Lesson 34 covers:

• Elementary Level: Addition (Sums up to 30)
• Mid Level: Understand Fractions
• High Level: Word Problems with Rational Numbers and Ratios

Elementary Level (Kinder to Grade 2)

Subject: Addition (Sums up to 30)

Alignment with Standards:

• CCSS.MATH.CONTENT.1.OA.A.1 – Use addition within 20 to solve word problems.
• CCSS.MATH.CONTENT.1.OA.C.5 – Relate counting to addition.
• CCSS.MATH.CONTENT.1.OA.C.6 – Add within 20, demonstrating fluency for sums within 10.
• CCSS.MATH.CONTENT.1.NBT.C.4 – Add within 100, including a two-digit number and a one-digit number.

Lesson Objectives:

By the end of this lesson, the student will be able to:

1. Solve addition problems with sums up to 30 using manipulatives and visual aids.
2. Count on from a given number to find the sum.
3. Write and solve simple addition equations (e.g., 12 + 5 = 17).
4. Apply addition skills to solve a word problem.

Materials Needed:

• Counting manipulatives (counters, blocks, buttons, or small toys)
• Number line (0-30)
• Whiteboard & markers
• Printed worksheets (simple addition problems up to 30)
• Flashcards (optional for reinforcement)
• Image Prompt (Visual Aid): A picture of a fruit basket with apples and oranges (e.g., 10 apples + 8 oranges = ?)

Lesson Procedure:

1. Warm-Up (5-10 minutes)

• Counting Practice: Count aloud from 1 to 30 together.
• Quick Review: Solve a few simple addition problems (sums up to 10) using fingers or counters.
  • Example: “If I have 3 blocks and add 4 more, how many do I have?”

2. Introduction to Addition up to 30 (15 minutes)

• Demonstrate with Manipulatives:
  • Give the student 15 counters (e.g., buttons).
  • Say: “Let’s add 12 buttons and 5 more. How many do we have now?”
  • Guide them to count all the buttons to find the sum (17).
• Use a Number Line:
  • Show how to “jump” forward to add (e.g., start at 10, jump 6 spaces to land on 16).
• Write Equations:
  • Model writing the problem: 12 + 5 = 17

3. Guided Practice (15 minutes)

• Worksheet Activity: Simple addition problems (e.g., 10 + 6, 14 + 3, 20 + 5).
• Word Problem:
  • “Emma has 15 stickers. She gets 7 more. How many does she have now?”
  • Solve using counters or a number line.

4. Independent Practice (10 minutes)

• Flashcard Game: Draw a flashcard (e.g., 18 + 4) and solve using preferred method.
• Drawing Activity:
  • Ask the student to draw two groups of objects (e.g., 13 stars + 6 moons) and count the total.

5. Wrap-Up & Review (5 minutes)

• Ask: “What did we learn today?”
• Solve one last problem together (e.g., 25 + 3).
• Praise effort and progress!

Assessment & Follow-Up:

• Observe if the student can:
  • Accurately count and add numbers up to 30.
  • Use multiple strategies (manipulatives, number line, mental math).
• Extension Activity (Optional):
  • Play a dice game (roll two dice, add numbers, and say the sum).

Mid Level (Grade 3 to 5)

Subject: Understanding Fractions (Parts of a Whole or Set)

Alignment with Standards:

• CCSS.MATH.CONTENT.4.NF.A.1 – Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b).
• CCSS.MATH.CONTENT.3.NF.A.1 – Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts.
• CCSS.MATH.CONTENT.4.NF.B.3 – Understand a fraction as a sum of unit fractions (e.g., 3/4 = 1/4 + 1/4 + 1/4).

Lesson Objectives:

By the end of this lesson, the student will be able to:

1. Define a fraction as part of a whole or a set.
2. Represent fractions visually using models (circles, rectangles, or objects).
3. Identify numerator and denominator in a fraction.
4. Compare simple fractions using concrete examples.

Materials Needed:

• Fraction circles or strips (printable or physical)
• Paper plates or construction paper (for drawing fractions)
• Colored pencils/markers
• Small objects (counters, beads, or LEGO pieces)
• Whiteboard & markers
• Printed worksheets (fraction shading & matching)
• Image Prompt (Visual Aid): A pizza divided into 8 slices with 3 slices eaten (to represent 3/8).

Lesson Procedure:

1. Warm-Up (10 minutes)

• Real-Life Fractions Discussion:
  • Ask: “Have you ever shared a pizza or a chocolate bar? How did you split it?”
  • Introduce the idea of fractions as equal parts.
• Quick Review of Basic Terms:
  • Draw a simple fraction (e.g., 1/2) and label the numerator (top number) and denominator (bottom number).

2. Introduction to Fractions (15 minutes)

• Hands-On Demonstration:
  • Use a paper plate to draw a circle and divide it into 4 equal parts. Shade 1 part to show 1/4.
  • Repeat with a rectangle divided into 3 parts, shading 2/3.
• Fraction of a Set:
  • Place 12 counters on the table. Ask: “If 3 are red, what fraction is red?” (Answer: 3/12 or simplified to 1/4).

3. Guided Practice (20 minutes)

• Activity 1: Fraction Circles/Strips
  • Have the student shade in fractions like 2/5, 3/6, etc., on printed templates.
• Activity 2: Object Groups
  • Give 10 LEGO pieces and ask: “What fraction is blue if 4 are blue?” (4/10 → simplify to 2/5).
• Worksheet Practice:
  • Match fractions to shaded shapes (e.g., link a picture of a half-shaded square to “1/2”).

4. Interactive Game (10 minutes)

• “Fraction Bingo”
  • Create bingo cards with fractions (e.g., 1/2, 2/3) and call out descriptions (“Shade two parts out of three!”).

5. Wrap-Up & Review (5 minutes)

• Ask: “How would you explain a fraction to a friend?”
• Solve a real-world problem: “If you ate 5 out of 8 cookies, what fraction is left?” (3/8).

Assessment & Follow-Up:

• Observation: Can the student accurately shade and name fractions?
• Exit Ticket: Draw 5/6 of a pie and explain the numerator/denominator.
• Extension Activity:
  • Bake cookies and divide them into fractions to share!

High Level (Grade 6 to 8)

Subject: Word Problems with Rational Numbers & Ratios

Alignment with Standards:

• CCSS.MATH.CONTENT.7.NS.A.3 – Solve real-world problems involving the four operations with rational numbers.
• CCSS.MATH.CONTENT.7.RP.A.3 – Use proportional relationships to solve ratio and percent problems (e.g., discounts, interest, taxes).
• CCSS.MATH.CONTENT.7.EE.B.3 – Solve multi-step real-life problems with positive and negative rational numbers.

Lesson Objectives:

By the end of this lesson, the student will be able to:

1. Identify rational numbers (positive/negative fractions, decimals, integers) in real-world contexts.
2. Apply arithmetic operations (+, −, ×, ÷) to solve word problems involving rational numbers.
3. Use ratios to solve problems involving proportions, unit rates, and percentages.
4. Justify solutions by explaining steps clearly.

Materials Needed:

• Whiteboard & markers
• Printed worksheets (real-world word problems)
• Calculator (for checking work)
• Play money (for financial scenarios)
• Grocery store ads (for price comparisons)
• Image Prompt: A receipt with discounts/taxes (to calculate final price)

Lesson Procedure:

1. Warm-Up (10 minutes)

Review Rational Numbers & Ratios:

• Quick examples:
  • “If the temperature drops from 5°C to -3°C, what’s the change?” (Answer: −8°C)
  • “A recipe uses 2 cups flour for 3 cups milk. What’s the ratio?” (Answer: 2:3 or ⅔)

2. Direct Instruction (15 minutes)

Key Concepts:

1. Rational Numbers in Context:
   • Money (profits/losses), temperatures, elevations, measurements.
2. Ratio/Proportion Strategies:
   • Unit rates (e.g., “$3.50 per pound”), scaling recipes, map scales.
3. Problem-Solving Steps:
   • Read the problem.
   • Understand what’s being asked.
   • Label numbers (positive/negative, units).
   • Execute the math.
   • Sense-check the answer.

3. Guided Practice (20 minutes)

Activity 1: Financial Word Problems

• “You have $50. You spend $50. You spend $12.75 on a book and earn $20 for babysitting. What’s your final balance?”
  • Solution: $50 − $50 − $12.75 + $20 = $7.25

Activity 2: Ratios in Recipes

• “A cookie recipe calls for 1.5 cups sugar for 4 dozen cookies. How much sugar for 2 dozen?”
  • Solution: Half the ratio → 0.75 cups

Activity 3: Temperature Change

• “It’s -4°F at night and rises 15°F by noon. What’s the new temperature?”
  • Solution: −4 + 15 = 11°F

4. Independent Practice (15 minutes)

Worksheet Problems:

1. Discounts/Taxes:“A $80 jacket is 25% off. Sales tax is 7%. What’s the final price?”
   • Solution: $80 × 0.75 = $60; $60 × 1.07 = $64.20
2. Speed/Distance:“A car travels 240 miles in 3.2 hours. What’s the speed in mph?”
   • Solution: 240 ÷ 3.2 = 75 mph

5. Wrap-Up & Reflection (10 minutes)

• Discussion:
  • “Which problem was hardest? How did you solve it?”
• Real-World Task:
  • Use a grocery ad to compare unit prices (e.g., 12 oz for $2.40 vs. 18oz for $2.40 vs. 18oz for $3.60).

Assessment & Follow-Up:

• Exit Ticket: Solve: “A 20% tip on a $45 meal is ____. Total cost = ____.”
• Project Extension: Track a week’s weather changes using negative numbers.

Differentiation Tips:

• For Struggling Learners: Use smaller numbers or highlight key words (e.g., “total,” “per”).
• For Advanced Learners: Introduce multi-step problems with mixed operations.