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LO: I can represent numbers in scientific notation (8MNA8)

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Use markers/colours to copy this poster into your book

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Learn about scientific notation and explore how it's used to represent very large or small numbers. Research examples from science, engineering, and real-world applications. Discuss with a classmate how scientific notation simplifies calculations.

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Choose two pairs of numbers in scientific notation and perform both addition and multiplication on the pairs. Use a calculator to check your work and discuss any trends you notice.

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LO: I can apply mathematical strategies to solve problems involving percentages, such as discount, tax, and interest (7MNA10)

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Imagine you have saved $1,000 in a bank account that gives simple interest. Decide your own interest rate (e.g., 3% per year). Calculate how much money you will have after 1, 2, and 3 years. Try a different rate or amount. What patterns do you notice about the growth?

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LO: I can solve problems using rates and unit rates (8MNA4)

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You are helping your family shop for Lunar New Year. Choose 10 different items from an online shop, each with a different percentage discount (e.g., 30%, 15%, 50%). Find their original prices and sale prices. Which item has the greatest absolute savings? Can you think of a way to compare the discounts fairly?

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After eating out with friends, the bill arrives with a 10% service charge and a 5% government tax. Design your own restaurant menu with at least five items. For a meal of two or more items, calculate the final bill including all charges. What strategies do you use to check your calculations?

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Create your own multi-step problem involving at least two different percentage operations (e.g., discount then tax; interest then donation). Solve it in as many ways as you can and explain your strategies. Share your problem with a classmate and solve theirs!

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Problem: Shopping Spree

Scenario:

You go to a store to buy a new jacket that costs $80. The store is offering a 25% discount on the jacket. After applying the discount, you have to pay a sales tax of 8% on the discounted price.

Tasks:

1. Calculate the Discounted Price:

Find the amount of the discount.

Subtract the discount from the original price to find the discounted price.

2. Calculate the Sales Tax:

Find the amount of sales tax based on the discounted price.

Add the sales tax to the discounted price to find the total amount you will pay.

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Scenario:
You buy a smartphone for $9500. It’s on sale for 15% off. After the discount, there’s a 10% recycling fee added to the discounted price.

Tasks:

1. Calculate the discounted price.

2. Calculate the recycling fee.

3. Find the total amount paid.

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The best menu ever

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Jonas 6GL

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Step 1: Choose Household Items

Select five common household items to analyse. For example:

1. Rice

2. Cooking Oil

3. Dishwashing liquid

4. Sugar

5. Tomato Sauce (ketchup)

Step 2: Gather Prices and Quantities

Find the price and quantity for each item. For example:

1. Rice: $73.00 for 8 kg

2. Cooking Oil: $35.50 for 1.5 litres

3. Dishwashing liquid: $19.00 for 1.3 litres

4. Sugar: $23.00 for 1 kg

5. Tomato Sauce: $22.50 for 500 ml

Step 3: Calculate Price Per Unit (per kg or litre)

Calculate the price per unit for each item using the formula: total price divided by quantity

Step 4: Summarise Unit Prices

Create a summary of the unit prices per litre orkg

***Deeper:

We have many tourists visiting HK. Do you think they find groceries cheaper here than their home country?

Choose a currency and do the conversions of how much these items would cost them if they were doing a direct exchange.

(PS: you can use the currency converter on your calculator app)

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You are organising a Founders Day picnic for 150 Year 2s and need to purchase snacks and drinks. You come across two options for snacks and drinks:

Cookies: A pack of 15 cookies costs $29.50.

Juice Boxes: A pack of 30 juice boxes costs $48.50.

1. Calculate the unit rate for both cookies and juice boxes (cost per item).

2. Which snack is more cost-effective based on the unit rates you calculated?

3. If you want each student to have 3 cookies and 2 juice boxes, how many packs of each will you need to purchase?

4. Include a detailed breakdown of your calculations, showing how you arrived at the number of packs needed for each item.

5. If your budget for snacks is $540, can you afford to buy enough cookies and juice boxes for all guests? Show all your calculations to justify your answer.

6. If you discover a special offer where buying 4 packs of cookies grants you 1 additional pack for free, how would this affect your purchasing decision? Calculate the new total cost and determine if it changes your budget situation.

*** Deeper:

During the event, you survey 75 guests from the picnic, and 30% say they prefer granola bars over cookies. If you want to maintain this preference ratio for upcoming events, how many cookies should you plan to purchase for 200 guests at the next event?

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Imagine you are planning a road trip with your family. You want to visit three different cities, and you need to calculate fuel costs and travel times to ensure a smooth journey.

1. Your car consumes 8 litres of fuel per 100 kilometers. If you know that the first city is 240 kilometers away, the second city is 320 kilometers from the first, and the third city is 150 kilometers from the second, calculate the total distance of the trip in kilometers. (Think of a different way to display this)

2. If petrol costs $26.60 per litre, how much will you spend on fuel for the entire trip? Show your calculations for each segment of the trip.

3. You also want to stop for lunch halfway to each city. If each lunch costs $130 per person and you have 4 family members, how much will you spend on lunches during the trip?

4. Finally, if you plan to travel at an average speed of 90 kilometers per hour, how long will it take to complete the entire trip in hours?

5. Explain your reasoning and the strategies you used in your calculations. What challenges did you face, and how did you overcome them?

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Chapter 8: Ratios and Rates

Rates

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Chapter 12: Exponents

Scientific Notation

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Convert the following numbers into scientific notation: 0.0075, 6340000, 5.89. Then, write these numbers in standard form from their scientific notation: 3.2 x 10^4, 7.89 x 10^-3. Swap with a partner and check each other's work.