Lesson 49 covers:

• Elementary Level: Missing Addend
• Mid Level: Multiplying Fractions by Whole Numbers
• High Level: Writing and Solving Equations from Word Problems

Elementary Level (Kinder to Grade 2)

Subject: Missing Addend (3 + __ = 7)

1. Alignment with Standards:

• 1.OA.D.8 – Determine the unknown whole number in an addition or subtraction equation relating three whole numbers (e.g., 3 + __ = 7).
• 1.OA.A.1 – Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing.

2. Learning Objectives:

By the end of the lesson, students will be able to:

• Understand that an equation must balance (both sides are equal).
• Find the missing addend in equations like 3 + __ = 7 using counting strategies, manipulatives, or subtraction.
• Explain their reasoning using words or drawings.

3. Materials Needed:

• Counters (e.g., buttons, blocks, or bear counters)
• Number line (0-10)
• Whiteboard & markers
• Worksheet with missing addend problems

Lesson Procedure

1. Warm-Up (5-10 minutes)

• Review Addition Facts:
  • Ask: *”What is 3 + 4?”* *”What is 2 + 5?”* (Use fingers or counters if needed.)
• Introduce the Concept of Equality:
  • Draw a simple balance scale on the board: 3 + 4 = 7.
  • Explain: *”Both sides must be the same. If 3 + something equals 7, how do we find the missing number?”*

2. Direct Instruction (10-15 minutes)

• Model with Counters:
  • Give the student 7 counters. Say: “If one part is 3, how many more make 7?”
  • Separate into two groups: 3 and 4. Write: 3 + 4 = 7.
• Use a Number Line:
  • Start at 3, jump forward until reaching 7. Count the jumps (4).
  • Write: 3 + __ = 7 → The missing number is 4.
• Introduce Subtraction Strategy:
  • Explain: *”If 3 + ? = 7, we can also do 7 – 3 = ?”*

3. Guided Practice (10-15 minutes)

• Hands-On Activity:
  • Give equations like 5 + __ = 8 and have the student use counters to solve.
  • Ask: “How did you find the missing number?”
• Number Line Practice:
  • Have the student solve 2 + __ = 6 using jumps on a number line.

4. Independent Practice (10 minutes)

• Worksheet with Missing Addends:
  • Include problems like:
    • 4 + __ = 9
    • __ + 2 = 5
    • 6 + __ = 10
• Word Problem (Optional):
  • “Jake has 5 marbles. He gets some more and now has 8. How many did he get?”

5. Wrap-Up & Assessment (5 minutes)

• Exit Ticket:
  • Ask: *”Solve 7 + __ = 10. Show your work with counters or a number line.”*
• Discussion:
  • “What strategies helped you find the missing number?”

Differentiation & Extensions:

• Support: Use smaller numbers (e.g., 2 + __ = 5) and physical counters.
• Challenge: Introduce word problems or larger numbers (up to 20).
• Game Idea: “Mystery Number” – One student thinks of a missing addend, and the other guesses.

Mid Level (Grade 3 to 5)

Subject: Multiplying Fractions by Whole Numbers

1. Alignment with Standards:

• 4.NF.B.4 – Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
  • 4.NF.B.4a – Understand a fraction *a/b* as a multiple of *1/b* (e.g., 5 × (1/4) = 5/4).
  • 4.NF.B.4b – Multiply a whole number by a fraction, interpreting the product as repeated addition.
  • 4.NF.B.4c – Solve word problems involving multiplication of fractions by whole numbers.

2. Learning Objectives:

By the end of the lesson, students will be able to:

• Represent multiplication of a whole number and a fraction using models (area models, number lines).
• Convert repeated addition of fractions into multiplication (e.g., 1/4 + 1/4 + 1/4 = 3 × 1/4).
• Solve real-world problems involving multiplying fractions by whole numbers.

3. Materials Needed:

• Fraction bars or circles (printable/manipulatives)
• Graph paper or drawing paper
• Whiteboard & markers
• Worksheet with practice problems

Lesson Procedure

1. Warm-Up (5-10 minutes)

• Review Prior Knowledge:
  • Ask: “What is 3 × 5?” (Repeated addition: 5 + 5 + 5).
  • Extend to fractions: *”What is 1/4 + 1/4 + 1/4?”* (Introduce as 3 × 1/4).
• Relate to Real-Life:
  • Show the pizza image prompt: “If one slice is ¼, how much is 3 slices?”

2. Direct Instruction (15-20 minutes)

A. Modeling with Fraction Bars/Circles

• Demonstrate 3 × 1/4:
  • Lay out three ¼ pieces. Show that together, they make ¾.
  • Write: 3 × 1/4 = 3/4.
• Area Model Example (Graph Paper):
  • Draw a rectangle divided into 4 equal parts. Shade 3 parts to show 3 × 1/4 = 3/4.

B. Number Line Approach

• Draw a number line from 0 to 1, divided into fourths.
• Jump ¼ three times: 1/4 → 2/4 → 3/4.
• Conclusion: 3 × 1/4 = 3/4.

C. Algorithm Introduction

• Explain: “Multiply numerator by whole number; denominator stays the same.”
  • Example: 2 × 3/5 = (2×3)/5 = 6/5 = 1 1/5.

3. Guided Practice (15 minutes)

• Hands-On Activity:
  • Give problems like 4 × 1/3 and have students model with fraction circles.
  • Ask: “How is this like repeated addition?”
• Word Problem:
  • *”A recipe needs 2/3 cup of sugar. If you triple the recipe, how much sugar is needed?”*

4. Independent Practice (15 minutes)

• Worksheet Problems:
  • Visual Models: Shade 5 × 1/6 in an area model.
  • Computation: Solve 7 × 2/3.
  • Word Problems: *”A runner runs 3/4 mile each day. How far in 5 days?”*

5. Wrap-Up & Assessment (10 minutes)

• Exit Ticket:
  • Solve: 5 × 3/8 (using any method).
• Discussion:
  • “Which strategy (models, number line, or algorithm) do you prefer? Why?”

Differentiation & Extensions:

• Support: Use smaller denominators (e.g., halves, fourths) and physical manipulatives.
• Challenge: Introduce mixed numbers (e.g., 2 × 1 1/2) or larger denominators.
• Real-World Connection: Adjust a recipe by doubling or tripling ingredient amounts.

Assessment Ideas:

• Oral Explanation: Have the student explain how they solved 4 × 2/5 using a model.
• Error Analysis: Provide a mistake (e.g., 3 × 1/2 = 1/6) and ask the student to correct it.

High Level (Grade 6 to 8)

Subject: Writing and Solving Equations from Word Problems

1. Alignment with Standards:

• 7.EE.B.4 – Use variables to represent quantities in real-world problems, and construct simple equations to solve problems.
• 7.EE.B.4a – Solve word problems leading to equations of the form px + q = r or p(x + q) = r, where *p*, *q*, and *r* are rational numbers.

2. Learning Objectives:

By the end of the lesson, students will be able to:

1. Identify key information in word problems to define variables.
2. Write equations in the form px + q = r or p(x + q) = r.
3. Solve equations using inverse operations and justify solutions in context.

3. Materials Needed:

• Whiteboard & markers
• Highlighters (for annotating word problems)
• Printed word problem worksheets
• Algebra tiles or digital equation tools (optional)

Lesson Procedure

1. Warm-Up (10 minutes)

Review Equation Basics:

• Solve simple equations:
  • *2x = 10* (→ *x = 5*)
  • *y − 7 = 3* (→ *y = 10*)
• Discuss: “How do inverse operations help us solve equations?”

Real-World Hook:

• Present a quick problem: “Lena has twice as many pencils as Marco. Together they have 18 pencils. How many does each have?”
• Guide students to see that *x + 2x = 18* leads to *x = 6*.

2. Direct Instruction (20 minutes)

Step 1: Translating Word Problems

• Teach the “Do-What” Strategy:
  • Do: Underline numbers/key phrases (e.g., “twice as many,” “total of”).
  • What: Identify the unknown (e.g., “Let *x* = Marco’s pencils”).
• Example Problem:

*”A gym charges $10/month plus $25 sign-up fee. If a member pays $85 total, how many months did they join for?”*

• • Equation: *10x + 25 = 85*

Step 2: Solving Equations

• Model solving *10x + 25 = 85*:
  1. Subtract 25: *10x = 60*
  2. Divide by 10: *x = 6*
• Emphasize checking the solution: *10(6) + 25 = 85 ✔*

Step 3: Equations with Parentheses

• Example: “5 times the sum of a number and 4 is 35.”
  • Equation: *5(x + 4) = 35* → Solve using distributive property or divide first.

3. Guided Practice (20 minutes)

Activity 1: Equation Matching

• Give students cards with word problems and equations. Match them (e.g., “A number tripled minus 5 is 13” → *3x − 5 = 13*).

Activity 2: Collaborative Problem-Solving

• Solve in pairs:

*”Rent-a-Car charges $50/day plus $0.20/mile. If a customer’s bill is $90 for 1 day, how many miles did they drive?”*

• • Equation: *50 + 0.20x = 90* → *x = 200 miles*

4. Independent Practice (20 minutes)

Worksheet Problems (Tiered Difficulty):

1. Basic: “Four more than twice a number is 22. Find the number.” (*2x + 4 = 22*)
2. Intermediate: “You buy 6 identical shirts for x each and spend x each and spend 30 total. Write and solve an equation.” (*6x = 30*)
3. Advanced: *”A phone plan costs $15/month plus $0.10/text. Your bill is $25. How many texts did you send?”* (*15 + 0.10x = 25*)

5. Wrap-Up & Assessment (10 minutes)

Exit Ticket:

• Solve: *”A landscaper charges $60 plus $25/hour. For a $135 job, how many hours did she work?”* (*60 + 25x = 135 → x = 3*)

Class Discussion:

• “What keywords helped you identify the operation (e.g., ‘per,’ ‘total’)?
• “Why is it important to check your solution in the original problem?”

Differentiation & Extensions

• Support: Use smaller numbers or diagrams (e.g., bar models).
• Challenge: Include multi-step problems (e.g., discounts, taxes).
• Real-World Project: Research a service (e.g., Uber, Netflix) and write/solve equations for their pricing.

Assessment Ideas:

1. Error Analysis: Provide an incorrect solution (e.g., *3x + 5 = 20 → x = 3*). Ask students to find and fix the mistake.
2. Create-a-Problem: Students write their own word problem and trade with a partner to solve.