| 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 | |
| What length (min) | 20 |
| What age group | Year or Grade 7 |
| Class size | 28 |
| What curriculum | CCSS |
| 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 | 6 |
| Create fill-in cards for students | |
| Create creative backup tasks for unexpected moments |
Understanding Proportions
Grade 7
Mathematics
20 minutes
28 students
This lesson adheres to the Common Core State Standards (CCSS) for Mathematics.
| Step Number | Step Title | Length | Details |
|---|---|---|---|
| 1 | Introduction | 2 min | Briefly introduce the concept of proportions using real-life examples. Explicitly state the learning objectives for the lesson. |
| 2 | Direct Instruction | 5 min | Present the definition of proportions, including ratios. Demonstrate how to set up and solve proportion equations with examples on the board. |
| 3 | Guided Practice | 5 min | Distribute handouts and work through a sample set of problems as a class. Encourage student participation by calling on volunteers. |
| 4 | Independent Practice | 5 min | Allow students to solve a few problems on their own using the handouts, walking around to offer support and feedback as needed. |
| 5 | Assign Homework | 1 min | Distribute a homework assignment related to proportions. Inform students that the homework will be checked without presentations in class. |
| 6 | Closing and Exit Ticket | 2 min | Recap the main points of the lesson. Distribute exit tickets for students to write down one thing they learned and one question they still have. Collect exit tickets as they leave. |
“Good morning, class! Today, we’re going to learn about proportions. Can anyone tell me what a proportion is or maybe give an example? (Pause for responses.) Great answers! A proportion is an equation that states that two ratios are equal. We’ll explore this concept today, and by the end of the lesson, you should be able to explain what proportions are, solve some simple proportion problems, and even apply what we’ve learned to real-world scenarios. Let’s dive into it!”
“First, let’s define proportions in a bit more detail. A proportion compares two ratios. For instance, if we have two ratios like 1:2 and 2:4, they can form a proportion since 1/2 equals 2/4. Now, I’ll show you how to set up a proportion. Let’s take an example where we want to find out how many apples can be bought for a certain amount of money.
If 3 apples cost $6, how much will 5 apples cost?
We can set up the proportion as:
3 apples / 6 dollars = 5 apples / x dollars
Now, to solve for x, we cross-multiply:
3x = 30
Dividing both sides by 3 gives us x = 10.
So, 5 apples will cost $10! Let’s do a couple more examples together on the board. (Write another example on the board and solve it with student participation.)”
“Now, it's your turn to work on some problems! I’m passing out handouts with practice problems. Let’s start with problem number one together.
What is the proportion here? (Wait for student responses.) Nice! Now, who can help solve it? (Call on a volunteer to help solve the first problem on the board.)
As we work through more of these, feel free to raise your hand to share your thoughts. I want to hear everyone’s ideas on how we can solve these proportions!”
“Fantastic job doing these problems together! Now, I’ll give you some time to work on the next few problems on your own. Please take about five minutes to complete problems two through four on your handouts. I’ll be walking around to help anyone who needs it, so don’t hesitate to ask questions. Remember, practice makes perfect!”
“Time’s up! Now that we’ve wrapped up our independent practice, I have a homework assignment for you. You will find additional proportion problems in your handouts that you should complete by next class. Remember, I’ll be checking your homework for completion, but you don’t need to present your work in class. Make sure to do your best!”
“Alright, class! Before we finish, let’s recap what we learned today about proportions. We defined what a proportion is, solved some examples, and practiced applying it to real-life situations.
As you leave, I want you to fill out an exit ticket I’m distributing. Write down one thing you learned today and one question you still have about proportions. You can drop those in the box on your way out. Thank you for your hard work today, and I’ll see you next time!”
| Slide Number | Image | Slide Content |
|---|---|---|
| 1 | {Image: A classroom with students} | - Introduction to Proportions - Define proportions: equation stating two ratios are equal - Learning goals: explain proportions, solve problems, apply knowledge |
| 2 | {Image: Visual of ratios, like 1:2} | - Detailed definition of proportions - Example of comparing ratios: 1:2 and 2:4 - Setting up a proportion: 3 apples / 6 dollars = 5 apples / x dollars - Cross-multiplication to solve for x |
| 3 | {Image: Students working on problems} | - Guided practice on proportion problems - Importance of class participation - Solving problems together on the board - Encouragement to share thoughts |
| 4 | {Image: Student focused on work} | - Independent practice on handouts - Time to work on problems 2-4 - Teacher available for questions - Reminder: "Practice makes perfect!" |
| 5 | {Image: Homework assignment sheet} | - Assignment of homework problems - Additional proportion problems to complete - Check for completion, no need to present in class - Encourage effort and commitment |
| 6 | {Image: Students leaving classroom} | - Recap of lesson on proportions - Summarized learning points: definitions, examples, applications - Exit ticket: one thing learned, one question remaining - Thank you for participation! |
Define what a proportion is in your own words. Provide an example of a proportion using two different ratios.
Solve the following proportion: If 4 pencils cost $8, how much would 7 pencils cost? Set up the proportion and show your work.
A car travels 150 miles on 5 gallons of gas. If the car continues to consume gas at this rate, how many gallons of gas will be needed to travel 300 miles? Set up the proportion and solve.
In a recipe, the ratio of sugar to flour is 2:5. If you want to use 10 cups of flour, how much sugar will you need? Show your calculations.
You are mixing paint in a ratio of blue to yellow of 3:2. If you want to make 25 liters of paint, how many liters of blue paint will you need? Set up the proportion and calculate.
Create your own proportion problem that involves a real-life scenario (such as shopping, cooking, or travel). Solve your problem and clearly show your work.
Reflect on what you learned about proportions in class. Write a paragraph summarizing your understanding and any areas you found challenging.