Algebraic Thinking: Patterns, Variables, and Equations for Fifth Graders

Question 1

What is the main difference between a variable and a constant?

Accepted Answer

A variable can change, while a constant is a specific number.

Answer

A variable is a specific number, while a constant can change.

Answer

Both variables and constants can change.

Question 2

Translate this verbal expression into a variable expression: The total of a number and 5

Accepted Answer

5 + x

Answer

x - 5

Answer

5x

Answer

x / 5

Question 3

In the equation y = 2x + 3, what is the slope and y-intercept?

Accepted Answer

Slope: 2, y-intercept: 3

Answer

Slope: 3, y-intercept: 2

Answer

Slope: -2, y-intercept: -3

Answer

Slope: 1, y-intercept: 0

Question 4

Examine the table below.

| Input | Output |
|---|---| 
| 1 | 4 |
| 2 | 7 |
| 3 | 10 |
| 4 | 13 |

What's the pattern between the input and output values? Write an equation that shows this pattern.

Accepted Answer

The pattern is to add 3 to the input. The equation is y = x + 3.

Answer

The pattern is to multiply the input by 3. The equation is y = 3x.

Answer

The pattern is to subtract 2 from the input. The equation is y = x - 2.

Question 5

Which of the following is a real-world situation that can be represented by the expression 4x + 2?

Accepted Answer

The total cost of buying 4 apples and 2 oranges, if an apple costs x cents and an orange costs 2 cents

Answer

The perimeter of a rectangle with a length of 4x cm and a width of 2 cm

Answer

The area of a triangle with a base of 4x cm and a height of 2 cm

Answer

The volume of a cube with a side length of 4x cm

Question 6

Solve for x: x - 5 = 3

Accepted Answer

x = 2

Answer

x = -2

Answer

x = 8

Answer

x = 10

Question 7

Which of the following expressions includes a variable?

Accepted Answer

y + 5

Answer

7 + 3

Answer

2 x 6

Answer

10

Question 8

Which of the following equations represents the relationship between the number of hours worked (h) and the amount earned (e) if the hourly rate is $10?

Accepted Answer

e = 10h

Answer

e = h / 10

Answer

e = 10 - h

Answer

e = h x 10

Question 9

Which of the following represents the pattern: 'add 3'?

Accepted Answer

n + 3

Answer

3n

Answer

n - 3

Answer

n / 3

Question 10

What is the slope of the line represented by the equation: y = -2x + 5?

Accepted Answer

-2

Answer

2

Answer

5

Answer

-5

Question 11

Which rule describes the pattern in this sequence: 2, 5, 8, 11, 14, ... ?

Accepted Answer

Add 3

Answer

Add 2

Answer

Multiply by 3

Answer

Divide by 3

Question 12

A rectangular garden's length is 3 feet more than its width. If the garden's area is 48 square feet, what are its dimensions?

Accepted Answer

Length: 8 feet, Width: 5 feet

Answer

Length: 6 feet, Width: 3 feet

Answer

Length: 9 feet, Width: 6 feet

Answer

Length: 7 feet, Width: 4 feet

Question 13

A plant grows 3 centimeters each day. On day 1, it's 5 centimeters tall. Which expression shows the plant's height, in centimeters, on day n?

Accepted Answer

3n + 5

Answer

3n - 5

Answer

5n + 3

Answer

5n - 3

Question 14

Which of these is an algebraic expression?

Accepted Answer

x + 3

Accepted Answer

2(x + 1)

Accepted Answer

3x - 2y

Answer

4 + 5

Question 15

A farmer sells apples at the market for 25 cents each. Write an expression to show how much money the farmer earns from selling x apples.

Accepted Answer

0.25x

Answer

x + 0.25

Answer

0.25 / x

Answer

x - 0.25

Question 16

Which of these is NOT an algebraic expression?

Accepted Answer

5 + 5

Answer

2x + 5

Answer

x - 3

Question 17

Which algebraic expression matches the pattern in this number sequence: 2, 5, 8, 11, 14, ...?

Accepted Answer

n + 3

Answer

3n

Answer

n - 2

Question 18

Which expression represents the pattern 2, 4, 6, 8, ...?

Accepted Answer

2n + 2

Answer

n + 3

Answer

2n - 2

Answer

3n + 1

Question 19

A pattern adds 3 to each number to get the next number. Which expression shows this pattern?

Accepted Answer

n + 3

Answer

3n

Answer

n^2

Question 20

What is the algebraic expression for 'Twice the sum of a number and 5'?

Accepted Answer

2(x + 5)

Answer

x + 2(5)

Answer

2x + 5

Question 21

A farmer has a rectangular plot of land that he wants to fence. The length of the plot is 3 feet more than 4 times its width. Express the area of the plot in terms of its width.

Accepted Answer

w(4w + 3)

Answer

4w + 3

Answer

3(w + 4)

Answer

4(w + 3)

Question 22

Which expression represents the number pattern 2, 5, 8, 11, ...?

Accepted Answer

n + 3

Answer

n - 3

Answer

3n

Answer

n^3

Question 23

An apple store sells apples for 50 cents each. If the store sells 'x' apples, what expression shows the total cost of the apples in dollars?

Accepted Answer

0.50x

Answer

0.50 + x

Answer

x / 0.50

Answer

x - 0.50

Question 24

Which algebraic expression represents the pattern 4, 7, 10, 13, ...?

Accepted Answer

n + 3

Answer

n - 3

Answer

3n

Question 25

Which sentence is true about the equation x + 5 = 10?

Accepted Answer

x is equal to 5

Answer

x is equal to 15

Answer

x is greater than 5

Answer

x is less than 5

Question 26

Which of the following is a linear function?

Accepted Answer

y = 2x + 1

Answer

y = 2^x

Answer

y = x^2

Answer

y = 1 / x

Question 27

Which expression represents the pattern: 2, 5, 8, 11, 14, ...?

Accepted Answer

n + 3

Answer

n - 3

Answer

3 - n

Answer

2 * n

Question 28

Which equation shows the relationship between x and y: y is 5 more than 4 times x?

Accepted Answer

y = 4x + 5

Answer

x = 4y + 5

Answer

x = 5y + 4

Answer

y = 5x + 4

Question 29

Which expression is the same as 3(x + 2)?

Accepted Answer

3x + 6

Answer

6x + 2

Answer

3x + 2

Answer

x + 6

Question 30

Which inequality shows that a number is less than 10?

Accepted Answer

n < 10

Answer

n ≥ 10

Answer

n > 10

Answer

n = 10

Question 31

Which of the following is a linear equation?

Accepted Answer

y = 2x + 1

Answer

y = x^2 + 2

Answer

y = √x

Answer

y = 1/(x + 1)

Question 32

What rule can we use to find the next number in the pattern 2, 5, 8, 11, 14, ...?

Accepted Answer

Add 3 to the previous number

Answer

Multiply the previous number by 2

Answer

Subtract 3 from the previous number

Question 33

A rectangle has a length of 5 units and a width of 'y' units.  What expression shows the area of the rectangle?

Accepted Answer

5y

Answer

5y * 5y

Answer

5 - y

Answer

y + 5

Question 34

Which number sentence is always true?

Accepted Answer

2(x + 3) = 2x + 6

Answer

2(x + 3) = x + 6

Answer

2(x - 3) = 2x + 6

Answer

2(x - 3) = x + 6

Question 35

Which pattern doesn't follow a rule where you add the same number each time?

Accepted Answer

2, 4, 6, 9, 13, ...

Answer

10, 8, 6, 4, 2, ...

Answer

1, 3, 5, 7, 9, ...

Answer

-1, 0, 1, 2, 3, ...

Question 36

Which table shows a relationship where 'y' is always double 'x'?

Accepted Answer

[table showing x | y values: (1, 2), (2, 4), (3, 6), (4, 8)]

Answer

[table showing x | y values: (1, 1), (2, 2), (3, 3), (4, 5)]

Answer

[table showing x | y values: (1, 3), (2, 5), (3, 9), (4, 12)]

Question 37

What is another way to write 2x(x + 3)?

Accepted Answer

2x^2 + 6x

Answer

x^2 + 3

Answer

2x + 6

Answer

4x^2 + 6

Question 38

Which expression describes the pattern: 3, 6, 9, 12, ...?

Accepted Answer

3n

Answer

n + 3

Answer

n x 2

Answer

3 + n

Question 39

If 'x' stands for a number, what is the value of 'x' in the equation x + 5 = 12?

Accepted Answer

7

Answer

17

Answer

2

Answer

5

Question 40

If 'y' is equal to 3, what is the value of '2y + 1'?

Accepted Answer

7

Answer

5

Answer

8

Answer

6

Question 41

Sarah has 's' stickers. Her friend gives her 5 more stickers. Which expression represents the total number of stickers Sarah has now?

Accepted Answer

s + 5

Answer

s - 5

Answer

5s

Question 42

A train travels at a speed of 'm' miles per hour. How many miles will it travel in 3 hours?

Accepted Answer

3m

Answer

m + 3

Answer

m / 3

Question 43

The pattern '2, 4, 6, 8, ...' follows which rule?

Accepted Answer

Add 2 to the previous number

Answer

Divide the previous number by 2

Answer

Multiply the previous number by 2

Answer

Subtract 2 from the previous number

Question 44

If 'a' is 5 and 'b' is 2, what is the value of 'a + b'?

Accepted Answer

7

Answer

3

Answer

2

Answer

10

Question 45

Which of the following represents a pattern that can be described by the rule "add 5"?

Accepted Answer

2, 7, 12, 17, 22

Answer

3, 5, 7, 9, 11

Answer

10, 8, 6, 4, 2

Question 46

Which of the following expressions is equivalent to 3x + 5?

Accepted Answer

5 + 3x

Answer

x + 5 + 3

Answer

5x + 3

Answer

3(x + 5)

Question 47

What is the value of x in the equation 2x - 5 = 11?

Accepted Answer

8

Answer

5

Answer

13

Answer

10

Question 48

Which of the following graphs represents the equation y = -x + 3?

Accepted Answer

Image of a line with a negative slope.

Answer

Image of a parabola.

Answer

Image of a circle.

Question 49

What is the probability of rolling a 6 on a standard six-sided die?

Accepted Answer

1 / 6

Answer

1 / 4

Answer

1 / 5

Answer

1 / 3

Question 50

Which of the following is a measure of central tendency?

Accepted Answer

Mean

Answer

Range

Answer

Mode

Answer

Median

Question 51

Which expression represents the pattern: 3, 6, 9, 12, ...?

Accepted Answer

3n

Answer

n / 3

Answer

3 * n - 3

Answer

n + 3

Question 52

Solve for x: x + 5 = 10

Accepted Answer

5

Answer

10

Answer

2

Answer

15

Question 53

Which of the following is equivalent to 2(x + 3)?

Accepted Answer

2x + 6

Answer

x + 2

Answer

6x

Answer

x + 6

Question 54

What is the value of y when 3y - 4 = 16?

Accepted Answer

6

Answer

8

Answer

4

Question 55

Which of the following represents an algebraic expression for 'the sum of two numbers increased by 5'?

Accepted Answer

x + y + 5

Answer

5(x + y)

Answer

x + 5y

Answer

(x + y) * 5

Question 56

What is the slope of the line represented by the equation y = 2x + 1?

Accepted Answer

2

Answer

-2

Answer

-1

Answer

1

Question 57

Which of the following is a factor of 12x^2 - 18x?

Accepted Answer

6x

Answer

x^2

Answer

6

Answer

3x

Question 58

What is the y-intercept of the line represented by the equation 2x - 3y = 6?

Accepted Answer

-2

Answer

-3

Answer

3

Answer

2

Question 59

Which of the following is NOT a strategy for solving algebraic equations?

Accepted Answer

Guessing and checking

Answer

Isolating the variable

Answer

Using inverse operations

Answer

Substituting values

Question 60

Which of the following is equivalent to the expression (2x + 3)(x - 1)?

Accepted Answer

2x^2 + x - 3

Answer

4x^2 - 2x - 3

Answer

x^2 + x - 3

Answer

2x^2 - 5x - 3

Question 61

What is the rule for the following pattern: 2, 4, 6, 8, 10?

Accepted Answer

Add 2 to the previous number

Answer

Subtract 2 from the previous number

Answer

Multiply the previous number by 2

Answer

Divide the previous number by 2

Question 62

If 'n' represents any number, which expression represents '5 less than a number'?

Accepted Answer

n - 5

Answer

5n

Answer

n + 5

Answer

5 / n

Question 63

Which of these equations represents the following scenario: 'Sarah has 3 apples, and she buys 4 more.'

Accepted Answer

3 + 4 = a

Answer

3 - 4 = a

Answer

3 / 4 = a

Answer

3 x 4 = a

Question 64

What is the missing number in the following pattern: 1, 3, 5, __, 9?

Accepted Answer

7

Answer

6

Answer

8