Grade 6 Math Worksheet — 70 Questions for 11-Year-Olds: Diagrams & Problem Solving (Place Value, Number System, Geometry, Fractions, Probability)

Section A: Place Value & Number System

1. Write 5,408,392 in words.
2. Write "Twelve million, sixty-two thousand, one hundred five" in standard form (using numbers).
3. What is the value of the digit 7 in the number 9,752,184?
4. Write 3,000,000 + 400,000 + 5,000 + 20 + 9 in standard form.
5. Order these numbers from smallest to largest: 890,123; 809,321; 891,023.
6. Round 4,567,890 to the nearest hundred thousand.
7. What number is 10,000 less than 2,005,150?

Section B: Fractions, Decimals, and Percentages

8. Convert 0.75 to a fraction in its simplest form.
9. Convert 3/5 to a decimal.
10. Convert 45% to a decimal.
11. Convert 0.8 to a percentage.
12. What is 25% of 80?
13. Arrange in order from smallest to largest: 0.5, 45%, 1/4.
14. A t-shirt costs $20. It is on sale for 10% off. What is the sale price?
15. Which is greater, 2/3 or 0.6?

Section C: Addition & Subtraction

16. 45,892 + 37,129 = ?
17. 90,000 - 12,345 = ?
18. A library has 15,472 books. It buys 2,150 more books. How many books does it have now?
19. Sam had $50.00. He bought a game for $29.95. How much money does he have left?
20. Calculate: 3,405 + 10,999 - 5,200 = ?
21. Find the missing number: 5,678 + ______ = 12,000.

Section D: Multiplication

22. 456 × 23 = ?
23. 708 × 150 = ?
24. A factory produces 350 toys a day. How many toys does it produce in 30 days?
25. A movie ticket costs $12. If 255 people go to the movie, how much money did the cinema collect?
26. What is 1,200 × 40?
27. A rectangular field is 85 meters long and 40 meters wide. What is its area? (Area = length × width)

Section E: Calculations with Fractions

28. 1/4 + 2/4 = ?
29. 5/8 - 2/8 = ?
30. 1/2 + 1/3 = ? (Remember to find a common denominator)
31. 7/10 - 1/5 = ?
32. 3/4 × 1/2 = ?
33. A recipe needs 1/2 cup of sugar and 3/4 cup of flour. How much more flour is needed than sugar?
34. A pizza has 8 slices. Mark eats 1/4 of the pizza. How many slices did he eat?

Section F: 2D Shapes and Angles

35. How many sides does a hexagon have?
36. What is the name of a polygon with 5 sides?
37. An angle measures exactly 90 degrees. What type of angle is it?
38. An angle measures 110 degrees. What type of angle is it?
39. An angle measures 45 degrees. What type of angle is it?
40. Imagine a perfect square. All its internal angles are _________ angles. (Fill in the blank)
41. A triangle has angles measuring 60°, 70°, and 50°. What type of triangle is it based on its angles? (Acute, Obtuse, or Right)

Section G: 3D Shapes and Volume

42. How many faces does a cube have?
43. How many vertices (corners) does a rectangular prism have?
44. What is the name of a 3D shape that is perfectly round like a ball?
45. A box has a length of 10 cm, a width of 5 cm, and a height of 4 cm. What is its volume? (Volume = length × width × height)
46. What is the volume of a cube with a side length of 3 cm?
47. Which 3D shape has a flat circular base and a single vertex (point) at the top?

Section H: The Coordinate Grid

For this section, imagine a standard coordinate grid with an x-axis (horizontal) and a y-axis (vertical). Points are written as (x, y).

48. What are the coordinates of a point that is 3 units to the right on the x-axis and 5 units up on the y-axis?
49. If you start at the origin (0,0) and move 6 units right and 2 units up, what are the coordinates of your new position?
50. Point A is at (2, 4). Point B is at (7, 4). What is the distance between Point A and Point B?
51. Imagine plotting these points on a grid: P(1,1), Q(5,1), R(5,4), S(1,4). What 2D shape do these points form when connected in order?
52. In which quadrant would you find the point (8, 9)? (Both numbers are positive).
53. What are the coordinates of the point located at the origin?

Section I: Reflection and Rotation

54. If the point (3, 5) is reflected across the x-axis, what are its new coordinates?
55. If the point (4, 2) is reflected across the y-axis, what are its new coordinates?
56. A shape is turned 90 degrees clockwise around a central point. What kind of transformation is this?
57. Look at the letter 'b'. If you reflect it across a vertical line, what letter do you get?
58. A triangle with vertices at A(1,1), B(3,1), and C(1,4) is rotated 180 degrees. This is the same as reflecting it across which two axes one after the other?
59. Which of these capital letters looks the same after a 180-degree rotation? A, F, H, G

Section J: Probability

60. You roll a standard six-sided die. What is the probability of rolling a 4? (Express as a fraction).
61. A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles (10 total). What is the probability of picking a blue marble at random?
62. Using the same bag from question 61, what is the probability of picking a marble that is NOT green?
63. You flip a fair coin. What is the probability of it landing on heads?
64. If an event is certain to happen (like the sun rising tomorrow), what is its probability? (Express as a number).
65. If an event is impossible (like rolling a 7 on a six-sided die), what is its probability? (Express as a number).

Section K: Mixed Problem Solving

66. Maria bought 3 notebooks at $2.50 each and a pack of pens for $4.75. If she paid with a $20 bill, how much change did she receive?
67. A rectangular park is 120 meters long and 80 meters wide. If you walk around the entire edge of the park once, what is the total distance you have walked? (This is the perimeter).
68. There are 28 students in a class. 3/4 of the students have brown hair. How many students do NOT have brown hair?
69. A train travels at a constant speed of 90 km per hour. How far will it travel in 3.5 hours?
70. John is saving for a bike that costs $250. He already has $70. He saves $15 each week from his allowance. How many weeks will it take him to save enough money to buy the bike?