December 2024

Reading in mathematics differs from other disciplines because the main idea is typically posed as a question or problem to solve at the end of the text rather than being introduced as a topic sentence near the beginning. The Three Reads routine, introduced in Routines for Reasoning (Kelemanik et al., 2016), provides a framework to help students comprehend word problems by emphasizing understanding before solving. This approach guides students through three distinct phases with a different purpose for reading in each stage: reading for context, identifying the question, and extracting relevant information.

In Chapter 4 of the Core Connections Geometry curriculum, students encounter the Statue of Liberty problem (4-45), which includes a narrative that blends historical context with a math challenge designed to spark curiosity. However, after reading through the problem, students may find it challenging to isolate the mathematical elements or visualize the context.

First Read: Understanding the Context

The problem begins with a narrative. For the first read, numbers can be omitted to focus on the context. 

Lindy gets nosebleeds whenever she is more than □ feet above the ground. During a class field trip, her teacher asked if she wanted to climb to the top of the Statue of Liberty. Since she does not want to get a nosebleed, she decided to take some measurements to figure out the height of the statue’s torch. She found a spot directly under the torch and then measured □ feet away and determined that the angle up to the torch was □°. Her eyes are □ feet above the ground. 

Emphasize to students that as they read the problem, they are figuring out the story and not figuring out the answer. Here, the numerical details and specific questions are omitted to encourage students to focus on the story itself. This can be useful for helping students to identify the context without being distracted by numbers or calculations. Teachers can ask students to summarize the story with a phrase, such as “heights and nosebleeds,” to capture the essence of the problem. Teachers do not need to take out the numbers in every problem.

Second Read: Determining the Question

The narrative remains the same, but the question is introduced:

Should she climb to the top or will she get a nosebleed? Draw a diagram that fits this situation. Justify your conclusion.

Students revisit the problem, now focusing on the goal: determining whether Lindy can safely ascend the statue. At this stage, students are encouraged to rephrase the question in their own words and discuss their interpretations with a partner. Sharing and comparing interpretations ensures a deeper understanding of the problem’s objective.

Read Three: Extracting Key Information

In this final step, the mathematical details are provided:

Lindy gets nosebleeds whenever she is more than 300 feet above the ground.  During a class field trip, her teacher asked if she wanted to climb to the top of the Statue of Liberty.  Since she does not want to get a nosebleed, she decided to take some measurements to figure out the height of the torch of the statue. She found a spot directly under the torch and then measured 42 feet away and determined that the angle up to the torch was 82º. Her eyes are 5 feet above the ground. 

Should she climb to the top or will she get a nosebleed? Draw a diagram that fits this situation. Justify your conclusion.

Students are tasked with identifying important details, such as measurements and relationships between quantities, and creating a diagram to visualize the scenario. This step emphasizes reasoning quantitatively, identifying patterns, and connecting the information to solve the problem.

Students may find it helpful to consider these questions with a partner or small group:

• What can be counted or measured? (Mathematical Practice 2)
• How are the quantities in this problem related to one another? (Mathematical Practice 2)
• How is this situation behaving and why is that important? (Mathematical Practice 7)
• Is there an underlying repeating process that I can generalize? (Mathematical Practice 8)

Depending on what students attend to, the teacher can record important information and guide students to connect the information with their path to the solution via the Standards for Mathematical Practice.

Supporting Students with Specific Needs

One common critique of CPM’s curricular materials is that the dense and complex reading can be challenging, especially for multilingual learners (MLs) and students with specific learning needs. The Three Reads routine offers a structured approach to help students process these texts by breaking them into manageable sections and encouraging multiple readings. This method supports comprehension by giving students opportunities to engage with the problem in different ways, fostering both understanding and the effective use of language.

Supporting Mathematical Thinking

Classic mathematics word problems are ubiquitous to secondary mathematics and have maintained a stable structure for centuries. First, there is a story that is often non-essential to the mathematics needed to solve the problem. Second, there is mathematical information, and finally, there is a mathematical question (Gerofsky, 2002). Because of the stability of this structure, students have been known to skip to the question of a word problem and then search for the relevant information. In contrast to the classic model, CPM’s problem-based approach integrates context and mathematical details throughout the narrative, requiring students to engage fully with the problem to identify relevant information.

In the Statue of Liberty problem, students are provided with the context of height with respect to Lindy and her nosebleeds and then asked to engage with that context as they answer the question, “Should she climb to the top or not?” The narrative, rather than appearing after the context, is established. If students skip right to the question at the end, they will not have any tools with which to solve the problem. 

The Three Reads routine helps disrupt the habit of working backward from the question. Instead, it encourages students to actively engage with the problem by focusing on understanding, exploring relationships, and constructing a clearer path to the solution.

References

Dietiker, L., Kysh, J., Sallee, T., & Hoey, B. (2024). Core Connections Geometry (L. Dietiker & M. Kassarjian, Eds. 2nd ed.). CPM Educational Program.

Gerofsky, S. (2002). A man left Albuquerque heading east: Word problems as genre in mathematics education. New York: Peter Lang Publishing. ISBN: 9780820458236.

Kelemanik, G., Lucenta, A., & Creighton, S. (2016). Routines for reasoning: Fostering the mathematical practices in all students. Portsmouth, NH: Heinemann.

National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, D.C.: Author. Retrieved from http://www.corestandards.org