Why Do We Use Letters in Math Anyway?

Lorna Balaguer

Tier 1

Lesson Plan

Algebra's Real-World Unveiling

Students will be able to identify variables in real-world contexts and understand their role in representing unknown quantities in algebraic expressions.

Understanding variables is fundamental to algebra, which is used to solve countless real-world problems from budgeting to engineering. This lesson helps students see the practical application of letters in math, making the abstract concrete and building a strong foundation for future mathematical concepts.

Audience

6th Grade Students

Time

45 minutes

Approach

Through relatable scenarios, discussion, and an interactive activity.

Materials

Whiteboard or Projector, Markers or Pens, Letters Have a Purpose Slide Deck, Everyday Algebra Brainstorm Discussion Guide, and Translate the Scenario Activity Sheet

Prep

Teacher Preparation

15 minutes

Review the Letters Have a Purpose Slide Deck and ensure all technological needs are met.
- Print or prepare for digital distribution the Everyday Algebra Brainstorm Discussion Guide and Translate the Scenario Activity Sheet.
- Ensure you have markers/pens and a whiteboard/projector ready.
- Review all generated materials as needed.

Step 1

Introduction: The Mystery of the Missing Number

5 minutes

Begin by asking students: "Have you ever wondered why we use letters in math? It seems a bit mysterious, right?"
2. Explain that today, they will uncover the secret power of letters in math – how they help us solve real-world puzzles.
3. Introduce the lesson's objective: Students will learn to see letters as placeholders for unknown numbers in everyday situations.

Step 2

Direct Instruction: Unveiling Variables with 'Letters Have a Purpose'

15 minutes

Use the Letters Have a Purpose Slide Deck to guide students through the concept of variables.
2. Define a variable as a letter representing an unknown number or quantity.
3. Present simple, relatable examples (e.g., 'If you have 'x' apples and I give you 3 more, how many do you have?')
4. Encourage questions and provide clear, simple explanations.

Step 3

Guided Practice: 'Everyday Algebra Brainstorm'

10 minutes

Facilitate a class discussion using the Everyday Algebra Brainstorm Discussion Guide.
2. Prompt students to think about situations in their own lives where they might not know an exact number.
3. Guide them to express these unknowns using letters (variables).
4. Write down their ideas on the board, showing how everyday language can be translated into mathematical expressions.

Step 4

Independent Practice: 'Translate the Scenario' Activity

10 minutes

Distribute the Translate the Scenario Activity Sheet.
2. Students will work individually or in pairs to read various scenarios and write an algebraic expression using a variable to represent the unknown.
3. Circulate to provide support and answer questions.

Step 5

Wrap-up: Reflect and Connect

5 minutes

Bring the class back together.
2. Ask students to share one thing they learned about why we use letters in math.
3. Reiterate that variables are powerful tools for solving problems when we don't know all the numbers.
4. Assign any unfinished activity as homework.

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Slide Deck

Why Are There Letters in Math Anyway?

It's a great question!
Today, we'll uncover the secret!
How do letters help us solve problems?

Welcome students and introduce the day's mystery: why are there letters in math? Engage them with a question to activate prior knowledge.

Meet the Variable!

A variable is a letter that represents a number we don't know yet.
It's like a placeholder or a mystery box waiting to be opened!
Common variables: x, y, a, b, n

Explain that letters in math are called variables. Define what a variable is in simple terms, emphasizing it's a placeholder for something unknown.

Everyday Unknowns

Imagine you have some cookies, but you don't know exactly how many.
You eat 2 cookies, and now you have 5 left.
How can we write this as a math problem?
Let 'c' be the number of cookies you started with.

Provide a simple, concrete example to illustrate how a variable works in a real-world scenario. Use a question to prompt thinking.

From Story to Math

Starting cookies (unknown) - 2 eaten = 5 left

c - 2 = 5

Here, 'c' is our variable! It represents the number of cookies we started with.

Show the algebraic expression for the previous slide's example. Explain how 'c' stands for the unknown number of cookies.

Another Mystery!

You have some money in your piggy bank.
Your aunt gives you $10 more.
Now you have $25.
How much money did you start with?
What letter could we use for the unknown amount?

Offer another relatable example, this time about money. Encourage students to think about what the variable would represent.

Money Matters

Starting money (unknown) + $10 received = $25 total

m + 10 = 25

'm' is our variable, representing your starting money.

Reveal the expression for the money example. Reinforce the idea that variables help us translate real-world problems into math.

The Power of Variables

Variables help us:

Represent numbers we don't know yet.
Turn everyday situations into mathematical expressions.
Solve problems!

Next, let's brainstorm more everyday algebra!

Summarize the key takeaway: variables help us deal with unknowns and solve problems. Look ahead to the next activity.

Discussion

Everyday Algebra Brainstorm

Objective: To connect the abstract concept of variables to students' real-world experiences by identifying situations with unknown quantities.

Instructions:

Introduction (2 minutes):
- Teacher: "We just learned that variables are letters that stand for unknown numbers. Now, let's think about our lives. Where in your day-to-day do you encounter things that are unknown, or quantities that change?"
- "For example, if you're saving money, you might not know exactly how much money you'll have next month. Or if you're making a recipe, you might need 'some' amount of an ingredient depending on how many people you're feeding."
Small Group Brainstorm (5 minutes):
- Divide students into small groups (2-3 students).
- Teacher: "In your groups, brainstorm as many everyday situations as you can where there's an unknown quantity. Think about school, home, sports, games, shopping – anywhere you don't know an exact number."
- "Try to come up with at least three ideas per group."
Whole Class Share and Translate (8 minutes):
- Teacher: "Let's hear some of your amazing ideas! When you share, first describe the situation, then tell us what the unknown quantity is, and finally, what letter (variable) you would use to represent it."
- As students share, write their ideas on the board. For each idea, guide them to identify the unknown and choose a variable.
- Example from Teacher:
  - Situation: "I'm planning a birthday party, and I don't know how many guests will RSVP."
  - Unknown: "The number of guests."
  - Variable: "I could use 'g' for guests."
- Discussion Prompts:
  - "Who has an idea to share?"
  - "What is the unknown in that situation?"
  - "What letter could we use as a variable for that unknown? Why did you choose that letter?"
  - "Can anyone think of a different letter we could use?"
  - "How is this like the cookie or money examples we saw?"
  - "Could we make a small math phrase from that situation? (e.g., 'g + 5' if 5 more people are invited)"
Wrap-up Question (Optional, 2 minutes):
- Teacher: "Based on our discussion, how do variables make it easier to talk about situations where we don't know everything yet?"

Example Scenarios for Teacher Guidance (if needed):

Situation: Number of points my favorite basketball team will score in their next game.
- Unknown: Points scored.
- Variable: p
Situation: How many pages I need to read to finish my book.
- Unknown: Pages left to read.
- Variable: P
Situation: The cost of a new video game if there's a special discount.
- Unknown: Final cost.
- Variable: c

Activity

Translate the Scenario: Variables in Action

Name: _____________________________

Date: _____________________________

Objective: For each scenario, identify the unknown quantity and write an algebraic expression using a variable.

Instructions: Read each situation carefully. In the space provided, identify what quantity is unknown, choose a letter to represent that unknown (your variable), and then write a mathematical expression or equation that describes the situation.

Scenario 1: The Pizza Party

You are ordering pizza for a party. Each pizza has 8 slices. You don't know how many pizzas you'll need, but you want to make sure you have enough slices for everyone.

Unknown Quantity:
Your Variable:
Algebraic Expression/Equation:

Scenario 2: Saving for a New Game

You have saved some money, and you want to buy a new video game that costs $60. You still need to save $15 more.

Unknown Quantity:
Your Variable:
Algebraic Expression/Equation:

Scenario 3: Mystery Books

Your library shelf has a certain number of mystery books. Your friend borrows 3 of them, and now there are 12 mystery books left on the shelf.

Unknown Quantity:
Your Variable:
Algebraic Expression/Equation:

Scenario 4: The School Trip Bus

Students are going on a school trip. Each bus can hold 40 students. You don't know how many students are going yet, but you need to figure out how many buses you'll need.

Unknown Quantity:
Your Variable:
Algebraic Expression/Equation:

Scenario 5: Baking Cookies

You are baking cookies. The recipe calls for 2 cups of flour for each batch. You want to make several batches, but you haven't decided how many yet.

Unknown Quantity:
Your Variable:
Algebraic Expression/Equation:

Challenge Scenario: Your Own Unknown!

Think of a situation in your own life where there's an unknown quantity. Describe the scenario, identify the unknown, choose a variable, and write an expression or equation.

Your Scenario Description:
Unknown Quantity:
Your Variable:
Algebraic Expression/Equation:

Answer Key

Translate the Scenario: Answer Key

This answer key provides possible solutions and reasoning for the "Translate the Scenario" activity. Students may use different variables, which is acceptable as long as they are consistently applied.