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## Understanding Mathematical Connections at the Third Grade Level

Written By: Deborah Armitage, M.Ed., Exemplars Math Consultant

This blog is Part 3 of a four-part series that explores mathematical connections and offers guidelines, strategies and suggestions for helping teachers elicit this type of thinking from their students.

In the first blog post we defined mathematical connections, examined the basis for making good mathematical connections and defined why the CCSSM, NCTM and Exemplars view them as critical elements of mathematics curriculum. We also reviewed the Exemplars rubric and offered strategies for teachers to try in their classrooms to help their students become more proficient in making mathematical connections.

As part of the second blog, we reviewed a first grade solution and how this student successfully included mathematical connections as well as the other problem-solving criteria of the Exemplars rubric in his or her work.

#### Blog 3: Mathematical Connections at the Third Grade Level

In today’s post, we’ll look at a third grade student’s solution for the task “Bracelets to Sell.” This task is one of a number of Exemplars tasks aligned to the Operations and Algebraic Thinking Standard 3.OA.3. It would be given toward the end of the learning time dedicated to this standard.

In addition to demonstrating the Exemplars criteria for Problem Solving, Reasoning and Proof, Communication, Connections and Representation from the assessment rubric, this anchor paper shows evidence that students can reflect on and apply mathematical connections successfully. For many students, mathematical connections begin with the other four criteria of the Exemplars rubric, regardless of their grade.

After reviewing our scoring rationales below, be sure to check out the tips for instructional support. Try these in your classroom along with the sample task and the Exemplars assessment rubric. How many mathematical connections can your students come up with?

#### 3rd Grade Task: Bracelets to Sell

Kathy has thirty-six bracelets to sell in her store. Kathy wants to display the bracelets in rows on a shelf. Kathy wants to have the same number of bracelets in each row. What are four different ways Kathy can display the bracelets in rows on the shelf? Each bracelet costs three dollars. If Kathy sells all the bracelets, how much money will she make? Show all of your mathematical thinking.

Common Core Alignments

• Content Standard 3.OA.3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
• Mathematical Practices: MP1, MP3, MP4, MP5, MP6

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