Original problems: These are newly authored practice questions, not copies of the official placement tests. Solve each problem and explain your method. Then reveal the worked answer to check your reasoning.
GRADE 3Place value#01
Write 4,508 in expanded form.
GRADE 3Mental arithmetic#02
Use compensation to find 398 + 257.
GRADE 3Division#03
Calculate 158 ÷ 6 and include the remainder.
GRADE 3Fractions#04
Calculate 1/10 + 5/10 in simplest form.
GRADE 3Comparison#05
Which is larger: 2/3 or 3/4? Why?
GRADE 3Measurement#06
Find 3 km 40 m − 1 km 750 m.
GRADE 3Area#07
An 8 × 6 rectangle has a 3 × 2 corner removed. Find the area.
GRADE 3Time#08
Find the elapsed time from 7:45 a.m. to 10:20 a.m.
GRADE 4Multiplication#09
Calculate 34 × 26 using an area model.
GRADE 4Factors#10
List the common factors of 12 and 18.
GRADE 4Mixed numbers#11
Express 17/5 as a mixed number.
GRADE 4Fraction arithmetic#12
Calculate 3/4 + 2/5.
GRADE 4Fraction of a whole#13
Find three-fourths of 28.
GRADE 4Decimals#14
Calculate 2.70 + 0.85.
GRADE 4Comparison model#15
Sarah has three times John’s stickers; together they have 72. Find each amount.
GRADE 4Cuboids#16
How many faces, edges and vertices has a cuboid?
GRADE 5Expressions#17
Evaluate 48 − 6 × (3 + 2).
GRADE 5Fraction multiplication#18
Calculate 3/4 × 2/3.
GRADE 5Fraction division#19
Calculate 3 ÷ 3/4.
GRADE 5Decimal multiplication#20
Calculate 2.4 × 0.35.
GRADE 5Triangle area#21
A triangle has base 10 cm and perpendicular height 6 cm. Find its area.
GRADE 5Ratio#22
Split $75 in ratio 2:3.
GRADE 5Percentage#23
Find 15% of 240 without a calculator.
GRADE 5Changing whole#24
Of 240 notebooks, 3/5 are sold; then 1/4 of the remainder are sold. How many remain?
After practice: Separate conceptual errors from representation gaps.
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