Singapore Math · Field Guide
ASSESS UNDERSTANDING

Practice library

Original questions, organized by grade, with expandable solutions and explanations.

Original problems: These are newly authored practice questions, not copies of the official placement tests. Have the student solve and explain independently, then reveal the worked answer.

GRADE 3Place value#01

Write 4,508 in expanded form.

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4,000 + 500 + 8. The tens digit is zero.

GRADE 3Mental arithmetic#02

Use compensation to find 398 + 257.

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400 + 257 − 2 = 655.

GRADE 3Division#03

Calculate 158 ÷ 6 and include the remainder.

View answer & explanation

26 remainder 2; check: 6 × 26 + 2 = 158.

GRADE 3Fractions#04

Calculate 1/10 + 5/10 in simplest form.

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6/10 = 3/5.

GRADE 3Comparison#05

Which is larger: 2/3 or 3/4? Why?

View answer & explanation

3/4. In twelfths, 2/3 = 8/12 while 3/4 = 9/12.

GRADE 3Measurement#06

Find 3 km 40 m − 1 km 750 m.

View answer & explanation

Regroup 3 km 40 m as 2 km 1,040 m; result 1 km 290 m.

GRADE 3Area#07

An 8 × 6 rectangle has a 3 × 2 corner removed. Find the area.

View answer & explanation

48 − 6 = 42 square units.

GRADE 3Time#08

Find the elapsed time from 7:45 a.m. to 10:20 a.m.

View answer & explanation

15 min to 8:00, then 120 min to 10:00, then 20 min = 155 min = 2 h 35 min.

GRADE 4Multiplication#09

Calculate 34 × 26 using an area model.

View answer & explanation

(30 + 4)(20 + 6) = 600 + 180 + 80 + 24 = 884.

GRADE 4Factors#10

List the common factors of 12 and 18.

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1, 2, 3 and 6.

GRADE 4Mixed numbers#11

Express 17/5 as a mixed number.

View answer & explanation

17 ÷ 5 = 3 remainder 2 → 3 2/5.

GRADE 4Fraction arithmetic#12

Calculate 3/4 + 2/5.

View answer & explanation

15/20 + 8/20 = 23/20 = 1 3/20.

GRADE 4Fraction of a whole#13

Find three-fourths of 28.

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28 ÷ 4 = 7, then 7 × 3 = 21.

GRADE 4Decimals#14

Calculate 2.70 + 0.85.

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3.55. Both values are expressed in hundredths.

GRADE 4Comparison model#15

Sarah has three times John’s stickers; together they have 72. Find each amount.

View answer & explanation

Four equal units → 72 ÷ 4 = 18; John 18, Sarah 54.

GRADE 4Cuboids#16

How many faces, edges and vertices has a cuboid?

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6 faces, 12 edges, 8 vertices.

GRADE 5Expressions#17

Evaluate 48 − 6 × (3 + 2).

View answer & explanation

(3 + 2) = 5; 6 × 5 = 30; 48 − 30 = 18.

GRADE 5Fraction multiplication#18

Calculate 3/4 × 2/3.

View answer & explanation

6/12 = 1/2.

GRADE 5Fraction division#19

Calculate 3 ÷ 3/4.

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There are 12 quarter-units in 3 wholes; four groups of 3 quarters fit. Answer 4.

GRADE 5Decimal multiplication#20

Calculate 2.4 × 0.35.

View answer & explanation

(24 × 35) / (10 × 100) = 840/1000 = 0.84.

GRADE 5Triangle area#21

A triangle has base 10 cm and perpendicular height 6 cm. Find its area.

View answer & explanation

(10 × 6) / 2 = 30 cm².

GRADE 5Ratio#22

Split $75 in ratio 2:3.

View answer & explanation

5 units worth $75 → $15/unit → $30 and $45.

GRADE 5Percentage#23

Find 15% of 240 without a calculator.

View answer & explanation

10% = 24 and 5% = 12, so 15% = 36.

GRADE 5Changing whole#24

Of 240 notebooks, 3/5 are sold; then 1/4 of the remainder are sold. How many remain?

View answer & explanation

2/5 of 240 = 96; retain 3/4 of 96 = 72.