Mastering Bar Models

Learning Objective

Students will be able to solve addition and subtraction word problems within 100 using bar models to represent and visualize quantities.

Learning Standards

This lesson aligns with the Common Core State Standards for Mathematics:

• 2.OA.A.1 - Use addition and subtraction within 100 to solve one- and two-step word problems.
• 2.NBT.B.5 - Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
• 2.MD.B.6 - Represent and interpret data (in this case, using bar models as visual data).

Key Vocabulary

• Bar model
• Sum
• Difference
• Addition
• Subtraction
• Unknown
• Part/Whole relationship

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Hook (Launch, Warm-Up) — 10 minutes

Activity: “Math Story Starter”

• Show two simple word problems on the board, e.g., "Emma has 45 marbles. She finds 20 more. How many does she have now?" and "Alex has 70 stickers. He gives 25 to his friend. How many does he have left?"
• Ask students to talk turn-by-turn with a partner what the problem is asking and how they might solve it.
• Brief whole-class share out of ideas to activate prior knowledge about addition and subtraction within 100.

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Learn (Explore)

Mini-lesson (I Do) — 15 minutes

Objective: Model how to use a bar model to represent addition and subtraction problems.

• Introduce the bar model as a visual tool, explaining that it helps “see” parts of a problem.
• Using a projector or large chart paper, write a word problem (e.g. 58 + 27 = ?).
• Draw a long bar divided into two parts: 58 and 27. Label each part. Then show how to find the total by combining the two bars.
• Repeat with subtraction: 83 - 39 = ? Draw a long bar for 83, then shade 39 to show the part taken away, and the remainder is the answer.
• Emphasize the part-whole relationship and how the bar model helps visualize the unknown part.

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Guided Practice (We Do) — 20 minutes

Activity: Partnered Bar Model Building

• Provide pairs with 4 word problems (two addition, two subtraction within 100).
• Give each pair large paper strips or bar model templates.
• Pairs read problems aloud, discuss how to draw the bar models, and solve problems collaboratively.
• Circulate offering support, questioning their choices ("How did you decide to split the bar?"), and encouraging them to explain their thinking.
• End with a few pairs sharing their bar models and strategies with the class.

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Independent Practice (You Do) — 20 minutes

Activity: Bar Model Problem Set

• Each student receives a set of 6 word problems (3 addition, 3 subtraction within 100) to solve independently using bar models.
• Encourage neat drawing of bar models with labels, and full sentence answers to show understanding.
• To engage different learners, include at least two problems where the unknown is in different positions (e.g., part missing, whole missing).
• Teacher circulates providing targeted reteach where needed.

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Closing (Synthesis, Discuss) — 10 minutes

• Gather students in a circle for a reflection discussion.
• Prompt questions: “How did bar models help you solve problems? Which problem was easiest/hardest? What could you do differently next time?”
• Write key points shared by students on chart paper for ongoing reference.
• Reinforce that bar models are a tool they can use anytime to help organize thinking during addition and subtraction.

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Fluency Focus — 10 minutes

Activity: Quick Bar Model Warm-Up

• Use a timed game: flash addition or subtraction facts (within 100) visually, students draw quick bar models in their notebooks and write answers as fast and accurately as possible in 2 minutes.
• Celebrate improvements by comparing results from earlier in class or previous days.

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Differentiation

• For struggling students: Provide partially completed bar models, use manipulatives (e.g., linking cubes) to physically build bars before drawing, and work in smaller groups with extra guidance.
• For advanced students: Challenge them to create their own word problems and corresponding bar models for classmates to solve; include two-step problems within 100 to deepen reasoning.
• Use varied modalities: visual (drawings), kinesthetic (manipulatives), and verbal explanations to enhance understanding.

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Assessment

• Formative: Teacher observation during guided and independent practice noting students’ ability to correctly draw and use bar models to solve problems.
• Cool Down: Exit ticket with two word problems requiring bar model solutions and explanation of reasoning in 2-3 sentences.
• Use exit ticket responses to identify students needing additional support or enrichment.

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Materials Needed:

• Chart paper and markers
• Bar model templates or paper strips
• Student notebooks or drawing paper
• Manipulatives (optional)
• Timers for fluency activity

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This engaging, standards-aligned lesson uses visual tools to deepen students’ understanding of addition and subtraction within 100, giving young learners both the conceptual foundation and practical strategies to master word problems.