Relationships Between Apples and Bananas

This lesson focuses on translating sentences into mathematical equations using variables. It begins by defining variables for apples and bananas, then constructs equations based on given sentences. The equations involve operations like equality, multiplication, addition, and subtraction. The lesson concludes with a complex equation involving the difference between triple the number of bananas and twice the number of apples. The aim is to help students understand how to form equations from word problems.

What do the variables 'a' and 'b' represent in this lesson?

• a is the number of bananas, b is the number of oranges

• a is the number of oranges, b is the number of grapes

• a is the number of apples, b is the number of bananas

• a is the number of bananas, b is the number of apples

If the number of apples is the same as the number of bananas, which equation represents this?

• a = b

• a = 3b

• a = b - 1

• a = b + 2

How would you express three times the number of apples equaling the number of bananas?

• b = a - 3

• b = 3a + 1

• 3a = b

• a = 3b

If 3a = b, what does this imply about the relationship between apples and bananas?

• The number of apples is equal to the number of bananas.

• The number of bananas is two more than the number of apples.

• The number of bananas is three times the number of apples.

• The number of apples is three times the number of bananas.

Which equation would you use if the number of apples is equal to the number of bananas?

• a = b - 2

• a = b

• a = 2b

• a = b + 3

Which equation represents four times the number of bananas equaling five times the number of apples?

• b = 5a + 4

• 4b = 5a

• 5b = 4a

• 4a = 5b

What does the equation 4b = 5a suggest about the quantities of apples and bananas?

• Four times the number of apples equals five times the number of bananas.

• The number of apples is four more than the number of bananas.

• Four times the number of bananas equals five times the number of apples.

• Five times the number of apples equals four times the number of bananas.

If the number of apples is two less than the number of bananas, which equation is correct?

• b = a + 2

• b = a - 2

• a = b - 2

• a = b + 2

How would you express the number of bananas being one more than the number of apples?

• b = a - 1

• b = a + 1

• a = b + 1

• a = b - 1

What is the equation for the difference between triple the number of bananas and twice the number of apples equaling three?

• 3b - 2a = 3

• 2b - 3a = 3

• 2a - 3b = 3

• 3a - 2b = 3