Strategy

Math Exemplar

Math Model Response

UDL 3.3 UDL 6.3

A math exemplar is a teacher-provided model of a math problem that has been correctly and fully completed. A math exemplar illustrates the key concepts, skills and steps required to successfully solve a given problem. Assessment criteria are demonstrated within the exemplar so that students know what is expected in order to meet the standards that will be assessed. As math exemplars make the problem-solving process explicit, students are taught to understand the embedded concepts and generalize them to novel tasks. Math exemplars can be used to highlight critical features of new concepts, or they can be utilized as a reference material that students can access as a support during guided or independent practice.

Implementation Tips

Making Exemplars
To create math exemplars, first obtain or design an assessment that addresses the targeted standard(s). Then, solve some of the problems yourself. Make note of any critical features of the problems as well as any misunderstandings that are likely to occur. Finally, create examples that reflect successful completion of the problems.
Multiple Strategies to Solve a Single Problem
Use a wide variety of exemplars that feature the same targeted skill and varied irrelevant attributes to hone students’ understanding of the targeted concept.
Using Same Strategy to Solve Multiple Problems
Present multiple exemplars containing the same concept in quick succession. This will help students to recognize patterns across situations.
Ascending Exemplars by Difficulty
Move from simple to complex exemplars. Including more complex examples prevents under-generalization on concepts.
Student Samples as Exemplars
Save strong student samples to use as exemplars. Seeing models of the work of a peer can be motivating for students. It's also an efficient practice for busy teachers.

Examples

Lower Elementary
When introducing the concept of adding money, a second grade teacher can use exemplars to illustrate how to successfully navigate the many signs present in such problems (e.g. addition, dollar and cents signs). First the teacher designs problems aligned to the assessment and standard (e.g. 3 nickels plus 2 dimes). She then reviews and/or introduces relevant symbols and concepts such as the addition sign, coin values, and the dollar sign. Next, she previews the process of solving the problem (e.g. identifying coin values, setting up the addition problem, then solving addition problem). Finally, the teacher can solidify the learning by modeling the process of solving each exemplar problem with her students.
Upper Elementary
When teachers are working with students to solve multistep word problems using the four operations, the teacher can anticipate misunderstandings that students are likely to have, and use exemplars to model the correct approach. For instance, a fourth grade teacher may include one exemplar in which the key words signaling the needed operations are not obvious. She may include another that requires students to distinguish between relevant and irrelevant information. Finally, the teacher can include one which illustrates the order of operations.
Middle School
A teacher can use math exemplars to support a group of students that is struggling to grasp how to draw geometric shapes when given information in a word problem. The teacher can provide the small group with exemplar word problems that illustrate conditions that they are likely to encounter. For instance, word problems that require students to identify and construct triangles from three measures of angles or sides that are stated within the example word problem.
High School
Teachers can send home exemplars as a support for students as they complete homework. For example, if a 10th grade student is struggling with graphing linear functions in his Algebra class, the teacher can provide exemplar problems to reference. The exemplar problems highlight key steps in solving the problems that the students will encounter in the homework, such as identifying intercepts, maxima, and minima.

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