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Mixing It Up: Adding Mixed Numbers!

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Lesson Plan

Mixing It Up: Adding Mixed Numbers!

Students will be able to fluently add mixed numbers with unlike denominators, demonstrating accurate conversion to equivalent fractions and proper simplification of sums within a 30-minute small group session.

Adding mixed numbers is a fundamental skill in math that applies to everyday situations, from baking and cooking to measuring and construction. Mastering this skill will build a strong foundation for more complex fraction operations and problem-solving in and out of the classroom.

Audience

5th Grade Small Group (Tier 2)

Time

30 minutes

Approach

Guided practice, visual aids, and direct instruction will clarify steps for adding mixed numbers.

Materials

Prep

Teacher Preparation

10 minutes

Step 1

Warm-Up: Fraction Frenzy Review

5 minutes

  1. Introduce the Warm-Up: "Welcome mathematicians! Today we're going to tackle adding mixed numbers. Let's start with a quick review of fractions."
    2. Review Equivalent Fractions: Ask students to find equivalent fractions for given examples (e.g., 1/2 = ?/4, 2/3 = ?/6). Discuss why finding a common denominator is important when adding fractions.
    3. Review Adding Fractions: Present a simple fraction addition problem (e.g., 1/4 + 1/2). Guide students to solve it, emphasizing finding a common denominator.

Step 2

Direct Instruction: Unlocking Mixed Numbers

10 minutes

  1. Introduce Mixed Numbers: Use Slide 1: What are Mixed Numbers? to remind students what mixed numbers are.
    2. Strategy 1: Separate Whole Numbers and Fractions:
    * Explain the process using Slide 2: Strategy 1 - Separate and Conquer.
    * Walk through an example: 1 1/2 + 2 1/4.
    * Emphasize finding common denominators for the fractional parts.
    * Demonstrate adding the fractions, then adding the whole numbers.
    * Show how to simplify or convert improper fractions in the sum.
    3. Strategy 2: Convert to Improper Fractions (Optional as a primary strategy, but good to review):
    * Briefly explain using Slide 3: Strategy 2 - Improper Impact.
    * Walk through an example: 1 1/2 + 2 1/4, converting both to improper fractions before adding. (Focus more on Strategy 1 as the main teaching point for this intervention group).
    4. Key Concept Check: Ask students to explain in their own words the first step when adding mixed numbers with different denominators.

Step 3

Guided Practice: Working It Out Together

10 minutes

  1. Distribute Worksheets: Hand out the Adding Mixed Numbers Practice Worksheet.
    2. Collaborative Solving: Work through the first two problems on the worksheet together as a group. Encourage students to explain their steps aloud.
    3. Individual Practice with Support: Allow students to work independently on the next few problems. Circulate, providing individual support and checking for understanding.
    4. Address Misconceptions: Pay close attention to common errors, such as forgetting to find a common denominator, incorrectly converting mixed numbers, or not simplifying the final answer. Provide immediate feedback and re-teach concepts as needed.

Step 4

Wrap-Up: Quick Check for Understanding

5 minutes

  1. Final Question: Pose one last mixed number addition problem (e.g., 2 1/3 + 1 1/6) for students to solve on their whiteboards or scratch paper.
    2. Share and Discuss: Ask a few students to share their answers and explain their process.
    3. Reinforce Learning: Briefly summarize the key steps for adding mixed numbers. Encourage students to continue practicing.
    4. Collect Worksheets: Collect the Adding Mixed Numbers Practice Worksheet to review student progress.
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Slide Deck

What Are Mixed Numbers?

A mixed number combines a whole number and a fraction.

  • Examples: 1 ½, 3 ¾, 5 ⅔

Think about 1 ½ pizzas: one whole pizza and half of another!

Greet students. Ask them to recall what a mixed number is. Facilitate a brief discussion to activate prior knowledge. Provide an example like 1 1/2 pizzas.

Strategy 1: Separate and Conquer!

Step 1: Find a Common Denominator for the fractions.

Step 2: Add the Fractions. (Remember to only add the numerators!)

Step 3: Add the Whole Numbers.

Step 4: Simplify if needed (e.g., convert improper fractions to mixed numbers and add to the whole number).

Introduce the first, and primary, strategy. Walk through an example step-by-step. Emphasize finding a common denominator for the fractions before adding them. Then add the whole numbers. Guide students on how to simplify if the fractional part is an improper fraction.

Strategy 2: Improper Impact (Optional)

Step 1: Convert both mixed numbers into improper fractions.

Step 2: Find a Common Denominator for the improper fractions.

Step 3: Add the Improper Fractions.

Step 4: Convert the final improper fraction back into a mixed number and simplify.

Briefly introduce the second strategy as an alternative, but reiterate that for this session, the 'Separate and Conquer' method is our focus. Quickly walk through one example of converting to improper fractions and then adding. This is good for students who might already be familiar or need a different approach.

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Worksheet

Adding Mixed Numbers Practice Worksheet

Name: ________________________

Part 1: Fraction Warm-Up! (Review)

  1. Find an equivalent fraction for each:
    a) 1/2 = ?/8



    b) 2/3 = ?/9


  2. Add the fractions. Remember to find a common denominator!
    a) 1/3 + 1/6 =





    b) 2/5 + 1/10 =




Part 2: Mixing It Up! (Adding Mixed Numbers)

Directions: Add the mixed numbers. Show your work! Remember to find a common denominator for the fractions first, then add the whole numbers and fractions separately. Simplify your answer if needed.

  1. 1 ½ + 2 ¼ =










  2. 3 ⅓ + 1 ⅙ =










  3. 2 ¾ + 1 ½ =










  4. 4 ⅖ + 1 ½ =










  5. 3 ⅚ + 2 ⅓ =










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Answer Key

Adding Mixed Numbers Answer Key

Part 1: Fraction Warm-Up! (Review)

  1. Find an equivalent fraction for each:
    a) 1/2 = 4/8
    * Thought Process: To change 2 to 8, you multiply by 4. So, you must also multiply the numerator (1) by 4. 1 x 4 = 4.
    b) 2/3 = 6/9
    * Thought Process: To change 3 to 9, you multiply by 3. So, you must also multiply the numerator (2) by 3. 2 x 3 = 6.

  2. Add the fractions. Remember to find a common denominator!
    a) 1/3 + 1/6 =
    * Thought Process: The common denominator for 3 and 6 is 6. Convert 1/3 to 2/6. Then add 2/6 + 1/6 = 3/6. Simplify 3/6 to 1/2.
    * Answer: 1/2
    b) 2/5 + 1/10 =
    * Thought Process: The common denominator for 5 and 10 is 10. Convert 2/5 to 4/10. Then add 4/10 + 1/10 = 5/10. Simplify 5/10 to 1/2.
    * Answer: 1/2

Part 2: Mixing It Up! (Adding Mixed Numbers)

Directions: Add the mixed numbers. Show your work! Remember to find a common denominator for the fractions first, then add the whole numbers and fractions separately. Simplify your answer if needed.

  1. 1 ½ + 2 ¼ =

    • Thought Process:
      • Find common denominator for ½ and ¼: It's 4. So ½ becomes 2/4.
      • Add fractions: 2/4 + 1/4 = 3/4.
      • Add whole numbers: 1 + 2 = 3.
      • Combine: 3 and 3/4.
    • Answer: 3 ¾

  2. 3 ⅓ + 1 ⅙ =

    • Thought Process:
      • Find common denominator for ⅓ and ⅙: It's 6. So ⅓ becomes 2/6.
      • Add fractions: 2/6 + 1/6 = 3/6.
      • Add whole numbers: 3 + 1 = 4.
      • Combine: 4 and 3/6. Simplify 3/6 to 1/2.
    • Answer: 4 ½

  3. 2 ¾ + 1 ½ =

    • Thought Process:
      • Find common denominator for ¾ and ½: It's 4. So ½ becomes 2/4.
      • Add fractions: 3/4 + 2/4 = 5/4 (which is 1 ¼).
      • Add whole numbers: 2 + 1 = 3.
      • Combine: 3 + 1 ¼ = 4 ¼.
    • Answer: 4 ¼

  4. 4 ⅖ + 1 ½ =

    • Thought Process:
      • Find common denominator for ⅖ and ½: It's 10. So ⅖ becomes 4/10 and ½ becomes 5/10.
      • Add fractions: 4/10 + 5/10 = 9/10.
      • Add whole numbers: 4 + 1 = 5.
      • Combine: 5 and 9/10.
    • Answer: 5 9/10

  5. 3 ⅚ + 2 ⅓ =

    • Thought Process:
      • Find common denominator for ⅚ and ⅓: It's 6. So ⅓ becomes 2/6.
      • Add fractions: 5/6 + 2/6 = 7/6 (which is 1 ⅙).
      • Add whole numbers: 3 + 2 = 5.
      • Combine: 5 + 1 ⅙ = 6 ⅙.
    • Answer: 6 ⅙
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Mixing It Up: Adding Mixed Numbers! • Lenny Learning