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.
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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