Work with Mixed Numbers
10 min
Narrative
The purpose of this Warm-up is to recall multiplication diagrams used in an earlier grade to find the product of 2 two digit numbers. This prepares students for finding the product of 2 mixed numbers in this lesson by decomposing the mixed number into a whole number and a fraction and then finding and adding partial products.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Sample Response
Students may notice:
- The diagrams all represent 34×21
- One of the diagrams is not divided into smaller parts.
- We saw diagrams like this in an earlier grade.
Students may wonder:
- What is the value of 34×21?
- Why are the diagrams partitioned in different ways?
- Are these different ways to find the value of 34×21?
Activity Synthesis (Teacher Notes)
- Display Diagram B.
- “How might we use this diagram to find the product of 34 x 21?”
- Record each partial product within the diagram and the addition of the partial products that produces the product of 34 x 21.
- If no students mention it, ask “How does decomposing and using the distributive property support this way of multiplying?”
Standards
Building On
- 4.NBT.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
- 4.NBT.B.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Building Toward
- 5.NF.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
- 5.NF.6·Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
- 5.NF.B.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
- 5.NF.B.6·Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
20 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Work with Mixed Numbers
10 min
Narrative
The purpose of this Warm-up is to recall multiplication diagrams used in an earlier grade to find the product of 2 two digit numbers. This prepares students for finding the product of 2 mixed numbers in this lesson by decomposing the mixed number into a whole number and a fraction and then finding and adding partial products.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Sample Response
Students may notice:
- The diagrams all represent 34×21
- One of the diagrams is not divided into smaller parts.
- We saw diagrams like this in an earlier grade.
Students may wonder:
- What is the value of 34×21?
- Why are the diagrams partitioned in different ways?
- Are these different ways to find the value of 34×21?
Activity Synthesis (Teacher Notes)
- Display Diagram B.
- “How might we use this diagram to find the product of 34 x 21?”
- Record each partial product within the diagram and the addition of the partial products that produces the product of 34 x 21.
- If no students mention it, ask “How does decomposing and using the distributive property support this way of multiplying?”
Standards
Building On
- 4.NBT.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
- 4.NBT.B.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Building Toward
- 5.NF.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
- 5.NF.6·Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
- 5.NF.B.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
- 5.NF.B.6·Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.