Exploring equal fractional values through Area Models, Aligned Number Lines, and Multiplication Rules
Represent and create equivalent fractions using subdivided blocks, aligned equal-length number lines, and multiplying top and bottom numbers.
DO: Project slide while students log in or sit on floor. Introduce lesson goal clearly.
WORK: Read WALT and WILF aloud with the class. Ask 2-3 students: "What does the word 'equivalent' sound like? Equal!"
RECORD: Ensure student math exercise books are open to today's heading: Equivalent Fractions.
FINISH: 2 minutes intro max.
CHECK: Quick thumbs up if students know what numerator and denominator mean.
When we slice a block into equal parts, we can cut across it horizontally to create smaller equal parts without changing the total shaded area!
🟩 Subdivided Block Support:
• Start with 2 thirds (23) shaded blue.
• Draw 1 line straight across the middle.
• Now you have 6 equal pieces in total, and 4 of them are shaded!
• So 23 is exactly equal to 46.
DO: Use the interactive controls on slide to show 2/3. Then select "2 Rows" to draw a horizontal line across the middle.
WORK: Ask students: "Did we add any more blue paint? No! We just cut the pieces into smaller parts! 2 thirds became 4 sixths."
RECORD: Have students draw a rectangle split into 3 vertical columns, shade 2, then draw 1 horizontal line through the middle to show 2/3 = 4/6 in their books.
FINISH: 5 minutes visual exploration.
CHECK: Ask: "If we split each third into 3 rows, what fraction would 2/3 become? 6/9!"
Fractions are equivalent if they sit at the exact same point on aligned number lines of equal length!
DO: Click on tick mark 1/3 on the top line. The laser guide will drop down straight through 2/6 on the middle line and 3/9 on the bottom line.
WORK: Point out Signpost Math 1:17 rule: "These two fractions are at the exact same point on the number line!"
RECORD: Have students record: 1/3 = 2/6 = 3/9 and 2/3 = 4/6 = 6/9 in their exercise books.
FINISH: 5 minutes exploration.
CHECK: Switch preset to "Fifths and Tenths". Ask: "What fraction on the tenths line is in line with 2/5? 4/10!"
DO: Click the multiplier buttons (×2, ×3, ×4, ×5) to show how top and bottom scale together.
WORK: Explain Signpost Math 1:19 concept: "Why does multiplying numerator and denominator by 5 give an equivalent fraction? Because 5/5 equals 1! Any number multiplied by 1 stays equal in value!"
RECORD: Have students copy: 1/3 × 2/2 = 2/6 and 1/3 × 5/5 = 5/15 into their books.
FINISH: 4 minutes.
CHECK: Ask: "If I multiply the numerator by 3, what MUST I do to the denominator? Multiply by 3!"
Solve these 4 core questions on your mini-whiteboard. Hold up your whiteboard when ready, then tap to check!
DO: Give students 60 seconds per question to write answers on mini-whiteboards and hold them up on "3, 2, 1... Show me!".
WORK: Tap each card to reveal the answer. Scan the room to spot misconceptions.
RECORD: Have students tick their whiteboard answers.
FINISH: 6 minutes class check.
CHECK: Ask students who got all 4 correct to give a high five to a partner.
Discuss these 4 reasoning questions with a partner. Write your answer on your mini-whiteboard, then tap to check!
DO: Give students 60 seconds to discuss each question with a shoulder partner before recording their whiteboards.
WORK: Tap cards to reveal answers. Ask 1-2 pairs to explain why adding to top and bottom (Q2 addition fallacy) breaks equivalence.
RECORD: Have students record key takeaway: "Multiply top and bottom, NEVER add!" in exercise books.
FINISH: 6 minutes class check.
CHECK: Thumbs up if students agree Maya and Ben ate the same amount of pizza in Q4.
Use this interactive tool to generate custom equivalent fraction problems on demand for extra whiteboard practice!
DO: Change the Numerator, Denominator, and Multiplier inputs live on screen during the lesson to produce fresh whiteboard challenge questions.
WORK: Call on different students to explain how they calculated the missing numerator or denominator.
RECORD: Have extension students create 3 custom equivalences in their exercise books.
FINISH: 4 minutes interactive practice.
CHECK: Ask: "What happens if we multiply by 10? 3/5 becomes 30/50!"
Solve for the missing numerator on your mini-whiteboard and hold it up high!
DO: Click "Generate New Question" to display a fresh prompt on screen. Give students 30-45 seconds to calculate the missing numerator on mini-whiteboards and call "3, 2, 1... Show me!".
WORK: Click "Reveal Answer" to show the complete working out and multiplier. Scan whiteboards across the class.
RECORD: Have students tick their whiteboards or record 3 generated equations in their exercise books.
FINISH: 6-8 minutes rapid-fire whiteboard practice.
CHECK: Questions cover halves, thirds, quarters, fifths, sixths, eighths, and twelfths.
Horizontal cuts increase the total parts without changing shaded value!
Equivalent fractions line up vertically at the exact same point!
Multiply top AND bottom by the same number (e.g. × 2, × 3, × 4).
Complete Sections 1 to 5 individually or in pairs. Ask for help if needed!
DO: Hand out printed 2-page student worksheets (or direct students to open the digital document).
WORK: Circulate around the room to provide targeted support to students who need extra practice on aligned number lines or multiplication rules.
RECORD: Students write full working out in their worksheets.
FINISH: 15-20 minutes independent work.
CHECK: Collect worksheets at end of lesson for formative assessment feedback.
Select a slide to see accompanying pedagogical notes and teaching tips.