Subtraction Algorithms (Part 3)
10 min
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
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?
Solution Steps (4)
- 1Notice left image→Shows 325 in expanded form: 300+20+5
- 2Notice right image→Shows 325 in standard form with regrouping notation (3→2, 2→12)
- 3Compare regrouping notation→Left: 300→200, 20→120; Right: 3→2 (hundreds), 2→12 (tens)
- 4Connect the representations→Both show decomposing 1 hundred into 10 tens for subtraction preparation
Sample Response
Students may notice:
- On the left is 325, written in expanded form. On the right is 325, written the regular way.
- Parts of the expression on the left are crossed out. The first two digits in the number on the right are crossed out.
- Both the expression and the number 325 have smaller numbers or digits written above them.
- The expression on the left shows 120 in the tens place, and the number on the right shows 12 in the tens place.
- The expression on the left shows 200, and the number on the right shows 2 for the hundreds.
- Both the expression and the number show a hundred decomposed into 10 tens and then added to the 2 tens that were already there.
- Why are parts of the expression and the number crossed out?
- What do the little numbers and the little digits represent?
- Why would we write a number like shown on the right?
- How is this related to what we did before?
Activity Synthesis (Teacher Notes)
- “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.)
Standards
Building Toward
- 3.NBT.2·Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
- 3.NBT.A.2·Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
20 min
15 min
Knowledge Components
All skills for this lesson
Role Legend
Target
Essential
Supporting
Foundational
All lesson KCs
2 skills
Press enter or space to select a node. You can then use the arrow keys to move the node around. Press delete to remove it and escape to cancel.
Press enter or space to select an edge. You can then press delete to remove it or escape to cancel.
Subtraction Algorithms (Part 3)
10 min
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
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?
Solution Steps (4)
- 1Notice left image→Shows 325 in expanded form: 300+20+5
- 2Notice right image→Shows 325 in standard form with regrouping notation (3→2, 2→12)
- 3Compare regrouping notation→Left: 300→200, 20→120; Right: 3→2 (hundreds), 2→12 (tens)
- 4Connect the representations→Both show decomposing 1 hundred into 10 tens for subtraction preparation
Sample Response
Students may notice:
- On the left is 325, written in expanded form. On the right is 325, written the regular way.
- Parts of the expression on the left are crossed out. The first two digits in the number on the right are crossed out.
- Both the expression and the number 325 have smaller numbers or digits written above them.
- The expression on the left shows 120 in the tens place, and the number on the right shows 12 in the tens place.
- The expression on the left shows 200, and the number on the right shows 2 for the hundreds.
- Both the expression and the number show a hundred decomposed into 10 tens and then added to the 2 tens that were already there.
- Why are parts of the expression and the number crossed out?
- What do the little numbers and the little digits represent?
- Why would we write a number like shown on the right?
- How is this related to what we did before?
Activity Synthesis (Teacher Notes)
- “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.)
Standards
Building Toward
- 3.NBT.2·Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
- 3.NBT.A.2·Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.