Elementary Level: Simple Subtraction (Up to 20)
Mid Level: Factors and Multiples
High Level: Percentages (Conversions and Applications)

Elementary Level (Kinder to Grade 2)

Subject: Simple Subtraction (Up to 20)

Alignment with Standards:

• Common Core State Standards (CCSS):
  • CCSS.MATH.CONTENT.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, with unknowns in all positions.
  • CCSS.MATH.CONTENT.1.OA.C.5: Relate counting to addition and subtraction (e.g., by counting back to subtract).
  • CCSS.MATH.CONTENT.1.OA.D.8: Determine the unknown whole number in an addition or subtraction equation relating three whole numbers (e.g., 6 – 4 = __).

Objectives

1. Understand subtraction as “taking away” or “removing” from a group.
2. Solve subtraction problems with numbers up to 20 using objects and stories.
3. Recognize and use the subtraction symbol (-) and complete simple equations.
4. Build confidence in counting back to find differences.

Materials

• Small objects for counting (e.g., 20 buttons, blocks, or cereal pieces)
• Paper cups or small containers (to hold objects)
• Number line (drawn or printed, 0-20)
• Blank paper or a whiteboard for writing equations
• Crayons, markers, or pencils
• Story props (e.g., toy animals, fruit pictures, or drawings)
• Worksheet with simple equations (e.g., 6 – 4 = __, 10 – 3 = __)

Activities

Day 1: Introduction to Subtraction with Objects (30-45 minutes)

1. Warm-Up (5-10 minutes):
   • Ask: “If you have 5 cookies and eat 2, how many are left?” Count together with fingers.
   • Say: “Today, we’re learning subtraction—it’s like taking things away!”
2. Direct Instruction (10 minutes):
   • Show 8 blocks. “I have 8 blocks. If I take away 3, how many are left?” Remove 3 blocks, count the rest (5).
   • Introduce the symbol: “We write it like this: 8 – 3 = 5.”
   • Repeat with another example (e.g., 10 – 4 = 6).
3. Hands-On Activity: Removing Objects (15-20 minutes):
   • Give the child 12 objects (e.g., buttons). Say: “Take away 5. How many are left?”
   • Count together, then write it: 12 – 5 = 7.
   • Try 2-3 more (e.g., 9 – 2, 15 – 6). Use a cup to “hide” the taken-away objects for fun.
4. Wrap-Up (5 minutes):
   • Ask: “What did we do to subtract? How did you know how many were left?”

Day 2: Subtraction Stories (45 minutes)

1. Review (10 minutes):
   • Recap: “Yesterday, we took things away. Show me 7 – 3 with your fingers or blocks.”
2. Hands-On Activity: Story Time (25 minutes):
   • Tell a subtraction story: “Five birds sat on a tree. Two flew away. How many stayed?”
   • Use props (e.g., 5 toy birds or drawings). Remove 2, count what’s left (3), write: 5 – 2 = 3.
   • Let the child make their own story: “Ten apples are in a basket. You eat some. How many are left?” Help them act it out with objects and write it (e.g., 10 – 4 = 6).
   • Use a number line: Start at 10, count back 4 steps to land on 6.
3. Wrap-Up (10 minutes):
   • Ask: “What was your favorite story? How did it help you subtract?”

Day 3: Practice and Assessment (45 minutes)

1. Warm-Up (10 minutes):
   • Play a quick game: “I have 8 toys. I give away 3. You tell me how many are left!” (Answer: 5)
2. Practice Activity (20 minutes):
   • Mix objects and stories: “Start with 15 blocks. Take away 7.” Write it (15 – 7 = 8).
   • Try a story: “Nine fish swim in a pond. Four swim away.” Use the number line or objects to solve (9 – 4 = 5).
3. Assessment (15 minutes):
   • Give a simple worksheet or write equations:
     • 6 – 4 = __ (2)
     • 10 – 3 = __ (7)
     • 8 – 5 = __ (3)
     • 12 – 6 = __ (6)
   • Let them use objects or the number line if needed. Check answers together.
4. Wrap-Up (5 minutes):
   • Celebrate: “You’re a subtraction star! What was the trickiest part?”

Assessment

• Informal Observation: Watch how they remove objects and count back during activities.
• Story Retelling: Check if they connect the story to the correct subtraction problem.
• Worksheet/Equations: Ensure they solve equations like 6 – 4 = 2 accurately, with or without tools.

Extensions

• Play “Subtraction Bingo” with numbers 0-20 and call out problems (e.g., 10 – 6).
• Use a favorite book with numbers (e.g., Ten Apples Up on Top! by Dr. Seuss) to make subtraction stories.
• Try subtracting backward: “I have 7 left after taking some from 10. How many did I take?” (10 – 7 = 3)

Mid Level (Grade 3 to 5)

Subject: Factors and Multiples

Alignment with Standards:

• Common Core State Standards (CCSS):
  • CCSS.MATH.CONTENT.4.OA.A.3: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted.
  • CCSS.MATH.CONTENT.5.OA.A.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols (Note: Grade 4 introduces foundational skills leading to this).
  • CCSS.MATH.CONTENT.4.NBT.B.4: Fluently add and subtract multi-digit whole numbers using the standard algorithm (as a prerequisite skill).

Objectives

1. Understand the order of operations using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
2. Solve multi-step equations accurately by following the PEMDAS sequence.
3. Apply order of operations through games and step-by-step practice.
4. Build problem-solving skills and confidence in handling numerical expressions.

Materials

• Whiteboard or paper for writing equations
• Markers, pencils, or pens
• Index cards or slips of paper for game equations
• Dice (2-3) for generating numbers in games
• PEMDAS reference chart (hand-drawn or printed, see image suggestion)
• Worksheet with PEMDAS problems (sample provided below)
• Optional: Calculator (for checking answers only after solving)

Activities

Day 1: Introduction to PEMDAS (45 minutes)

1. Warm-Up (10 minutes):
   • Ask: “What’s 3 + 4 × 2? Is it 14 or 11?” (Solve both ways to show why order matters: 3 + 8 = 11, not 7 × 2 = 14.)
   • Say: “Today, we’re learning a secret code to solve math problems right every time!”
2. Direct Instruction (15 minutes):
   • Introduce PEMDAS with a chant: “Please Excuse My Dear Aunt Sally!”
     • P: Parentheses first
     • E: Exponents (skip for Grade 4 or mention as “power” for later)
     • MD: Multiplication and Division (left to right)
     • AS: Addition and Subtraction (left to right)
   • Solve together: “6 + 3 × 2 = ?” (3 × 2 = 6, then 6 + 6 = 12, not 9 + 2 = 11.)
   • Try with parentheses: “(6 + 3) × 2 = ?” (9 × 2 = 18.)
3. Practice (15 minutes):
   • Write 3 simple equations (e.g., 5 + 4 × 3, 10 – 2 + 4, 8 × 2 – 5). Solve step-by-step together.
4. Wrap-Up (5 minutes):
   • Ask: “Why do we need PEMDAS? What happens if we don’t use it?”

Day 2: Equation Games (45 minutes)

1. Review (10 minutes):
   • Recap: “What does PEMDAS stand for? Solve this quick: 4 + 5 × 2.” (Answer: 14)
2. Hands-On Activity: PEMDAS Dice Game (25 minutes):
   • Roll 3 dice to get numbers (e.g., 3, 4, 6).
   • Write an equation using all three, plus operations and parentheses (e.g., (3 + 4) × 6).
   • Solve it together: (3 + 4) = 7, 7 × 6 = 42.
   • Take turns making 3-5 equations. For fun, award a point for each correct answer!
   • Variation: Use index cards with pre-written equations (e.g., 10 – 3 × 2, 8 + 4 ÷ 2) and race to solve.
3. Wrap-Up (10 minutes):
   • Discuss: “Which equation was trickiest? How did PEMDAS help?”

Day 3: Step-by-Step Solving and Assessment (45 minutes)

1. Warm-Up (10 minutes):
   • Solve a fun problem: “You have 12 candies. Eat 3, then split the rest in half. How many left?” (12 – 3 = 9, 9 ÷ 2 = 4.5, round to 4.)
2. Practice Activity: Step-by-Step Solving (15 minutes):
   • Solve 3 equations aloud, showing steps:
     • 7 + 2 × 4 = ? (2 × 4 = 8, 7 + 8 = 15)
     • (10 – 5) + 3 = ? (10 – 5 = 5, 5 + 3 = 8)
     • 12 ÷ 3 + 6 = ? (12 ÷ 3 = 4, 4 + 6 = 10)
   • Encourage them to explain each step.
3. Assessment: PEMDAS Worksheet (15 minutes):
   • Provide a worksheet with 5-7 problems:
     • 5 + 3 × 2 = __ (11)
     • 10 – 4 + 6 = __ (12)
     • (8 + 2) × 3 = __ (30)
     • 12 ÷ 4 + 5 = __ (8)
     • 9 – 2 × 3 = __ (3)
   • Solve independently, then check together.
4. Wrap-Up (5 minutes):
   • Celebrate: “You cracked the PEMDAS code! What was your favorite part?”

Assessment

• Informal Observation: Note their understanding of order during games and practice.
• Game Accuracy: Check if they apply PEMDAS correctly in dice equations.
• Worksheet: Ensure they solve at least 80% of problems correctly (e.g., 4/5 or 6/7), showing steps.

Extensions

• Add a challenge: “Write your own PEMDAS problem for me to solve!”
• Explore real-life scenarios (e.g., “Buy 2 apples at $3 each, add $4 tax, subtract $2 coupon”).
• Play an online PEMDAS game (e.g., Math Playground’s “Order of Operations”).

High Level (Grade 6 to 8)

Subject: Percentages (Conversions and Applications)

Alignment with Standards:

• Common Core State Standards (CCSS):
  • CCSS.MATH.CONTENT.7.RP.A.3: Use proportional relationships to solve multistep ratio and percent problems (e.g., simple interest, tax, markups and markdowns, gratuities, and commissions).
  • CCSS.MATH.CONTENT.6.RP.A.3.C: Find a percent of a quantity as a rate per 100; solve problems involving finding the whole, given a part and the percent (Note: Grade 7 builds on this).
  • CCSS.MATH.CONTENT.7.NS.A.2.D: Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates or eventually repeats.

Objectives

1. Understand percentages as parts of 100 and convert between fractions, decimals, and percentages.
2. Apply percentage skills to real-world scenarios like discounts, taxes, and tips.
3. Solve multi-step problems involving percentages with confidence.
4. Develop number sense and practical math application skills.

Materials

• Notebook or paper for calculations
• Pencil, pen, or calculator (for checking, not solving initially)
• Fraction-decimal-percent conversion chart (hand-drawn or printed)
• Play money or fake receipts (optional for realism)
• Index cards or slips for practice problems
• Worksheet with conversion and application problems (sample below)
• Optional: Ads or menus (online or paper) for discount/tip practice

Activities

Day 1: Converting Between Fractions, Decimals, and Percentages (45 minutes)

1. Warm-Up (10 minutes):
   • Ask: “If you ate half a pizza, what percent is that?” (Hint: Half is 50%.)
   • Say: “Today, we’re learning how percentages connect to fractions and decimals!”
2. Direct Instruction (15 minutes):
   • Explain: “Percent means ‘per 100.’ 50% is 50 out of 100, or 50/100.”
   • Show conversions:
     • Fraction to Decimal: 1/4 = 0.25 (divide 1 by 4).
     • Decimal to Percent: 0.25 × 100 = 25%.
     • Percent to Fraction: 75% = 75/100 = 3/4 (simplify).
   • Practice together: Convert 1/2 (0.5, 50%), 0.8 (80%, 4/5), 20% (0.2, 1/5).
3. Practice (15 minutes):
   • Write 5 conversions (e.g., 3/4, 0.6, 15%). Solve step-by-step together.
4. Wrap-Up (5 minutes):
   • Ask: “What’s an easy way to turn a percent into a decimal? Why do we move the decimal point?”

Day 2: Applying Percentages – Discounts, Tax, and Tips (45 minutes)

1. Review (10 minutes):
   • Recap: “Convert 25% to a decimal and fraction.” (0.25, 1/4)
   • Say: “Now, let’s use percentages in real life!”
2. Hands-On Activity: Real-World Calculations (25 minutes):
   • Discounts: “A $20 shirt is 25% off. How much do you save?”
     • 25% = 0.25, 0.25 × 20 = $5 saved. New price: 20 – 5 = $15.
   • Tax: “A $10 toy has 10% tax. How much tax do you pay?”
     • 10% = 0.1, 0.1 × 10 = $1 tax. Total: 10 + 1 = $11.
   • Tip: “Dinner costs $30. You leave a 20% tip. How much is the tip?”
     • 20% = 0.2, 0.2 × 30 = $6 tip. Total: 30 + 6 = $36.
   • Use play money or receipts to act it out.
3. Wrap-Up (10 minutes):
   • Discuss: “Which was easiest—discount, tax, or tip? Why do we use percentages for these?”

Day 3: Practice and Mixed Applications (45 minutes)

1. Warm-Up (10 minutes):
   • Quick challenge: “Convert 2/5 to a percent. Then find 2/5 of 20.” (40%, 8)
2. Practice Activity: Step-by-Step Solving (20 minutes):
   • Solve mixed problems together:
     • “A $50 game is 30% off. What’s the sale price?” (30% of 50 = 15, 50 – 15 = $35)
     • “A $25 meal has 8% tax and a 15% tip. What’s the total?” (Tax: 0.08 × 25 = 2, Tip: 0.15 × 25 = 3.75, Total: 25 + 2 + 3.75 = $30.75)
   • Use index cards with problems for a “pick and solve” game.
3. Assessment: Worksheet (15 minutes):
   • Provide a worksheet:
     • Convert: 1/2 = __% (50%), 0.75 = __/100 (75/100 = 3/4), 40% = __ (0.4)
     • Apply: $60 jacket, 20% off = __ ($48), $15 meal, 10% tip = __ ($1.50, total $16.50)
   • Check together, focusing on steps.
4. Wrap-Up (5 minutes):
   • Ask: “How do percentages help us in real life? What was your favorite problem?”

Assessment

• Informal Observation: Note their ability to convert and calculate during activities.
• Practice Accuracy: Check steps in discount/tax/tip problems for correct use of percentages.
• Worksheet: Ensure at least 80% accuracy (e.g., 4/5 correct) in conversions and applications.

Extensions

• Shop online (pretend): Find items, apply discounts, and calculate totals.
• Explore interest: “Save $100 at 5% interest for a year. How much do you earn?” (5% of 100 = $5)
• Create a “store” with items and percentage challenges for family.