How to Teach Equivalent Fractions to 5th Graders With 4 Hands-On Activities

How to Teach Equivalent Fractions to 5th Graders With 4 Hands-On Activities

By 5th grade, most children have seen equivalent fractions before. In the Common Core sequence they're introduced in Grade 4 (standard 4.NF.1). In Grade 5 they become a tool children rely on: adding and subtracting fractions with unlike denominators (5.NF.1) only works if a child can turn 2/3 into 8/12 without stopping to think. If that step is shaky, every problem after it is shaky too.

The four activities below take a child from seeing that 1/2 and 2/4 are the same amount to understanding why multiplying the top and bottom by the same number works. Do them in order, one or two per sitting, about 15–20 minutes each.

Activity 1: Paper Folding

Give your child three identical strips of paper, each about 2 inches by 11 inches.

  • Fold the first strip in half and shade 1 part. Label it 1/2.
  • Fold the second strip in half, then in half again, to make 4 parts. Shade 2 parts and label it 2/4.
  • Fold the third strip into 8 parts by halving three times. Shade 4 parts and label it 4/8.

Line the strips up. All three shaded areas end at the same point. Then ask: "Each time we folded, what happened to the number of parts? What happened to the shaded parts?" Both doubled. That's the rule they'll need later, and here they can see it on paper.

Activity 2: Build a Fraction Wall

Cut seven strips of the same length from cardstock. Leave one whole, then mark the others into halves, thirds, fourths, sixths, eighths, and twelfths. Stack them like bricks, with the whole strip on top.

Have your child find every fraction that lines up with 1/3. They should find 2/6, 4/12, and nothing among the halves, fourths, or eighths. That last part matters. It shows that not every denominator can produce an equivalent for every fraction, which sets up the idea of common multiples. A good follow-up question: "Which rows match 3/4?" (Answer: 6/8 and 9/12.)

Activity 3: Grid Paper Area Models

This activity connects the picture to multiplication. On grid paper, draw a 4-by-3 rectangle (12 squares). Shade 3 of the 4 columns, which shows 3/4 of the rectangle.

Now count. Each column holds 3 squares, so the shaded part is 3 × 3 = 9 squares out of 4 × 3 = 12. Your child has just shown 3/4 = 9/12, and seen why. Cutting each column into 3 rows multiplied both the number of shaded pieces and the total pieces by 3.

Repeat with a 2/5 rectangle cut into 2 rows (2/5 = 4/10), then 4 rows (2/5 = 8/20). After three or four of these, most children can drop the grid and just multiply.

Activity 4: Matching Card Game

Write 24 index cards to make 8 sets of 3 equivalent fractions. For example:

  • 1/2, 3/6, 5/10
  • 2/3, 4/6, 8/12
  • 3/5, 6/10, 9/15
  • 1/4, 3/12, 4/16

Shuffle the cards and lay them face down. Players flip three at a time and keep the set if all three are equal. To claim a set, a player has to say the multiplier aloud: "2/3 times 4 over 4 is 8/12." Saying the multiplier out loud means the game practices the rule, not just memory.

Which Activity Does What

ActivityMaterialsWhat It ShowsTime
Paper folding3 paper stripsSame amount, more pieces10–15 min
Fraction wall7 cardstock strips, rulerWhich denominators match20 min
Grid area modelsGrid paper, colored pencilsWhy you multiply top and bottom15–20 min
Matching card game24 index cardsFast recall and naming the multiplier15 min

Worked Example: Putting It to Use

Here's the Grade 5 problem these activities prepare for: 2/3 + 1/4.

  • Step 1: Find a number both 3 and 4 divide into. The multiples of 3 are 3, 6, 9, 12. The multiples of 4 are 4, 8, 12. Use 12.
  • Step 2: Convert 2/3. Since 3 × 4 = 12, multiply the top by 4 too: 2/3 = 8/12.
  • Step 3: Convert 1/4. Since 4 × 3 = 12, multiply the top by 3: 1/4 = 3/12.
  • Step 4: Add: 8/12 + 3/12 = 11/12.

If your child gets stuck at Step 2, go back to the grid. Draw a 3-by-4 rectangle and shade 2 of the 3 columns, which gives 8 of 12 squares.

Common Mistakes to Watch For

  • Adding instead of multiplying: writing 1/2 = 3/4 because they added 2 to the top and bottom. Check it on the fraction wall: 3/4 is clearly longer than 1/2.
  • Changing only one number: writing 2/3 = 2/12. Ask: "If the pieces got 4 times smaller, how many pieces do you need now?"
  • Thinking bigger numbers mean a bigger fraction: believing 4/8 is more than 1/2. The folded strips settle this quickly.

Once the hands-on work clicks, a few minutes of written practice each day will make the skill automatic. You can print free equivalent fraction and fraction addition worksheets at mathsignal.co.kr/sheet/en. They're Korean-style math drills in English, organized by grade and topic.

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