Factor Detectives Unit

1. (NC.4.NBT.7) Write the following numbers in order from least to greatest:

0.8 0.08 0.79 0.82

Order:

2. (NC.4.NBT.7) Maya's pencil is 0.35 meters long. Marcus's pencil is 0.4 meters long. Marcus says his pencil is shorter because 4 is less than 35. Explain his mistake.

3. (NC.4.NBT.1) Complete: \(600 \times 10 =\) ________, and \(60,000 \div 10 =\) ________. How many tens are in 4,500? ________

Cut or Fold Along Line

Day 3 Exit Ticket • Factor Search & Stopping Rule NC.4.OA.4

Part A: Find all factor pairs of 32 using a systematic search.

Part B: Is 32 prime or composite? Explain using division.

Part C: Is 32 a multiple of 8? Explain.

Part D (Challenge): Without finding every single factor, explain how you know 37 is prime. What numbers did you test?

Grade 4 Mathematics • Daily Checkpoint Page 3 of 5 • Day 3

Day 4 Checkpoint • Grade 4 Math

Daily Do Now & Exit Ticket

Name: Date:

Day 4 Do Now • Spiral Review NC.4.NBT.7 (Decimals) • NC.4.NBT.2

1. (NC.4.NBT.7) Select ALL statements that are TRUE:

\(0.6 > 0.59\) \(0.3 = 0.03\) \(0.07 < 0.70\) \(0.92 < 0.9\)

2. (NC.4.NBT.7) Write \(\frac{4}{10}\) and \(\frac{72}{100}\) as decimals. Then, compare them using \(>\), \(<\), or \(=\).

3. (NC.4.NBT.2) Write 304,050 in expanded notation and word form.

Cut or Fold Along Line

Day 4 Exit Ticket • Area Models NC.4.OA.4

Part A: Draw two different area models for 20 with dimensions labeled.

Model 1 Model 2

Part B: List all factor pairs of 20.

Part C: Explain why 20 is composite using models.

Part D (Challenge): Can you build more than one area model for 19? Explain why or why not using mathematical reasoning.

Grade 4 Mathematics • Daily Checkpoint Page 4 of 5 • Day 4

Day 5 Checkpoint • Grade 4 Math

Daily Do Now & Exit Ticket

Name: Date:

Day 5 Do Now • Cumulative Spiral Check NC.4.NBT.7 • NC.4.NBT.1 • NC.4.NBT.4

1. (NC.4.NBT.7) In a track meet, Liam jumped 1.45 meters, Carlos jumped 1.5 meters, and Devon jumped 1.39 meters. Write their names in order from furthest jump to shortest jump.

2. (NC.4.NBT.1) True or False: 40 hundreds is equal to 4 thousands. Prove your answer using place value.

3. (NC.4.NBT.4) An amusement park had 63,412 visitors on Saturday and 48,975 visitors on Sunday. How many more visitors attended on Saturday than Sunday?

Show vertical subtraction:

Cut or Fold Along Line

Day 5 Exit Ticket • Prime & Composite Mastery NC.4.OA.4

Part A: Circle ALL the prime numbers in the list below:

3 4 5 6 7 9 11 13

Part B: Find factor pairs of 9. Prime or composite? Explain.

Part C: Is 13 prime or composite? Justify with multiplication/division.

Part D (Challenge): A student says: "31 is composite because it is greater than 30." Do you agree or disagree? Defend your answer with mathematical evidence.

Grade 4 Mathematics • Daily Checkpoint Page 5 of 5 • Day 5

Number Detective Challenge:

Find a whole number between 1 and 50 that has exactly three factor pairs. List the number, its factor pairs, and explain how you know you found them all:

Math Journal • Constructed Response

Comparison Proof

Prompt: Compare the numbers 25 and 30. Explain their factor pairs, whether each is prime or composite, how you know 25 is a multiple of one of its factors, and what patterns you notice.

NC.4.OA.4 • Factor Detectives Workbook Page 3 of 5 • Day 3 Practice

Day 4 Student Practice • NC.4.OA.4

Area Model & Geometry Investigation

Name: Date:

Directions: Complete the area model investigation for the target numbers below. Every area model represents \(\text{Length} \times \text{Width} = \text{Area}\) and relates directly to division.

Area Model Comparison: Number 16 vs. Number 18 Square vs. Non-Square

Area = 16

Which rectangle is a square? Explain why.

Area = 18

Which rectangle has the greatest perimeter?

Multi-Number Area Model Explorer

Record dimensions and equations for 14, 21, 24, and 25:

Area = 14:

Area = 21:

Area = 24:

Area = 25:

Area Model Extension:

Which whole number from 10 to 30 has the greatest number of area models? Support your answer with evidence.

Math Journal • Constructed Response

Geometry Proof

Prompt: Use area models to compare 20 and 25. Explain all factor pairs, which number has a square array and why, and how area models prove whether each number is prime or composite.

NC.4.OA.4 • Factor Detectives Workbook Page 4 of 5 • Day 4 Practice

Day 5 Summative • NC.4.OA.4

EOG Rigor Multiple-Choice Assessment

Name: Score: / 6

1. (DOK 1) Which list shows ALL the factor pairs of 24?

A. (1, 24), (2, 12), (3, 8), (4, 6)

B. (1, 24), (2, 10), (3, 9)

C. (1, 12), (2, 6), (3, 9)

D. (1, 24), (3, 7), (4, 6)

2. (DOK 2) Which number is a multiple of BOTH 2 and 3?

A. 9

B. 10

C. 12

D. 15

3. (DOK 3) Jason says 25 is a prime number. Is Jason correct? Explain.

A. Yes, because 25 has only 2 factors.

B. No, because 25 has more than 2 factors (1, 5, 25).

C. Yes, because 25 is only divisible by 5.

D. No, because all odd numbers are composite.

4. (DOK 1) Which number is NOT composite?

A. 21

B. 17

C. 30

D. 18

5. (DOK 3) You have 16 chairs. Can you arrange them in equal rows more than one way? What does this tell you about 16?

A. Yes; 16 must be a prime number.

B. Yes; 16 is composite because it has multiple factor pairs.

C. No; 16 can only be arranged in 1 row of 16.

D. No; 16 is even, so it can only have 2 rows.

6. (DOK 3 Constructed Response) James claims: "17 is a composite number because it is an odd number." Use what you know about factors and factor pairs to explain whether James is correct or incorrect.

NC.4.OA.4 • Factor Detectives Workbook Page 5 of 5 • Day 5 Assessment

NC.4.OA.4 • Teacher Answer Guide Page 1 of 4 • Days 1 & 2 Solutions

Teacher Resource • NC.4.OA.4 & NC.4.NBT

Master Solutions Teacher Key (Days 3 & 4)

Days 3 – 4 Checkpoints

Day 3 Do Now Solutions (NC.4.NBT.7 & NBT.1) Spiral Standards

1. (NBT.7): Least to greatest order: 0.08, 0.79, 0.8, 0.82 (rewritten with equal place values: 0.08, 0.79, 0.80, 0.82).

2. (NBT.7): Marcus made a place-value error. 0.4 equals 4 tenths or 40 hundredths (\(0.40\)). Since 40 hundredths is greater than 35 hundredths (\(0.35\)), Marcus's pencil is actually longer.

3. (NBT.1): \(600 \times 10 = \mathbf{6,000}\); \(60,000 \div 10 = \mathbf{6,000}\); There are 450 tens in 4,500.

Day 3 Exit Ticket Solutions (NC.4.OA.4) Exemplar Rubric

Part A: Factor pairs of 32: \((1, 32), (2, 16), (4, 8)\). Factors: 1, 2, 4, 8, 16, 32.

Part B: Composite because \(32 \div 2 = 16\) and \(32 \div 4 = 8\); it has 6 total factors, which is more than two factors.

Part C: Yes, 32 is a multiple of 8 because \(8 \times 4 = 32\).

Part D (Challenge): To test 37, you only need to test whole numbers up to 6 (\(6 \times 6 = 36\)). 37 is not divisible by 2 (odd), 3 (\(3 \times 12 = 36\)), 4, 5, or 6. Since none divide evenly, 37 must be prime.

Day 4 Do Now Solutions (NC.4.NBT.7 & NBT.2) Decimal & Notation

1. (NBT.7): True statements: \(0.6 > 0.59\) and \(0.07 < 0.70\). (False: \(0.3 = 0.03\) and \(0.92 < 0.9\)).

2. (NBT.7): \(\frac{4}{10} = 0.4\) (or 0.40); \(\frac{72}{100} = 0.72\). Comparison: \(0.4 < 0.72\) (or \(\frac{4}{10} < \frac{72}{100}\)).

3. (NBT.2): \(300,000 + 4,000 + 50\). Word form: Three hundred four thousand, fifty.

Day 4 Exit Ticket Solutions (NC.4.OA.4) Exemplar Rubric

Part A: Student draws two models from: \(1 \times 20\), \(2 \times 10\), or \(4 \times 5\).

Part B: Factor pairs of 20: \((1, 20), (2, 10), (4, 5)\).

Part C: 20 is composite because it can be represented by three different rectangular area models, showing it has more than one factor pair.

Part D (Challenge): No, you cannot build more than one area model for 19. The only model is \(1 \times 19\) because 19 is prime and has no other factors.

NC.4.OA.4 • Teacher Answer Guide Page 2 of 4 • Days 3 & 4 Solutions

Teacher Resource • NC.4.OA.4 & NC.4.NBT

Day 5 Checkpoints & Practice Key

Day 5 & Workbook Keys

Day 5 Do Now Solutions (NC.4.NBT Cumulative Spiral) Cumulative

1. (NBT.7): Furthest to shortest: Carlos (1.5 m), Liam (1.45 m), Devon (1.39 m). (Note: \(1.5 = 1.50\)).

2. (NBT.1): True. 40 hundreds \(= 40 \times 100 = 4,000\). 4 thousands \(= 4 \times 1,000 = 4,000\).

3. (NBT.4): \(63,412 - 48,975 = \mathbf{14,437}\) more visitors.

Day 5 Exit Ticket Solutions (NC.4.OA.4 Mastery) Exemplar Rubric

Part A (Circle Prime Numbers): Prime numbers circled: 3, 5, 7, 11, 13. (Composite numbers left uncircled: 4, 6, 9).

Part B: Factor pairs of 9: \((1, 9), (3, 3)\). Composite because it has 3 factors: 1, 3, 9.

Part C: 13 is prime because only \(1 \times 13 = 13\). No other whole numbers divide evenly into 13.

Part D (Challenge): Disagree. A number's size does not determine if it is prime or composite. 31 is greater than 30, but its only factor pair is \((1, 31)\). Therefore, 31 is prime.

Day 3 Factor Search Table Master Key

Detective Challenge Answer: Numbers with exactly 3 factor pairs (6 factors) include 12 (\((1,12), (2,6), (3,4)\)), 18 (\((1,18), (2,9), (3,6)\)), 20, 28, 32, 44, 45, and 50.

NC.4.OA.4 • Teacher Answer Guide Page 3 of 4 • Day 5 & Practice Solutions

Teacher Resource • NC.4.OA.4 Assessment

Day 5 Assessment Key & Distractor Rationale

EOG Standards Item Analysis

Question 1 • Correct Answer: A DOK 1

Rationale: 24 has four factor pairs: \((1, 24), (2, 12), (3, 8), (4, 6)\). Distractor B has incorrect sums \((2, 10)\), C is missing pairs, and D uses non-factors \((3, 7)\).

Question 2 • Correct Answer: C DOK 2

Rationale: 12 is a common multiple (\(2 \times 6 = 12\) and \(3 \times 4 = 12\)). 9 and 15 are multiples of 3 only; 10 is a multiple of 2 only.

Question 3 • Correct Answer: B DOK 3

Rationale: 25 has three factors (1, 5, 25). Since it has more than two factors, it is composite. Distractor D represents the common student misconception that all odd numbers are prime.

Question 4 • Correct Answer: B DOK 1

Rationale: "NOT composite" means prime. 17 has only two factors (1 and 17). 21 (\(3 \times 7\)), 30 (\(3 \times 10\)), and 18 (\(2 \times 9\)) are all composite.

Question 5 • Correct Answer: B DOK 3

Rationale: 16 chairs can be arranged in \(1 \times 16\), \(2 \times 8\), and \(4 \times 4\). Multiple arrangements directly signify that 16 is composite.

Question 6 (Constructed Response) • Scoring Rubric 2-Point EOG Rubric

Score Point 2 (Full Credit): Student states James is incorrect and provides sound mathematical reasoning (e.g., "Even though 17 is odd, it is prime because its only factors are 1 and 17. Being odd does not make a number composite; numbers like 9, 15, and 21 are odd but composite.").

Score Point 1 (Partial Credit): Student identifies that James is incorrect or that 17 is prime, but provides incomplete explanation or lacks mention of factor pairs.

Score Point 0: Incorrect claim (agrees with James) or irrelevant explanation.

Math Journal Holistic Scoring Guide

Full credit responses across Days 1–4 journals must include: (1) All accurate factor pairs listed systematically, (2) Correct classification using precise terminology ("prime", "composite"), (3) Visual evidence connected to arrays/area models, and (4) Clear linkage between factors and multiples.

NC.4.OA.4 • Teacher Answer Guide Page 4 of 4 • Assessment Key & Rubrics

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

COMPOSITE NUMBERS

More than two factors (at least one other pair).

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25...

Misconception Buster: Odd DOES NOT equal Prime! 15 is odd, but \(3 \times 5 = 15\) (Composite)!