Test 3 (Unit 6) is Completed & Locked

Verified Grade: 40 / 53 (75.5% • Grade C • 30 min game time) • Total Time: 35m 6s • Completed October 15, 2026 at 7:53 PM.

Test Submitted & Graded

Verified Grade: 40 / 53 (75.5% • Grade C • 30 min game time)

Total Time Taken: 35m 6s (Initial: 20m 2s + Retake: 15m 4s / 45:00 limit)

All answers have been evaluated. Newly corrected retake answers were added directly to the total score.

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4th Grade Math Diagnostic Test — Unit 6

Factors, Multiples, Prime & Composite Numbers, and Number Patterns. Official Diagnostic Completed October 15, 2026.

Question 1

Factor Pairs up to 100

Score: 16 / 22 pts (Verified)

Part A: Find all factor pairs of 36. Fill in the factor pairs in order from smallest to largest first factor.

Pair 1: × = 36 Correct
Pair 2: × = 36 Correct
Pair 3: × = 36 Correct
Pair 4: × = 36 Verified Accepted (1 / 2 pt • True Commutative Fact)
Pair 5: × = 36 Verified Accepted (1 / 2 pt • True Commutative Fact)

Part B: How many total unique factors does 36 have? Incorrect (0 / 1 pt) factors. (Pass 1: 5 • Retake: 3)

Part C: Find all factor pairs of 48 in order from smallest first factor.

Pair 1: × = 48 Correct
Pair 2: × = 48 Correct
Pair 3: × = 48 Correct
Pair 4: × = 48 Verified Accepted (1 / 2 pt • True Commutative Fact)
Pair 5: × = 48 Verified Accepted (1 / 2 pt • True Commutative Fact)

Total unique factors of 48: Incorrect (0 / 1 pt) factors. (Pass 1: 5 • Retake: 3)

Official Solution:

Factor pairs of 36: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6.
Unique factors of 36 (9 total): 1, 2, 3, 4, 6, 9, 12, 18, 36 (6 is listed only once because 6 × 6 = 36).

Factor pairs of 48: 1 × 48, 2 × 24, 3 × 16, 4 × 12, 6 × 8.
Unique factors of 48 (10 total): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

Concept & Review Notes (Systematic Factor Listing & Counts)

1. Systematic Testing vs. Commutative Duplicates: When finding factor pairs, test integers in order: 1, 2, 3, 4, 5, 6... Reversing a pair you already wrote (such as 9 × 4 when you already have 4 × 9, or 8 × 6 when you already have 6 × 8) is the exact same pair due to the commutative property. Missing pairs were 2 × 18 and 3 × 12 for 36, and 3 × 16 and 4 × 12 for 48.

2. Unique Factors Count: To count unique factors, list out all distinct numbers that divide the target with no remainder. For 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 (9 unique factors). For 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 (10 unique factors).

Question 2

Multiples of Whole Numbers

Score: 7 / 7 pts (100%)

Part A: Write the first six multiples of 8 starting from 8 × 1:

Correct Correct Correct Correct Correct Correct

Part B: Is 72 a multiple of 8?

Correct
Official Solution:

First six multiples of 8: 8, 16, 24, 32, 40, 48.
Is 72 a multiple of 8? Yes, because 8 × 9 = 72 (or 72 ÷ 8 = 9 with 0 remainder).

Concept & Review Notes (Full Credit Mastery)

Excellent work! Jing demonstrated complete mastery on multiples of 8 and identifying that 72 is in the 8 times table (8 × 9 = 72).

Question 3

Prime vs. Composite Numbers

Score: 5 / 7 pts (Pass 1: 2 / 7)

Part A: Classify each number as Prime or Composite:

29 Correct
39 Correct
51 Corrected on Retake (Pass 1: Prime)
67 Corrected on Retake (Pass 1: Composite)
91 Corrected on Retake (Pass 1: Prime)

Part B: What is the smallest prime number? Incorrect (0 / 1 pt) (Pass 1: 29 • Retake: left blank)

Part C: Is the number 1 prime, composite, or neither?

Incorrect (0 / 1 pt)
Official Solution:

• 29: Prime (only 1 × 29)
• 39: Composite (3 × 13 = 39)
• 51: Composite (3 × 17 = 51)
• 67: Prime (only 1 × 67)
• 91: Composite (7 × 13 = 91)
• Smallest prime number: 2 (also the only even prime number)
• The number 1: Neither prime nor composite (a prime number must have exactly two distinct factors; 1 only has one factor).

Concept & Review Notes (Tricky Composites & Special Numbers)

1. Retake Recovery: Jing successfully caught and fixed 51 (3 × 17), 67 (prime), and 91 (7 × 13) on the retake, jumping Part A from 2/5 to a perfect 5/5!

2. Smallest Prime: The smallest prime number is 2 (factors: 1 and 2). It is the only even prime number because every other even number is divisible by 2.

3. Why 1 is Special: A prime number must have exactly two distinct factors (1 and itself). Since the number 1 only has one factor (itself), it is classified as Neither prime nor composite.

Question 4

Distinguishing Factors vs. Multiples

Score: 0 / 4 pts

Part A: Choose whether the first number is a Factor or a Multiple of the second number:

1. 6 is a of 24. Incorrect (0 / 1 pt)
2. 30 is a of 5. Incorrect (0 / 1 pt)
3. 9 is a of 72. Incorrect (0 / 1 pt)

Part B: Write a whole number between 20 and 30 that is a multiple of both 3 and 4:

Incorrect (0 / 1 pt) (Must be between 20 and 30)
Official Solution:

1. 6 is a factor of 24 (6 × 4 = 24).
2. 30 is a multiple of 5 (5 × 6 = 30).
3. 9 is a factor of 72 (9 × 8 = 72).
Part B: Multiples of 3 between 20-30: 21, 24, 27. Multiples of 4 between 20-30: 24, 28. The number that is a multiple of both is 24 (since 3 × 8 = 24 and 4 × 6 = 24).

Concept & Review Notes (Factor vs. Multiple Mental Anchor)

1. The Size Rule: A factor is smaller than or equal to the number. It is a building block that fits inside evenly (e.g., 6 fits into 24 four times, so 6 is a factor). A multiple is larger than or equal to the number. It is the product when you multiply (e.g., 5 × 6 = 30, so 30 is a multiple of 5). Jing inverted these three relationships in Part A.

2. Common Multiples in a Range: In Part B, 6 is a multiple of 3, but not of 4, and 6 is not between 20 and 30. Looking in the range [20, 30]: 3 × 8 = 24 and 4 × 6 = 24, giving 24.

Question 5

Number Rules & Input/Output Tables

Score: 9 / 9 pts (100% on Retake!)

Part A: A pattern starts at 5 and follows the rule: “Add 6 each time.”
Write the first 5 numbers of this pattern:

Corrected on Retake (Pass 1: 6, 12, 18, 24, 30)

What will always be true of every number in this pattern?

Corrected on Retake (Pass 1: even)

Part B: An input/output table follows the rule: Output = (Input × 4) + 3.
Fill in the missing values in the table:

Input Output Status
2 11 Example
5 Corrected on Retake
8 Corrected on Retake
43 Corrected on Retake
Official Solution:

Part A: Start at 5, add 6 each time: 5, 11, 17, 23, 29.
Feature: All numbers are odd (5 is odd, and adding an even number like 6 always keeps the sum odd: Odd + Even = Odd).
Part B:
• Input 5 → (5 × 4) + 3 = 20 + 3 = 23.
• Input 8 → (8 × 4) + 3 = 32 + 3 = 35.
• Output 43 → Work backward: 43 − 3 = 40; 40 ÷ 4 = 10.

Concept & Review Notes (Flawless Retake Recovery)

Outstanding turnaround! In Pass 1, Jing started at 6 and listed multiples of 6 (0 / 9). On the retake, Jing carefully read the prompt, started at 5, calculated every term correctly (5, 11, 17, 23, 29), correctly identified the odd feature, and executed all forward and inverse input/output table calculations for a perfect 9 / 9 (+9 pts)!

Question 6

Applied Word Problems: Arrays & Grouping

Score: 3 / 4 pts (Pass 1: 1 / 4)

A school gym has 60 folding chairs. The custodian needs to arrange all 60 chairs into equal rows with no chairs left over.

Part A: Can she arrange them into rows of 8 chairs?

Correct

Part B: If she sets up rows of 5 chairs, how many rows will there be?

Corrected on Retake (Pass 1: 40) rows.

Part C: Name two other possible numbers of chairs per row she could use (other than 1, 5, 8, or 60):

Option 1: chairs per row Disallowed by Prompt (0 / 1 pt)
Option 2: chairs per row Correct (1 / 1 pt)

(Pass 1: 5 and 8 • Retake: 5 and 12)

Official Solution:

Part A: No, because 60 ÷ 8 = 7 R 4 (there would be 4 chairs left over; 8 is not a factor of 60).
Part B: 60 ÷ 5 = 12 rows.
Part C: Any two other factors of 60: 2, 3, 4, 6, 10, 12, 15, 20, or 30 chairs per row.

Concept & Review Notes (Reading Prompt Restrictions)

1. Division and Factors: In Part B, Jing fixed 40 → 12 on the retake (60 ÷ 5 = 12), and in Part C successfully named 12 as a valid row size (12 × 5 = 60).

2. Prompt Exclusions: Option 1 was 5, but the question explicitly asked for numbers "other than 1, 5, 8, or 60". Remind Jing to always re-read constraints in word problems to avoid using excluded values.