WGU D128 Mathematics for Elementary Educators
Objective Assessment - 2026/2027 Edition | Math
Content & Pedagogical Knowledge
80 Multiple-Choice Items | 100 % Correct Key & Dual-Focus Rationale
Domain 1 – Number & Operations (24 items)
Q1
A 4th-grade student writes:
307
– 48
141
She explains, “I crossed out the 3 and made it 2, then put a 1 next to the 0 so 10 – 8 = 2,
and 2 – 4 = 2.” Which misconception is MOST evident?
A. Incorrect basic subtraction facts
B. Misapplication of the standard algorithm’s “borrowing” sequence
C. Failure to regroup across zero correctly (treated middle 0 as 9 instead of 10)
D. Ignoring place value by subtracting 8 from 0 directly
Correct: C
,Rationale: Math: After the first regroup, the tens place should be 9 (not 10) because 1
hundred was moved to the tens as 10 tens, then 1 ten moved to the ones. Pedagogy:
Student needs place-value language: “We trade 1 hundred for 10 tens, then trade 1 ten
for 10 ones,” supported by base-ten blocks. Distractors: A is fact accurate; B is vague; D
ignores the regroup that did occur.
Q2
When introducing ⅖ × 3, a teacher wants to build conceptual understanding. Which
representation is MOST appropriate?
A. Jumping 3 steps of 0.4 on a number line
B. Overlaying 3 copies of a 2-part-out-of-5 strip on the same whole
C. Calculating 2 × 3 = 6 and writing 6/5
D. Repeating ⅖ fifteen times because 3 = 15⁄5
Correct: B
Rationale: Math: ⅖ × 3 means 3 groups of ⅖; visually laying three identical fraction strips
each showing 2/5 builds the iteration meaning. Pedagogy: Strips allow students to see
the product 6⁄5 as “one whole and one-fifth.” Number-line jumps (A) are abstract; C skips
the model; D mis-scales the unit.
Q3
A 3rd grader says, “0.4 is less than 0 because 4 is less than zero.” Which experience
BEST addresses this idea?
A. Placing 0 and 0.4 on a 0-1 decimal strip and discussing distance from 0
,B. Rounding 0.4 to the nearest whole number
C. Converting 0.4 to 4⁄10 and comparing to 0⁄10
D. Showing the rule “zeros on the left are smaller”
Correct: A
Rationale: Math: 0.4 > 0; the strip shows magnitude visually. Pedagogy: Kinesthetic
placement and measuring “how far from 0” confronts the zero-is-smaller-than-anything
misconception. Rounding (B) hides the decimal; C is correct but less intuitive; D is
procedural.
Q4
A student computes 48 × 6 mentally by finding 50 × 6 = 300 and subtracting 2 × 6 = 12
to get 288. Which property did the student use?
A. Associative property of multiplication
B. Distributive property over subtraction
C. Commutative property
D. Identity property
Correct: B
Rationale: Math: 48 × 6 = (50 – 2) × 6 = 50×6 – 2×6. Pedagogy: Recognizing the strategy
legitimizes flexible mental math and introduces the distributive principle; teachers
should highlight and name it. Associative (A) groups factors; commutative (C) reorders;
identity (D) uses 1.
Q5
, While multiplying 234 × 6, a fifth grader writes partial products: 1200 (200×6), 180
(30×6), 24 (4×6) and adds them. Which statement BEST describes this algorithm?
A. It is incorrect because place value is ignored.
B. It is a valid expanded-form application of the distributive property.
C. It only works for even factors.
D. It is the lattice method.
Correct: B
Rationale: Math: 234 × 6 = (200 + 30 + 4) × 6. Pedagogy: Encouraging expanded form
before compact algorithm deepens place-value understanding. Lattice (D) is different
grid model.
Q6
A student divides 3 by 4 and writes 1 remainder 1. When asked for a decimal, she says,
“You can’t divide 3 by 4.” Which intervention is MOST effective?
A. Reminding her that 4 goes into 3 zero times, then trade 3 for 30 tenths and continue
B. Showing 3⁄4 = 0.75 with a calculator
C. Re-teaching long-division steps
D. Providing extra worksheets with remainders
Correct: A
Objective Assessment - 2026/2027 Edition | Math
Content & Pedagogical Knowledge
80 Multiple-Choice Items | 100 % Correct Key & Dual-Focus Rationale
Domain 1 – Number & Operations (24 items)
Q1
A 4th-grade student writes:
307
– 48
141
She explains, “I crossed out the 3 and made it 2, then put a 1 next to the 0 so 10 – 8 = 2,
and 2 – 4 = 2.” Which misconception is MOST evident?
A. Incorrect basic subtraction facts
B. Misapplication of the standard algorithm’s “borrowing” sequence
C. Failure to regroup across zero correctly (treated middle 0 as 9 instead of 10)
D. Ignoring place value by subtracting 8 from 0 directly
Correct: C
,Rationale: Math: After the first regroup, the tens place should be 9 (not 10) because 1
hundred was moved to the tens as 10 tens, then 1 ten moved to the ones. Pedagogy:
Student needs place-value language: “We trade 1 hundred for 10 tens, then trade 1 ten
for 10 ones,” supported by base-ten blocks. Distractors: A is fact accurate; B is vague; D
ignores the regroup that did occur.
Q2
When introducing ⅖ × 3, a teacher wants to build conceptual understanding. Which
representation is MOST appropriate?
A. Jumping 3 steps of 0.4 on a number line
B. Overlaying 3 copies of a 2-part-out-of-5 strip on the same whole
C. Calculating 2 × 3 = 6 and writing 6/5
D. Repeating ⅖ fifteen times because 3 = 15⁄5
Correct: B
Rationale: Math: ⅖ × 3 means 3 groups of ⅖; visually laying three identical fraction strips
each showing 2/5 builds the iteration meaning. Pedagogy: Strips allow students to see
the product 6⁄5 as “one whole and one-fifth.” Number-line jumps (A) are abstract; C skips
the model; D mis-scales the unit.
Q3
A 3rd grader says, “0.4 is less than 0 because 4 is less than zero.” Which experience
BEST addresses this idea?
A. Placing 0 and 0.4 on a 0-1 decimal strip and discussing distance from 0
,B. Rounding 0.4 to the nearest whole number
C. Converting 0.4 to 4⁄10 and comparing to 0⁄10
D. Showing the rule “zeros on the left are smaller”
Correct: A
Rationale: Math: 0.4 > 0; the strip shows magnitude visually. Pedagogy: Kinesthetic
placement and measuring “how far from 0” confronts the zero-is-smaller-than-anything
misconception. Rounding (B) hides the decimal; C is correct but less intuitive; D is
procedural.
Q4
A student computes 48 × 6 mentally by finding 50 × 6 = 300 and subtracting 2 × 6 = 12
to get 288. Which property did the student use?
A. Associative property of multiplication
B. Distributive property over subtraction
C. Commutative property
D. Identity property
Correct: B
Rationale: Math: 48 × 6 = (50 – 2) × 6 = 50×6 – 2×6. Pedagogy: Recognizing the strategy
legitimizes flexible mental math and introduces the distributive principle; teachers
should highlight and name it. Associative (A) groups factors; commutative (C) reorders;
identity (D) uses 1.
Q5
, While multiplying 234 × 6, a fifth grader writes partial products: 1200 (200×6), 180
(30×6), 24 (4×6) and adds them. Which statement BEST describes this algorithm?
A. It is incorrect because place value is ignored.
B. It is a valid expanded-form application of the distributive property.
C. It only works for even factors.
D. It is the lattice method.
Correct: B
Rationale: Math: 234 × 6 = (200 + 30 + 4) × 6. Pedagogy: Encouraging expanded form
before compact algorithm deepens place-value understanding. Lattice (D) is different
grid model.
Q6
A student divides 3 by 4 and writes 1 remainder 1. When asked for a decimal, she says,
“You can’t divide 3 by 4.” Which intervention is MOST effective?
A. Reminding her that 4 goes into 3 zero times, then trade 3 for 30 tenths and continue
B. Showing 3⁄4 = 0.75 with a calculator
C. Re-teaching long-division steps
D. Providing extra worksheets with remainders
Correct: A
