| Full lesson | Create for a teacher a set of content for giving a lesson, beginning with the lesson plan. Each new block of materials must begin with an H1 heading (other subheaders must be H2, H3, etc). When you describe required pictures, write those descriptions in curly brackets, for example: {A picture of a triangle} |
| Which subject | Mathematics |
| What topic | Equations with percents |
| What length (min) | 30 |
| What age group | Year or Grade 8 |
| Class size | 20 |
| What curriculum | |
| Include full script | |
| Check previous homework | |
| Ask some students to presents their homework | |
| Add a physical break | |
| Add group activities | |
| Include homework | |
| Show correct answers | |
| Prepare slide templates | |
| Number of slides | 5 |
| Create fill-in cards for students | |
| Create creative backup tasks for unexpected moments |
Mathematics
Equations with Percents
Year/Grade 8
Approximately 13-14 years old
30 minutes
20 students
This lesson is designed to meet the expectations outlined in the Canadian Mathematics Curriculum for Grade 8, focusing on algebraic reasoning and problem-solving with percentages.
| Step Number | Step Title | Length | Details |
|---|---|---|---|
| 1 | Introduction to Percents | 5 minutes | Begin with a brief review of percentages. Engage students with a question about where they encounter percentages in daily life. |
| 2 | Setting Up Equations | 5 minutes | Explain how to convert word problems into equations involving percentages. Provide examples on the board. |
| 3 | Guided Practice | 10 minutes | Work through a couple of examples as a class. Ask students to volunteer answers and explain their reasoning. |
| 4 | Independent Practice | 5 minutes | Distribute worksheets with practice problems. Students work individually to reinforce their understanding. |
| 5 | Review and Clarification | 3 minutes | Go over practice questions, clarifying any common misconceptions. Encourage peer discussion for shared learning. |
| 6 | Homework Assignment | 2 minutes | Briefly explain the homework assignment, ensuring students understand the expectations without asking for presentations. |
"Good morning, everyone! Today we are going to talk about an important topic in mathematics: equations with percents.
To start, can anyone tell me where you might encounter percentages in your daily life? Perhaps in sales, taxes, or maybe when calculating tips at a restaurant?
Think about what a percentage actually represents. It’s a way of expressing a part of a whole, right? For example, if something is 20% off, that means you get to pay only 80% of the original price.
Now let's dive deeper into how we can set up and solve equations involving percentages!"
"Now that we've revisited what a percentage is, let’s learn how to convert word problems into mathematical equations.
When we encounter a word problem that involves a percentage, the first step is to identify the whole and the part represented by the percentage.
For example, let’s say we have a problem stating: 'A sweater originally costs $50 but is on sale for 20% off.'
Can anyone help me set up the equation?
That's right! We know that 20% of $50 is the amount we’d subtract from the original price. We can express that as:
[ \text{Discount} = 0.20 \times 50 ]
Then, we can find the sale price by subtracting that discount from the original price."
"Okay, now let’s practice together. I’ll present another example on the board.
'If you scored 75% on your math test which had 40 questions, how many questions did you get correct?'
Can anyone suggest how we might set up the equation for this?
Good! We can express 75% of 40, which gives us:
[ \text{Correct Answers} = 0.75 \times 40 ]
Let's calculate that. What do we get?
Absolutely! You got 30 questions correct.
Now, I want you to turn to your neighbor and discuss how you would solve this next problem:
'A store has a sale where 15% of all items are discounted. If you were buying shoes that originally cost $80, how much do you save?'
Who wants to share their approach?"
"Great discussions, everyone! Now it's your turn to work on some practice on your own.
I’m handing out worksheets with a few problems related to equations with percents.
Please read through each problem carefully and set up the equations as we practiced.
You will have 5 minutes for this, and if you have any questions, please feel free to raise your hand."
"Alright, time's up! Let’s review the answers to the worksheets together.
I’ll go through a couple of the problems, and I want you all to be ready to share your thought processes.
If you struggled with any particular question, don’t hesitate to ask!
Let’s clarify any misconceptions together. For example, how did you solve problem number 3?
Excellent answers, everyone! Keep talking to each other about your methods."
"Before we wrap up, I want to explain your homework assignment.
You’ll have a set of questions that will ask you to apply what we learned about equations with percents.
Make sure you read each of the problems carefully and show your work step by step.
This assignment is important for reinforcing today’s lesson, and it will be due next class.
If you have any questions at home, feel free to email me or ask me before class next time.
Thank you all for your hard work today!"
A jacket originally priced at $120 is on sale for 25% off. What is the sale price of the jacket? Show your calculations.
You earned a score of 85% on a quiz that had 50 questions. How many questions did you answer correctly? Write out the equation used to find your answer.
A store is offering a promotion where 10% of every purchase goes to charity. If you spend $200, how much money will be donated to charity? Set up and solve the equation.
A restaurant bill comes to $75, and you want to leave a 15% tip. How much do you plan to tip? Show your workings.
A pair of sneakers cost $90, but there is a discount of 30%. How much do you save on the sneakers? What is the final price after applying the discount? Clearly present your calculations.
If a book priced at $40 is now at a 35% discount, what is the discounted price? Write the steps you took to arrive at your answer.
During a sale, you bought items that cost a total of $150 before tax. If there’s a tax of 13%, what will be the final amount you pay? Include all calculations in your response.
Your friend scored 60% on a test with 30 questions. How many questions did they get wrong? Generate the equation used to solve the problem and present your answer.
A bicycle costs $500, and there's a sale offering 20% off the price. If you want to buy it, how much money will you save? Calculate the amount saved and the new price after the discount.
You want to buy a laptop that costs $1,200. There is a student discount of 15%. What is your total saving and what will be the price after applying the discount? Document your calculations.