Unit 3, Lesson 10
Subtraction Algorithms (Part 3)
Grade 3
Warm-up
Notice and Wonder: Digits That Disappear
Instructional Routines
Notice and Wonder
to see where instructional routines fit in your journey.
Materials
To Gather
Base-ten blocks
Activity Narrative
The purpose of this Warm-up is to elicit the observation that a hundred decomposed into more tens can be recorded, using a condensed notation, which will be useful later in the lesson when students decompose hundreds and tens to facilitate subtraction. While students may notice and wonder many things about these numbers, the important discussion point is how the decomposition is recorded. Base-ten blocks or diagrams can be used during the discussion if students need additional support in making sense of the condensed notation.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Activity
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
What do you notice? What do you wonder?
Student Response
Loading...
Advancing Student Thinking
Activity Synthesis
- “Both the expression in expanded form and the number show a unit decomposed into smaller units. Where do you see this in each case?” (The 300 has been turned into 200 in both examples. The 200 is shown as 200 in the first example, but as just a 2 in the second example. The 2 tens have been turned into 12 tens in both examples. The 12 tens is shown as 120 in the first example, but as just a 12 in the tens place in the second example.)
Activity 1
A New Subtraction Algorithm
Instructional Routines
to see where instructional routines fit in your journey.
Materials
None
Activity Narrative
The purpose of this activity is for students to learn a subtraction algorithm that records the difference in each place-value position as a single digit. The algorithm also records a decomposed hundred as a single digit in the hundreds place and as two digits in the tens place. Students carefully analyze and discuss two different ways to subtract, highlighting similarities and differences, and explaining how and why they work (MP6).
Launch
- Groups of 2
- Display Andre and Clare’s work.
- “How are the two algorithms alike?” (Both are stacked vertically. They show the same two numbers, 528 and 271. Both show a hundred decomposed into 10 tens.)
- “How are they different?” (One pair of numbers is written in expanded form, but the other pair is not. In Andre’s case, the decomposition of a hundred is recorded as 400 and 120. In Clare’s case, it is written as 4 in the hundreds place and 12 in the tens place.)
- 1 minute: quiet think time
- 2 minutes: partner discussion
- Share and record responses. Emphasize the different ways of recording the decompositions.
- “We noticed that this new algorithm uses fewer digits by not writing out the value of each digit. We just record up to 2 digits in each place to tell how many hundreds, tens, or ones there are.”
Activity
- “Take a few quiet minutes to work on the activity. Afterward, discuss your responses with your partner.”
- 3–5 minutes: independent work time
- 2–3 minutes: partner discussion
Andre and Clare found the value of
Andre's algorithm
Clare's algorithm
- Complete both algorithms to find the difference.
- Andre and Clare started their subtraction in different ways. How did their way of starting affect the steps needed to find the difference?
Student Response
Loading...
Advancing Student Thinking
Activity Synthesis
- Invite students to share their work for completing each algorithm.
- “What did you do differently as you completed each problem?” (With Andre’s work, I subtracted all the place values, and then I added up all the parts of the difference. With Clare’s work, once I subtracted the digits in each place value, the answer was complete.)
Activity 2
Try Clare’s Algorithm
Instructional Routines
to see where instructional routines fit in your journey.
Materials
None
Activity Narrative
The purpose of this activity is for students to practice using the algorithm they learned in the previous activity, in which the difference in each place-value position is recorded with one digit, and the decomposition of a place-value unit is recorded with one or two digits.
MLR8 Discussion Supports. Display sentence frames to support partner discussion: “First I _____ because . . . ,” and “Then I _____ because . . . .”
Advances: Speaking, Listening Representation: Internalize Comprehension. Synthesis: Invite students to identify which details were most important/needed to solve the problems. Display the sentence frame: “The next time I subtract, using Clare’s algorithm, I will look for . . . .”
Supports accessibility for: Conceptual Processing
Advances: Speaking, Listening Representation: Internalize Comprehension. Synthesis: Invite students to identify which details were most important/needed to solve the problems. Display the sentence frame: “The next time I subtract, using Clare’s algorithm, I will look for . . . .”
Supports accessibility for: Conceptual Processing
Launch
- Groups of 2
- “Now let's try using the algorithm you learned in the last activity to subtract some numbers. You can use the steps you recorded from our last activity, or use Clare’s work as an example.”
Activity
- 3–5 minutes: independent work time
- “Share your work and solutions with your partner.”
- 2–3 minutes: partner discussion
Clare used an algorithm to find the value of
Try using her algorithm to find the value of each difference.
Student Response
Loading...
Advancing Student Thinking
Activity Synthesis
- Display students' work on the first expression.
- “Where do we see the 91 after the 9 and the 1 have been crossed out?” (The 8 and the 11 represent 80 and 11, which is 91.)
Have a correction or suggestion?
Tell us about a typo, a broken link, or an improvement you’d like to see. We read every submission but can’t reply.
Have a question or need support instead? Visit our Contact Us page to reach our team.