Algebraic Thinking: Solving Equations and Inequalities for Fourth Graders

Question 1

An apple vendor sells apples for 50 cents each. If you buy x apples, how much will you pay in total?

Accepted Answer

50x cents

Answer

x - 50 cents

Answer

50 + x cents

Answer

x / 50 cents

Question 2

We have a number, let's call it x. If we divide x by 6, the result is 5. Which equation shows this?

Accepted Answer

x ÷ 6 = 5

Answer

x + 6 = 5

Answer

x - 6 = 5

Answer

6 ÷ x = 5

Question 3

What is the formula for the area of a circle with a radius of 'r' centimeters?

Accepted Answer

πr^2

Answer

2πr

Answer

2πr^2

Answer

r^2

Question 4

You buy b books, and each book costs $4. Which expression shows how much money you will spend?

Accepted Answer

4b

Answer

b/4

Answer

4 + b

Answer

b - 4

Question 5

Which inequality shows that the difference between twice a number x and 5 is more than 10?

Accepted Answer

2x - 5 > 10

Answer

2x - 5 < 10

Answer

5 - 2x > 10

Question 6

A train travels at a steady speed of 60 miles per hour. If the train travels for 't' hours, which algebraic expression represents the total distance the train traveled?

Accepted Answer

60t

Answer

t + 60

Answer

60/t

Question 7

A bicyclist travels at a speed of 15 miles per hour. Write an algebraic expression that represents the total distance covered if the bicyclist travels for t hours.

Accepted Answer

15t

Answer

15 + t

Answer

t / 15

Answer

15 / t

Question 8

Simplify the algebraic expression: 3(x + 2) - (x - 5)

Accepted Answer

2x + 11

Answer

3x + 7

Answer

2x - 3

Answer

3x - 2

Question 9

Examine the pattern in this sequence: 1, 4, 9, 16, 25, ... What is the next number in the pattern and explain why?

Accepted Answer

The pattern is a sequence of perfect squares, so the next number is 36.

Answer

The pattern is a sequence of odd numbers, so the next number is 27.

Answer

The pattern is a sequence of increasing numbers, so the next number is 31.

Answer

The pattern is a sequence of prime numbers, so the next number is 29.

Question 10

Which equation shows the number x is 10 less than y?

Accepted Answer

x = y - 10

Answer

x = y + 10

Answer

y = x + 10

Answer

y = x - 10

Question 11

The length of a rectangle is 5 cm more than its width. If the width is x cm, what is the length of the rectangle?

Accepted Answer

x + 5 cm

Answer

x cm

Answer

x - 5 cm

Answer

5x cm

Question 12

Which number sentence represents 'Five is less than ten'?

Accepted Answer

10 > 5

Answer

5 > 10

Answer

5 = 10

Answer

10 = 5

Question 13

If x = 6 and y = 8, what is x + y?

Accepted Answer

14

Answer

2

Answer

8

Answer

24

Question 14

Which inequality shows that the number x is less than or equal to 10?

Accepted Answer

x ≤ 10

Answer

x > 10

Answer

x < 10

Answer

x ≥ 10

Question 15

Solve the inequality:

|2x - 5| is greater than 3

Accepted Answer

x is less than 4 or x is greater than 1

Answer

x is greater than 4 or x is less than 1

Answer

x is less than 2 or x is greater than 3

Question 16

Which of the following represents an algebraic expression for the phrase 'the sum of three times a number and 5'?

Accepted Answer

3x + 5

Answer

5 + 3x

Answer

5 - 3x

Answer

x + 5

Question 17

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

Accepted Answer

3x + 5

Answer

5x + 3

Answer

x + 3 + 5

Answer

5x

Question 18

Which inequality represents the statement 'The product of a number and 4 is at least 12'?

Accepted Answer

n × 4 ≥ 12

Answer

n + 4 ≥ 12

Answer

n - 4 ≥ 12

Answer

n ÷ 4 ≥ 12

Question 19

In the number sequence 5, 10, 15, 20, 25, ... what is the pattern? Write an algebraic expression that represents the nth term of the sequence.

Accepted Answer

The pattern is adding 5 to each number. The algebraic expression for the nth term is 5n.

Answer

The pattern is multiplying each number by 2. The algebraic expression for the nth term is 2n.

Answer

The pattern is alternating between adding 5 and subtracting 5. The algebraic expression for the nth term is 5 + (-1)^n.

Question 20

What's the key difference between an expression and an equation?

Accepted Answer

An expression doesn't have an equal sign (=), but an equation does.

Answer

Equations aren't always harder than expressions.

Answer

Both expressions and equations can use variables.

Answer

Equations can be used to solve problems, but expressions can't.

Question 21

A rectangle's width is 'x' centimeters. If the rectangle is 5 centimeters longer than it is wide, how long is the rectangle?

Accepted Answer

x + 5 cm

Answer

x - 5 cm

Answer

5x cm

Answer

5 cm

Question 22

Which inequality represents 'x is less than or equal to 10'?

Accepted Answer

x ≤ 10

Answer

x > 10

Answer

x = 10

Answer

x < 10

Question 23

An apple costs 25 cents. If you buy 5 apples, how much will it cost?

Accepted Answer

$1.25

Answer

$0.50

Answer

$1.00

Answer

$1.50

Question 24

Which symbol correctly represents 'x is less than or equal to 5'?

Accepted Answer

x ≤ 5

Answer

x > 5

Answer

x < 5

Answer

x ≥ 5

Question 25

Simplify the expression: 2(3x + 4) - 5x + 7

Accepted Answer

6x + 15

Answer

x + 15

Answer

12x + 7

Answer

5x + 15

Question 26

A rectangular garden's length is 5 centimeters more than its width. If the width is represented by the variable w, which expression shows the length of the garden?

Accepted Answer

w + 5

Answer

w - 5

Answer

5 - w

Question 27

Observe the sequence: 2, 5, 8, 11, 14, ... What number comes next? Explain your thinking.

Accepted Answer

17

Answer

15

Answer

18

Answer

16

Question 28

Which inequality represents that the number x is less than or equal to 10?

Accepted Answer

x ≤ 10

Answer

x ≥ 10

Answer

x = 10

Question 29

Look at this sequence: 1, 4, 9, 16, 25, .... What's the pattern? Explain your answer.

Accepted Answer

Squaring natural numbers

Answer

Adding odd numbers together

Answer

Multiplying prime numbers

Answer

No pattern

Question 30

Solve the inequality: 2x - 5 is greater than 11

Accepted Answer

x is greater than 8

Answer

x is less than 8

Answer

x is greater than 16

Answer

x is less than 16

Question 31

What is the algebraic expression for the total cost of buying 'b' books, if each book costs $4?

Accepted Answer

4b

Answer

b + 4

Answer

4 - b

Answer

b / 4

Question 32

Which expression matches the phrase '3 times a number, x, minus 5'?

Accepted Answer

3x minus 5

Answer

3x plus 5

Answer

5 minus 3x

Answer

5 plus 3x

Question 33

Which equation shows the line passing through the points (2, 5) and (4, 9)?

Accepted Answer

y equals 2x plus 3

Answer

y equals x plus 3

Answer

y equals 2x plus 1

Answer

y equals x plus 5

Question 34

Observe the sequence: 2, 4, 8, 16, 32, .... Describe the rule that governs this pattern. Explain your reasoning.

Accepted Answer

Each number is obtained by multiplying the previous number by 2.

Answer

Each number is obtained by adding 2 to the previous number.

Answer

Each number is obtained by multiplying the previous number by 3.

Question 35

You rent a car for 'd' days. The daily rental cost is $30. What is the total cost of renting the car?

Accepted Answer

30d

Answer

d + 30

Answer

d - 30

Answer

30 - d

Question 36

Peter has 5 apples. His friend gives him more apples represented by the variable "x". Which expression shows the total number of apples Peter has now?

Accepted Answer

5 + x

Answer

5 - x

Answer

x - 5

Answer

5 / x

Question 37

Solve the equation: x + 3 = 7

Accepted Answer

4

Answer

10

Answer

7

Answer

11

Question 38

Write an inequality to represent: The number of pencils John has is less than 10

Accepted Answer

John < 10

Answer

John > 10

Answer

John = 10

Answer

10 < John

Question 39

Complete the pattern: 2, 5, 8, 11, ___, 17

Accepted Answer

15

Answer

12

Answer

14

Answer

16

Question 40

Simplify the expression: 3(x + 2)

Accepted Answer

3x + 6

Answer

6x + 2

Answer

x + 6

Answer

3x + 2

Question 41

Solve for x: x - 5 = 10

Accepted Answer

15

Answer

5

Answer

10

Answer

20

Question 42

Translate this situation into an equation: The total number of students is 25. The number of girls is "x". The number of boys is 3 more than the number of girls.

Accepted Answer

x + 3 = 25

Answer

x - 3 = 25

Answer

25 - 3 = x

Answer

25 + 3 = x

Question 43

Find the value of 'x' in the equation: 'x + 3 = 7

Accepted Answer

x = 4

Answer

x = 7

Answer

x = 10

Answer

x = 3

Question 44

Which inequality means 'The number of marbles is less than 12'?

Accepted Answer

Marbles < 12

Answer

Marbles > 12

Answer

Marbles ≥ 12

Answer

Marbles ≤ 12

Question 45

In the expression '3x + 5', what is 'x' called?

Accepted Answer

Variable

Answer

Number

Answer

Expression

Answer

Term

Question 46

Write an equation for the perimeter of a rectangle with length 'l' and width 'w'.

Accepted Answer

2l + 2w

Answer

l + w

Answer

l - w

Answer

2l - 2w

Question 47

Which equation has endless solutions?

Accepted Answer

x + 3 = x + 4

Answer

x - 5 = 5

Answer

2x = 10

Answer

x + y = 10

Question 48

Which expression is equivalent to 5 times the sum of x and 3?

Accepted Answer

5x + 15

Answer

15x + 3

Answer

x + 3 + 5

Answer

5(x - 3)

Question 49

Which inequality represents 'the number y is greater than or equal to 5'?

Accepted Answer

y ≥ 5

Answer

y ≠ 5

Answer

y > 5

Answer

y ≤ 5

Question 50

Which expression has a value of 12 when x equals 4?

Accepted Answer

3x + 6

Answer

x + 12

Answer

4x + 4

Answer

2x + 8

Question 51

A store sells apples for $0.50 each and oranges for $0.75 each. You buy 3 apples and some oranges for a total of $5. Which equation can you use to find the number of oranges you bought?

Accepted Answer

0.50(3) + 0.75x = 5

Answer

3x + 0.50 = 5

Answer

0.75(3) + 0.50x = 5

Answer

5x + 0.75 = 3

Question 52

Which of the following is NOT a variable?

Accepted Answer

10

Answer

x

Answer

y

Answer

a

Question 53

Identify the pattern in the sequence: 3, 7, 11, 15, ...

Accepted Answer

Each number is 4 more than the previous number.

Answer

Each number is 3 less than the previous number.

Answer

Each number is twice the previous number.

Answer

There is no pattern.

Question 54

Which of the following is an example of a linear equation?

Accepted Answer

y = 2x + 3

Answer

y = √x

Answer

y = x^2 + 1

Question 55

Which expression below is equivalent to 5x + 3?

Accepted Answer

3x + 5x

Answer

3x - 5x

Answer

5 + 3x

Answer

5x - 3

Question 56

Which equation matches the situation: There are 4 more apples in the basket than oranges?

Accepted Answer

Apples = Oranges + 4

Answer

Oranges = Apples + 4

Answer

Oranges = Apples - 4

Answer

Apples = Oranges - 4

Question 57

Which inequality represents the statement: The number of students in the class is greater than or equal to 20?

Accepted Answer

Students ≥ 20

Answer

Students > 20

Answer

Students < 20

Question 58

Which variable represents the unknown number in the equation: x + 7 = 12?

Accepted Answer

x

Answer

7

Answer

x + 7

Answer

12

Question 59

Which expression represents the area of a rectangle that is 5 units long and 3 units wide?

Accepted Answer

5 x 3

Answer

3 - 5

Answer

5 + 3

Answer

5 - 3

Question 60

Which inequality represents the set of numbers less than -5?

Accepted Answer

x < -5

Answer

x ≤ -5

Answer

x ≥ -5

Answer

x > -5

Question 61

Which equation represents the statement: The total of two numbers is 15?

Accepted Answer

x + y = 15

Answer

x + x = 15

Answer

x - y = 15

Answer

y - x = 15

Question 62

Which number continues the pattern: 10, 15, 20, 25, ...?

Accepted Answer

30

Answer

32

Answer

28

Question 63

Which expression represents the perimeter of a square with a side length of s?

Accepted Answer

4s

Answer

s + s + s + s

Answer

s x s

Answer

2s

Question 64

Which inequality represents the following situation: A number decreased by 4 is greater than or equal to -2?

Accepted Answer

x - 4 ≥ -2

Answer

x - 4 ≤ -2

Answer

-2 - x ≥ 4

Answer

4 - x ≥ -2