Content category I of the Elementary Education: Mathematics Subtest (5003): about 20 of the 50 questions (40%). The topics ETS lists, how they are tested and practice questions with explanations.
50 questions on the real 65-minute clock, weighted like the ETS test, with a score by content category and an explanation for every answer.
Or start the free Numbers and Operations drillFrom the ETS Elementary Education: Mathematics Subtest (5003) Study Companion, content category I.
The largest category: place value and rounding, the four operations with whole numbers, fractions and decimals, properties of operations, ratios, rates and percents, factors, multiples and primes, and estimation. Several questions show a student’s computation and ask what misconception it reveals or which model represents it.
Answer each question, then open the explanation.
Question 1
A recipe uses 3/4 cup of oats for 6 servings. How many cups of oats are needed for 10 servings at the same rate?
Answer: C: 1.25
Each serving requires (3/4) ÷ 6 = 1/8 cup. Ten servings require 10 × 1/8 = 1.25 cups; multiplying by 6/10 reverses the scale factor.
Question 2
Which expression is the prime factorization of 180?
Answer: D: 2² × 3² × 5
The factorization 180 = 4 × 45 = 2² × 3² × 5 uses only prime factors. Although 4 × 9 × 5 also equals 180, the factors 4 and 9 are composite.
Question 3
A school has reached 72% of its goal by collecting 324 books. How many books are in the goal? Enter your answer as a whole number.
Numeric entry: answer in books.
Answer: 450 books
The equation 0.72 × goal = 324 represents the situation. Dividing 324 by 0.72 gives a goal of 450 books; multiplying by 0.72 would find a percent of the collected amount.
Question 4
A teacher models 3 ÷ 1/4 using three whole paper strips. Which action completes a measurement-division model?
Answer: B: Partition each strip into fourths and count all the fourth-size pieces.
Measurement division asks how many groups of size one-fourth fit into 3 wholes. Partitioning all three wholes into fourths produces 12 pieces; keeping one-fourth of each whole instead models multiplication by one-fourth.
Take the full test under the real clock
50 questions on the real 65-minute clock, weighted like the ETS test, with a score by content category and an explanation for every answer.
Or start the free Numbers and Operations drillETS lists about 20 of the 50 questions in Numbers and Operations, about 40% of the test.
Understands the place value system; Understands operations and properties of rational numbers; Understands proportional relationships and percents; Knows how to use basic concepts of number theory; Knows a variety of strategies to determine the reasonableness of results.
The largest category: place value and rounding, the four operations with whole numbers, fractions and decimals, properties of operations, ratios, rates and percents, factors, multiples and primes, and estimation. Several questions show a student’s computation and ask what misconception it reveals or which model represents it.
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