Grade 5 · Maths · curriculum collection
Grade 5 Maths, Common Core domains
8 units for Grade 5 maths, organised by Common Core domain: Operations and Algebraic Thinking, Number and Operations in Base Ten, Number and Operations: Fractions, Measurement and Data. Each unit has a short lesson, a practice worksheet and a review worksheet, both with answer keys.
Answer-checked and approved on 29 October 2026
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Aligned by StudyBrix at domain level. Not an official publication of, or endorsed by, the standards' authors. Framework: Common Core State Standards for Mathematics.
Units in teaching order
5.OA Operations and Algebraic Thinking
Arithmetic
Order of operations.
Short lesson: Find the remainder
Study guide for Grades 3 to 5: 2 worked examples and 2 practice questions. The remainder is at least zero and smaller than the positive divisor.
dividend = divisor × quotient + remainder
The remainder is at least zero and smaller than the positive divisor.
Worked example
What is the remainder when 78 is divided by 4?
78 = 4 × 19 + 2
Answer: 2
Worksheets
A practice worksheet and a review worksheet, 12 and 12 questions.
Practice worksheet: 12 questions
39 + 12 × 6 = ?
67 + 8 × 2 = ?
80 + 18 × 14 = ?
60 + 12 × 8 = ?
47 + 18 × 10 = ?
32 + 7 × 4 = ?
11 + 12 × 14 = ?
78 + 12 × 16 = ?
59 + 8 × 10 = ?
32 + 17 × 5 = ?
65 + 6 × 12 = ?
45 + 11 × 3 = ?
Answer key
- 111 12 × 6 = 72; 39 + 72 = 111
- 83 8 × 2 = 16; 67 + 16 = 83
- 332 18 × 14 = 252; 80 + 252 = 332
- 156 12 × 8 = 96; 60 + 96 = 156
- 227 18 × 10 = 180; 47 + 180 = 227
- 60 7 × 4 = 28; 32 + 28 = 60
- 179 12 × 14 = 168; 11 + 168 = 179
- 270 12 × 16 = 192; 78 + 192 = 270
- 139 8 × 10 = 80; 59 + 80 = 139
- 117 17 × 5 = 85; 32 + 85 = 117
- 137 6 × 12 = 72; 65 + 72 = 137
- 78 11 × 3 = 33; 45 + 33 = 78
Review worksheet: 12 questions
7 + 6 × 11 = ?
6 + 15 × 10 = ?
37 + 6 × 18 = ?
32 + 8 × 10 = ?
61 + 9 × 2 = ?
30 + 12 × 18 = ?
36 + 8 × 18 = ?
19 + 8 × 8 = ?
33 + 16 × 6 = ?
9 + 9 × 10 = ?
83 + 18 × 3 = ?
56 + 18 × 18 = ?
Answer key
- 73 6 × 11 = 66; 7 + 66 = 73
- 156 15 × 10 = 150; 6 + 150 = 156
- 145 6 × 18 = 108; 37 + 108 = 145
- 112 8 × 10 = 80; 32 + 80 = 112
- 79 9 × 2 = 18; 61 + 18 = 79
- 246 12 × 18 = 216; 30 + 216 = 246
- 180 8 × 18 = 144; 36 + 144 = 180
- 83 8 × 8 = 64; 19 + 64 = 83
- 129 16 × 6 = 96; 33 + 96 = 129
- 99 9 × 10 = 90; 9 + 90 = 99
- 137 18 × 3 = 54; 83 + 54 = 137
- 380 18 × 18 = 324; 56 + 324 = 380
5.OA Operations and Algebraic Thinking
Number patterns
Number patterns.
Short lesson: Number patterns
In a number pattern, the same rule takes you from each number to the next.
- Find the rule. Work out the difference between neighbouring numbers. If it is always the same, that is the rule.
- Check the rule. Make sure the rule works for every pair of numbers, not only the first two.
- Continue the pattern. Apply the rule to the last number to find the next one.
Worked example
What comes next? 47, 63, 79, 95, ...
Each number is 16 more than the one before: 63 is 47 + 16, and so on. So the next number is 95 + 16 = 111.
Answer: 111
Worksheets
A practice worksheet and a review worksheet, 12 and 12 questions.
Practice worksheet: 12 questions
What comes next? 32, 34, 36, 38, …
What comes next? 89, 102, 115, 128, …
What comes next? 54, 77, 100, 123, …
What comes next? 80, 99, 118, 137, …
What comes next? 83, 105, 127, 149, …
What comes next? 54, 59, 64, 69, …
What comes next? 88, 112, 136, 160, …
What comes next? 33, 56, 79, 102, …
What comes next? 63, 72, 81, 90, …
What comes next? 21, 35, 49, 63, …
What comes next? 15, 24, 33, 42, …
What comes next? 77, 82, 87, 92, …
Answer key
- 40 38 + 2 = 40
- 141 128 + 13 = 141
- 146 123 + 23 = 146
- 156 137 + 19 = 156
- 171 149 + 22 = 171
- 74 69 + 5 = 74
- 184 160 + 24 = 184
- 125 102 + 23 = 125
- 99 90 + 9 = 99
- 77 63 + 14 = 77
- 51 42 + 9 = 51
- 97 92 + 5 = 97
Review worksheet: 12 questions
What comes next? 79, 98, 117, 136, …
What comes next? 63, 68, 73, 78, …
What comes next? 65, 87, 109, 131, …
What comes next? 27, 35, 43, 51, …
What comes next? 71, 92, 113, 134, …
What comes next? 18, 28, 38, 48, …
What comes next? 77, 79, 81, 83, …
What comes next? 36, 45, 54, 63, …
What comes next? 40, 54, 68, 82, …
What comes next? 61, 78, 95, 112, …
What comes next? 44, 57, 70, 83, …
What comes next? 86, 97, 108, 119, …
Answer key
- 155 136 + 19 = 155
- 83 78 + 5 = 83
- 153 131 + 22 = 153
- 59 51 + 8 = 59
- 155 134 + 21 = 155
- 58 48 + 10 = 58
- 85 83 + 2 = 85
- 72 63 + 9 = 72
- 96 82 + 14 = 96
- 129 112 + 17 = 129
- 96 83 + 13 = 96
- 130 119 + 11 = 130
5.NBT Number and Operations in Base Ten
Place value
Place value.
Short lesson: Greatest common factor
Study guide for Grades 4 to 7: 2 worked examples and 2 practice questions. A factor divides a whole number without a remainder.
gcd(a,b) = gcd(b, a mod b)
A factor divides a whole number without a remainder.
Worked example
Find the greatest common factor of 123 and 50.
gcd(123, 50) = 1
Answer: 1
Worksheets
A practice worksheet and a review worksheet, 12 and 12 questions.
Practice worksheet: 12 questions
What is the value of the hundreds digit in 9171?
What is the value of the hundreds digit in 2779?
What is the value of the hundreds digit in 7538?
What is the value of the hundreds digit in 4553?
What is the value of the hundreds digit in 5832?
What is the value of the hundreds digit in 2607?
What is the value of the hundreds digit in 4387?
What is the value of the hundreds digit in 6887?
What is the value of the hundreds digit in 8341?
What is the value of the hundreds digit in 6860?
What is the value of the hundreds digit in 7107?
What is the value of the hundreds digit in 4925?
Answer key
- 100 1 × 100 = 100
- 700 7 × 100 = 700
- 500 5 × 100 = 500
- 500 5 × 100 = 500
- 800 8 × 100 = 800
- 600 6 × 100 = 600
- 300 3 × 100 = 300
- 800 8 × 100 = 800
- 300 3 × 100 = 300
- 800 8 × 100 = 800
- 100 1 × 100 = 100
- 900 9 × 100 = 900
Review worksheet: 12 questions
What is the value of the hundreds digit in 3909?
What is the value of the hundreds digit in 4270?
What is the value of the hundreds digit in 4959?
What is the value of the hundreds digit in 9363?
What is the value of the hundreds digit in 2975?
What is the value of the hundreds digit in 9636?
What is the value of the hundreds digit in 3323?
What is the value of the hundreds digit in 9331?
What is the value of the hundreds digit in 6719?
What is the value of the hundreds digit in 4442?
What is the value of the hundreds digit in 7112?
What is the value of the hundreds digit in 6752?
Answer key
- 900 9 × 100 = 900
- 200 2 × 100 = 200
- 900 9 × 100 = 900
- 300 3 × 100 = 300
- 900 9 × 100 = 900
- 600 6 × 100 = 600
- 300 3 × 100 = 300
- 300 3 × 100 = 300
- 700 7 × 100 = 700
- 400 4 × 100 = 400
- 100 1 × 100 = 100
- 700 7 × 100 = 700
5.NBT Number and Operations in Base Ten
Multi-digit calculation
Dividing whole numbers and multiplying whole numbers.
Short lesson: Find the remainder
Study guide for Grades 3 to 5: 2 worked examples and 2 practice questions. The remainder is at least zero and smaller than the positive divisor.
dividend = divisor × quotient + remainder
The remainder is at least zero and smaller than the positive divisor.
Worked example
What is the remainder when 78 is divided by 4?
78 = 4 × 19 + 2
Answer: 2
Worksheets
A practice worksheet and a review worksheet, 12 and 12 questions.
Practice worksheet: 12 questions
31 × 11 = ?
250 ÷ 5 = ?
41 × 12 = ?
483 ÷ 23 = ?
10 × 17 = ?
52 ÷ 13 = ?
5 × 23 = ?
360 ÷ 15 = ?
39 × 20 = ?
174 ÷ 3 = ?
30 × 24 = ?
153 ÷ 3 = ?
Answer key
- 341 31 × 11 = 341
- 50 5 × 50 = 250
- 492 41 × 12 = 492
- 21 23 × 21 = 483
- 170 10 × 17 = 170
- 4 13 × 4 = 52
- 115 5 × 23 = 115
- 24 15 × 24 = 360
- 780 39 × 20 = 780
- 58 3 × 58 = 174
- 720 30 × 24 = 720
- 51 3 × 51 = 153
Review worksheet: 12 questions
1166 ÷ 22 = ?
8 × 20 = ?
112 ÷ 2 = ?
18 × 23 = ?
384 ÷ 24 = ?
37 × 19 = ?
96 ÷ 16 = ?
41 × 17 = ?
528 ÷ 22 = ?
15 × 9 = ?
33 ÷ 11 = ?
38 × 7 = ?
Answer key
- 53 22 × 53 = 1166
- 160 8 × 20 = 160
- 56 2 × 56 = 112
- 414 18 × 23 = 414
- 16 24 × 16 = 384
- 703 37 × 19 = 703
- 6 16 × 6 = 96
- 697 41 × 17 = 697
- 24 22 × 24 = 528
- 135 15 × 9 = 135
- 3 11 × 3 = 33
- 266 38 × 7 = 266
5.NBT Number and Operations in Base Ten
Decimals
Adding decimals, multiplying decimals, dividing decimals and tenths as decimals.
Short lesson: Divide decimals
Study guide for Grades 5 to 7: 2 worked examples and 2 practice questions. Scale both numbers by the same power of ten.
(a × 10ⁿ)/(b × 10ⁿ) = a/b, b ≠ 0
Scale both numbers by the same power of ten.
Worked example
27.5 ÷ 0.5 = ?
275 ÷ 5 = 55
Answer: 55
Worksheets
A practice worksheet and a review worksheet, 12 and 12 questions.
Practice worksheet: 12 questions
28.6 × 38 = ?
18.29 + 21.71 = ?
18 ÷ 0.5 = ?
Write 57/10 as a decimal.
26.6 × 15 = ?
42.33 + 6.59 = ?
6.6 ÷ 1.1 = ?
Write 19/10 as a decimal.
41.4 × 41 = ?
22.31 + 3.59 = ?
70 ÷ 1.4 = ?
Write 63/10 as a decimal.
Answer key
- 1086.8 286 × 38 = 10868; 10868 ÷ 10 = 1086.8
- 40 18.29 + 21.71 = 40
- 36 180 ÷ 5 = 36
- 5.7 57 ÷ 10 = 5.7
- 399 266 × 15 = 3990; 3990 ÷ 10 = 399
- 48.92 42.33 + 6.59 = 48.92
- 6 66 ÷ 11 = 6
- 1.9 19 ÷ 10 = 1.9
- 1697.4 414 × 41 = 16974; 16974 ÷ 10 = 1697.4
- 25.9 22.31 + 3.59 = 25.9
- 50 700 ÷ 14 = 50
- 6.3 63 ÷ 10 = 6.3
Review worksheet: 12 questions
42 ÷ 0.7 = ?
1.3 × 11 = ?
49.15 + 13.21 = ?
Write 27/10 as a decimal.
55.2 ÷ 1.2 = ?
22.8 × 44 = ?
5.98 + 37.22 = ?
Write 52/10 as a decimal.
2.8 ÷ 1.4 = ?
39.7 × 9 = ?
27.8 + 29.08 = ?
Write 23/10 as a decimal.
Answer key
- 60 420 ÷ 7 = 60
- 14.3 13 × 11 = 143; 143 ÷ 10 = 14.3
- 62.36 49.15 + 13.21 = 62.36
- 2.7 27 ÷ 10 = 2.7
- 46 552 ÷ 12 = 46
- 1003.2 228 × 44 = 10032; 10032 ÷ 10 = 1003.2
- 43.2 5.98 + 37.22 = 43.2
- 5.2 52 ÷ 10 = 5.2
- 2 28 ÷ 14 = 2
- 357.3 397 × 9 = 3573; 3573 ÷ 10 = 357.3
- 56.88 27.8 + 29.08 = 56.88
- 2.3 23 ÷ 10 = 2.3
5.NF Number and Operations: Fractions
Fraction concepts and operations
Multiplying fractions, comparing fractions, adding fractions, subtracting mixed numbers, simplifying fractions and equivalent fractions.
Short lesson: Fractions of a set
Study guide for Grades 3 to 6: 2 worked examples and 2 practice questions. Split into equal groups using the denominator, then take the numerator groups.
(a/b) × N = a × (N ÷ b)
Split into equal groups using the denominator, then take the numerator groups.
Worked example
Find 4/8 of 136.
136 ÷ 8 × 4 = 68
Answer: 68
Worksheets
A practice worksheet and a review worksheet, 12 and 12 questions.
Practice worksheet: 12 questions
Find 7/12 of 240.
Choose <, > or =: 7/5 □ 6/12
- <
- >
- =
Simplify 80/230.
Calculate 7 8/11 − 6 6/11. Give a fraction in simplest form.
12/4 × 8/6 = ?
7/10 + □ = 1
6/10 + 5/15 = ?
10/15 = □/105
14/16 − 8/16 = ?
Find 4/5 of 40.
Choose <, > or =: 10/16 □ 1/19
- <
- >
- =
Simplify 121/374.
Answer key
- 140 240 ÷ 12 × 7 = 140
- > 7 × 12 = 84; 6 × 5 = 30
- 8/23 80/230 = 8/23
- 13/11 (85 − 72)/11 = 13/11
- 4 (12 × 8)/(4 × 6) = 4
- 3/10 7/10 + 3/10 = 10/10 = 1
- 14/15 90/150 + 50/150 = 14/15
- 70 10 × 7 = 70; 15 × 7 = 105
- 3/8 (14 − 8)/16 = 3/8
- 32 40 ÷ 5 × 4 = 32
- > 10 × 19 = 190; 1 × 16 = 16
- 11/34 121/374 = 11/34
Review worksheet: 12 questions
Choose <, > or =: 7/15 □ 12/14
- =
- <
- >
4/8 + 3/20 = ?
3/16 = □/48
Calculate 3 2/5 − 1 1/5. Give a fraction in simplest form.
5/2 × 1/7 = ?
Find 1/6 of 18.
8/15 + □ = 1
Simplify 15/120.
7/11 − 5/11 = ?
Choose <, > or =: 7/14 □ 10/2
- <
- =
- >
7/12 + 1/17 = ?
8/11 = □/99
Answer key
- < 7 × 14 = 98; 12 × 15 = 180
- 13/20 80/160 + 24/160 = 13/20
- 9 3 × 3 = 9; 16 × 3 = 48
- 11/5 (17 − 6)/5 = 11/5
- 5/14 (5 × 1)/(2 × 7) = 5/14
- 3 18 ÷ 6 × 1 = 3
- 7/15 8/15 + 7/15 = 15/15 = 1
- 1/8 15/120 = 1/8
- 2/11 (7 − 5)/11 = 2/11
- < 7 × 2 = 14; 10 × 14 = 140
- 131/204 119/204 + 12/204 = 131/204
- 72 8 × 9 = 72; 11 × 9 = 99
5.MD Measurement and Data
Area, perimeter and volume
Volume of combined rectangular prisms and volume of rectangular prisms.
Short lesson: Volume of two joined boxes
Study guide for Grades 5 to 8: 2 worked examples and 2 practice questions. Add the volumes only when the boxes do not overlap.
V = l₁w₁h₁ + l₂w₂h₂
Add the volumes only when the boxes do not overlap.
Worked example
Two non-overlapping rectangular boxes measure 7×8×6 cm and 2×4×3 cm. Find their total volume in cm³.
336 + 24 = 360
Answer: 360 cm³
Worksheets
A practice worksheet and a review worksheet, 12 and 12 questions.
Practice worksheet: 12 questions
Two non-overlapping rectangular boxes measure 6×10×5 cm and 6×3×2 cm. Find their total volume in cm³.
Find the volume of a cuboid measuring 2 cm × 24 cm × 9 cm, in cm³.
Two non-overlapping rectangular boxes measure 10×9×5 cm and 9×7×5 cm. Find their total volume in cm³.
Find the volume of a cuboid measuring 26 cm × 12 cm × 18 cm, in cm³.
Two non-overlapping rectangular boxes measure 12×10×4 cm and 3×5×6 cm. Find their total volume in cm³.
Find the volume of a cuboid measuring 30 cm × 22 cm × 20 cm, in cm³.
Two non-overlapping rectangular boxes measure 5×8×8 cm and 5×2×2 cm. Find their total volume in cm³.
Find the volume of a cuboid measuring 18 cm × 13 cm × 20 cm, in cm³.
Two non-overlapping rectangular boxes measure 3×4×4 cm and 5×6×4 cm. Find their total volume in cm³.
Find the volume of a cuboid measuring 15 cm × 4 cm × 2 cm, in cm³.
Two non-overlapping rectangular boxes measure 5×8×6 cm and 8×7×8 cm. Find their total volume in cm³.
Find the volume of a cuboid measuring 9 cm × 15 cm × 20 cm, in cm³.
Answer key
- 336 cm³ 300 + 36 = 336
- 432 cm³ 2 × 24 × 9 = 432 cm³
- 765 cm³ 450 + 315 = 765
- 5616 cm³ 26 × 12 × 18 = 5616 cm³
- 570 cm³ 480 + 90 = 570
- 13200 cm³ 30 × 22 × 20 = 13200 cm³
- 340 cm³ 320 + 20 = 340
- 4680 cm³ 18 × 13 × 20 = 4680 cm³
- 168 cm³ 48 + 120 = 168
- 120 cm³ 15 × 4 × 2 = 120 cm³
- 688 cm³ 240 + 448 = 688
- 2700 cm³ 9 × 15 × 20 = 2700 cm³
Review worksheet: 12 questions
Find the volume of a cuboid measuring 13 cm × 10 cm × 12 cm, in cm³.
Two non-overlapping rectangular boxes measure 3×3×3 cm and 7×7×2 cm. Find their total volume in cm³.
Find the volume of a cuboid measuring 19 cm × 21 cm × 9 cm, in cm³.
Two non-overlapping rectangular boxes measure 2×8×7 cm and 5×3×4 cm. Find their total volume in cm³.
Find the volume of a cuboid measuring 23 cm × 16 cm × 14 cm, in cm³.
Two non-overlapping rectangular boxes measure 12×2×3 cm and 7×2×7 cm. Find their total volume in cm³.
Find the volume of a cuboid measuring 11 cm × 20 cm × 17 cm, in cm³.
Two non-overlapping rectangular boxes measure 8×3×6 cm and 7×3×8 cm. Find their total volume in cm³.
Find the volume of a cuboid measuring 19 cm × 16 cm × 2 cm, in cm³.
Two non-overlapping rectangular boxes measure 5×4×4 cm and 4×5×3 cm. Find their total volume in cm³.
Find the volume of a cuboid measuring 30 cm × 16 cm × 10 cm, in cm³.
Two non-overlapping rectangular boxes measure 4×2×2 cm and 3×3×4 cm. Find their total volume in cm³.
Answer key
- 1560 cm³ 13 × 10 × 12 = 1560 cm³
- 125 cm³ 27 + 98 = 125
- 3591 cm³ 19 × 21 × 9 = 3591 cm³
- 172 cm³ 112 + 60 = 172
- 5152 cm³ 23 × 16 × 14 = 5152 cm³
- 170 cm³ 72 + 98 = 170
- 3740 cm³ 11 × 20 × 17 = 3740 cm³
- 312 cm³ 144 + 168 = 312
- 608 cm³ 19 × 16 × 2 = 608 cm³
- 140 cm³ 80 + 60 = 140
- 4800 cm³ 30 × 16 × 10 = 4800 cm³
- 52 cm³ 16 + 36 = 52
5.MD Measurement and Data
Measurement & time
Converting metres and centimetres and converting kilograms and grams.
Short lesson: Kilograms and grams
Study guide for Grades 4 to 6: 2 worked examples and 2 practice questions. Multiply kilograms by one thousand to express the same mass in grams.
1 kg = 1,000 g
Multiply kilograms by one thousand to express the same mass in grams.
Worked example
Convert 22.5 kg to g.
22.5 × 1000 = 22500
Answer: 22500 g
Worksheets
A practice worksheet and a review worksheet, 12 and 12 questions.
Practice worksheet: 12 questions
Convert 22.1 kg to g.
Convert 49.73 metres to centimetres.
Convert 20.6 kg to g.
Convert 60.05 metres to centimetres.
Convert 40.7 kg to g.
Convert 63.03 metres to centimetres.
Convert 43.9 kg to g.
Convert 85.84 metres to centimetres.
Convert 47.4 kg to g.
Convert 10.86 metres to centimetres.
Convert 27.4 kg to g.
Convert 61.92 metres to centimetres.
Answer key
- 22100 g 22.1 × 1000 = 22100
- 4973 cm 49.73 × 100 = 4973
- 20600 g 20.6 × 1000 = 20600
- 6005 cm 60.05 × 100 = 6005
- 40700 g 40.7 × 1000 = 40700
- 6303 cm 63.03 × 100 = 6303
- 43900 g 43.9 × 1000 = 43900
- 8584 cm 85.84 × 100 = 8584
- 47400 g 47.4 × 1000 = 47400
- 1086 cm 10.86 × 100 = 1086
- 27400 g 27.4 × 1000 = 27400
- 6192 cm 61.92 × 100 = 6192
Review worksheet: 12 questions
Convert 13 metres to centimetres.
Convert 22.6 kg to g.
Convert 35.73 metres to centimetres.
Convert 61.6 kg to g.
Convert 4.13 metres to centimetres.
Convert 84.9 kg to g.
Convert 39.29 metres to centimetres.
Convert 23.7 kg to g.
Convert 94.36 metres to centimetres.
Convert 61 kg to g.
Convert 78.24 metres to centimetres.
Convert 65.7 kg to g.
Answer key
- 1300 cm 13 × 100 = 1300
- 22600 g 22.6 × 1000 = 22600
- 3573 cm 35.73 × 100 = 3573
- 61600 g 61.6 × 1000 = 61600
- 413 cm 4.13 × 100 = 413
- 84900 g 84.9 × 1000 = 84900
- 3929 cm 39.29 × 100 = 3929
- 23700 g 23.7 × 1000 = 23700
- 9436 cm 94.36 × 100 = 9436
- 61000 g 61 × 1000 = 61000
- 7824 cm 78.24 × 100 = 7824
- 65700 g 65.7 × 1000 = 65700