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Basic Algebra Foundations
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Basic Algebra Foundations
🔢 Part 1: Understanding Equations
1. Circle the correct meaning of the equals sign (=):
The answer is coming next
Both sides are the same as each other
Add the numbers together
2. Fill in the blanks to complete these number sentences:
a) 7 + 5 = _____
b) 10 - _____ = 3
c) _____ + 4 = 12
d) 15 = 9 + _____
📐 Part 2: Solving One-Step Equations
3. Solve these equations. Show your working using inverse operations:
Example: t + 7 = 12
a) x + 5 = 13
b) 2s = 14
c) m - 3 = 8
d) 4y = 20
4. Check all the equations that have the solution x = 6:
x + 2 = 8
3x = 18
x - 4 = 2
x + 1 = 5
🔄 Part 3: Properties of Operations
5. The commutative property says we can change the order. Circle which examples show the commutative property:
3 × b = b × 3
a + 5 = 5 + a
2(x + 1) = 2x + 2
7 + m = m + 7
6. Use the distributive property to expand these expressions:
a) 2(x + 3) = _____________
b) 4(y + 1) = _____________
c) 3(a + 5) = _____________
7. Match the algebraic expression with its meaning:
1. 3b
2. x + 7
3. 2(y + 4)
4. m - 5
A. Seven more than x
B. Three times b
C. Five less than m
D. Two times the sum of y and 4
🎨 Part 4: Visual Algebra
8. Draw algebra tiles or shapes to represent the equation x + 3 = 7:
9. Use pictures or symbols to show how you would solve 2n = 10:
10. Explain in your own words what it means to "keep an equation balanced":
🧠 Part 5: Challenge Questions
11. Write an equation for this word problem: "Sarah has some stickers. After giving away 4 stickers, she has 9 left. How many stickers did she start with?"
12. If 3x + 1 = 16, what is the value of x?
13. Circle the expressions that are equivalent to 4a + 8:
4(a + 2)
2(2a + 4)
4a + 2 + 6
8 + 4a
14. Reflection: What was the most challenging part of this worksheet for you?
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