Teacher says a number, students have to write it in powers of 10 on their mini-whiteboards. E.g. if the teacher says "1000," students would write "10^3." If the teacher says "0.01," they would write "10^2." To make it a bit more competitive, the last student to show the correct answer is out of the round.

🎯 Target Number Challenge

• What you need: Whiteboard or projector.

• How it works:

  1. Write a "target number" on the board (e.g., 500).

  2. Provide a set of 4-5 other numbers (e.g., 24, 78, 19, 5).

  3. The challenge is for students to use two or more of the numbers and any operation (+, -, ×, ÷) to get an answer as close as possible to the target number.

  4. Encourage them to talk through their estimation process first. For example, "I know 24 is close to 25, and 19 is close to 20. So, 25 × 20 is 500. Let me check what 24 × 19 actually is."

🎈 Hot Air Balloon Maths

This is a powerful visual metaphor for understanding vertical movement with integers, especially for addition and subtraction.

• What you need: A whiteboard or large piece of paper.

• How it works:

  1. Draw a large vertical number line. The top is the sky (positive), the bottom is the sea (negative), and the middle is sea level (0). Your hot air balloon starts at 0.

  2. Use "gas burns" 🔥 to represent adding a positive number (moves the balloon UP) and "sandbags" 🛍️ to represent adding a negative number (moves the balloon DOWN).

  3. Example: "The balloon is at +10m. We add 3 sandbags (-3). Where does it go?" (It moves down 3 units to +7m).

  4. To model subtraction, talk about removing items. Crucially, removing a sandbag (subtracting a negative) makes the balloon lighter and causes it to go UP. This is a fantastic way to explain why - (-a) = +a.

Objective

The goal is for teams to correctly convert fractions, decimals, and percentages and race to the finish line. This game works well for a class of about 20–30 students, divided into 4–6 teams.

Materials

• Index cards with different values written in either fraction, decimal, or percentage form (e.g., 1/4, 0.5, 75%). Make sure you have at least 15–20 cards per team.

• Three large posters or whiteboards, each with a heading: Fractions, Decimals, and Percentages.

• Tape or blu-tack.

• Markers or pens for each team.

How to Play

1. Setup: Divide the class into teams. At one end of the classroom, place a stack of the mixed-value index cards for each team. At the other end, set up the three posters/whiteboards.

2. The Relay: The first person from each team grabs an index card. They must then run to the posters and write the equivalent values for that card in the correct category. For example, if they pick up the card with "1/2", they would write "0.5" under the Decimals poster and "50%" under the Percentages poster.

3. Tag and Repeat: Once they have written their answers, they run back and tag the next person in their team. The next person repeats the process with a new card.

4. Winning: The first team to correctly convert and write the equivalent values for all their cards wins the race.

Variations and Extensions

• Difficulty: Vary the difficulty of the cards. Start with simple fractions like 1/2, 1/4, and 1/10, and then introduce more complex ones like 3/8 or 2/3.

• Individual Challenge: Instead of a relay, turn it into a "scavenger hunt." Hide the cards around the room and have students work individually or in pairs to find them and fill out a conversion sheet.

Materials

• "Original Price Tag" cards (Large cards with whole number amounts, e.g., $60, $120, $450, $80, $20). Make one set of 5-10 cards.

• "Discount/Sale Sign" cards (Large cards with simple percentages/fractions, e.g., 25% off, 41​ off, 50% off, 10% GST, 30% off). Make one set.

• Whiteboard/Projector for recording answers and calculations.

• Mini-whiteboards or paper for students to work out their calculations.

Part 1: Find a Percentage of a Whole Number (The Discount)

Goal: Calculate the discount amount and the new sale price.

Procedure

1. Introduction (5 mins): Explain that they are a team of retail managers preparing for a sale. Review how to convert simple percentages to fractions (e.g., 50%=21​, 25%=41​, 10%=101​).

2. The Challenge:

   • Display one Original Price Tag (e.g., $80).

   • Display one Discount/Sale Sign (e.g., 25% off).

   • Task 1 (Individual/Pair Work): Students work on their whiteboards to calculate:

     • A) The Discount Amount: (25% of $80).

     • B) The New Sale Price: ($80 - Discount Amount).

3. Check and Share (5 mins): Ask for a volunteer to explain their calculation for the discount amount (e.g., "25% is 41​. 41​ of $80 is $20"). Record the correct answers.

4. Repeat: Repeat this process 2-3 times with different Price Tag and Sale Sign combinations.

Part 2: Find a Whole Amount Given a Simple Fraction or Percentage (The Mystery Price)

Goal: Use the discount amount or sale price to work backward and find the original price.

Procedure

1. The Mystery Scenario (5 mins): Explain that a clumsy customer has torn the original price tag, but the sales slip only shows the discount amount or the final sale price, and the discount rate. They must find the Original Price.

2. Set-up 1 (Finding the Whole from the Discount):

   • Write a sentence on the board: "The sale sign said 50% off, and the customer saved $15 on the shirt."

   • Task 2 (Individual/Pair Work): Students must determine the Original Price.

   • Logic Check: Guide them with a question: "If $15 is 50% (or half) of the price, what was the whole price?" (Answer: $30)

3. Set-up 2 (Finding the Whole from the Sale Price): (This is slightly more challenging and great for Year 8).

   • Write a new sentence on the board: "The sale sign said 25% off, and the final price paid was $45."

   • Analysis: Ask the class: "If it was 25% off, what percentage of the original price did the customer pay?" (Answer: 100%−25%=75%).

   • Task 3 (Individual/Pair Work): Students work out the Original Price.

     • Calculation: If $45 is 75% (or 43​) of the price, first find 25% (or 41​). $45÷3=$15.

     • The full price is 4×$15=$60.

4. Repeat: Provide 1-2 more examples using simple percentages like 10%, 20%, or 75%.

Extension/Wrap-up

• Error Check: Present a common student error (e.g., calculating 25% of $60 as $25) and have the students collaboratively find and fix the mistake.

• "Create Your Own": Challenge students to create their own 'Mystery Price' problem and swap it with a partner to solve.

Materials

• Large Visual Aids: Draw or print three large circles (representing pizzas).

  • Pizza 1: Divided into halves (21​).

  • Pizza 2: Divided into thirds (31​).

  • Pizza 3: Divided into quarters (41​).

• A "Conversion Grid" (on the whiteboard/projector) to record equivalent fractions.

• Mini-whiteboards/Paper for students' individual calculations.

• Coloured Markers (for shading the pizzas).

Part 1: Addition – The Sharing Challenge

Goal: Understand the need for a Common Denominator (finding the Lowest Common Multiple - LCM).

Procedure

1. Set the Scene (5 mins): Tell students two friends brought pizzas to a party. One brought 21​ of a pepperoni pizza and the other brought 31​ of a cheese pizza. The task is to find the total amount of pizza.

2. The Problem: Write the equation on the board:
   21​+31​=?

3. Visual Exploration:

   • Shade 21​ of Pizza 1.

   • Shade 31​ of Pizza 2.

   • Ask: "Can we just add the '1's on top and the '2' and '3' on the bottom?" (No). "Why not?" (The pieces are different sizes; you can't add apples and oranges).

4. Finding the Common Denominator:

   • Guide the students to find the LCM of 2 and 3, which is 6.

   • Draw a third line on the whiteboard labeled "Sixths" and physically re-cut (draw lines) on the 21​ pizza to show it's now 63​, and on the 31​ pizza to show it's now 62​.

5. Equivalent Fractions: Use the Conversion Grid:

   • 21​=63​ (Multiply numerator and denominator by 3)

   • 31​=62​ (Multiply numerator and denominator by 2)

6. Solve: Now that the pieces are the same size (sixths), we can add them:
   63​+62​=65​
   The total pizza is 65​.

Part 2: Subtraction – The Leftovers

Goal: Apply the common denominator method to subtraction.

Procedure

1. Set the Scene (5 mins): Imagine a group ordered 43​ of a large vegetarian pizza, but they ate 21​ of it. How much is left?

2. The Problem: Write the equation on the board:
   43​−21​=?

3. Finding the Common Denominator:

   • Ask students for the LCM of 4 and 2. (It's 4).

   • Tell them, "We only need to change the 21​ fraction, as quarters is already the smallest common piece size."

4. Equivalent Fractions:

   • 21​=42​ (Multiply numerator and denominator by 2)

5. Visual and Solve:

   • On the whiteboard, draw a pizza cut into quarters. Shade 43​.

   • Ask them to physically erase/cross out 42​ (which is the 21​ they ate).

   • Solve the equation:
     43​−42​=41​
     The amount of pizza left is 41​.

Whole-Class Practice (10 mins)

Task: Put up several problems on the board. Students work individually on mini-whiteboards. They must show the equivalent fractions step.

1. 41​+81​=

2. 32​−61​=

3. 51​+101​=

4. 107​−53​=

• Review: Have students show their mini-whiteboards. Focus feedback on the process of correctly finding the LCM and multiplying the numerators and denominators consistently to create the equivalent fraction.

This hands-on activity uses a ratio recipe to demonstrate how the concept of "parts" works when sharing unequally.

• Concept Focus: Understanding that a ratio defines the total number of "parts" in the whole.

• Materials: Large bags of three different coloured counters/tokens (or small packets of snack items like dried fruit and nuts), and ratio cards.

• Activity:

  1. Introduce the Recipe: Tell the class they are making a "Ratio Mix." Display a ratio card, such as 3:2:1 (e.g., for every 3 blue, 2 red, and 1 yellow token).

  2. Calculate the Total Parts: Students first add the ratio numbers to find the total number of parts: 3+2+1=6 total parts.

  3. Set the Whole: Give the groups a specific total amount of items (e.g., 60 tokens). This is the "whole" that needs to be divided into 6 equal parts.

  4. Find the Value of One Part: Students calculate the value of a single part: 60 tokens/6 parts=10 tokens per part.

  5. Calculate the Share: Students use the single part value to find each share:

     • Blue (3 parts): 3×10=30 tokens.

     • Red (2 parts): 2×10=20 tokens.

     • Yellow (1 part): 1×10=10 tokens.

  6. Check (Inverse): Groups physically combine and count the tokens to ensure the total is 60. Then, they divide the pile according to their calculated shares.

This is a challenging inverse problem that requires students to work backward from a known share to find the original ratio and total.

• Concept Focus: Working backward from the value of a known share to determine the value of a single part and the total amount.

• Materials: Whiteboard/Projector.

• Activity:

  1. The Budget Problem: Present a problem where a specific share is given, not the total.
     Scenario: Three siblings, Tom, Ben, and Chloe, share an inheritance in a ratio. We know Ben gets $45,000 and Chloe gets $30,000.

  2. Find the Ratio: Students simplify the two known shares to find their base ratio.

     • Ben : Chloe = 45,000:30,000. This simplifies by dividing by 15,000 to 3 : 2. (This represents 3 parts and 2 parts, respectively).

  3. Introduce the Third Share: Add the final piece of information: The full ratio is Tom : Ben : Chloe is 5 : 3 : 2.

  4. Find the Unit Value: Since the 3 parts (Ben's share) equals $45,000, students can find the value of one part: $45,000/3=$15,000 per part.

  5. Calculate the Missing Shares and Total:

     • Tom (5 parts): 5×$15,000=$75,000

     • Total Inheritance: 75,000+45,000+30,000=$150,000

  6. This process reinforces that the core concept (the value of one part) can be found using any known component of the problem.

This game uses visual representation and quick mental math to practice dividing a total into proportional parts.

• Concept Focus: Visually partitioning a total into unit blocks based on a ratio.

• Materials: Whiteboard or large paper, markers, pre-written ratio cards (e.g., 1:3, 2:5, 3:4).

• Activity:

  1. Set the Total: Write a total number on the board (e.g., 49 apples 🍎).

  2. Display the Ratio: Show a ratio card, such as 3:4.

  3. Find the Parts: Students quickly calculate the total number of parts (3+4=7 parts).

  4. Find the Unit: Students calculate the value of one unit: 49÷7=7 per part.

  5. The Sort: Students then quickly calculate the final shares (Person A gets 3×7=21; Person B gets 4×7=28).

  6. Quick Check: Have students shout out the final shares and then the total (21+28=49).

  7. Gamification: Create a 3×3 grid on the board. Each square contains a total amount (e.g., 27, 35, 60, 100). Teams take turns rolling a die to determine which square they tackle, and then the teacher provides a random two-part ratio. The first team to correctly calculate both shares and verify the total wins the square.

This activity focuses on comparing weekly, monthly, and yearly costs for the same essential service, reinforcing the need to convert periods for a fair comparison.

• Concept Focus: Converting weekly costs to yearly costs (and vice versa) to find the cheapest option.

• Materials: Whiteboard, worksheet with three fictional phone plans.

• The Plans: Create three fictional mobile phone plans for students to analyze:

  1. Weekly Prepaid Plan: $10 per week (No contract).

  2. Monthly Contract Plan: $45 per month (12-month lock-in).

  3. Yearly Bulk Plan: $480 per year (Paid upfront).

• Activity:

  1. Conversion Challenge: Students must convert all plans to a single unit (e.g., yearly cost) to compare them accurately.

     • Weekly to Yearly: $10×52 weeks = $520

     • Monthly to Yearly: $45×12 months = $540

     • Yearly: $480

  2. Comparison and Discussion: Ask students: Which plan is cheapest? Why?

  3. Variable Introduction: Introduce a realistic variable, such as a one-time yearly fee (e.g., a $20 account fee added to the yearly bulk plan) or a cancellation fee (e.g., $100 to break the monthly contract). Students must recalculate and determine if the cheapest plan still holds its value. This highlights how finance plans have hidden costs.

This hands-on budgeting activity demonstrates the power of consistent, smaller contributions versus sporadic, larger ones.

• Concept Focus: Creating and tracking savings plans over different periods to reach a single goal.

• Materials: Whiteboard, individual tracking sheets, calculators.

• The Goal: The class decides on a savings target (e.g., saving $600 for a new scooter).

• Activity:

  1. Weekly Plan: Students calculate the amount needed to save weekly to reach the goal in one year: $600/52 weeks ≈ $11.54 per week.

  2. Monthly Plan: Students calculate the amount needed to save monthly to reach the goal in one year: $600/12 months = $50 per month.

  3. Budgeting Simulation: Students select one plan. They then track the required savings on a blank monthly calendar or a simulated budget.

  4. Introducing Budget Shocks: Halfway through the simulation (after six months), introduce a random "budget shock" that only affects one payment period:

     • Weekly Plan: You had a big holiday, and missed two weeks of savings. You must catch up on the $23.08 deficit in the next payment.

     • Monthly Plan: Your car needed a repair; you can only contribute $25 this month instead of $50.

  5. Comparison: Students compare the two plans and discuss: Which plan provides more flexibility? Which plan is easier to stick to? This helps them evaluate which financial frequency is "better" for a given goal.

This practical activity reinforces applying percentages and comparing prices to make a financial decision.

• Concept Focus: Calculating the discount amount and final price, then comparing deals.

• Materials Needed:

  1. "Sale" Item Cards: A series of cards for the same item but at different stores (e.g., "T-shirt").

     • Store A: $50, 30% off

     • Store B: $45, 20% off

     • Store C: $60, 40% off

  2. A calculation sheet for teams to show their working.

• How to Play (Small Groups/Whole Class):

  1. The Challenge: Give each small group the set of "Sale" Item Cards. Their task is to determine which store offers the best deal (i.e., the lowest final price) and why.

  2. Calculate: Each group must calculate the final price for all three stores. Encourage the use of the decimal multiplier method (e.g., 50×0.70) for efficiency.

  3. The Report (Inverse Check): Once a group has a winner, they must present their findings to the class. As an inverse check, they must also state the actual dollar value of the savings (the amount discounted).

     • Example: "Store A is $35. We saved $15 ($50−$35)."

  4. Whole-Class Vote: Groups vote on the best deal. The group with the correct winning store, and the best-explained calculations and savings, wins the round.

  5. Extension: Introduce a "Loyalty Card" rule that adds a fixed dollar discount after the percentage has been applied (e.g., "Take an extra $5 off").