Strategy

Annotated Example Problem

Process Log, Double-entry Journal, Annotated Exemplar

UDL 2.3 UDL 6.2

An annotated example problem is a specific type of reference material that provides students step-by-step instructions for completing a certain type of math problem. It usually includes the worked-out solution to a sample problem and a written explanation of each step in the problem-solving process. Similar to a “think aloud” on paper, the example problem reveals the thinking that happens while moving through each step of the problem and answers questions like: How can I tell what the problem is asking?, What do I need to do first?, What parts of the problem are tricky or challenging? -and- How do I check my work? The purpose of the annotated example math problem is to grow students’ problem-solving and reasoning skills as they apply the strategies provided in the example to solve similar problems. As the strategy exposes the problem-solving process, all students would stand to benefit from an annotated example problem. Those students that struggle with organization, memory or attention may find the strategy especially powerful as they work to solve complex problems.

Ready-to-Use Resources

Graphic Organizer

Step-by-Step Graphic Organizers for Annotated Example Problems

A set of templates for creating annotated example problems. Each template includes space for annotating mathematical steps and reasoning for multi-step problems. Great for creating step-by-step models and reinforcing mathematical algorithms and problem solving strategies

Grade 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 · Math · 3 pages


Graphic Organizer

T-Chart for Annotated Example Problems

A T-Chart template for creating annotated example problems. Great for reinforcing mathematical algorithms and problem solving strategies.

Grade 6, 7, 8, 9, 10, 11, 12 · Math · 1 pages


Templates

Template with Guiding Questions for Annotated Example Problems

A template for annotated word problems. Template includes guiding questions and space for describing mathematical steps and reasoning. Great for creating models and reinforcing mathematical algorithms and problem solving strategies.

Grade 3, 4, 5, 6, 7, 8 · Math · 1 pages


Implementation Tips

Consider the Level of Language Used
When creating an annotated example problem, use everyday language in the written explanations for each step. It is important to consider the reading ability of the student(s) receiving the annotated example to ensure that the listed steps can be easily followed. Clarify any terms or math vocabulary that must be understood to solve the problem. Also, include visuals and other representations of the problem as appropriate to better show the problem-solving process.
Ongoing Access to Examples
As you develop annotated examples throughout the year for different skills (e.g. solving problems using the order of operations, finding volume, etc.) store them all in a binder that is accessible to the class. Encourage students to use the binder as a resource when they need a refresher of how to solve a certain type of problem. If possible, try to obtain copies of any annotated examples teachers in lower grades have created and include them in your classroom binder as well. This could be especially helpful for middle school and high school grades as math concepts often build on each other.
Student Highlighting the Annotated Example
Encourage students to mark up any annotated example problem they receive by highlighting it or adding notes as they use it to solve problems. This can increase student engagement, build reasoning skills, and further help students internalize the steps they are practicing.

Examples

Elementary
When students are learning how to solve multi-digit division problems, create an annotated example problem that details each step of the process that students can use as a reference tool. Provide clarification for how students should deal with remainders and how to check their answers. To help build confidence as students are mastering this new skill, allow them to use the annotated example until they feel comfortable solving problems without it.
Middle/High School
Create an annotated example that outlines how to solve complex word problems (e.g. problems involving sales tax and discount). Include information about how to determine what a question is asking as well as how to perform specific calculations.
Use in Guided Practice
During guided practice or review, have the whole class help you create an annotated example problem of the concept just taught. Using chart paper, write a sample problem at the top of the sheet. Ask students to help you write out the steps for solving the problem. As you work through the problem together, create a chart that shows the problem broken down mathematically into smaller chunks with written explanations of each step. The annotated example can be posted in the classroom as an additional reference for students.
Student-created Annotated Examples
After teaching a new concept, have students create an annotated example with a partner explaining how to solve a similar problem. By making their own annotated examples, students reflect on their problem solving and can work together to clarify misunderstandings. Have students share their annotated example with others to ensure that the steps are clearly and accurately explained. Student-created annotated example problems are a great way to challenge students and help them solidify and retain new learning.

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