Represent Situations with Multiplication and Division
10 min
Narrative
This Number Talk encourages students to think about multiplication and division involving a whole number and unit fraction. While the order of the factors does not matter for multiplication, as seen in the first two expressions, it does matter for division, as seen in the second pair of expressions. Monitor for students who find the value of the two division expressions using multiplication since the relationship between multiplication and division is the focus of this lesson.
Launch
Display one expression.
“Give me a signal when you have an answer and can explain how you got it.”
1 minute: quiet think time
Teacher Instructions
Record answers and strategy.
Keep expressions and work displayed.
Repeat with each expression.
Student Task
Find the value of each expression mentally.
3×101
101×3
101÷3
3÷101
Sample Response
103: It’s 3 tenths.
103: It’s the same as 3×101.
301: It’s 31×101.
30: There are ten 101s in 1 and 3 times as many in 3.
Activity Synthesis (Teacher Notes)
“How did you find the value of 3÷101?” (I know that there are ten 101s in 1 so there are thirty 101s in 3.)
Standards
Addressing
5.NF.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
5.NF.7·Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
5.NF.B.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
5.NF.B.7·Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.<span>Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.</span>
15 min
20 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Represent Situations with Multiplication and Division
10 min
Narrative
This Number Talk encourages students to think about multiplication and division involving a whole number and unit fraction. While the order of the factors does not matter for multiplication, as seen in the first two expressions, it does matter for division, as seen in the second pair of expressions. Monitor for students who find the value of the two division expressions using multiplication since the relationship between multiplication and division is the focus of this lesson.
Launch
Display one expression.
“Give me a signal when you have an answer and can explain how you got it.”
1 minute: quiet think time
Teacher Instructions
Record answers and strategy.
Keep expressions and work displayed.
Repeat with each expression.
Student Task
Find the value of each expression mentally.
3×101
101×3
101÷3
3÷101
Sample Response
103: It’s 3 tenths.
103: It’s the same as 3×101.
301: It’s 31×101.
30: There are ten 101s in 1 and 3 times as many in 3.
Activity Synthesis (Teacher Notes)
“How did you find the value of 3÷101?” (I know that there are ten 101s in 1 so there are thirty 101s in 3.)
Standards
Addressing
5.NF.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
5.NF.7·Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
5.NF.B.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
5.NF.B.7·Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.<span>Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.</span>