Understanding Multiplication and Division Misconceptions

This lesson teaches how to describe relationships between expressions involving fractions or decimals without direct calculation. It addresses common misunderstandings about multiplication and division, showing that multiplying by a fraction can result in a smaller number, while dividing by a fraction can result in a larger number. Through examples, the lesson demonstrates how to compare expressions by understanding the effects of multiplication and division, emphasizing that multiplying by one does not change a number's value, while dividing by a fraction increases it.

What is a common misunderstanding about multiplication?

• It always results in a smaller number.

• It has no effect on the number.

• It always results in a larger number.

• It always results in zero.

What happens when you multiply a number by a fraction less than 1?

• The number becomes larger.

• The number becomes zero.

• The number becomes smaller.

• The number remains the same.

What is a common misunderstanding about division?

• It always results in a larger number.

• It always results in a smaller number.

• It always results in zero.

• It has no effect on the number.

What happens when you divide a number by a fraction less than 1?

• The number becomes larger.

• The number becomes smaller.

• The number remains the same.

• The number becomes zero.

How can you compare 7 plus 1 and 1 half times 7 plus 1?

• 7 plus 1 is half as large.

• 7 plus 1 is twice as large.

• They are equal.

• 1 half times 7 plus 1 is larger.

What is the effect of multiplying a number by 1?

• The number becomes smaller.

• The number remains the same.

• The number becomes larger.

• The number becomes zero.

How can you compare 10 minus 5 and 10 minus 5 divided by 0.25?

• They are equal.

• 10 minus 5 is half as large.

• 10 minus 5 is four times larger.

• 10 minus 5 divided by 0.25 is four times larger.

What is the effect of dividing a number by 1?

• The number becomes larger.

• The number becomes smaller.

• The number remains the same.

• The number becomes zero.

How can you compare 42 times 7 and 42 times 7 divided by 1 third?

• 42 times 7 divided by 1 third is three times larger.

• They are equal.

• 42 times 7 is half as large.

• 42 times 7 is three times larger.

What is the relationship between dividing by 1 and dividing by a fraction less than 1?

• Dividing by 1 results in a larger number.

• Dividing by a fraction less than 1 results in a smaller number.

• Dividing by a fraction less than 1 results in a larger number.

• They have the same effect.