Squares, Cubes and Number Patterns Class 8 Maths Worksheet with Quiz and Activities
Solve the locker puzzle, build squares from odd numbers and meet the taxicab number 1729. On WitKnowLearn you get the Squares, Cubes and Number Patterns Class 8 online quiz, online activities and interactive games, a square and cube lab, a virtual lab and a worksheet-style practice sheet for Class 8 Maths.
Squares, Cubes and Number Patterns Class 8 Online Quiz
20 questions: 10 easy, 5 average and 5 thinking. Tap an answer and the next question comes up.
Squares, Cubes and Number Patterns Class 8 Activities
👆 Tap a tab to switch: Learn, Games, Labs, Challenges, Virtual Lab and Practice sheet
Squares, Cubes and Number Patterns: The Locker Puzzle, Odd Numbers and Taxicab 1729
A short read for Class 8 before you play. These notes cover A Square and A Cube: squares, cubes and number patterns.
🔐 The locker puzzle
A hundred people toggle a hundred lockers: person k flips every kth locker. A locker is flipped once for each of its factors, so only lockers with an odd number of factors stay open. Those are exactly the square numbers: 1, 4, 9, 16 and so on.
➕ Odd numbers and squares
Adding the first n odd numbers gives n squared, because each new L-shaped layer of tiles completes a bigger square. The nth odd number is 2n - 1, so 1 + 3 + 5 + 7 = 16 and the 36th odd number is 71.
🚕 Cubes and taxicab 1729
A cube is n × n × n. Ramanujan noticed that 1729 is the smallest number that is the sum of two cubes in two ways: 1³ + 12³ and 9³ + 10³. Roots undo powers, and ancient Indian words varga (square), ghana (cube) and mula (root) show how old these ideas are.
Squares, Cubes and Number Patterns Class 8 Maths Activities
Follow every step on the Number Train. Earn up to 3 stars in every activity.
This page covers A Square and A Cube: squares, cubes and number patterns for Class 8 maths. It covers perfect squares, square roots, odd number patterns, perfect cubes, cube roots, the locker puzzle and taxicab numbers.
The activities are pitched at Class 8 level. Solve the locker puzzle, build squares from odd-number layers in the studio, sort squares from cubes and find taxicab pairs. Explore more Class 8 maths worksheets on WitKnowLearn after this chapter.
Key ideas and facts to know
| n | n squared | n cubed |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 4 | 8 |
| 3 | 9 | 27 |
| 4 | 16 | 64 |
| 5 | 25 | 125 |
How to use this page
- Flip the six cards and try the Square and Cube Lab in the Learn tab.
- Play the five games and the five labs to practise each idea.
- Finish the five challenges to collect up to 15 points.
- Do two virtual experiments and build squares from odd-number layers in the studio.
- Take the 20-question online quiz, with assertion and reason and case study questions, and fill in the practice sheet.
Worked examples
324 = 2 × 2 × 3 × 3 × 3 × 3. Every prime pairs up, so it is 18 squared.
3375 = 3 × 3 × 3 × 5 × 5 × 5 = (3 × 5) cubed, so the cube root is 15.
This Squares, Cubes and Number Patterns worksheet for Class 8 science gives you online activities and interactive games that make the chapter clear. Every activity has a goal, a hint and a short fact, so students learn while they enjoy.
Complete Guide: Class 8 Maths Squares, Cubes and Number Patterns
This guide is for Class 8 students, parents and teachers. It covers A Square and A Cube: squares, cubes and number patterns for Class 8 maths and shows how to use the quiz, labs and games on this page.
Introduction to Squares, Cubes and Number Patterns
This chapter turns a puzzle about lockers into the idea of perfect squares, then follows the pattern of odd numbers and moves on to cubes, roots and a famous number.
What is there in this chapter
- Factors and the locker puzzle
- Squares and their patterns
- Square roots
- Cubes and taxicab numbers
- Cube roots
Learning objectives
- Explain why squares have an odd number of factors.
- Use patterns of odd numbers.
- Find square and cube roots by prime factors.
- Reason with assertions and case studies.
Learning outcomes
- I can spot squares and cubes.
- I can use odd number patterns.
- I can find roots with prime factors.
Squares, Cubes and Number Patterns Class 8 resources on this page
| Resource | What it gives |
|---|---|
| Online quiz | 20 questions: 10 easy, 5 average and 5 thinking, with assertion and reason and case study questions and a full review |
| Flip cards | 6 picture cards with one-line rules |
| Square and Cube Lab | A hands-on lab with 3 rounds |
| Games | 5 interactive games |
| Labs | 5 activity labs |
| Virtual Lab | 2 experiments plus a studio that builds squares from L-shaped odd-number layers |
| Challenges | 5 challenges, 15 points in all |
| Practice sheet | A worksheet-style sheet with 16 questions, name and date lines and a live score |
Key facts
| Idea | Rule |
|---|---|
| Squares end in | 0, 1, 4, 5, 6, 9 |
| Odd count of factors | only squares |
| Sum of first n odd numbers | n squared |
| 1729 | 1³ + 12³ and 9³ + 10³ |
| Roots | undo powers |
Types of questions you may see
- Is it a perfect square or cube
- Smallest multiplier to make a square or cube
- Assertion and reason on factors
- Odd number sums and patterns
Solved examples
72 = 2 × 2 × 2 × 3 × 3. One 2 is left unpaired, so multiply by 2 to get 144.
2 × 36 - 1 = 71.
Common mistakes
| Mistake | Correct idea |
|---|---|
| Thinking 2 times a number is its square | Square means n × n |
| Forgetting that perfect cubes can end in any digit | Check 8 cubed is 512 |
| Pairing factors in threes for a square | Pairs for squares, triplets for cubes |
Squares, Cubes and Number Patterns in daily life
Squares and cubes appear in floor tiles, areas, volumes of boxes and tanks, game grids, pixel screens and puzzles that use patterns.
Tips for parents and teachers
- Learn squares to 20 and cubes to 10.
- Check the units digit before you try a root.
- Practise one assertion and one case study each week.
Related Class 8 Maths Worksheets
- 🔵Class 8 Maths Worksheet: Squares and Square Roots
- 🧊Class 8 Maths Worksheet: Cubes and Cube Roots
- 🌳Class 8 Maths Worksheet: More Squares and Roots
- 🧊Class 8 Maths Worksheet: Cube Roots Practice
- ✖Class 8 Maths Worksheet: Exponents and Powers
- 🧠Class 8 Maths Notes and Mind Maps
- 📚Class 8 Maths Worksheets, page 1
- 📚Class 8 Maths Worksheets, page 2
Squares, Cubes and Number Patterns Class 8 FAQs
Why do squares have an odd number of factors?
Factors come in pairs, but in a square one pair has two equal numbers, so that factor is counted once and the total is odd.
How can odd numbers make squares?
Each L-shaped layer of tiles uses the next odd number and completes the next bigger square, so the first n odd numbers add up to n squared.
What is special about 1729?
It is the smallest number that can be written as the sum of two cubes in two ways: 1³ + 12³ and 9³ + 10³.
How do I know if a number is a perfect cube?
Write its prime factors. If they can be grouped into complete triplets, the number is a perfect cube.
What can students do on this page?
Students can take a 20-question online quiz with assertion and reason and case study questions, play five games, try five online activities, finish five challenges, run the Square and Cube Lab, do two virtual experiments, build the squares 1, 4, 9, 16 and 25 from L-shaped layers in the layers and totals views,, and fill in a 16-question practice sheet with a Show answers button.
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