🧪Unlocking Equivalent Fractions: Same Amount, Different Names!

Lesson plan

Objectives

• Students will be able to define equivalent fractions using their own words.
• Students will be able to identify equivalent fractions using visual models (e.g., fraction strips, circles).
• Students will be able to generate equivalent fractions by multiplying both the numerator and denominator by the same non-zero number.
• Students will be able to generate equivalent fractions by dividing both the numerator and denominator by a common factor (simplifying).
• Students will be able to explain why two fractions are equivalent.

Materials

• Whiteboard or projector
• Dry erase markers or pens
• Pre-cut fraction strips or circles (sets for 1/2, 1/3, 1/4, 1/6, 1/8, 1/12)
• Individual whiteboards and markers (optional)
• Equivalent Fractions Worksheet (provided)
• Pencils
• Colored pencils or crayons (for worksheet)

Warm-up

Begin by displaying a picture of a pizza cut into 8 equal slices with 4 slices remaining. Ask students: 'What fraction of the pizza is left?' (Expected answer: 4/8). Then ask: 'Is there another way to describe the amount of pizza left?' Guide them to think about how they might cut the pizza differently to represent the same amount with a different fraction. This sets the stage for thinking about different fractions representing the same quantity.

Direct instruction

1. **1. Review Fractions:** Start by quickly reviewing what a fraction is (a part of a whole) and identifying the numerator (how many parts we have) and denominator (how many total parts make up the whole). Use a simple example like 1/2 of an apple.
2. **2. Introduce Equivalent Fractions:** Explain that 'equivalent' means 'equal' or 'the same amount.' So, equivalent fractions are fractions that represent the same part of a whole, even though they look different. Write 'Equivalent = Equal' on the board.
3. **3. Visual Exploration with Models:** Distribute fraction strips or circles. Have students take out a 1/2 strip. Ask: 'What other strips can you use to cover exactly the same amount as 1/2?' Guide them to discover that two 1/4 strips cover 1/2, or three 1/6 strips cover 1/2. Write these equivalencies on the board: 1/2 = 2/4 = 3/6.
4. **4. The 'Fancy One' Rule (Multiplication):** Explain that we can find equivalent fractions by multiplying the numerator and the denominator by the SAME non-zero number. This is like multiplying by a 'fancy one' (e.g., 2/2, 3/3, 4/4), which doesn't change the value of the fraction. Demonstrate: 'If we have 1/2, and we multiply the top and bottom by 2, we get (1×2)/(2×2) = 2/4. This shows 1/2 and 2/4 are equivalent.'
5. **5. Practice Generating Equivalent Fractions:** Work through several examples together using multiplication. For instance, 'Find an equivalent fraction for 1/3.' (Multiply by 2/2 to get 2/6, or by 3/3 to get 3/9). 'Find an equivalent fraction for 2/5.' (Multiply by 2/2 to get 4/10). Emphasize that you can choose any number to multiply by, as long as it's the same for both numerator and denominator.
6. **6. The 'Fancy One' Rule (Division / Simplifying):** Explain that we can also find equivalent fractions by dividing the numerator and the denominator by the SAME non-zero number (a common factor). This is often called 'simplifying' or 'reducing' fractions. Demonstrate: 'If we have 4/8, what number can we divide both 4 and 8 by?' (2 or 4). 'If we divide by 4/4, we get (4÷4)/(8÷4) = 1/2. This shows 4/8 and 1/2 are equivalent.'
7. **7. Practice Simplifying Fractions:** Work through examples like 'Simplify 6/9.' (Divide by 3/3 to get 2/3). 'Simplify 10/12.' (Divide by 2/2 to get 5/6). Remind students that they should divide by the greatest common factor for the simplest form, but any common factor will create an equivalent fraction.

Guided practice

Let's work through some examples together on our whiteboards or in our notebooks. First, I'll show you how to find an equivalent fraction for 3/4. I want to find a fraction with a denominator of 8. So, I need to think: 'What do I multiply 4 by to get 8?' The answer is 2. So, I must also multiply the numerator, 3, by 2. This gives me (3 × 2) / (4 × 2) = 6/8. So, 3/4 is equivalent to 6/8. Now, try this one: Find a fraction equivalent to 2/6 that has a denominator of 3. Think: 'What do I divide 6 by to get 3?' (2). So, divide the numerator, 2, by 2. (2 ÷ 2) / (6 ÷ 2) = 1/3. So, 2/6 is equivalent to 1/3. Let's do one more: Use your fraction strips to find a fraction equivalent to 1/3. Show me your strips. (Students should show 2/6 or 3/9).

Independent practice

Students will complete the 'Equivalent Fraction Explorer' worksheet. They will work individually to identify shaded equivalent fractions, find missing numerators or denominators, and draw models to represent equivalency. Circulate around the room to provide individual support and check for understanding. Encourage students to use their fraction strips as a tool if they are struggling with a problem.

Closure

Bring the class back together. Ask students to share one thing they learned about equivalent fractions today. 'What does it mean for two fractions to be equivalent?' (They represent the same amount). 'How can we find an equivalent fraction?' (Multiply or divide the numerator and denominator by the same number). For an exit ticket, have students answer the following prompt on an index card or small piece of paper: 'Draw a model to show 1/3. Then, draw a model to show an equivalent fraction and write the fraction next to it.'

Assessment

Mastery will be assessed through observation during guided practice, completion and accuracy of the 'Equivalent Fraction Explorer' worksheet, and the successful completion of the exit ticket demonstrating understanding of equivalent fractions through models.

Differentiation

For struggling learners: Provide pre-made fraction strips or circles for all problems. Allow them to work with a partner to discuss and solve problems. Focus initially on identifying equivalent fractions using only visual models before moving to multiplication/division. Provide a multiplication chart for reference. For advanced learners: Challenge them to find three different equivalent fractions for a given fraction. Ask them to write a word problem that requires finding an equivalent fraction. Have them explain the concept of multiplying by 'a fancy one' in their own words, connecting it to the identity property of multiplication.

Equivalent Fraction Explorer

Read each problem carefully and follow the instructions. Show your work or explain your reasoning for each answer. You may use fraction strips or draw models to help you.

1. Shade 1/2 of the circle. Then, shade 2/4 of the circle. Are these fractions equivalent? Explain why or why not.
2. Shade 1/3 of the rectangle. Then, shade 2/6 of another identical rectangle. Are these fractions equivalent? Explain why or why not.
3. Look at the two fraction models. Write the fraction for each shaded part. Are the fractions equivalent?
4. Fill in the missing numerator to make the fractions equivalent: 1/3 = ?/6
5. Fill in the missing denominator to make the fractions equivalent: 2/5 = 4/?
6. Find a fraction equivalent to 3/4. Show your multiplication.
7. Find a fraction equivalent to 2/3. Show your multiplication.
8. Simplify the fraction 6/12. Show your division.
9. Simplify the fraction 8/10. Show your division.
10. Draw a picture to show that 1/4 is equivalent to 2/8. Label your drawings clearly.
11. Is 3/5 equivalent to 6/10? Explain how you know.
12. Which fraction is NOT equivalent to 1/2? Circle your answer. A) 2/4 B) 3/6 C) 4/10 D) 5/10

Equivalent Fractions Quick Check

1. What does it mean for two fractions to be equivalent?
   • They have the same numerator.
   • They have the same denominator.
   • They represent the same amount of a whole.
   • They are written with the same numbers.
   Answer: They represent the same amount of a whole.
2. Which fraction is equivalent to 1/3?
   • 2/3
   • 1/6
   • 3/9
   • 2/4
   Answer: 3/9
3. Look at the image of a circle divided into 4 equal parts, with 2 parts shaded. Which fraction is equivalent to the shaded part?
   • 1/4
   • 3/4
   • 1/2
   • 4/8
   Answer: 1/2
4. To find an equivalent fraction for 2/5, you can multiply the numerator and denominator by:
   • Any number
   • Only 2
   • The same non-zero number
   • A different number each time
   Answer: The same non-zero number
5. Which fraction is equivalent to 6/8?
   • 1/2
   • 2/3
   • 3/4
   • 4/5
   Answer: 3/4
6. Fill in the blank: 1/4 = ?/8
   • 1
   • 2
   • 4
   • 8
   Answer: 2
7. Which of these pairs of fractions are NOT equivalent?
   • 1/2 and 5/10
   • 2/3 and 4/6
   • 3/4 and 6/12
   • 1/5 and 2/10
   Answer: 3/4 and 6/12
8. If you have 4/6 of a chocolate bar, which other fraction represents the same amount?
   • 1/3
   • 2/3
   • 3/4
   • 1/2
   Answer: 2/3

Equivalent Fractions at Home

Dear Families, This week in math, we are learning about equivalent fractions. Equivalent fractions are different fractions that represent the same amount or part of a whole. For example, 1/2 is equivalent to 2/4. We are using visual models and multiplication/division to find and create equivalent fractions. Please help your child complete the following tasks to reinforce their understanding of this important concept. This homework will help them see how fractions are used in everyday life.

• Explain to a family member what an equivalent fraction is using your own words. Give them an example.
• Draw two identical rectangles. Shade 1/2 of the first rectangle and 3/6 of the second rectangle. Are they equivalent? Write a sentence explaining why.
• Find two different equivalent fractions for 1/4. Show your work using multiplication.
• Find two different equivalent fractions for 3/5. Show your work using multiplication.
• Simplify the fraction 5/10 to its simplest form. Show your work using division.
• Simplify the fraction 6/9 to its simplest form. Show your work using division.
• Look around your house for examples of equivalent fractions. For instance, 'Half of the cookies are gone, which is the same as 3/6 of the cookies.' Write down at least two examples you find.
• Challenge: Can you find a fraction equivalent to 1/2 that has a denominator of 100? Show your work.

Vocabulary

fraction · noun

A number that represents a part of a whole.

"The recipe called for 1/2 cup of sugar."

numerator · noun

The top number in a fraction, showing how many parts are being considered.

"In the fraction 3/4, the numerator is 3."

denominator · noun

The bottom number in a fraction, showing the total number of equal parts the whole is divided into.

"In the fraction 3/4, the denominator is 4."

equivalent · adjective

Having the same value or amount.

"One dollar is equivalent to four quarters."

equivalent fractions · noun

Fractions that represent the same amount or part of a whole, even though they have different numerators and denominators.

"1/2 and 2/4 are equivalent fractions because they both represent half of something."

whole · noun

All of something; a complete unit.

"I ate the whole apple by myself."

half · noun

One of two equal parts of a whole; 1/2.

"He shared half of his sandwich with his friend."

third · noun

One of three equal parts of a whole; 1/3.

"A third of the class raised their hands."

fourth · noun

One of four equal parts of a whole; 1/4.

"We ate a fourth of the pie for dessert."

simplify · verb

To reduce a fraction to its lowest terms by dividing the numerator and denominator by their greatest common factor.

"Can you simplify the fraction 4/8 to 1/2?"

common factor · noun

A number that divides exactly into two or more other numbers.

"The common factors of 6 and 9 are 1 and 3."

product · noun

The result of multiplying two or more numbers.

"The product of 2 and 3 is 6."

Activities

• Fraction Matching Game · 10 minutes

  Prepare cards with various fractions (e.g., 1/2, 2/4, 3/6, 1/3, 2/6, 4/12). Students work in small groups to match equivalent fraction pairs. This can be done as a memory game where cards are face down, or simply by matching face-up cards. This activity reinforces visual recognition of equivalency.

• Equivalent Fraction Puzzles · 10 minutes

  Create jigsaw-style puzzles where each piece has a fraction, and only pieces representing equivalent fractions fit together. For example, one piece might have '1/2' and another '2/4' that fit to form a larger shape. Students work individually or in pairs to assemble the puzzles, visually connecting different fraction representations.

• Fraction Race using Strips · 10 minutes

  Divide the class into small teams. Give each team a set of fraction strips. Call out a fraction (e.g., '1/2'). Teams must quickly build an equivalent fraction using different strips (e.g., two 1/4 strips or three 1/6 strips). The first team to correctly show an equivalent fraction wins a point. This promotes quick thinking and visual understanding.

• Build a Fraction Wall · 15 minutes

  Provide students with paper strips of equal length. Each student or pair creates a 'fraction wall' by folding and labeling strips to represent a whole, then halves, thirds, fourths, etc. They then identify and color-code equivalent fractions on their wall (e.g., 1/2 and 2/4 are both colored blue). This hands-on activity builds a strong visual foundation for equivalent fractions.