Unit 2 RTD • Writing Ratios • Page 2 of 4 Set B
4 Questions Total
2
Select TWO true statements.
Count each shape group and write down the total before testing the statements.
★ ★ ★ ★ ★ ★ Total Stars = ____
♥ ♥ ♥ ♥ Total Hearts = ____
◻ ◻ ◻ ◻ ◻ ◻ Total Circles = ____
a) The ratio of hearts to circles is 3:2.
b) There are two stars for every heart.
c) The ratio of stars to circles is 6 to 8.
d) The ratio of hearts to circles is 2:3.
e) There are two hearts for every star.
Test Each Statement Below:
Write ratio & divide by GCF:
3
The library has 45 fiction books and 27 nonfiction books on a shelf. Which of the following statements correctly describes the ratio of nonfiction books to fiction books?
a) The ratio of nonfiction to fiction books is 15:9
b) The ratio of nonfiction to fiction books is 5:3
c) The ratio of nonfiction to fiction books is 18:1
d) The ratio of nonfiction to fiction books is 3:5
Words First & Division Setup:
Words: :
Divide 27 and 45 by common factor (9):
Unit 2 RTD • Writing Ratios • Page 3 of 4 Set B
4
The basketball team played 40 games this season. They won 32 games and lost 8 games. Which of the following statements correctly describes the ratio of losses to wins?
a) The ratio of losses to wins is 24:1
b) The ratio of losses to wins is 1:4
c) The ratio of losses to wins is 4:1
d) The ratio of losses to wins is 16:4
Words first & divide by 8:
Exit Ticket
Score: ____ / 2
1
A pet store has 24 hamsters and 42 goldfish. Which describes the ratio of goldfish to hamsters?
a) The ratio of hamsters to goldfish is 21:12
b) The ratio of hamsters to goldfish is 4:7
c) The ratio of hamsters to goldfish is 18:1
d) The ratio of hamsters to goldfish is 7:4
Fluency Divide (\(\div 6\)):
2
Select TWO true statements.
4 Smileys • 8 Diamonds • 10 Circles
a) Ratio of circles to diamonds is 4:5.
b) Two smiley faces for every diamond.
c) Ratio of smiley faces to diamonds is 4 to 8.
d) Ratio of smiley faces to circles is 4:8.
e) Ratio of circles to diamonds is 5:4.
Test work:
Homework
Due Tomorrow
1. A baker has 35 chocolate cupcakes and 14 vanilla cupcakes. What is the ratio of chocolate to vanilla in simplest form?
Words: : Simplest:
Divide by 7:
2. A runner ran 12 miles on weekdays and 8 miles on weekends. Which describes the ratio of weekend miles to weekday miles?
a) 3:2 b) 2:3 c) 4:1 d) 8:20
Words first:
Unit 2 RTD • Writing Ratios • Page 4 of 4 Set B
CFU: "If there are 12 dogs and 60 cats, why is cats to dogs 5:1 and NOT 1:5?"
Daily Routine: Co-Teacher Sync • Answer Key Master • Reduced-Load Packets Page 1 of 4 • Context, Co-Teacher Sync & HOTL
★
First Starred Independent Practice Question • Core Conceptual & Fluency Checkpoint
Item: Ind. Practice #1 (Roses 18 & Tulips 54 → Tulips to Roses)
Identify 2–3 Potential Errors & Break It Down (BID) Prompts
| Anticipated Error / Misconception | BID / Teacher Prompt (Scaffold Question) |
|---|---|
| 1. Inverts ratio order: Computes roses to tulips (18:54 → 1:3), selecting option (a) because roses was listed first in the sentence stem. | "Look at the question sentence: Does it ask for roses to tulips, or tulips to roses? Write the labels right now: Tulips first, Roses second. What number goes with Tulips?" |
| 2. Subtracts terms: Calculates \(54 - 18 = 36\) and selects option (b) 36:1, confusing multiplicative comparison with additive difference. | "Are ratios about subtracting numbers or comparing by dividing equal groups? Use your reference sheet: Step 4 says divide by a common factor." |
| 3. Multi-digit fluency drop: Struggles to divide 54 by 18, assumes no common factor or misdivides mentally. | "Open your fluency scratch box. Both 54 and 18 are multiples of 9. What is \(54 \div 9\)? What is \(18 \div 9\)? Now simplify \(6:2\) by dividing by 2!" |
Plan a Mini-RTD for Most Likely Error (Easel Script):
"Pencils down in 3-2-1. Look at my chart. The problem says 18 roses and 54 tulips. BUT what does the question ask? 'Ratio of tulips to roses!' Tulips MUST go first. Tulips = 54. Roses = 18. Never let the sentence fool you—follow the question!"
Script a Stamp (MPS 1 Key Takeaway):
"To write any ratio, the first word named in the question MUST become the first number. Write labels first (\(\text{Tulips} : \text{Roses}\), then divide both numbers by the common factor to simplify."
Name Your AM Laps 1 – 6 (Specific Look-Fors for Each Lap) • Live Push-In Scans
Lap 1 Underlines "tulips to roses"
Lap 2 Writes words first: \(\text{Tulips} : \text{Roses}\)
Lap 3 Matches values: \(54 : 18\)
Lap 4 Divides fluently by 9 or 18
Lap 5 Selects (c) 3:1
Lap 6 Multiplication check: \(3 \times 18 = 54\)
Real-Time Student Data Tracker (6 Laps • 8 Students) Mark: ✓ Mastered | ✗ Error | • BID Prompted
| Student Name | L1 | L2 | L3 | L4 | L5 | L6 | Error Code / Observation | BID Delivered |
|---|---|---|---|---|---|---|---|---|
| 1. __________________ | □ | □ | □ | □ | □ | □ | ||
| 2. __________________ | □ | □ | □ | □ | □ | □ | ||
| 3. __________________ | □ | □ | □ | □ | □ | □ | ||
| 4. __________________ | □ | □ | □ | □ | □ | □ | ||
| 5. __________________ | □ | □ | □ | □ | □ | □ | ||
| 6. __________________ | □ | □ | □ | □ | □ | □ | ||
| 7. __________________ | □ | □ | □ | □ | □ | □ | ||
| 8. __________________ | □ | □ | □ | □ | □ | □ |
Push-In Move: If 2+ students make Error #1 on Lap 2, execute 45-second Mini-RTD at easel. Page 2 of 4 • MPS 1 Error Analysis & 6-Lap Tracking
★
Second Starred Independent Practice • Context Rigor & Multi-Step Fluency Transfer
Item: Ind. Practice #5/6 (Library 45 Fiction & 27 Nonfiction • Nonfiction to Fiction)
Identify 2–3 Potential Errors & Break It Down (BID) Prompts
| Anticipated Error / Misconception | BID / Teacher Prompt (Scaffold Question) |
|---|---|
| 1. Inverts order of categories: Sets up 45:27 (5:3) instead of 27:45 (3:5), selecting option (b). | "Step 1: Underline the ratio question: 'nonfiction books to fiction books'. Nonfiction is 27! Which number must go on the left?" |
| 2. Incomplete simplification: Divides by 3 to get 9:15, or divides by 9 incorrectly and selects 15:9. | "You divided by 3 to get 9:15. Can 9 and 15 both divide again? Divide by 3 one more time. What is \(9 \div 3\)? \(15 \div 3\)?" |
| 3. Multi-digit division stall: Struggles to recall 9 times tables for 27 and 45. | "Use your reference factor chart. \(2 + 7 = 9\) and \(4 + 5 = 9\). Both are divisible by 9! Count by 9s to 27: 9, 18, 27 (3). To 45: 9, 18, 27, 36, 45 (5)!" |
Plan a Mini-RTD for Most Likely Error (Easel Script):
"Look at 27 and 45. Some students divided by 3 and stopped at 9:15. Always test: Are there any more common factors? Yes! Both still divide by 3 to reach 3:5. Keep dividing until only 1 fits in both!"
Script a Stamp (MPS 2 Key Takeaway):
"In word problems with larger numbers, write the labels first. If you don't find the biggest factor right away, keep dividing step-by-step until the ratio cannot be divided further."
Name Your AM Laps 1 – 6 (Specific Look-Fors for Each Lap) • Live Push-In Scans
Lap 1 Underlines "nonfiction to fiction"
Lap 2 Writes \(\text{NF} : \text{F}\) words first
Lap 3 Matches values \(27 : 45\)
Lap 4 Fluently divides by 9 (or 3 twice)
Lap 5 Selects option (d) 3:5
Lap 6 Multiplication check: \(3 \times 9 = 27\), \(5 \times 9 = 45\)
Real-Time Student Data Tracker (6 Laps • 8 Students) Mark: ✓ Mastered | ✗ Error | • BID Prompted
| Student Name | L1 | L2 | L3 | L4 | L5 | L6 | Error Code / Observation | BID Delivered |
|---|---|---|---|---|---|---|---|---|
| 1. __________________ | □ | □ | □ | □ | □ | □ | ||
| 2. __________________ | □ | □ | □ | □ | □ | □ | ||
| 3. __________________ | □ | □ | □ | □ | □ | □ | ||
| 4. __________________ | □ | □ | □ | □ | □ | □ | ||
| 5. __________________ | □ | □ | □ | □ | □ | □ | ||
| 6. __________________ | □ | □ | □ | □ | □ | □ | ||
| 7. __________________ | □ | □ | □ | □ | □ | □ | ||
| 8. __________________ | □ | □ | □ | □ | □ | □ |
Push-In Priority: Ensure students do not stop at partial simplification; enforce the inverse check. Page 3 of 4 • MPS 2 Error Analysis & 6-Lap Tracking
✓
Backwards Planning Core • Mandatory In-Class Assessment Collection
Mandatory Non-Negotiable
Exit Ticket Aggressive Monitoring Focus & Stamp (Immediate Live Scans: Goldfish 42 & Hamsters 24 • Goldfish to Hamsters)
ET Lap 1 (Order & Setup) Scans setup: Did student write \(\text{Goldfish} : \text{Hamsters}\) and match \(42 : 24\)? Immediate stop if \(24:42\).
ET Lap 2 (Fluency Simplification) Scans division: Did student divide both by 6 to reach \(7:4\) (option d) rather than \(4:7\) (option b)?
Conceptual Stamp / Key Rule "Goldfish came first in the question, so 42 goes on top/first. Divide both by 6 to get \(7:4\)."
Push-In Student Assessment Data Collection Tool (8 Students) Fill during collection / grading • Live Mastered vs. Gap Tally
| Student Name | Score / % | Level | Primary Misconception / Gap | Tomorrow's Push-In Action |
|---|---|---|---|---|
| 1. __________________ | ____ / 2 | L / M / H | ||
| 2. __________________ | ____ / 2 | L / M / H | ||
| 3. __________________ | ____ / 2 | L / M / H | ||
| 4. __________________ | ____ / 2 | L / M / H | ||
| 5. __________________ | ____ / 2 | L / M / H | ||
| 6. __________________ | ____ / 2 | L / M / H | ||
| 7. __________________ | ____ / 2 | L / M / H | ||
| 8. __________________ | ____ / 2 | L / M / H |
Next-Day Push-In Priority & Strategy
Priority Standard / Gap to Target:
Order conservation in part-to-part and part-to-whole word problems; multi-digit division fluency when finding GCF without arithmetic calculation stall.
Planned Grouping / Push-In Delivery:
Tier II (Kidney Table): 4 students for a 5-minute Do Now reteach using color-coded word cards.
Tier III (Station Teaching): Co-teacher leads station using multi-digit division factor charts and structured ratio templates.
Data Cycle Complete: Use this Exit Ticket data to fuel tomorrow's Section 1 Reflection and Tier II/III grouping. Page 4 of 4 • Exit Ticket & Assessment Tracker
