Justify using the sentence frame: "I compared the ______ place because..."

Error Analysis (DOK 3)

Student writes: 85,763 < 86,093 because "3 is smaller than 9."

Which place should have been compared? Rewrite the correct explanation:

Check for Understanding

Compare 92,804 and 92,840. Explain why the 4 does NOT have the same value in both numbers:

Independent Practice: Record >, <, or = and Justify

56,810 _____ 56,801

Which place determined comparison?

91,304 _____ 91,340

Explain using place value:

100,000 _____ 99,999

Why is 100,000 greater?

62,587 _____ 62,578

Write a complete sentence comparison:

Real-World Application: Canned Food Drive

School A collected 84,975 cans. School B collected 84,795 cans. Which school collected more? Explain without saying "because 975 is bigger."

Grade 4 Mathematics • Unit: Number Champions Day 3 • NC.4.NBT.7

Compare & Defend

Name:   Date:  

Warm-Up: Which Comparison is Correct?

45,681 _____ 45,681

72,000 _____ 71,999

88,392 _____ 89,103

Which comparison required looking past the first two digits? Why?

We Do: Comparison Organizer (91,028 vs. 91,820)

Why didn't we need to compare the tens or ones places?

Error Analysis (DOK 3)

Student writes: 64,205 > 64,502 because "205 is bigger than 502 because 2 is bigger than 5." Correct the error:

Expanded Form Comparison

Compare 64,205 and 60,000 + 4,000 + 500 + 2. Which place value determines the symbol?

You Do: Complete All 4 Parts

57,108 _____ 57,801

66,932 _____ 66,923

89,240 _____ 89,240

45,987 _____ 46,098

Real-World Application: Book Drive

School A collected 75,008 books. School B collected 75,800 books. Which school collected more? Prove your answer without simply saying "800 is bigger."

Grade 4 Mathematics • Unit: Number Champions Day 4 • Real-World Contexts

Multi-Step Showdown

Name:   Date:  

Warm-Up: Compare and Defend

Newton Pop.: 92,485 | Harrisville Pop.: 94,203

Which town has more people? Write the comparison and place value reason:

Truck A: 86,450 mi | Truck B: 84,999 mi

Which truck traveled farther? Which place value determined your answer?

We Do: Maple Elementary vs. River Elementary

Maple Elementary collected 36,418 cans in Week 1 and 22,350 cans in Week 2. River Elementary collected 41,980 cans total. Who collected more?

Step 1: Calculate Maple's Total

Step 2: Compare & Explain

Error Analysis (DOK 3)

A student solved: \(36,418 + 22,350 = 48,768\) and concluded "48,768 > 41,980 so Maple wins." Is the addition correct? How did this mistake impact their argument?

Independent Practice: Multi-Step Word Problems

Problem 1: Factory Production

Texas Factory: 72,416 cars. Ohio Factory: 75,023 cars. Which factory produced more? Defend:

Problem 2: City Visitors

Bellview: 43,920 visitors. Milltown: 42,756 visitors. Compare using >, <, or = and explain:

Problem 3: Bookstore Sales

Bookstore A: Mar (21,845) + Apr (25,900). Bookstore B: 48,999. Who sold more books? Show all steps:

Problem 4: Step Challenge

Runner A: Mon (56,230) + Tue (41,906). Runner B: 97,001. Who took more steps? Justify:

DOK 3 Question: Why must we solve calculations before comparing values in multi-step problems?

Grade 4 Mathematics • Unit: Number Champions Day 5 • Mastery & Synthesis

Mastery & Review

Name:   Date:  

Warm-Up: Which Comparison is True?

73,492 _____ 73,429

Which place value determined the symbol? Why not the ones?

58,301 _____ 58,301

Explain your reasoning in one complete mathematical sentence:

We Do: Comparison Organizer (78,642 vs. 78,624)

Error Analysis (DOK 3)

Student writes: 52,701 > 52,710 because "701 is bigger than 710 because 7 is bigger than 7." Rewrite using place value:

Synthesis: Estimation & Comparison

Estimate the sum of 48,675 and 48,657 to the nearest hundred. Then compare the two numbers using >, <, or =:

Independent Review: Practice Problems

38,100 _____ 38,001

47,920 _____ 48,102

65,754 _____ 65,745

90,300 _____ 89,999

Enrichment: Order from Least to Greatest

65,709 • 65,790 • 65,970 • 65,079 • 65,907

"For Part A, I compared the ____________ place because..."

Part D (Constructed Response): A student claims: "84,325 is greater because 5 is greater than 2." Do you agree or disagree? Use place-value vocabulary (digits, place, values) to prove your answer:

NC.4.NBT.7 Mastery Rubric & Feedback Guide

Teacher Evaluation Scale

Intervention Notes / Small Group Focus:

Student Next Steps:

Warm-Up Quick Compare

34,205 < 34,502 (Hundreds place: 200 < 500)

67,319 = 67,319 (All places identical)

89,002 < 90,001 (Ten-thousands place: 80,000 < 90,000)

We Do Organizer (74,315 vs 73,915)

Ten-thousands: 7 = 7 (Same)

Thousands: 4 vs 3 (Different!)

Conclusion: 74,315 > 73,915 because 4 thousands (4,000) is greater than 3 thousands (3,000).

Error Analysis & CFU

Error Correction: The student compared the ones place instead of left-to-right. The thousands place decides: 5,000 < 6,000, so 85,763 < 86,093.

CFU (92,804 vs 92,840): In 92,804 the 4 is in the ones place (value = 4). In 92,840 the 4 is in the tens place (value = 40). 92,804 < 92,840.

Independent Practice & Context

56,810 > 56,801 (Tens: 10 > 0)

91,304 < 91,340 (Tens: 0 < 40)

100,000 > 99,999 (Hundred-thousands: 100k > 0)

62,587 > 62,578 (Tens: 80 > 70)

Canned Food Drive: School A (84,975) > School B (84,795) because 9 hundreds (900) > 7 hundreds (700).

NC.4.NBT.7 Instructional Resource • Number Champions Page 1 of 3 • Teacher Edition

Grade 4 Mathematics • Unit: Number Champions Teacher Solutions & Scoring Guide

Practice Packet Key: Days 3, 4 & 5

Multi-Step Showdown & Review

Day 3 • Compare & Defend Page 3 Student Packet

Warm-Up & Organizer

45,681 = 45,681

72,000 > 71,999 (Thousands 2 > 1)

88,392 < 89,103 (Thousands 8 < 9)

91,028 vs 91,820: Stop at hundreds (0 < 8). Tens/ones are irrelevant.

Misconceptions & Forms

Error Fix: 64,205 < 64,502. The student compared 2 vs 5 in isolation. In hundreds place, 200 < 500.

Expanded Form: 64,205 < 64,502 (Expanded: 60,000+4,000+500+2). Hundreds place (200 < 500) decides.

You Do & Book Drive

57,108 < 57,801 (Hundreds: 100 < 800)

66,932 > 66,923 (Tens: 30 > 20)

89,240 = 89,240

45,987 < 46,098 (Thousands: 5k < 6k)

Books: School B (75,800) > School A (75,008) (Hundreds 800 > 0).

Day 4 • Multi-Step Showdown Page 4 Student Packet

We Do: Maple vs. River

Step 1 (Maple Total): 36,418 + 22,350 = 58,768 cans.

Step 2 (Compare): 58,768 > 41,980 (Ten-thousands place: 50,000 > 40,000).

Error Analysis: The student forgot to regroup 10,000 into the ten-thousands column (got 48,768). Although the conclusion was Maple, the mathematical evidence was false.

Independent Word Problems

1. Cars: Ohio (75,023) > Texas (72,416) (Thousands: 5,000 > 2,000).

2. Visitors: Bellview (43,920) > Milltown (42,756) (Thousands: 3,000 > 2,000).

3. Books: Bookstore A = 21,845 + 25,900 = 47,745. Bookstore B (48,999) > Bookstore A (47,745). Bookstore B sold more!

4. Steps: Runner A = 56,230 + 41,906 = 98,136. Runner A (98,136) > Runner B (97,001). Runner A took more!

Day 5 • Mastery & Synthesis Review Page 5 Student Packet

Warm-Up & Organizer

73,492 > 73,429 (Tens: 90 > 20)

58,301 = 58,301 (Equal)

78,642 vs 78,624: Ten-thousands (7), thousands (8), and hundreds (6) equal. Tens place: 40 > 20, so 78,642 > 78,624.

Error & Synthesis

Error Fix: 52,701 < 52,710. Hundreds are both 700. In tens place, 0 tens < 1 ten (0 < 10).

Synthesis: 48,675 + 48,657 ≈ 48,700 + 48,700 = 97,400. Compare: 48,675 > 48,657 (Tens 70 > 50).

Independent & Ordering

38,100 > 38,001 (Hundreds 1 > 0)

47,920 < 48,102 (Thousands 7k < 8k)

65,754 > 65,745 (Tens 50 > 40)

90,300 > 89,999 (Ten-thousands 9 > 8)

Enrichment Order: 65,079 < 65,709 < 65,790 < 65,907 < 65,970

NC.4.NBT.7 Instructional Resource • Number Champions Page 2 of 3 • Teacher Edition

Grade 4 Mathematics • Unit: Number Champions Mastery Assessment Guide

Daily Mastery Exit Tickets Key (Days 1–5)

Standards Rubric & Feedback Exemplars

Exit Ticket 1: Precision Estimation 4 Pts

Problem: Estimate sum of \(5,249 + 6,872\)

Part A (Hundred): 5,200 + 6,900 = 12,100 (1 pt)

Part B (Thousand): 5,000 + 7,000 = 12,000 (1 pt)

Part C: Hundreds estimate is closer because exact sum is 12,121; 12,100 is off by only 21, whereas 12,000 is off by 121. (1 pt)

Part D: Closer to 12,000. 12,121 is 121 away from 12,000 but 879 away from 13,000. (1 pt)

Exit Ticket 2: Place Value Comparisons 4 Pts

Part A: 70,983 > 70,839 (1 pt)

Part B: Hundreds place determined answer (900 > 800). (1 pt)

Part C: Incomplete because digits must be compared starting from greatest place value (left). Only after confirming ten-thousands and thousands are equal does the hundreds place decide. (1 pt)

Part D: 45,001 > 44,998. The thousands digit 5 has a value of 5,000, while the thousands digit 4 has a value of 4,000. 5,000 > 4,000. (1 pt)

Exit Ticket 3: Defend Your Symbol 4 Pts

Part A: 57,108 < 57,801 (1 pt)

Part B: Hundreds place determined answer. (1 pt)

Part C: Ten-thousands (5) and thousands (7) are equal. In the hundreds place, 100 is less than 800, so we stop and conclude 57,108 < 57,801. (1 pt)

Part D (100,000 vs 99,999): 100,000 has 1 in the hundred-thousands place (value 100,000); 99,999 has 0 hundred-thousands. Highest place value always decides regardless of individual digit values. (1 pt)

Exit Ticket 4: Real-World Comparisons 4 Pts

Part A: 83,728 > 82,901 (1 pt)

Part B: Thousands place (3,000 > 2,000). (1 pt)

Part C: Calculation: 83,728 - 82,901 = 827 more views. (1 pt)

Part D: Disagree. The student compared hundreds instead of starting with the greatest place value. The thousands place (3,000 vs 2,000) decided the comparison before ever looking at 728 or 901. (1 pt)

Exit Ticket 5: Unit Mastery Assessment (NC.4.NBT.7) 4 Pts

Part A: 84,325 < 84,352 (1 pt)

Part B: 91,406 = 91,406 (1 pt)

Part C: "For Part A, I compared the tens place because ten-thousands (8), thousands (4), and hundreds (3) are all identical, and 2 tens (20) < 5 tens (50)." (1 pt)

Part D (Constructed Response): Disagree. While 5 is greater than 2 in the ones place, multi-digit numbers must be compared from left to right. In the tens place, 20 is less than 50. Since 2 tens < 5 tens, the number 84,325 is smaller regardless of the ones place. (1 pt)

Teacher Grading Rubric & Action Plan Benchmark: 80% (16/20 pts unit total)

Level 4: Exceeds (4/4)

Flawless comparisons, identifies exact place value, and justifies using expanded place value vocabulary.

Level 3: Meets (3/4)

Correct symbols and identifies place value. Explanations clear but may omit explicit value statements (e.g. 5,000).

Level 2: Developing (2/4)

Correct symbols on simple pairs, but relies on digit size rather than place value (e.g., "728 vs 901"). Needs reteaching.

Level 1: Emerging (0-1/4)

Misconceptions comparing right-to-left or reversing symbols (> vs <). Place-value chart intervention required.

NC.4.NBT.7 Instructional Resource • Number Champions Page 3 of 3 • Teacher Edition