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Mixed Up Numbers

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Lesson Plan

Mixed Number Conversion Guide

Students will be able to confidently convert between improper fractions and mixed numbers, understanding the relationship between the two forms.

Mastering conversions between improper fractions and mixed numbers is essential for simplifying answers and performing various operations with fractions, building a strong foundation for future math concepts.

Audience

Elementary School Students

Time

45 minutes

Approach

Hands-on activities and visual aids will make abstract fraction concepts concrete.

Materials

Prep

Prepare Materials

15 minutes

Step 1

Introduction & Hook: What's So Mixed Up?

5 minutes

  • Begin by asking students what they know about fractions. Introduce the idea that sometimes fractions can be 'mixed up' and have a 'whole' and a 'part'.
    - Display an improper fraction (e.g., 7/4) and a mixed number (e.g., 1 3/4) on the board or projector. Ask students to share any observations or prior knowledge.

Step 2

Guided Instruction: Improper to Mixed Magic

15 minutes

  • Use the Improper to Mixed Magic Slide Deck to guide students through the concept of improper fractions and mixed numbers.
    - Explain that an improper fraction has a numerator larger than or equal to its denominator, meaning it represents one or more whole units.
    - Introduce the process of converting an improper fraction to a mixed number using division. Demonstrate with examples from the slide deck.
    - Emphasize how the remainder becomes the new numerator and the divisor remains the denominator, with the quotient being the whole number.

Step 3

Activity: Building Mixed Numbers

15 minutes

  • Distribute the 'Building Mixed Numbers Activity Kits' to small groups.
    - Guide students through the Building Mixed Numbers Activity Kit, where they will use manipulatives to physically convert improper fractions into mixed numbers.
    - Provide several improper fractions for them to work with (e.g., 5/2, 7/3, 9/4). Encourage them to discuss their strategies within their groups.

Step 4

Practice & Application: Convert and Conquer

8 minutes

  • Hand out the Convert and Conquer Worksheet.
    - Students will independently work on the worksheet, applying the conversion methods learned.
    - Circulate and provide support as needed. Remind students to show their work.

Step 5

Conclusion & Share Out

2 minutes

  • Briefly review one or two problems from the Convert and Conquer Worksheet as a class.
    - Ask students to share one new thing they learned or one strategy they found helpful.
    - Reiterate the importance of being able to convert between improper fractions and mixed numbers for simplifying and future math.
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Slide Deck

Mixed Up Numbers: Can Fractions Be Whole?

What do you know about fractions?

Sometimes fractions are a little 'mixed up'! They have a whole part AND a fraction part. Let's explore!

Greet students and start with a quick fraction warm-up question or a think-pair-share about what fractions they already know. Introduce the idea of 'mixed-up' numbers.

What's an Improper Fraction?

An improper fraction is when the numerator (top number) is bigger than or equal to the denominator (bottom number).

It means you have one or more whole things!

Example: You have a pizza cut into 4 slices. If you have 7 slices (7/4), you have more than one whole pizza!

Explain what an improper fraction is using simple language. Emphasize that the top number (numerator) is bigger than or equal to the bottom number (denominator). Use the pizza example to make it relatable.

What's a Mixed Number?

A mixed number combines a whole number and a proper fraction.

Example: If you have 7 slices of pizza (from pizzas cut into 4 slices each), that's like having 1 whole pizza and 3 extra slices. So, 7/4 is the same as 1 3/4.

Introduce mixed numbers. Explain how they combine a whole number and a proper fraction. Connect it back to the previous pizza example.

Improper to Mixed: The Magic Steps!

How do we change an improper fraction into a mixed number?

1. Divide the numerator by the denominator.
(The numerator goes inside the division symbol!)
2. The quotient (the answer to the division) becomes your whole number.
3. The remainder becomes your new numerator.
4. The denominator stays the same!

Clearly outline the steps for converting an improper fraction to a mixed number. Walk through an example visually or on a whiteboard. Stress the importance of division.

Let's Practice! Convert 7/4

Convert 7/4 to a Mixed Number:

1. Divide 7 by 4.
7 ÷ 4 = 1 with a remainder of 3

2. Whole number: 1
3. New numerator: 3
4. Denominator: 4 (stays the same)

So, 7/4 = 1 3/4

Show a clear example. Verbally walk through the steps again with the example 7/4. Encourage students to follow along or try it on scratch paper.

Your Turn! Convert 9/2

Try to convert 9/2 to a Mixed Number.

Remember the steps:
1. Divide numerator by denominator.
2. Quotient is the whole number.
3. Remainder is the new numerator.
4. Denominator stays the same.



What did you get?

Provide another example for students to try independently or with a partner before revealing the answer. This helps check for understanding.

Answer: 9/2 is 4 1/2

Let's check your work for 9/2:

1. Divide 9 by 2.
9 ÷ 2 = 4 with a remainder of 1

2. Whole number: 4
3. New numerator: 1
4. Denominator: 2 (stays the same)

So, 9/2 = 4 1/2

Great job!

Reveal the answer to the previous slide's practice problem. Address any misconceptions and clarify.

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Activity

Building Mixed Numbers: A Hands-On Adventure!

Objective: To use manipulatives to visually understand and convert improper fractions into mixed numbers.

Materials per group:

  • Fraction circles or bars (enough to make several whole units and various fractional parts like 1/2s, 1/3s, 1/4s)
  • Activity sheet to record conversions
  • Pencil

Instructions:

  1. Gather Your Tools: Each group should have a set of fraction manipulatives.

  2. Understand Improper Fractions: Your teacher will give you an improper fraction. For example, let's start with 5/2.

  3. Build the Improper Fraction: Using your fraction manipulatives, build the improper fraction. For 5/2, you would take 5 halves (1/2 pieces).

  4. Make Wholes! Now, look at your pieces. Can you combine any of them to make a whole unit? (For 5/2, two 1/2 pieces make one whole.)

  5. Count Your Wholes: Count how many whole units you were able to make.

  6. Count Your Leftovers: How many fractional pieces are left over? This will be the fraction part of your mixed number.

  7. Write It Down: On your activity sheet, record the improper fraction and the mixed number you built.
    Example: 5/2 = 2 1/2

Challenge Fractions to Build:

Work with your group to build and convert these improper fractions. Record your answers below!

  1. 7/3











  2. 9/4











  3. 10/3











  4. 11/5











  5. 6/2











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Worksheet

Convert and Conquer: Improper to Mixed Fractions!

Name: ____________________________

Date: ____________________________

Directions: For each improper fraction, show your work and convert it into a mixed number. Remember, you can use division to help you conquer these conversions!

Example:

$$\frac{7}{3}$$

Think: 7 divided by 3.

  • How many times does 3 go into 7? 2 times.
  • What's left over? 1.
  • The denominator stays the same: 3.

So, $\frac{7}{3}$ = $$2\frac{1}{3}$$

  1. $$\frac{5}{2}$$






  2. $$\frac{11}{4}$$






  3. $$\frac{13}{5}$$






  4. $$\frac{9}{2}$$






  5. $$\frac{10}{3}$$






  6. $$\frac{17}{6}$$






  7. $$\frac{14}{3}$$






  8. $$\frac{23}{7}$$






  9. $$\frac{12}{5}$$






  10. $$\frac{15}{4}$$






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Answer Key

Convert and Conquer: Improper to Mixed Fractions! - Answer Key

Directions: For each improper fraction, the steps for converting it into a mixed number are shown below.

  1. $$\frac{5}{2}$$

    • Thought Process: Divide 5 by 2. 2 goes into 5 two times (2 * 2 = 4) with 1 left over (5 - 4 = 1). The denominator remains 2.
    • Answer: $$2\frac{1}{2}$$




  2. $$\frac{11}{4}$$

    • Thought Process: Divide 11 by 4. 4 goes into 11 two times (2 * 4 = 8) with 3 left over (11 - 8 = 3). The denominator remains 4.
    • Answer: $$2\frac{3}{4}$$




  3. $$\frac{13}{5}$$

    • Thought Process: Divide 13 by 5. 5 goes into 13 two times (2 * 5 = 10) with 3 left over (13 - 10 = 3). The denominator remains 5.
    • Answer: $$2\frac{3}{5}$$




  4. $$\frac{9}{2}$$

    • Thought Process: Divide 9 by 2. 2 goes into 9 four times (4 * 2 = 8) with 1 left over (9 - 8 = 1). The denominator remains 2.
    • Answer: $$4\frac{1}{2}$$




  5. $$\frac{10}{3}$$

    • Thought Process: Divide 10 by 3. 3 goes into 10 three times (3 * 3 = 9) with 1 left over (10 - 9 = 1). The denominator remains 3.
    • Answer: $$3\frac{1}{3}$$




  6. $$\frac{17}{6}$$

    • Thought Process: Divide 17 by 6. 6 goes into 17 two times (2 * 6 = 12) with 5 left over (17 - 12 = 5). The denominator remains 6.
    • Answer: $$2\frac{5}{6}$$




  7. $$\frac{14}{3}$$

    • Thought Process: Divide 14 by 3. 3 goes into 14 four times (4 * 3 = 12) with 2 left over (14 - 12 = 2). The denominator remains 3.
    • Answer: $$4\frac{2}{3}$$




  8. $$\frac{23}{7}$$

    • Thought Process: Divide 23 by 7. 7 goes into 23 three times (3 * 7 = 21) with 2 left over (23 - 21 = 2). The denominator remains 7.
    • Answer: $$3\frac{2}{7}$$




  9. $$\frac{12}{5}$$

    • Thought Process: Divide 12 by 5. 5 goes into 12 two times (2 * 5 = 10) with 2 left over (12 - 10 = 2). The denominator remains 5.
    • Answer: $$2\frac{2}{5}$$




  10. $$\frac{15}{4}$$

    • Thought Process: Divide 15 by 4. 4 goes into 15 three times (3 * 4 = 12) with 3 left over (15 - 12 = 3). The denominator remains 4.
    • Answer: $$3\frac{3}{4}$$




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