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Worksheet (with Solutions): Algebraic Thinking

# Grade 5 Math Worksheet: Algebraic Thinking

Section A: Multiple Choice Questions

Q1: Sarah wrote the expression \(5 + n\) to represent the total number of pencils she has. If she has 12 pencils in total, what is the value of \(n\)?
(a) 5
(b) 7
(c) 12
(d) 17

Q2: Which expression represents "8 less than a number \(x\)"?
(a) \(8 - x\)
(b) \(x - 8\)
(c) \(x + 8\)
(d) \(8x\)

Q3: What is the next number in the pattern: 3, 7, 11, 15, ___?
(a) 17
(b) 18
(c) 19
(d) 20

Q4: If \(m \times 6 = 48\), what is the value of \(m\)?
(a) 6
(b) 7
(c) 8
(d) 9

Q5: Which equation matches this statement: "A number divided by 4 equals 9"?
(a) \(4n = 9\)
(b) \(n \div 4 = 9\)
(c) \(n + 4 = 9\)
(d) \(9 \div n = 4\)

Q6: Evaluate the expression \(3 \times (4 + 2)\).
(a) 14
(b) 18
(c) 20
(d) 24

Q7: If the rule for a pattern is "multiply by 2, then add 1," what number comes after 5?
(a) 7
(b) 10
(c) 11
(d) 12

Q8: Which property is shown by the equation \(7 + 8 = 8 + 7\)?
(a) Associative Property
(b) Commutative Property
(c) Distributive Property
(d) Identity Property

Section B: Fill in the Blanks

Q9: A letter or symbol that represents an unknown number is called a(n) __________.
Q10: In the expression \(5x + 3\), the number 5 is called the __________.
Q11: To solve the equation \(x + 9 = 15\), you need to subtract __________ from both sides.
Q12: The pattern 2, 4, 8, 16, 32 follows the rule: multiply by __________.
Q13: An equation is a mathematical sentence that uses an __________ sign to show two expressions are equal.
Q14: When you replace a variable with a number and calculate the result, you are __________ the expression.

Section C: Word Problems

Q15: Maria has some stickers in her collection. She receives 12 more stickers from her friend, and now she has 35 stickers in total. Write an equation to represent this situation and solve it to find how many stickers Maria had originally.
Q16: A school bus route drops off students at several stops. At each stop, 6 students get off the bus. If 42 students got off the bus in total, how many stops did the bus make? Write and solve an equation.
Q17: Jake is thinking of a number. When he multiplies his number by 4 and then adds 5, he gets 29. What number is Jake thinking of?
Q18: A bakery packages cookies in boxes. Each box contains the same number of cookies. If 8 boxes contain 72 cookies in total, how many cookies are in each box?
Q19: Emma creates a number pattern starting at 5. Her rule is: "Add 7 to get the next number." Write the first five numbers in Emma's pattern.
Q20: A rectangular garden has a width of 8 feet. The length is unknown, but the perimeter of the garden is 36 feet. Write an equation using the perimeter formula \(P = 2l + 2w\) and solve it to find the length of the garden.
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