenal of research-based strategies—from critically reading the problem using the three reads strategy to creating effective visual representations—to support their own language access and math learning. With strategies in hand, students can confidently make sense of math problems and develop a deeper understanding of proportional reasoning, setting them up for success in algebra and beyond.

Completed Jelly Beans sheet

Example of a completed task, using the “three reads” strategy and visual representations.

Resources for ongoing learning

Want to learn more about the bridge event and access resources? Details and event materials are available on the REL Appalachia website here:

In addition, research supporting the strategies used in this bridge event came from the collection of IES practice guides, including:

To learn more about how REL Appalachia supported these Virginia school divisions in increasing algebra readiness, explore this partnership resource collection.



1National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. U.S. Department of Education: Washington, DC 20008.

2Tierney, W. G., Bailey, T., Constantine, J., Finkelstein, N., & Hurd, N. F. (2009). Helping students navigate the path to college: What high schools can do (NCEE No. 2009-4066). National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.

3Woodward, J., Beckmann, S., Driscoll, M., Franke, M., Herzig, P., Jitendra, A., ...Ogbuehi, P. (2012). Improving mathematical problem solving in grades 4 through 8: A practice guide (NCEE 2012-4055). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from

4Baker, S., Lesaux, N., Jayanthi, M., Dimino, J., Proctor, C. P., Morris, J., Gersten, R., Haymond, K., Kieffer, M. J., Linan-Thompson, S., et al. (2014). Teaching academic content and literacy to English learners in elementary and middle school (NCEE 2014-4012). Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education.