Elementary Level: Addition and Subtraction Relationship
Mid Level: Review and Practice of Number Operations
High Level: Solving Percent Problems

Elementary Level (Kinder to Grade 2)

Subject: Addition and Subtraction Relationship

Alignment with Standards:

National Standards Alignment

• Common Core State Standards (CCSS):
  • CCSS.MATH.CONTENT.1.OA.B.3: Apply properties of operations as strategies to add and subtract (e.g., if 2 + 3 = 5 is known, then 5 – 3 = 2 is also known—fact families).
  • CCSS.MATH.CONTENT.1.OA.C.6: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.
  • CCSS.MATH.CONTENT.1.OA.D.7: Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.

Objectives

1. Understand that addition and subtraction are related operations (e.g., adding and then taking away gets you back where you started).
2. Recognize and use fact families to show how numbers connect through addition and subtraction.
3. Create number bonds and fact families to explore these relationships.
4. Build confidence in solving basic addition and subtraction problems within 10.

Materials

• Small objects for counting (e.g., 10 blocks, buttons, or cereal pieces)
• Paper cups or containers (to group objects)
• Whiteboard or paper for writing equations
• Crayons, markers, or pencils
• Number bond template (circle with 2 parts and a whole, printable or hand-drawn)
• Fact family worksheet (e.g., blank triangles or houses for 3 numbers)
• Optional: Dice, flashcards, or a number line (0-10)

Activities

Day 1: Exploring Addition and Subtraction Together (30-45 minutes)

1. Warm-Up (5-10 minutes):
   • Ask: “If I have 3 cookies and add 2 more, how many do I have? (5) What if I eat 2—how many then? (3)”
   • Say: “Today, we’re learning how adding and subtracting are best friends!”
     
2. Direct Instruction (10 minutes):
   • Show with objects: “I have 4 blocks. Add 3 more—count them (7). Now take 3 away—back to 4!”
   • Explain: “Addition puts things together. Subtraction takes them apart. They work together like a team!”
   • Write: “4 + 3 = 7, 7 – 3 = 4.” Say: “See how they switch places?”
     
3. Practice (15-20 minutes):
   • Use 5 objects: “Add 2 (7). Take 2 away (5).” Write: “5 + 2 = 7, 7 – 2 = 5.”
   • Try another: “3 + 4 = 7, 7 – 4 = 3.” Count with blocks each time.
     
4. Wrap-Up (5 minutes):
   • Ask: “How are adding and subtracting connected? Tell me one pair you made!”
     

Day 2: Number Bonds (45 minutes)

1. Review (10 minutes):
   • Recap: “Yesterday, we saw 5 + 2 = 7 and 7 – 2 = 5. What’s the big number? (7) The little ones? (5, 2)”
   • Quick game: “I say 6 + 3 = 9. You say the subtraction!” (9 – 3 = 6)
     
2. Hands-On Activity: Number Bonds (25 minutes):
   • Draw a number bond: Big circle (whole) with 2 small circles (parts).
   • Example: Write 7 in the big circle, 4 and 3 in the small ones.
     • “4 + 3 = 7 (parts make the whole). 7 – 3 = 4 (whole minus a part).”
   • Try with objects: 6 blocks total—split into 2 and 4. Fill in a bond: 6 (whole), 2 and 4 (parts).
     • Write: “2 + 4 = 6, 6 – 4 = 2.”
   • Do 2 more (e.g., 8 with 5 and 3, 10 with 7 and 3). Draw and write equations.
     
3. Wrap-Up (10 minutes):
   • Ask: “What’s a number bond show us? How does it help with subtracting?”
     

Day 3: Fact Families and Assessment (45 minutes)

1. Warm-Up (10 minutes):
   • Say: “If 3 + 5 = 8, what’s a subtraction?” (8 – 5 = 3) “Another?” (8 – 3 = 5)
   • Introduce: “These are a fact family—3 numbers that stick together!”
     
2. Hands-On Activity: Fact Families (20 minutes):
   • Draw a triangle or house: Put 6, 4, 2 at the corners.
     • Write all facts: “4 + 2 = 6, 2 + 4 = 6, 6 – 2 = 4, 6 – 4 = 2.”
   • Use objects: Start with 7, split into 3 and 4. Write the family: “3 + 4 = 7, 4 + 3 = 7, 7 – 4 = 3, 7 – 3 = 4.”
   • Try one more (e.g., 5, 3, 2).
     
3. Assessment (15 minutes):
   • Give 2 sets of numbers:
     • 5, 3, 2: Write fact family (3 + 2 = 5, 2 + 3 = 5, 5 – 2 = 3, 5 – 3 = 2).
     • 8, 5, 3: Write fact family (5 + 3 = 8, 3 + 5 = 8, 8 – 5 = 3, 8 – 3 = 5).
   • Use blocks or a number line if needed. Check together.
     
4. Wrap-Up (5 minutes):
   • Celebrate: “You made fact families! How do they show adding and subtracting are buddies?”

Assessment

• Informal Observation: Note their understanding of the relationship during activities.
• Number Bonds: Check if they connect parts to whole (e.g., 6 = 2 + 4, 6 – 4 = 2).
• Fact Families: Ensure they write all 4 facts correctly for at least one set (e.g., 3 + 2 = 5, etc.).

Extensions

• Roll dice: Add the numbers, then write the fact family.
• Story problems: “You have 6 apples, give 2 away—what’s left?” Link to a family.
• Play “Fact Family Match”: Mix up equations, sort into families.

Mid Level (Grade 3 to 5)

Subject: Review and Practice of Number Operations

National Standards Alignment

• Common Core State Standards (CCSS):
  • CCSS.MATH.CONTENT.4.NBT.B.4: Fluently add and subtract multi-digit whole numbers using the standard algorithm.
  • CCSS.MATH.CONTENT.4.NBT.B.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations.
  • CCSS.MATH.CONTENT.4.NBT.B.6: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.

Objectives

1. Review and reinforce fluency in addition and subtraction with multi-digit numbers.
2. Practice multiplication of up to two-digit numbers by one-digit numbers and explore basic two-digit by two-digit multiplication.
3. Strengthen division skills with one-digit divisors and understand remainders.
4. Build confidence and problem-solving skills through mixed operation practice.

Materials

• Whiteboard or paper for calculations
• Pencil, pen, or markers
• Number cards or dice (for generating problems)
• Base-10 blocks or counters (for visual support)
• Mixed operations worksheet (sample provided below)
• Math game supplies: deck of cards, spinner, or online tool (e.g., Math Playground)
• Optional: Calculator (for checking answers only after solving)

Activities

Day 1: Addition and Subtraction Review (45 minutes)

1. Warm-Up (10 minutes):
   • Ask: “What’s 25 + 37? Now take away 12—what’s left?” (62, then 50)
   • Say: “We’re brushing up on all our number skills—starting with adding and subtracting!”
     
2. Direct Instruction (15 minutes):
   • Review addition: “Line up 143 + 258.” Model stacking and carrying (401).
   • Review subtraction: “576 – 239.” Model borrowing (337).
   • Emphasize place value: “Tens stay with tens, ones with ones!”
     
3. Practice (15-20 minutes):
   • Solve together: 324 + 187 (511), 493 – 265 (228). Use blocks if needed.
   • Quick mix: Write 5 problems (e.g., 56 + 78, 142 – 89), they pick 3 to solve.
     
4. Wrap-Up (5 minutes):
   • Ask: “What’s trickier—adding or subtracting? Why?”

Day 2: Multiplication Review (45 minutes)

1. Review (10 minutes):
   • Recap: “What’s 4 × 6? (24) How about 12 + 12? (24) Same answer, different ways!”
   • Quick drill: “5 × 3, 7 × 4” (15, 28).
     
2. Hands-On Activity: Mixed Multiplication (25 minutes):
   • Practice one-digit: “346 × 3.” Break it down (300 × 3 = 900, 40 × 3 = 120, 6 × 3 = 18; total 1,038).
   • Try two-digit: “14 × 12.” Use area model or stacking (10 × 12 = 120, 4 × 12 = 48; 168).
   • Game: Roll 2 dice (e.g., 5, 4), multiply (20). Do 5 rounds, add scores.
     
3. Wrap-Up (10 minutes):
   • Discuss: “How does knowing 5 × 3 help with 50 × 3? What’s fun about multiplying?”
     

Day 3: Division and Mixed Operations (45 minutes)

1. Warm-Up (10 minutes):
   • Ask: “If 6 × 4 = 24, what’s 24 ÷ 4? (6) See the connection?”
     
2. Hands-On Activity: Division and Mix (25 minutes):
   • Review division: “48 ÷ 3.” Model sharing (16) or repeated subtraction (48 – 3 = 45, etc.).
   • With remainder: “25 ÷ 4” (6 R1). Use counters to show.
   • Mixed review game: Use cards—draw 2 numbers, spin for operation (+, -, ×, ÷).
     • E.g., 15, 6, + = 21; 20, 4, ÷ = 5. Solve 5 problems, check together.
   • Worksheet sample:
     • 245 + 378 = __ (623)
     • 512 – 196 = __ (316)
     • 23 × 4 = __ (92)
     • 45 ÷ 5 = __ (9)
       
3. Wrap-Up (10 minutes):
   • Ask: “Which operation was easiest today? How do they all fit together?”

Assessment

• Informal Observation: Note fluency and strategies during practice and games.
• Game Accuracy: Check if they solve mixed problems correctly (e.g., 4/5 right).
• Worksheet: Ensure at least 80% accuracy across all operations (e.g., 7/9 correct).

Extensions

• Word problems: “You have 48 cookies, split them into 6 bags—how many each?” (8)
• Math relay: Time 5 mixed problems, beat the clock next time.
• Create a “Number Story”: Use all 4 operations in a short tale (e.g., “I had 10 apples, added 5, ate 3, split 12 into 4 friends…”).

High Level (Grade 6 to 8)

Subject: Solving Percent Problems

Alignment with Standards:

National Standards Alignment

• Common Core State Standards (CCSS):
  • CCSS.MATH.CONTENT.7.RP.A.3: Use proportional relationships to solve multistep ratio and percent problems (e.g., percent increase/decrease, markups, discounts).
  • CCSS.MATH.CONTENT.7.EE.B.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form, using tools strategically.
  • CCSS.MATH.CONTENT.6.RP.A.3.C: Find a percent of a quantity as a rate per 100 (Note: Grade 7 extends this to complex applications).

Objectives

1. Understand how to calculate percent increase and decrease in various contexts.
2. Solve problems involving percent change using proportions or decimal methods.
3. Apply percent skills to real-world scenarios like sales discounts and population growth.
4. Develop problem-solving and critical thinking skills through practical applications.

Materials

• Notebook or paper for calculations
• Pencil, pen, or calculator (for checking, not solving initially)
• Fake money or receipts (optional for sales practice)
• Percent problem worksheet (sample provided below)
• Real-world examples (e.g., sale ads, population stats from online or books)
• Index cards or slips for practice problems
• Optional: Graph paper for visualizing changes

Activities

Day 1: Understanding Percent Increase and Decrease (45 minutes)

1. Warm-Up (10 minutes):
   • Ask: “If a shirt costs $20 and goes up by 25%, what’s the new price?” (Hint: 25% of 20 = 5, so 20 + 5 = $25.)
   • Say: “We’re tackling percent problems—like price hikes and discounts!”
2. Direct Instruction (15 minutes):
   • Explain:
     • Percent Increase: Original + (Original × Percent as decimal).
       • E.g., $20 + (20 × 0.25) = $25.
     • Percent Decrease: Original – (Original × Percent as decimal).
       • E.g., $20 – (20 × 0.20) = $16 (20% off).
   • Percent Change: |(New – Original) ÷ Original| × 100.
     • E.g., 20 to 25 = (25 – 20) ÷ 20 = 0.25 × 100 = 25%.
   • Show both methods: Decimal (0.25 × 20) or proportion (25/100 = x/20).
3. Practice (15-20 minutes):
   • Solve: $50 with 30% increase ($65), $40 with 15% decrease ($34).
   • Check change: 50 to 65 = 30% increase? Yes!
4. Wrap-Up (5 minutes):
   • Ask: “What’s easier—decimal or proportion? Where do we see percent changes?”

Day 2: Real-World Sales Applications (45 minutes)

1. Review (10 minutes):
   • Recap: “What’s 20% off $30? (6 off, so $24) How do you know?”
2. Hands-On Activity: Sales Problems (25 minutes):
   • Scenario 1: “A $60 jacket is 25% off. New price?”
     • 0.25 × 60 = 15, 60 – 15 = $45.
   • Scenario 2: “A $25 game increases 10% after a sale. New price?”
     • 0.1 × 25 = 2.5, 25 + 2.5 = $27.50.
   • Game: Use fake receipts or ads. Pick 3 items, apply discounts (e.g., 20%, 15%), calculate totals.
   • Check: “Original $80, now $64—what’s the percent decrease?” (20%)
3. Wrap-Up (10 minutes):
   • Discuss: “How do sales use percents? What’s a good deal you found?”

Day 3: Population Growth and Mixed Practice (45 minutes)

1. Warm-Up (10 minutes):
   • Ask: “A town of 100 grows by 10%. New population?” (110)
2. Hands-On Activity: Population and Mix (25 minutes):
   • Scenario 1: “A city has 1,000 people. It grows 15%. New total?”
     • 0.15 × 1,000 = 150, 1,000 + 150 = 1,150.
   • Scenario 2: “A park had 500 birds, now 425. Percent decrease?”
     • (500 – 425) ÷ 500 = 0.15 × 100 = 15%.
   • Worksheet sample:
     • $90, 20% off = __ ($72)
     • 200 people, 5% increase = __ (210)
     • 50 to 40, % change = __ (20% decrease)
   • Solve 5 problems, mix sales and growth.
3. Wrap-Up (10 minutes):
   • Ask: “How do percents help with populations? What’s your favorite problem type?”

Assessment

• Informal Observation: Note their ability to apply methods during activities.
• Practice Accuracy: Check steps in sales/population problems (e.g., 4/5 correct).
• Worksheet: Ensure at least 80% accuracy (e.g., 4/5 right) in mixed problems.

Extensions

• Shop challenge: Find online items, apply discounts, compare savings.
• Graph it: Plot population growth (e.g., 100 to 110 to 121) over 3 years.
• Reverse it: “New price $36 after 20% off—what’s original?” ($45)