Grade 6 · Maths · curriculum collection
Grade 6 Maths, Common Core domains
8 units for Grade 6 maths, organised by Common Core domain: Ratios and Proportional Relationships, The Number System, Expressions and Equations, Geometry, Statistics and Probability. 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
6.RP Ratios and Proportional Relationships
Percentages
Percent of a quantity, finding the whole from a percent and percents as fractions.
Short lesson: Find the original whole
Study guide for Grades 6 to 9: 2 worked examples and 2 practice questions. Divide by the percentage as a decimal, not by the whole-number percent.
whole = part ÷ (p/100)
Divide by the percentage as a decimal, not by the whole-number percent.
Worked example
40% of a number is 392. What is the number?
392 ÷ 0.4 = 980
Answer: 980
Worksheets
A practice worksheet and a review worksheet, 12 and 12 questions.
Practice worksheet: 12 questions
Find 83% of 380.
Write 16% as a fraction in simplest form.
20% of a number is 220. What is the number?
Find 83% of 70.
Write 72% as a fraction in simplest form.
50% of a number is 100. What is the number?
Find 94% of 140.
Write 8% as a fraction in simplest form.
25% of a number is 90. What is the number?
Find 6% of 480.
Write 1% as a fraction in simplest form.
75% of a number is 135. What is the number?
Answer key
- 315.4 83/100 × 380 = 315.4
- 4/25 16/100 = 4/25
- 1100 220 ÷ 0.2 = 1100
- 58.1 83/100 × 70 = 58.1
- 18/25 72/100 = 18/25
- 200 100 ÷ 0.5 = 200
- 131.6 94/100 × 140 = 131.6
- 2/25 8/100 = 2/25
- 360 90 ÷ 0.25 = 360
- 28.8 6/100 × 480 = 28.8
- 1/100 1/100 = 1/100
- 180 135 ÷ 0.75 = 180
Review worksheet: 12 questions
Find 21% of 240.
50% of a number is 190. What is the number?
Write 17% as a fraction in simplest form.
Find 54% of 540.
40% of a number is 424. What is the number?
Write 42% as a fraction in simplest form.
Find 51% of 160.
10% of a number is 120. What is the number?
Write 29% as a fraction in simplest form.
Find 6% of 190.
40% of a number is 360. What is the number?
Write 46% as a fraction in simplest form.
Answer key
- 50.4 21/100 × 240 = 50.4
- 380 190 ÷ 0.5 = 380
- 17/100 17/100 = 17/100
- 291.6 54/100 × 540 = 291.6
- 1060 424 ÷ 0.4 = 1060
- 21/50 42/100 = 21/50
- 81.6 51/100 × 160 = 81.6
- 1200 120 ÷ 0.1 = 1200
- 29/100 29/100 = 29/100
- 11.4 6/100 × 190 = 11.4
- 900 360 ÷ 0.4 = 900
- 23/50 46/100 = 23/50
6.RP Ratios and Proportional Relationships
Converting units and rates
Converting kilograms and grams and converting rates.
Short lesson: Convert speed units
Study guide for Grades 6 to 9: 2 worked examples and 2 practice questions. One kilometre is 1000 metres; one hour is 3600 seconds.
1 m/s = 3.6 km/h
One kilometre is 1000 metres; one hour is 3600 seconds.
Worked example
Convert 19 m/s to km/h.
19 × 3.6 = 68.4
Answer: 68.4 km/h
Worksheets
A practice worksheet and a review worksheet, 12 and 12 questions.
Practice worksheet: 12 questions
Convert 37.1 kg to g.
Convert 7 m/s to km/h.
Convert 58.5 kg to g.
Convert 40 m/s to km/h.
Convert 53.3 kg to g.
Convert 11 m/s to km/h.
Convert 49.3 kg to g.
Convert 72 m/s to km/h.
Convert 43.3 kg to g.
Convert 77 m/s to km/h.
Convert 64.8 kg to g.
Convert 69 m/s to km/h.
Answer key
- 37100 g 37.1 × 1000 = 37100
- 25.2 km/h 7 × 3.6 = 25.2
- 58500 g 58.5 × 1000 = 58500
- 144 km/h 40 × 3.6 = 144
- 53300 g 53.3 × 1000 = 53300
- 39.6 km/h 11 × 3.6 = 39.6
- 49300 g 49.3 × 1000 = 49300
- 259.2 km/h 72 × 3.6 = 259.2
- 43300 g 43.3 × 1000 = 43300
- 277.2 km/h 77 × 3.6 = 277.2
- 64800 g 64.8 × 1000 = 64800
- 248.4 km/h 69 × 3.6 = 248.4
Review worksheet: 12 questions
Convert 66.7 kg to g.
Convert 54 m/s to km/h.
Convert 74.1 kg to g.
Convert 76 m/s to km/h.
Convert 80.7 kg to g.
Convert 53 m/s to km/h.
Convert 87.1 kg to g.
Convert 80 m/s to km/h.
Convert 74.5 kg to g.
Convert 49 m/s to km/h.
Convert 49.1 kg to g.
Convert 6 m/s to km/h.
Answer key
- 66700 g 66.7 × 1000 = 66700
- 194.4 km/h 54 × 3.6 = 194.4
- 74100 g 74.1 × 1000 = 74100
- 273.6 km/h 76 × 3.6 = 273.6
- 80700 g 80.7 × 1000 = 80700
- 190.8 km/h 53 × 3.6 = 190.8
- 87100 g 87.1 × 1000 = 87100
- 288 km/h 80 × 3.6 = 288
- 74500 g 74.5 × 1000 = 74500
- 176.4 km/h 49 × 3.6 = 176.4
- 49100 g 49.1 × 1000 = 49100
- 21.6 km/h 6 × 3.6 = 21.6
6.NS The Number System
Factors, multiples and absolute value
Greatest common factor, absolute value and least common multiple.
Short lesson: Absolute value
Study guide for Grades 6 to 8: 2 worked examples and 2 practice questions. Distance is never negative.
|x| = distance from x to 0
Distance is never negative.
Worked example
|101| = ?
|101| = 101
Answer: 101
Worksheets
A practice worksheet and a review worksheet, 12 and 12 questions.
Practice worksheet: 12 questions
Find the least common multiple of 14 and 11.
|99| = ?
Find the greatest common factor of 42 and 42.
Find the least common multiple of 17 and 24.
|303| = ?
Find the greatest common factor of 95 and 127.
Find the least common multiple of 25 and 28.
|266| = ?
Find the greatest common factor of 78 and 110.
Find the least common multiple of 14 and 27.
|142| = ?
Find the greatest common factor of 19 and 84.
Answer key
- 154 14 × 11 ÷ 1 = 154
- 99 |99| = 99
- 42 gcd(42, 42) = 42
- 408 17 × 24 ÷ 1 = 408
- 303 |303| = 303
- 1 gcd(95, 127) = 1
- 700 25 × 28 ÷ 1 = 700
- 266 |266| = 266
- 2 gcd(78, 110) = 2
- 378 14 × 27 ÷ 1 = 378
- 142 |142| = 142
- 1 gcd(19, 84) = 1
Review worksheet: 12 questions
Find the greatest common factor of 9 and 72.
|-342| = ?
Find the least common multiple of 26 and 17.
Find the greatest common factor of 66 and 37.
|305| = ?
Find the least common multiple of 10 and 5.
Find the greatest common factor of 112 and 34.
|150| = ?
Find the least common multiple of 25 and 26.
Find the greatest common factor of 16 and 144.
|-201| = ?
Find the least common multiple of 10 and 29.
Answer key
- 9 gcd(9, 72) = 9
- 342 |-342| = 342
- 442 26 × 17 ÷ 1 = 442
- 1 gcd(66, 37) = 1
- 305 |305| = 305
- 10 10 × 5 ÷ 5 = 10
- 2 gcd(112, 34) = 2
- 150 |150| = 150
- 650 25 × 26 ÷ 1 = 650
- 16 gcd(16, 144) = 16
- 201 |-201| = 201
- 290 10 × 29 ÷ 1 = 290
6.NS The Number System
Decimal operations
Adding decimals, multiplying decimals and dividing 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
18.59 + 15.65 = ?
59.4 ÷ 1.1 = ?
7.9 × 22 = ?
1.78 + 49.12 = ?
19.2 ÷ 0.6 = ?
23.9 × 5 = ?
49.92 + 18.42 = ?
5.6 ÷ 0.2 = ?
49.1 × 29 = ?
26.3 + 39.42 = ?
25.6 ÷ 0.8 = ?
2.1 × 19 = ?
Answer key
- 34.24 18.59 + 15.65 = 34.24
- 54 594 ÷ 11 = 54
- 173.8 79 × 22 = 1738; 1738 ÷ 10 = 173.8
- 50.9 1.78 + 49.12 = 50.9
- 32 192 ÷ 6 = 32
- 119.5 239 × 5 = 1195; 1195 ÷ 10 = 119.5
- 68.34 49.92 + 18.42 = 68.34
- 28 56 ÷ 2 = 28
- 1423.9 491 × 29 = 14239; 14239 ÷ 10 = 1423.9
- 65.72 26.3 + 39.42 = 65.72
- 32 256 ÷ 8 = 32
- 39.9 21 × 19 = 399; 399 ÷ 10 = 39.9
Review worksheet: 12 questions
35.7 ÷ 0.7 = ?
47.4 × 4 = ?
21.62 + 49.55 = ?
24 ÷ 1 = ?
30.8 × 21 = ?
47.14 + 38.62 = ?
10.5 ÷ 0.3 = ?
0.7 × 19 = ?
6.91 + 18.29 = ?
73.5 ÷ 1.5 = ?
47.8 × 33 = ?
10.23 + 14.06 = ?
Answer key
- 51 357 ÷ 7 = 51
- 189.6 474 × 4 = 1896; 1896 ÷ 10 = 189.6
- 71.17 21.62 + 49.55 = 71.17
- 24 240 ÷ 10 = 24
- 646.8 308 × 21 = 6468; 6468 ÷ 10 = 646.8
- 85.76 47.14 + 38.62 = 85.76
- 35 105 ÷ 3 = 35
- 13.3 7 × 19 = 133; 133 ÷ 10 = 13.3
- 25.2 6.91 + 18.29 = 25.2
- 49 735 ÷ 15 = 49
- 1577.4 478 × 33 = 15774; 15774 ÷ 10 = 1577.4
- 24.29 10.23 + 14.06 = 24.29
6.EE Expressions and Equations
Order of operations
Order of operations.
Short lesson: Subtract signed integers
Study guide for Grades 6 to 8: 2 worked examples and 2 practice questions. Subtracting a negative is adding its opposite.
a − b = a + (−b)
Subtracting a negative is adding its opposite.
Worked example
(41) − (-53) = ?
(41) + (53) = 94
Answer: 94
Worksheets
A practice worksheet and a review worksheet, 12 and 12 questions.
Practice worksheet: 12 questions
61 + 9 × 2 = ?
60 + 9 × 14 = ?
55 + 12 × 3 = ?
65 + 16 × 2 = ?
4 + 10 × 12 = ?
80 + 15 × 4 = ?
50 + 2 × 12 = ?
55 + 17 × 6 = ?
50 + 7 × 14 = ?
35 + 15 × 6 = ?
57 + 11 × 10 = ?
6 + 12 × 16 = ?
Answer key
- 79 9 × 2 = 18; 61 + 18 = 79
- 186 9 × 14 = 126; 60 + 126 = 186
- 91 12 × 3 = 36; 55 + 36 = 91
- 97 16 × 2 = 32; 65 + 32 = 97
- 124 10 × 12 = 120; 4 + 120 = 124
- 140 15 × 4 = 60; 80 + 60 = 140
- 74 2 × 12 = 24; 50 + 24 = 74
- 157 17 × 6 = 102; 55 + 102 = 157
- 148 7 × 14 = 98; 50 + 98 = 148
- 125 15 × 6 = 90; 35 + 90 = 125
- 167 11 × 10 = 110; 57 + 110 = 167
- 198 12 × 16 = 192; 6 + 192 = 198
Review worksheet: 12 questions
23 + 2 × 12 = ?
90 + 10 × 11 = ?
23 + 4 × 4 = ?
74 + 17 × 7 = ?
73 + 12 × 9 = ?
56 + 9 × 2 = ?
81 + 9 × 5 = ?
59 + 8 × 10 = ?
84 + 16 × 16 = ?
31 + 7 × 14 = ?
75 + 3 × 5 = ?
40 + 12 × 6 = ?
Answer key
- 47 2 × 12 = 24; 23 + 24 = 47
- 200 10 × 11 = 110; 90 + 110 = 200
- 39 4 × 4 = 16; 23 + 16 = 39
- 193 17 × 7 = 119; 74 + 119 = 193
- 181 12 × 9 = 108; 73 + 108 = 181
- 74 9 × 2 = 18; 56 + 18 = 74
- 126 9 × 5 = 45; 81 + 45 = 126
- 139 8 × 10 = 80; 59 + 80 = 139
- 340 16 × 16 = 256; 84 + 256 = 340
- 129 7 × 14 = 98; 31 + 98 = 129
- 90 3 × 5 = 15; 75 + 15 = 90
- 112 12 × 6 = 72; 40 + 72 = 112
6.EE Expressions and Equations
Algebra
Evaluating expressions, one-step equations and combining like terms.
Short lesson: Combine like terms
Study guide for Grades 6 to 9: 2 worked examples and 2 practice questions. Only terms with the same variable part can be combined this way.
ax + bx = (a + b)x
Only terms with the same variable part can be combined this way.
Worked example
Find the coefficient of x after simplifying 32x + 33x.
(32 + 33)x = 65x
Answer: 65
Worksheets
A practice worksheet and a review worksheet, 12 and 12 questions.
Practice worksheet: 12 questions
Evaluate 13x + 22 when x = -5.
Find the coefficient of x after simplifying 20x + 22x.
Solve for x: 23x = 736
Evaluate 10x + 11 when x = -14.
Find the coefficient of x after simplifying 10x + 2x.
Solve for x: 10x = 330
Evaluate 10x + 22 when x = 10.
Find the coefficient of x after simplifying 30x + 11x.
Solve for x: 23x = 138
Evaluate 13x + 20 when x = -2.
Find the coefficient of x after simplifying 16x + 18x.
Solve for x: 19x = 551
Answer key
- -43 13 × (-5) + 22 = -43
- 42 (20 + 22)x = 42x
- 32 x = 736 ÷ 23 = 32
- -129 10 × (-14) + 11 = -129
- 12 (10 + 2)x = 12x
- 33 x = 330 ÷ 10 = 33
- 122 10 × (10) + 22 = 122
- 41 (30 + 11)x = 41x
- 6 x = 138 ÷ 23 = 6
- -6 13 × (-2) + 20 = -6
- 34 (16 + 18)x = 34x
- 29 x = 551 ÷ 19 = 29
Review worksheet: 12 questions
Evaluate 13x + 4 when x = 2.
Solve for x: 28x = 1512
Find the coefficient of x after simplifying 34x + 8x.
Evaluate 13x + 23 when x = 2.
Solve for x: 14x = 14
Find the coefficient of x after simplifying 25x + 29x.
Evaluate 3x + 27 when x = 2.
Solve for x: 15x = 660
Find the coefficient of x after simplifying 8x + 28x.
Evaluate 7x + 15 when x = -3.
Solve for x: 13x = 286
Find the coefficient of x after simplifying 26x + 28x.
Answer key
- 30 13 × (2) + 4 = 30
- 54 x = 1512 ÷ 28 = 54
- 42 (34 + 8)x = 42x
- 49 13 × (2) + 23 = 49
- 1 x = 14 ÷ 14 = 1
- 54 (25 + 29)x = 54x
- 33 3 × (2) + 27 = 33
- 44 x = 660 ÷ 15 = 44
- 36 (8 + 28)x = 36x
- -6 7 × (-3) + 15 = -6
- 22 x = 286 ÷ 13 = 22
- 54 (26 + 28)x = 54x
6.G Geometry
Geometry
Area of trapezoids, volume of rectangular prisms and area of triangles.
Short lesson: Area of a trapezoid
Study guide for Grades 6 to 9: 2 worked examples and 2 practice questions. A and b are the parallel sides; h is the perpendicular distance between them.
A = (a + b)h/2
a and b are the parallel sides; h is the perpendicular distance between them.
Worked example
A trapezoid has parallel sides 13 cm and 21 cm and height 22 cm. Find its area in cm².
(13 + 21) × 22 ÷ 2 = 374
Answer: 374 cm²
Worksheets
A practice worksheet and a review worksheet, 12 and 12 questions.
Practice worksheet: 12 questions
A triangle has base 66 cm and perpendicular height 5 cm. Find its area in cm².
A trapezoid has parallel sides 15 cm and 7 cm and height 14 cm. Find its area in cm².
Find the volume of a cuboid measuring 21 cm × 22 cm × 6 cm, in cm³.
A triangle has base 36 cm and perpendicular height 12 cm. Find its area in cm².
A trapezoid has parallel sides 7 cm and 8 cm and height 23 cm. Find its area in cm².
Find the volume of a cuboid measuring 17 cm × 7 cm × 3 cm, in cm³.
A triangle has base 64 cm and perpendicular height 7 cm. Find its area in cm².
A trapezoid has parallel sides 19 cm and 16 cm and height 24 cm. Find its area in cm².
Find the volume of a cuboid measuring 20 cm × 6 cm × 20 cm, in cm³.
A triangle has base 30 cm and perpendicular height 31 cm. Find its area in cm².
A trapezoid has parallel sides 17 cm and 18 cm and height 19 cm. Find its area in cm².
Find the volume of a cuboid measuring 15 cm × 12 cm × 4 cm, in cm³.
Answer key
- 165 cm² (66 × 5) ÷ 2 = 165 cm²
- 154 cm² (15 + 7) × 14 ÷ 2 = 154
- 2772 cm³ 21 × 22 × 6 = 2772 cm³
- 216 cm² (36 × 12) ÷ 2 = 216 cm²
- 172.5 cm² (7 + 8) × 23 ÷ 2 = 172.5
- 357 cm³ 17 × 7 × 3 = 357 cm³
- 224 cm² (64 × 7) ÷ 2 = 224 cm²
- 420 cm² (19 + 16) × 24 ÷ 2 = 420
- 2400 cm³ 20 × 6 × 20 = 2400 cm³
- 465 cm² (30 × 31) ÷ 2 = 465 cm²
- 332.5 cm² (17 + 18) × 19 ÷ 2 = 332.5
- 720 cm³ 15 × 12 × 4 = 720 cm³
Review worksheet: 12 questions
A triangle has base 16 cm and perpendicular height 54 cm. Find its area in cm².
Find the volume of a cuboid measuring 19 cm × 16 cm × 6 cm, in cm³.
A trapezoid has parallel sides 20 cm and 21 cm and height 10 cm. Find its area in cm².
A triangle has base 37 cm and perpendicular height 34 cm. Find its area in cm².
Find the volume of a cuboid measuring 27 cm × 2 cm × 20 cm, in cm³.
A trapezoid has parallel sides 17 cm and 13 cm and height 14 cm. Find its area in cm².
A triangle has base 51 cm and perpendicular height 2 cm. Find its area in cm².
Find the volume of a cuboid measuring 13 cm × 22 cm × 3 cm, in cm³.
A trapezoid has parallel sides 10 cm and 5 cm and height 18 cm. Find its area in cm².
A triangle has base 41 cm and perpendicular height 12 cm. Find its area in cm².
Find the volume of a cuboid measuring 30 cm × 16 cm × 12 cm, in cm³.
A trapezoid has parallel sides 18 cm and 7 cm and height 8 cm. Find its area in cm².
Answer key
- 432 cm² (16 × 54) ÷ 2 = 432 cm²
- 1824 cm³ 19 × 16 × 6 = 1824 cm³
- 205 cm² (20 + 21) × 10 ÷ 2 = 205
- 629 cm² (37 × 34) ÷ 2 = 629 cm²
- 1080 cm³ 27 × 2 × 20 = 1080 cm³
- 210 cm² (17 + 13) × 14 ÷ 2 = 210
- 51 cm² (51 × 2) ÷ 2 = 51 cm²
- 858 cm³ 13 × 22 × 3 = 858 cm³
- 135 cm² (10 + 5) × 18 ÷ 2 = 135
- 246 cm² (41 × 12) ÷ 2 = 246 cm²
- 5760 cm³ 30 × 16 × 12 = 5760 cm³
- 100 cm² (18 + 7) × 8 ÷ 2 = 100
6.SP Statistics and Probability
Statistics & probability
The mean, the median and range of a data set.
Short lesson: Range of a data set
Study guide for Grades 4 to 8: 2 worked examples and 2 practice questions. Sort the data or find its two extreme values.
range = maximum − minimum
Sort the data or find its two extreme values.
Worked example
Find the range of: 139, 48, 42, 141, 58, 112.
141 − 42 = 99
Answer: 99
Worksheets
A practice worksheet and a review worksheet, 12 and 12 questions.
Practice worksheet: 12 questions
Find the range of: 120, 110, 91, 68, 118, 10.
Find the median of 16, 27, 41, 46, 37.
Find the mean of 48, 11, 21, 36.
Find the range of: 148, 81, 136, 54, 132, 40.
Find the median of 69, 61, 90, 98, 75.
Find the mean of 4, 22, 27, 7.
Find the range of: 42, 133, 27, 138, 84, 132.
Find the median of 50, 55, 84, 8, 62.
Find the mean of 4, 6, 11, 38.
Find the range of: 33, 41, 9, 35, 109, 120.
Find the median of 26, 72, 30, 90, 75.
Find the mean of 30, 26, 49, 16.
Answer key
- 110 120 − 10 = 110
- 37 16 ≤ 27 ≤ 37 ≤ 41 ≤ 46 → 37
- 29 (48 + 11 + 21 + 36) ÷ 4 = 29
- 108 148 − 40 = 108
- 75 61 ≤ 69 ≤ 75 ≤ 90 ≤ 98 → 75
- 15 (4 + 22 + 27 + 7) ÷ 4 = 15
- 111 138 − 27 = 111
- 55 8 ≤ 50 ≤ 55 ≤ 62 ≤ 84 → 55
- 14.75 (4 + 6 + 11 + 38) ÷ 4 = 14.75
- 111 120 − 9 = 111
- 72 26 ≤ 30 ≤ 72 ≤ 75 ≤ 90 → 72
- 30.25 (30 + 26 + 49 + 16) ÷ 4 = 30.25
Review worksheet: 12 questions
Find the range of: 38, 73, 80, 33, 121, 114.
Find the median of 41, 98, 86, 25, 65.
Find the mean of 4, 5, 37, 15.
Find the range of: 64, 4, 73, 130, 86, 13.
Find the median of 33, 42, 69, 19, 75.
Find the mean of 19, 23, 30, 3.
Find the range of: 52, 100, 90, 108, 51, 104.
Find the median of 20, 68, 27, 94, 24.
Find the mean of 40, 4, 33, 31.
Find the range of: 121, 82, 32, 66, 36, 66.
Find the median of 99, 78, 44, 86, 59.
Find the mean of 15, 29, 36, 50.
Answer key
- 88 121 − 33 = 88
- 65 25 ≤ 41 ≤ 65 ≤ 86 ≤ 98 → 65
- 15.25 (4 + 5 + 37 + 15) ÷ 4 = 15.25
- 126 130 − 4 = 126
- 42 19 ≤ 33 ≤ 42 ≤ 69 ≤ 75 → 42
- 18.75 (19 + 23 + 30 + 3) ÷ 4 = 18.75
- 57 108 − 51 = 57
- 27 20 ≤ 24 ≤ 27 ≤ 68 ≤ 94 → 27
- 27 (40 + 4 + 33 + 31) ÷ 4 = 27
- 89 121 − 32 = 89
- 78 44 ≤ 59 ≤ 78 ≤ 86 ≤ 99 → 78
- 32.5 (15 + 29 + 36 + 50) ÷ 4 = 32.5