Using Algorithms with Partial Products: 2 Two-Digit Numbers
10 min
Narrative
The purpose of this Warm-up is for students to compare ways to keep track of composing units in addition problems and in multiplication problems in which the partial products have a newly composed unit. While students may notice and wonder many things about these ways of recording, the important discussion point is to invite students to consider whatever way they currently record composing a new unit when they add, and then to use it when they multiply if there’s a need to compose a new unit when they add up the partial products.
This prompt gives students opportunities to look for and make use of structure (MP7) as they attend to ways to record newly composed units when they add 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 numbers that are added up are the same in each problem but their order is different.
- Some columns have little 1s.
- In both problems, there is a small 1 written in the hundreds and thousands place.
Students may wonder:
- Why is there a 1 in the hundreds (or thousands) column?
- What does the 1 in the hundreds (or thousands) column represent?
- Does it matter how you record the work?
Activity Synthesis (Teacher Notes)
- ”In both examples, the same numbers are added up. How would you explain what happens when adding the tens and hundreds?” (Add 5 tens and 5 tens to get 10 tens, which is 1 hundred or 100. Show that 100 with 0 in the tens place and either record a 1 at the top. To add the hundreds, 300 +700+100=1100, so record 1 in the hundreds place and then show that we also have 1000 to add.)
- “How does place value help us understand what the additional 1s represent?” (If the 1 is in the hundreds column, it represents 100. If it is in the thousands column, it represents 1000.)
- “When you add up partial products, keep track of the composed units in a way that makes sense to you.”
Standards
- 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.
25 min
10 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Using Algorithms with Partial Products: 2 Two-Digit Numbers
10 min
Narrative
The purpose of this Warm-up is for students to compare ways to keep track of composing units in addition problems and in multiplication problems in which the partial products have a newly composed unit. While students may notice and wonder many things about these ways of recording, the important discussion point is to invite students to consider whatever way they currently record composing a new unit when they add, and then to use it when they multiply if there’s a need to compose a new unit when they add up the partial products.
This prompt gives students opportunities to look for and make use of structure (MP7) as they attend to ways to record newly composed units when they add 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 numbers that are added up are the same in each problem but their order is different.
- Some columns have little 1s.
- In both problems, there is a small 1 written in the hundreds and thousands place.
Students may wonder:
- Why is there a 1 in the hundreds (or thousands) column?
- What does the 1 in the hundreds (or thousands) column represent?
- Does it matter how you record the work?
Activity Synthesis (Teacher Notes)
- ”In both examples, the same numbers are added up. How would you explain what happens when adding the tens and hundreds?” (Add 5 tens and 5 tens to get 10 tens, which is 1 hundred or 100. Show that 100 with 0 in the tens place and either record a 1 at the top. To add the hundreds, 300 +700+100=1100, so record 1 in the hundreds place and then show that we also have 1000 to add.)
- “How does place value help us understand what the additional 1s represent?” (If the 1 is in the hundreds column, it represents 100. If it is in the thousands column, it represents 1000.)
- “When you add up partial products, keep track of the composed units in a way that makes sense to you.”
Standards
- 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.