# Lesson Plan: Equivalent Fractions (Year 4/5 Mathematics) **Unit:** Number & Algebra — Fractions & Decimals **Lesson Title:** Equivalent Fractions **Textbook Mapping:** Signpost Mathematics Lessons 1:17 & 1:19 **Curriculum Alignment:** Australian Curriculum v9 (AC9M4N04 / AC9M5N03) **Target Duration:** 60 Minutes --- ## 🎯 Learning Intentions & Success Criteria ### WALT (We Are Learning To) - Represent and generate **equivalent fractions** using subdivided blocks (area models), aligned equal-length number lines, and multiplication rules. ### WILF (What I'm Looking For) 1. Explain in plain words why two fractions with different numerators and denominators can represent the **same total value**. 2. Perform horizontal cuts across area blocks to convert thirds into sixths or ninths. 3. Identify aligned fraction points on equal-length number lines ($\frac{1}{3} = \frac{2}{6} = \frac{3}{9}$). 4. Multiply numerator and denominator by the same non-zero whole number ($\times k$) to generate equivalent fractions. --- ## 📚 Curriculum & Pedagogical Context - **AC9M4N04**: Find equivalent fractions using visual representations and number lines. - **AC9M5N03**: Compare and order fractions with common denominators and find equivalent fractions using multiplication and division. - **Signpost 1:17 Focus**: Equal-length stacked number lines (Thirds, Sixths, Ninths; Fifths, Tenths; Halves, Quarters, Eighths). - **Signpost 1:19 Focus**: The multiplication rule ($\frac{a \times k}{b \times k} = \frac{c}{d}$), showing that multiplying by $\frac{k}{k}$ is equivalent to multiplying by $1$. --- ## 🛠️ Instructional Sequence & Time Breakdown ``` ┌─────────────────────────────────────────────────────────────┐ │ 1. Warm-Up & Learning Intentions (5 mins) │ │ 2. Model 1: Subdivided Area Blocks (8 mins) │ │ 3. Model 2: Aligned Stacked Number Lines (8 mins) │ │ 4. Model 3: The Multiplication Rule (8 mins) │ │ 5. Mini-Whiteboard Check Set 1 (Slide 5) (5 mins) │ │ 6. Partner Discussion Check Set 2 (Slide 6)(6 mins) │ │ 7. Teacher Tools Sandbox (Slide 7) (4 mins) │ │ 8. Rapid-Fire Missing Numerator (Slide 8) (6 mins) │ │ 9. Independent Practice & Worksheet (10 mins) │ └─────────────────────────────────────────────────────────────┘ ``` --- ### Step 1: Warm-Up & Learning Intentions (5 Mins) - **Slide:** Slide 1 (Title, WALT & WILF) - **Teacher Script:** > *"Class, today we are exploring equivalent fractions. Look at the word 'equivalent'. What word does it start with? Equal! Equivalent fractions look different because they have different numbers, but they represent the EXACT same amount of pizza, chocolate, or length on a number line!"* - **Logistics (Notes):** - **DO:** Project Slide 1. - **WORK:** Read WALT & WILF aloud with the class. - **RECORD:** Ensure student math exercise books are open to today's heading: *Equivalent Fractions*. - **CHECK:** Thumbs up for numerator/denominator definitions. --- ### Step 2: Model 1 — Subdivided Area Blocks (8 Mins) - **Slide:** Slide 2 (Subdivided Block Interactive Visualiser) - **Teacher Script:** > *"Look at this rectangle split into 3 vertical columns. We have shaded 2 columns. That's 2 thirds ($\frac{2}{3}$). Now watch what happens when I draw 1 line straight across the middle! Did we add any more blue paint? No! But how many equal pieces do we have in total now? 6! How many are shaded? 4! So 2 thirds is EXACTLY equal to 4 sixths!"* - **Interactive Tool Action:** Use the interactive buttons on Slide 2 to switch between 1 Row (thirds), 2 Rows (sixths), and 3 Rows (ninths). - **Logistics (Notes):** - **DO:** Demonstrate horizontal cuts live on screen. - **WORK:** Have students sketch a rectangle with 3 columns, shade 2, and cut across with a red pencil. - **RECORD:** Write $\frac{2}{3} = \frac{4}{6}$ in exercise books. - **CHECK:** Ask: "What fraction would $\frac{2}{3}$ become if we cut it into 3 rows? $\frac{6}{9}$!" --- ### Step 3: Model 2 — Aligned Stacked Number Lines (8 Mins) - **Slide:** Slide 3 (Aligned Stacked Number Lines Visualiser) - **Teacher Script:** > *"When number lines are the exact same length from 0 to 1, equivalent fractions sit at the EXACT SAME VERTICAL POINT! Look at our laser guide line. When I place it at $\frac{1}{3}$, it drops straight through $\frac{2}{6}$ on the sixths line and $\frac{3}{9}$ on the ninths line!"* - **Interactive Tool Action:** Click tick marks on line 1 ($\frac{1}{3}$, $\frac{2}{3}$) to trigger the animated Laser Guide. Switch preset to *Fifths & Tenths* and *Halves, Quarters, Eighths*. - **Logistics (Notes):** - **DO:** Click different tick marks to drop the laser guide. - **WORK:** Compare $\frac{2}{3} = \frac{4}{6} = \frac{6}{9}$ and $\frac{2}{5} = \frac{4}{10}$. - **RECORD:** Write aligned fraction pairs in exercise books. - **CHECK:** Ask: "Which fraction in ninths lines up with $\frac{2}{3}$? $\frac{6}{9}$!" --- ### Step 4: Model 3 — The Multiplication Rule (8 Mins) - **Slide:** Slide 4 (The Multiplication Golden Rule & Stepper) - **Teacher Script:** > *"Now for the math magic! You don't always need to draw pictures to find equivalent fractions. The Golden Rule is: Multiply the top AND bottom by the exact same number! Why does this work? Because $\frac{2}{2}$, $\frac{3}{3}$, or $\frac{5}{5}$ is equal to 1 whole, and multiplying by 1 never changes the value!"* - **Interactive Tool Action:** Click the multiplier buttons ($\times 2, \times 3, \times 4, \times 5$) to scale top and bottom dynamically. - **Logistics (Notes):** - **DO:** Chant "Multiply top and bottom by the same number!" with the class. - **WORK:** Show $\frac{1}{3} \times \frac{2}{2} = \frac{2}{6}$ and $\frac{1}{3} \times \frac{5}{5} = \frac{5}{15}$. - **RECORD:** Copy rule and examples into books. - **CHECK:** Ask: "If I multiply top by 4, what MUST I multiply bottom by? 4!" --- ### Step 5: Mini-Whiteboard Check Set 1 (5 Mins) - **Slide:** Slide 5 (Class Practice: Mini-Whiteboard Check Set 1) - **Activity:** 1. Q1: Area block cut ($\frac{3}{4}$ cut in half $\rightarrow \frac{6}{8}$). 2. Q2: Aligned number line ($\frac{2}{3} = \frac{6}{9}$). 3. Q3: True/False ($\frac{2}{5} = \frac{4}{10}$ $\rightarrow$ True). 4. Q4: Chain completion ($\frac{1}{4} = \frac{2}{8} = \frac{3}{12} = \frac{4}{16}$). --- ### Step 6: Reasoning & Discussion Check Set 2 (6 Mins) - **Slide:** Slide 6 (Class Practice: Reasoning & Discussion Check Set 2 💬) - **Activity:** 1. Q1: Conceptual reasoning (cutting $\frac{1}{2}$ into 3 rows $\rightarrow \frac{3}{6}$). 2. Q2: Spot the mistake! (Sam added 1 to top and bottom: $\frac{1}{3} \neq \frac{2}{4}$ — addition fallacy). 3. Q3: Twelfths on number line ($\frac{3}{4} = \frac{9}{12}$). 4. Q4: Real-world pizza sharing ($\frac{2}{5} = \frac{4}{10}$ — equal amounts). --- ### Step 7: Teacher Tools Sandbox (4 Mins) - **Slide:** Slide 7 (Teacher Tools Drawer 🛠️) - **Teacher Action:** Enter custom numerators, denominators, and multipliers to generate on-demand whiteboard prompts. --- ### Step 8: Rapid-Fire Missing Numerator Challenge (6 Mins) - **Slide:** Slide 8 (Whiteboard Challenge: Find the Missing Numerator 🎯) - **Teacher Action:** Click `🎲 Generate New Question` to cycle randomly through curated fraction questions covering halves, thirds, quarters, fifths, sixths, eighths, and twelfths. --- ### Step 9: Independent Practice & Worksheet Launch (10 Mins) - **Slide:** Slide 9 (Lesson Wrap-Up & Student Worksheet Launch) - **Student Work:** Distribute printed 2-page student worksheet: `Lesson_1_17_Equivalent_Fractions_Worksheet.docx`. --- ## 📦 File Package Artifacts 1. `Lesson_1.17_Presentation.html` — Full-viewport interactive slide presentation (9 slides). 2. `slides_content.html` — Slide HTML markup with interactive widgets & teacher notes drawer. 3. `Lesson_1_17_Equivalent_Fractions_Worksheet.docx` — Printable 2-page student worksheet. 4. `generate_worksheet.py` — Automated Python document builder script. 5. `Lesson_Plan_Equivalent_Fractions.md` — This pedagogical master plan.