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Number and Algebra Basics

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Number and Algebra Basics

Number and Algebra Basics

Mathematical symbols and numbers illustration

🔢 Part 1: Number Structure

1. Write these numbers in order from smallest to largest:

10³, 10⁻¹, 10², 0.001, 100

2. Find the prime factorisation of 48. Show your work using a factor tree:
3. Circle the correct answer for the Highest Common Factor (HCF) of 24 and 36:

6

12

18

24

4. What is the Least Common Multiple (LCM) of 4 and 6?

✖️➗ Part 2: Operations - Multiplication, Division & Estimation

5. Estimate the product of 247 × 32 by rounding to the nearest 10:

247 rounds to _______ and 32 rounds to _______

Estimated answer: _______ × _______ = _______

6. Calculate 4154 ÷ 8. Show your working and express any remainder as a decimal:
7. Round these numbers to the nearest hundred:

a) 3,847 = _______

b) 12,351 = _______

c) 7,050 = _______

8. Check all the strategies that help with estimation:

Rounding to the nearest 10

Using place value

Ignoring all digits

Rounding to the nearest 100

📐 Part 3: Algebraic Expressions

9. Simplify these expressions by collecting like terms:

a) 4x + 3x - 5x + 6 = _______

b) 7y + 2 - 3y + 5 = _______

c) 5a + 2b - 3a + 4b = _______

10. Expand these expressions using the distributive property:

a) 2(x + 3) = _______

b) 5(2y - 4) = _______

c) 3(a + 2b) = _______

11. Circle the expressions that are equivalent to 6x + 12:

6(x + 2)

3(2x + 4)

2(3x + 6)

x + 18

⚖️ Part 4: Solving Linear Equations

12. Solve these one-step equations. Show your working:

a) x + 7 = 15

b) 3y = 21

13. Solve these two-step equations:

a) 2x + 5 = 13

b) 4t - 7 = 9

14. Write and solve an equation for this word problem:

"Five times a number plus 3 equals 18. Find the number."

Equation: _______________________

Answer: The number is _______

🎯 Part 5: Mathematical Vocabulary

15. Match the mathematical terms with their definitions:
1. Variable
2. Prime factorisation
3. Distributive property
4. Like terms
A. Terms with the same variable part
B. A letter representing an unknown number
C. Breaking down a number into prime factors
D. a(b + c) = ab + ac
16. Fill in the blanks using the words: inverse, estimation, exponent, simplify

a) To solve an equation, we use _______ operations.

b) We can _______ an expression by collecting like terms.

c) In 10³, the number 3 is called an _______.

d) _______ helps us check if our answer is reasonable.

🧠 Part 6: Problem Solving Challenge

17. Sarah has $45. She buys some books that cost $8 each and has $13 left over. How many books did she buy?

Write an equation: _______________________

Answer: Sarah bought _______ books.

18. A rectangle has a length of (3x + 2) metres and a width of 4 metres. Write an expression for the perimeter and simplify it:
19. Reflection: What was the most challenging part of this worksheet for you? How did you overcome it?

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