Lesson 37 covers:

• Elementary Level: Subtraction (Up to 30)
• Mid Level: Equivalent Fractions
• High Level: Algebraic Expressions

Elementary Level (Kinder to Grade 2)

Subject: Subtraction (Up to 30)

Alignment with Standards:

• 1.OA.A.1 – Use subtraction within 20 to solve word problems.
• 1.OA.C.6 – Add and subtract within 20, demonstrating fluency for subtraction within 10.
• 1.NBT.C.6 – Subtract multiples of 10 in the range 10-30.

Lesson Objectives

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

1. Subtract numbers up to 30 using manipulatives, drawings, and number lines.
2. Solve simple word problems involving subtraction (e.g., “There are 15 apples, and 6 are eaten. How many are left?”).
3. Recognize subtraction as “taking away” and relate it to real-life scenarios.

Materials Needed

✔ Counters (e.g., buttons, beans, small toys)
✔ Number line (0-30)
✔ Whiteboard & markers
✔ Subtraction flashcards (up to 30)
✔ Printed worksheets (with visuals & word problems)
✔ Ten frames (for visual grouping)

Lesson Activities

1. Warm-Up (10 minutes)

Objective: Review basic subtraction concepts within 10.

• Oral Practice:
  • “If I have 8 candies and I eat 3, how many are left?” (Use fingers or counters.)
  • Quick flashcard drills (e.g., 7 – 2 = ?, 10 – 4 = ?).
• Number Line Practice:
  • Demonstrate 12 – 5 using a number line (start at 12, jump back 5).

2. Direct Instruction (15 minutes)

Objective: Introduce subtraction up to 30 with manipulatives.

• Demonstration with Counters:
  • “Let’s subtract 14 – 6. Count out 14 counters, then take away 6. How many remain?”
• Ten Frames Method:
  • Show subtraction using ten frames (e.g., 18 – 5: Cross out 5 dots).
• Word Problem:
  • “There are 25 birds on a tree. 7 fly away. How many are left?” (Solve together.)

3. Guided Practice (15 minutes)

Objective: Reinforce learning with hands-on activities.

• Worksheet Activity:
  • Simple subtraction problems (e.g., 20 – 8, 25 – 12) with pictures.
• Interactive Game:
  • “Subtraction Bowling” (Set up 10 cups, knock some down, write the equation).

4. Independent Practice (10 minutes)

Objective: Assess understanding with independent work.

• Flashcard Challenge:
  • Time the student to solve 5 subtraction problems (e.g., 22 – 9, 30 – 15).
• Drawing Subtraction:
  • “Draw 17 stars, cross out 9. Write the equation.”

5. Wrap-Up & Review (5 minutes)

• Exit Question:
  • “If you have 28 stickers and give 13 to a friend, how many do you keep?”
• Real-Life Connection:
  • Discuss when we use subtraction (e.g., sharing toys, saving money).

Assessment & Follow-Up

• Observation: Check if the student uses strategies (counters, number line) correctly.
• Worksheet Review: Provide feedback on errors.
• Next Lesson Preview: Introduce subtraction with regrouping (if ready).

Mid Level (Grade 3 to 5)

Subject: Equivalent Fractions

Alignment with Standards:

• 4.NF.A.1 – Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) using visual models and reasoning.
• 4.NF.A.2 – Compare fractions using benchmarks and equivalence.

Lesson Objectives

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

1. Define equivalent fractions as fractions that represent the same value despite having different numerators and denominators.
2. Generate equivalent fractions using multiplication and division.
3. Identify equivalent fractions using visual models (fraction strips, number lines).
4. Apply the concept to compare fractions (e.g., 1/2 = 2/4 = 4/8).

Materials Needed

✔ Fraction strips or circles (printed or physical manipulatives)
✔ Whiteboard & markers
✔ Grid paper (for shading fractions)
✔ Index cards (for matching games)
✔ Digital tool (optional: interactive fraction apps like Fractions by Brainingcamp)
✔ Worksheet with practice problems

Lesson Activities

1. Warm-Up (10 minutes)

Objective: Activate prior knowledge of fractions.

• Quick Review:
  • “What is a fraction? Can you name the parts?” (Numerator = top, denominator = bottom).
  • Show a visual (e.g., a circle cut into halves and fourths) and ask: Are 1/2 and 2/4 the same amount?
• Real-World Connection:
  • “If you eat 2 slices of a pizza cut into 8 slices, is that the same as 1 slice from a pizza cut into 4 slices?”

2. Direct Instruction (20 minutes)

Objective: Teach how to generate and identify equivalent fractions.

• Visual Models:
  • Use fraction strips to show 1/2 = 2/4 = 3/6. Fold paper strips to demonstrate scaling.
  • Shade grid paper to prove 3/4 = 6/8 (see Image Prompt below).
• Mathematical Rule:
  • “Multiply or divide the numerator and denominator by the same number to find equivalent fractions.”
  • Example: 1/3 × 2/2 = 2/6

3. Guided Practice (15 minutes)

Objective: Hands-on exploration of equivalence.

• Matching Game:
  • Lay out index cards with fractions (e.g., 1/2, 2/4, 3/6). Have the student group equivalents.
• Number Line Activity:
  • Plot 1/2, 2/4, and 4/8 on the same number line to show they align.

4. Independent Practice (10 minutes)

Objective: Reinforce learning with problem-solving.

• Worksheet Problems:
  • Fill-in-the-blank: 2/3 = __/6 = __/9.
  • Circle equivalent fractions: Which of these match 3/5? (6/10, 9/15, 4/8).
• Word Problem:
  • “A recipe uses 2/3 cup of flour. If you double the recipe, what’s an equivalent fraction?”

5. Wrap-Up & Reflection (5 minutes)

• Exit Ticket:
  • Write two fractions equivalent to 4/5.
• Real-Life Application:
  • “Why might equivalent fractions be useful when cooking or measuring?”

Assessment & Differentiation

• Formative: Observe during matching game and worksheet.
• Accommodations:
  • Visual Learners: Use more manipulatives.
  • Advanced Learners: Introduce simplifying fractions (e.g., 6/8 = 3/4).

Extension Activity

• Fraction War Card Game: Modify the classic “War” game by comparing fractions (e.g., 1/2 vs. 3/6—declare a “war” if equivalent!).

High Level (Grade 6 to 8)

Subject: Algebraic Expressions

Alignment with Standards:

• 7.EE.A.1 – Apply properties of operations to simplify linear algebraic expressions.
• 7.EE.A.2 – Rewrite expressions in different forms to solve problems.
• 7.EE.B.4 – Use variables to represent quantities in real-world problems.

Lesson Objectives

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

1. Define variables and construct algebraic expressions from word problems.
2. Apply the distributive property and combine like terms to simplify expressions.
3. Evaluate expressions for given values of variables.
4. Connect algebra to real-world scenarios (e.g., calculating costs, distances).

Materials Needed

✔ Whiteboard & markers
✔ Algebra tiles (or printed cutouts)
✔ Index cards with word problems
✔ Worksheets with practice problems
✔ Digital tool (optional: Desmos or Khan Academy Algebra Intro)

Lesson Activities

1. Warm-Up (10 minutes)

Objective: Review pre-algebra concepts.

• Oral Drill:
  • “If a pizza costs $12 and you buy n pizzas, how much do you spend?” (Answer: 12n)
  • “What is the difference between an expression and an equation?” (Expression has no equals sign.)
• Quick Challenge:
  • Simplify: 3 + 2x + 5 – x (Answer: x + 8).

2. Direct Instruction (20 minutes)

Objective: Teach how to write and simplify expressions.

• Variables in Real Life:
  • Example: “A plumber charges $50 for a visit plus $25/hour. Write an expression for h hours.” (50 + 25h)
• Algebra Tiles Demo:
  • Use tiles to show 3x + 2 + x – 4 → Combine like terms to get 4x – 2.
• Distributive Property:
  • Example: Simplify 2(x + 4) → 2x + 8.

3. Guided Practice (20 minutes)

Objective: Hands-on application.

• Word Problem Cards:
  • Draw a card (e.g., “A gym membership costs $30/month plus a $10 sign-up fee. Write an expression.”).
  • Solve in pairs and simplify (e.g., 10 + 30m).
• Error Analysis:
  • “Spot the mistake: 5 + 3(x – 2) = 8x – 10.” (Correct: 3x – 1.)

4. Independent Practice (15 minutes)

Objective: Reinforce skills.

• Tiered Worksheet:
  • Level 1: Write expressions (e.g., “7 less than twice a number” → 2n – 7).
  • Level 2: Simplify 4(2y + 3) – y (Answer: 7y + 12).
• Real-World Task:
  • “You buy x $5 books and a $20 backpack. Write and simplify an expression.” (5x + 20).

5. Wrap-Up (10 minutes)

• Exit Ticket:
  • Simplify 6k + 3 – 2k + 10 and write an expression for: “A rectangle has length L and width 5. Find the perimeter.” (4k + 13; 2L + 10).
• Reflection Question:
  • “Why might simplifying expressions be useful in budgeting?”

Assessment & Differentiation

• Formative: Monitor during guided practice; check worksheet steps.
• Accommodations:
  • Struggling Learners: Use color-coding for like terms (e.g., highlight all x terms in blue).
  • Advanced Learners: Introduce substitution (e.g., “If x = 3, evaluate 2x + 5”).

Extension Activity

• Algebraic Expressions Scavenger Hunt:
  • Hide word problems around the house. Solve and simplify to unlock a “code” (e.g., 3x + 2x = 15 → x = 3).