Fractions & Percentages

Learning Objectives:

• Understand how to apply fractions and percentages to solve real-world problems.
• Enhance critical thinking and problem-solving skills.
• Strengthen fluency in converting between fractions, decimals, and percentages.

Curriculum Area:

Common Core State Standards (Grade 8):

• CCSS.MATH.CONTENT.7.RP.A.3: Use proportional relationships to solve multistep ratio and percent problems. Extend this standard to Grade 8 to include real-world connections.
• CCSS.MATH.CONTENT.7.NS.A.1.D: Apply and extend previous understandings of operations with fractions to situations involving real-life contexts.

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Materials Needed:

• Whiteboard/marker
• Calculator (optional)
• Worksheet with real-life fraction and percentage problems
• Grocery store circulars (printed or brought in by teacher)

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Lesson Outline:

1. Warm-Up Activity (5 minutes)

Objective: Reinforce prior knowledge and introduce the concept.

• Pose this relatable problem on the board:
  "You’re baking cookies. The recipe calls for ¾ cup of sugar, but you want to half the recipe. How much sugar will you need?"
  (Guide the student to divide ¾ by 2. Solution: ⅜ cups of sugar.)
• Follow up with a question about percentages:
  "You’re shopping, and a jacket that costs $80 is 25% off. How much will you save?"
  (Guide them to calculate 25% of $80 = $20 saved.)

Transition:

Explain how fractions and percentages are useful tools in daily life, from cooking to shopping to budgeting.

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2. Core Lesson: Real-World Applications (20 minutes)

Activity 1: Fractions in Grocery Shopping (10 minutes)

1. Hand the student a grocery store circular (or write an example if using the whiteboard).
   Example:
   • "Oranges cost $3.99 for 6 lbs. But you only want 2 lbs. How much should you pay?"
2. Walk them through the math:
   • Step 1: Find the cost per pound (divide by 6).
   • Step 2: Multiply by 2 to find the final cost.
3. Expand with additional scenarios, e.g., splitting a large pack of items or calculating tax using fractional amounts.

Activity 2: Discounts and Sales Tax (10 minutes)

1. Set up this scenario:
   "A video game costs $60, but it’s on sale for 20% off. Sales tax in your area is 8%. What will the final price be after the discount and tax?"
   • Step 1: Find the discount amount (20% of $60 = $12).
   • Step 2: Subtract the discount from the original price ($60 - $12 = $48).
   • Step 3: Calculate sales tax on the discounted price (8% of $48 = $3.84).
   • Step 4: Add tax back to the discounted price ($48 + $3.84 = $51.84).
     Solution: Final price = $51.84.
2. Have the student solve a similar problem, changing values and percentages. Give the student just enough support as needed to promote independent thinking.

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3. Guided Practice: DIY Problem Solving (10 minutes)

Activity: Designing Real-Life Scenarios

Have the student create their own real-world fraction or percentage problem.

• For example, they might think of:
  • "How many slices of pizza are left if you ate ⅓ of a pizza with 12 slices?"
  • "If the school bookstore has a 15% discount during a sale, how much will you pay for a $25 backpack?"
• Encourage imagination while keeping scenarios practical.
• Swap roles where the teacher solves the problem they’ve created. This helps them think critically while seeing the utility of math.

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4. Wrap-Up and Reflection (5 minutes)

Quick Discussion:

• Ask open-ended questions:
  • Where else do you think fractions or percentages are necessary in real life? (e.g., splitting a bill at a restaurant, calculating tips, budgeting for monthly expenses, tracking grades.)
  • What was challenging about today’s lesson, and what felt easy?

Exit Ticket Question:
Leave them with one last problem to solve independently:

• "You want to tip your hairstylist 18% on a $45 haircut. How much is the tip?"

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Homework (Optional/Challenge):

Ask the student to involve a parent, guardian, or sibling in solving three real-life fraction or percentage problems around the house. For example:

• Split a recipe into smaller portions.
• Calculate a tip for a meal.
• Figure out the savings on an item from a receipt if it was discounted by a certain percentage.

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Teacher’s Note:

This lesson centers on bridging classroom learning with everyday life. It's designed to make math feel approachable by tying it to familiar, practical experiences students encounter regularly. Encourage the student to identify where fractions and percentages pop up outside math class throughout the week!