Elementary Level: Ordinal Numbers (First to Tenth)

Mid Level: Problem Solving with Number Operations

High Level: Multi-Step Ratio and Percentage Problems

Elementary Level (Kinder to Grade 2)

Subject: Ordinal Numbers (First to Tenth)

Alignment with Standards:

• Common Core State Standards (CCSS):
  • CCSS.MATH.CONTENT.1.NBT.A.1: Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral (builds counting skills for ordinals).
  • CCSS.MATH.CONTENT.K.CC.B.4: Understand the relationship between numbers and quantities; connect counting to cardinality (extends to ordinal positions).
  • CCSS.ELA-LITERACY.SL.1.1: Participate in collaborative conversations with diverse partners about grade 1 topics and texts with peers and adults in small and larger groups (used in activities).

Objectives

1. Understand that ordinal numbers (first, second, third, etc.) show position or order rather than quantity.
2. Recognize and use ordinal numbers from “first” to “tenth” in spoken and written forms.
3. Apply ordinal numbers in line-up games and a scavenger hunt to reinforce their meaning.
4. Build counting, sequencing, and listening skills through hands-on practice.

Materials

• 10 small toys or objects (e.g., blocks, cars, stuffed animals)
• Number cards (1st to 10th, written as words or abbreviations: 1st, 2nd, 3rd, etc.)
• Paper or notebook for drawing/writing
• Crayons, markers, or pencils
• Scavenger hunt list (e.g., “Find the 3rd book on the shelf”)
• Optional: Storybook with order (e.g., The Very Hungry Caterpillar by Eric Carle), a line-up mat

Activities

Day 1: Introducing Ordinal Numbers (30-45 minutes)

1. Warm-Up (5-10 minutes):
   • Ask: “If you’re in a race, who gets the gold medal? (First!) Today, we’re learning words for order!”
   • Say: “First, second, third—these are ordinal numbers!”
2. Direct Instruction (10 minutes):
   • Line up 5 toys: “This car is first, this bear is second, this block is third…” Count to fifth.
   • Show cards: “1st, 2nd, 3rd, 4th, 5th.” Say them together.
   • Explain: “Ordinal numbers tell us ‘which one’ in line—not how many!”
3. Practice (15-20 minutes):
   • Read a book page (e.g., The Very Hungry Caterpillar: “On the first day…”). Spot “first,” “second.”
   • Point and say: “Who’s third? (block!) Fifth?”
4. Wrap-Up (5 minutes):
   • Ask: “What’s the 1st thing you do in the morning? Tell me in order!”

Day 2: Line-Up Games (45 minutes)

1. Review (10 minutes):
   • Recap: “What’s after first? (second) Show me 3rd with your fingers!” (3rd finger up)
   • Quick line: 3 toys—“Who’s 2nd?”
2. Hands-On Activity: Line-Up Games (25 minutes):
   • Toy Race: Line up 10 toys. “Put the car 4th. Make the doll 1st.” Shuffle and try again.
   • Family Line: Use family members or toys: “Mom is 1st, I’m 3rd, who’s 5th?”
   • Card Match: Lay out toys, place cards (1st-10th) under them. “Switch 7th and 2nd!”
   • Say it: “The bear is 6th!” They point and repeat.
3. Wrap-Up (10 minutes):
   • Ask: “Which spot was your favorite? Who was 10th in our line?”

Day 3: Scavenger Hunt and Quiz (45 minutes)

1. Warm-Up (10 minutes):
   • Say: “Line up these 5 blocks. Who’s 3rd? 1st?”
   • Prep: “We’re hunting with ordinal numbers today!”
2. Hands-On Activity: Scavenger Hunt (20 minutes):
   • List (read aloud):
     • “Find the 2nd book on the shelf.”
     • “Touch the 5th toy in your room.”
     • “Point to the 1st chair you see.”
     • Add 3 more (e.g., 7th step, 4th cup).
   • Hunt together: “What’s 2nd? Show me!” Draw or write one find (e.g., “2nd book—red”).
3. Assessment: Ordinal Number Quiz (15 minutes):
   • Line up 10 objects. Ask:
     • “Who’s 3rd? 8th? 1st?” (Point or say.)
     • “Put this card (5th) under the right toy.”
     • Write: “Draw 4 toys. Circle the 2nd.”
   • Check: Can they name/match 1st-10th?
4. Wrap-Up (5 minutes):
   • Celebrate: “You’re an ordinal expert! What’s 1st on your fun list today?”

Assessment

• Informal Observation: Note their ability to order objects during games.
• Scavenger Hunt: Check if they find items by position (e.g., 4/6 correct).
• Quiz: Ensure they identify/write at least 80% of positions (e.g., 8/10 right).

Extensions

• Race story: “First I ran, second I jumped…”—add to 10th.
• Ordinal song: Sing “1st, 2nd, 3rd” to “Twinkle, Twinkle.”
• Outside hunt: “What’s the 3rd tree you see?”

Mid Level (Grade 3 to 5)

Subject: Problem Solving with Number Operations

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.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.

Objectives

1. Understand how to break down multi-step word problems into manageable parts.
2. Apply addition, subtraction, multiplication, and division to solve real-world scenarios.
3. Solve multi-step problems involving all four operations with whole numbers.
4. Develop critical thinking and mathematical reasoning skills through practical applications.

Materials

• Notebook or paper for calculations
• Pencil, pen, or markers
• Word problem cards or worksheet (samples provided below)
• Real-world props: play money, small toys (e.g., cars), measuring cups (optional)
• Whiteboard or chart paper for modeling
• Optional: Calculator (for checking after solving), dice for random numbers

Activities

Day 1: Introduction to Multi-Step Problems (45 minutes)

1. Warm-Up (10 minutes):
   • Ask: “If you have 5 candies and get 3 more, then share them equally with a friend, how many do you each get?” (8 ÷ 2 = 4)
   • Say: “Today, we’re solving big problems with all our math skills!”
2. Direct Instruction (15 minutes):
   • Explain: “Multi-step problems need more than one operation—like adding then dividing.”
   • Model: “You have 12 marbles. You buy 8 more, then split them into 4 bags. How many per bag?”
     • Step 1: 12 + 8 = 20 (add).
     • Step 2: 20 ÷ 4 = 5 (divide).
     • Answer: 5 marbles per bag.
   • Show: Write steps, underline key words (buy = +, split = ÷).
3. Practice (15-20 minutes):
   • Try: “Sara has 15 cookies. She eats 3, then triples what’s left. How many now?”
     • 15 – 3 = 12, 12 × 3 = 36. Answer: 36 cookies.
   • Discuss: “What did we do first? Why?”
4. Wrap-Up (5 minutes):
   • Ask: “What’s one operation you used? Where do you see math like this?”

Day 2: Real-World Scenarios—Shopping and Sharing (45 minutes)

1. Review (10 minutes):
   • Recap: “What’s 10 + 5 – 3? (12) Now divide by 2? (6) Multi-step magic!”
2. Hands-On Activity: Problem Solving (25 minutes):
   • Scenario 1: “You have $20. You buy a $7 toy and a $5 book. How much is left?”
     • 20 – 7 = 13, 13 – 5 = 8. Answer: $8.
   • Scenario 2: “A store has 24 shirts. They sell 6, then get 18 more. How many now?”
     • 24 – 6 = 18, 18 + 18 = 36. Answer: 36 shirts.
   • Scenario 3: “You bake 30 cookies, give away 10, split the rest into 5 jars. How many per jar?”
     • 30 – 10 = 20, 20 ÷ 5 = 4. Answer: 4 cookies per jar.
   • Use play money/toys: Act out Scenario 1, check with math.
3. Wrap-Up (10 minutes):
   • Discuss: “Which step was trickiest? How’s this like real shopping?”

Day 3: Mixed Operations and Challenges (45 minutes)

1. Warm-Up (10 minutes):
   • Quickie: “6 × 3 – 4 = ?” (18 – 4 = 14) “What’s first?” (Multiply!)
2. Hands-On Activity: Advanced Scenarios (25 minutes):
   • Scenario 1: “A farm has 15 chickens. They double, then 8 run away. How many left?”
     • 15 × 2 = 30, 30 – 8 = 22. Answer: 22 chickens.
   • Scenario 2: “You earn $12, spend $3, then split the rest with 3 friends (including you). How much each?”
     • 12 – 3 = 9, 9 ÷ 3 = 3. Answer: $3 each.
   • Challenge: “A party needs 4 cups of juice per guest. You have 28 cups for 5 guests. How much left?”
     • 4 × 5 = 20, 28 – 20 = 8. Answer: 8 cups left.
   • Write one: “Make your own problem!” (e.g., “I have 10 apples, add 5, split into 3—how many each?”)
3. Wrap-Up (10 minutes):
   • Share: “Read your problem! How did you solve the party one?”

Assessment

• Informal Observation: Note their ability to identify steps during discussions.
• Scenario Solutions: Check for correct operations and answers (e.g., 4/5 right).
• Student Problem: Ensure it uses 2+ operations with a clear solution.

Extensions

• Shop game: Use real ads, calculate totals after discounts.
• Reverse it: “You end with 6 cookies after 2 steps—what happened?”
• Story chain: Each adds a step to a problem (e.g., “I had 10, added 5, you subtract…”).

High Level (Grade 6 to 8)

Subject: Multi-Step Ratio and Percentage Problems

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, percent increase/decrease).
  • 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.7.RP.A.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.

Objectives

1. Understand how to solve multi-step problems combining ratios and percentages.
2. Apply proportional reasoning to real-world scenarios involving multiple operations.
3. Solve challenging word problems that integrate ratios and percentages with addition, subtraction, multiplication, or division.
4. Develop analytical and problem-solving skills through complex mathematical challenges.

Materials

• Notebook or paper for calculations
• Pencil, pen, or calculator (for checking after solving)
• Word problem cards or worksheet (samples provided below)
• Real-world props: measuring cups, play money, or small objects (e.g., marbles)
• Whiteboard or chart paper for modeling
• Optional: Graph paper, ratio table templates

Activities

Day 1: Introduction to Ratios and Percentages in Multi-Step Problems (45 minutes)

1. Warm-Up (10 minutes):
   • Ask: “If 2:3 is the ratio of cats to dogs and there are 10 cats, how many dogs? (15) What if 20% run away?” (12 left)
   • Say: “We’re tackling tough problems with ratios and percents together!”
2. Direct Instruction (15 minutes):
   • Review:
     • Ratio: Part-to-part or part-to-whole (e.g., 2:3 = 2 cats for 3 dogs).
     • Percentage: Part of 100 (e.g., 20% = 0.2).
   • Model: “A recipe has a 3:2 flour-to-sugar ratio. You use 15 cups flour. Sugar is 50% more than flour. Total cups?”
     • Step 1: 3:2 → 15 flour = 3 parts, 1 part = 5, sugar = 2 × 5 = 10.
     • Step 2: 50% more flour = 15 × 0.5 = 7.5, new sugar = 10 + 7.5 = 17.5.
     • Step 3: 15 + 17.5 = 32.5 cups total.
   • Emphasize: Break it into steps, find key numbers.
3. Practice (15-20 minutes):
   • Try: “A 4:5 ratio of red to blue marbles. 20 red. 25% of blue are lost. How many blue left?”
     • 4:5 → 20 red = 4 parts, 1 part = 5, blue = 5 × 5 = 25. 25% of 25 = 6.25, 25 – 6.25 = 18.75 (round to 19).
4. Wrap-Up (5 minutes):
   • Ask: “What’s the trickiest part? Where do ratios show up?”

Day 2: Real-World Ratio and Percent Challenges (45 minutes)

1. Review (10 minutes):
   • Recap: “3:4 ratio, 12 is 3 parts. What’s 4 parts? (16) Add 10%? (17.6)”
2. Hands-On Activity: Word Problems (25 minutes):
   • Problem 1: “A store mixes juice in a 2:3 ratio of orange to apple. They use 14 orange. 20% of apple spoils. Total left?”
     • 2:3 → 14 orange = 2 parts, 1 part = 7, apple = 3 × 7 = 21. 20% of 21 = 4.2, 21 – 4.2 = 16.8. Total = 14 + 16.8 = 30.8 (31).
   • Problem 2: “A team has a 5:2 win-to-loss ratio. 15 wins. Losses increase by 30%. New total games?”
     • 5:2 → 15 wins = 5 parts, 1 part = 3, losses = 2 × 3 = 6. 30% of 6 = 1.8, 6 + 1.8 = 7.8 (8). Total = 15 + 8 = 23.
   • Use props: Measure 2:3 cups, “spoil” 20% apple—check math.
3. Wrap-Up (10 minutes):
   • Discuss: “How did ratios help? What’s a real-life mix like this?”

Day 3: Advanced Multi-Step Problems (45 minutes)

1. Warm-Up (10 minutes):
   • Quickie: “1:4 ratio, 5 is 1 part. 4 parts? (20) 15% off 20? (17)”
2. Hands-On Activity: Challenging Scenarios (25 minutes):
   • Problem 1: “A garden has a 3:7 ratio of roses to tulips. 21 roses. Tulips grow by 10%, then 5 are picked. Final total?”
     • 3:7 → 21 roses = 3 parts, 1 part = 7, tulips = 7 × 7 = 49. 10% of 49 = 4.9 (5), 49 + 5 = 54, 54 – 5 = 49. Total = 21 + 49 = 70.
   • Problem 2: “A sale has a 2:5 ratio of shirts to pants. 16 shirts. Pants are 25% off original stock. New ratio?”
     • 2:5 → 16 shirts = 2 parts, 1 part = 8, pants = 5 × 8 = 40. 25% of 40 = 10, 40 – 10 = 30. New ratio = 16:30 (8:15).
   • Write one: “3:4 ratio, 12 is 3. 20% more of 4 part. Total?” (21.6)
3. Wrap-Up (10 minutes):
   • Share: “What’s your problem? How do percents twist the ratio?”

Assessment

• Informal Observation: Note their step-by-step reasoning during activities.
• Problem Solutions: Check for correct ratios and percent calculations (e.g., 4/5 right).
• Student Problem: Ensure it combines ratio and percent with a clear answer.

Extensions

• Ratio remix: Adjust a recipe (e.g., 2:3 to 4:6), add 10% more.
• Percent shift: “Old ratio 1:2, new 1:3—what’s the % change?”
• Graph it: Plot ratio totals before/after percent change.