Disk Decomposers Lesson Plan
Small Group Facilitation Guide
Two Different Ways: Hundreds & Tens
Grade 2 Math • Unit 2: Place Value • Day 2 of Place Value Disks • 45 Minutes
Small Group (4–6 Scholars)
Standards: 2.NBT.A.1, 2.NBT.A.2
Lesson Objective
Scholars will represent 3-digit numbers in standard form, then trade 1 hundred for 10 tens to represent the exact same number in a different way, proving numerical equivalence.
Core Mathematical Habit
Flexible Representation:
Numbers are not fixed to one appearance. Decomposing units allows mathematicians to rename quantities (e.g., 140 = 1 H 4 T = 14 T) without altering total value.
Manipulatives & Tools
- Place value disks (100s red, 10s blue)
- Double-sided H-T-O chart mats
- Two Different Ways Worksheets
- Dry-erase markers & felt erasers
Small Group Instructional Architecture (45 Minutes)
| Segment | Time | Focus & Scholar Action |
|---|
| 1. Do Now & Hook | 7 min | Balance equations (_ + 5 = 16 + 2). Hook: Two different ways to equal 18—today we do this with 3-digit numbers! |
| 2. Concrete Modeling | 10 min | The "Two Ways" routine on mats: Build 120 (Way 1: 1 H, 2 T). Trade 1 hundred for 10 tens (Way 2: 12 T). |
| 3. Guided Practice | 13 min | Worksheet Page 1: Represent target numbers 120 and 140 in two different ways in the large drawing charts. |
| 4. Extra Practice | 10 min | Worksheet Page 2: Represent 200 and 230 in two different ways using the extra-large drawing boxes. |
| 5. Exit Ticket | 5 min | Independent assessment: represent 130 and 200 in two different ways. |
Segment 1: Do Now & Conceptual Hook (7 Minutes)
Minutes 0–7
1. Independent Solve (3 min): Scholars use the large work areas to solve \(13 + 5 = 16 + 2\) and \(17 + 4 = 18 + 3\).
2. Bridging Hook (4 min): "Look at equation 1: \(13 + 5\) and \(16 + 2\) are TWO DIFFERENT WAYS to make the number 18! Today in small group, we are going to see how place value disks let us show 3-digit numbers in TWO DIFFERENT WAYS by trading hundreds for tens!"
Segment 2: Concrete Modeling — The "Two Different Ways" Routine (10 Minutes)
Minutes 7–17
Step 1: Build Way 1 (Standard): "Let's represent 120. Put 1 hundred and 2 tens on your place value mat. What number is this? (120). That is Way 1."
Step 2: Challenge for Way 2 (Different Way!): "Now, I want you to show 120 in a DIFFERENT way without changing the value. How can we do that? What can we trade?"
Step 3: Execute the Trade: Guide scholars to trade the 1 red hundred disk for 10 blue ten disks. "How many tens are from the trade? (10). How many were already there? (2). How many tens in all? (12 tens!). Count by tens to prove it: 10, 20... 120!"
💬 Key Anchor:
"Way 1: 1 hundred 2 tens = 120. Way 2: 12 tens = 120. Two different ways, but the EXACT same number!"
Small Group Math Guide • Page 1 of 2 • See Page 2 for Guided Practice & Error Diagnosis
Instructional Delivery & Error Correction Matrix
Two Different Ways Framework • Diagnostic Moves & High-Leverage Discourse
Disk Decomposers • Page 2
Segment 3: Guided Practice
13 min
Transition to Worksheet Page 1:
- Problem 1 (Target: 120): Draw Way 1 (1 H, 2 T) and Way 2 (0 H, 12 T). Prompt scholars to draw tens in organized 5-groups inside the large drawing boxes.
- Problem 2 (Target: 140): Scholars draw Way 1 first, then physically trade the hundred on their mat before drawing Way 2 (14 tens).
Segment 4: Extra Practice
10 min
Scholars work in pairs on Page 2 in the extra-large drawing boxes:
- Problem 3 (Target: 200): Way 1 = 2 hundreds. Way 2 = trade ONE hundred, resulting in 1 hundred and 10 tens (or 20 tens).
- Problem 4 (Target: 230): Way 1 = 2 H 3 T. Way 2 = 1 H 13 T.
- Peer Check: Partners verify that each way totals the target number by counting aloud together.
Diagnostic Error Response Protocol
Identified Scholar Misconception
Underlying Confusion
Immediate Corrective Prompt / Move
Error 1: Draws identical disks in both charts
Does not understand the prompt "a different way".
"Look at Way 1. Can you trade one of those hundreds for tens so it looks different but has the same value?"
Error 2: Adds 10 tens without removing hundred
Accumulates disks instead of making a 1-to-10 trade.
"If you take 10 tens from the bank, you must give the bank your 100 disk! What would happen to the number if you kept both?"
Error 3: Forgets the original tens (writes 10 tens for 140)
Focuses only on the traded hundred.
"You traded the hundred for 10 tens. But what about the 4 tens that were already in 140? 10 + 4 = 14 tens!"
Small Group Discourse Prompts
1. Equivalence Prompt:
"Why do Way 1 and Way 2 have the exact same value even though they look completely different?"
Expected Answer: "Because ten 10s has the exact same value as 1 hundred."
2. Flexibility Prompt:
"When might it be helpful in math to show 140 as 14 tens instead of 1 hundred 4 tens?"
Expected Answer: "When we need to subtract tens and don't have enough!"
Segment 5: Exit Ticket Administration (5 Minutes)
Minutes 40–45
Administer independently. Prompt scholars to draw their disks clearly inside each chart. Mastery Criteria: Scholar correctly shows target number 130 in two different ways (1 H 3 T and 13 T) and target number 200 in two different ways (2 H and 1 H 10 T or 20 T).
Unit 2: Place Value Disks • Two Different Ways Lesson Plan Success Benchmark: 80%+ exit ticket mastery
Disk Decomposers Worksheet
Small Group Math
Show Numbers in Two Different Ways
2nd Grade • Day 2
Name:
Date:
DO NOW Make both sides equal. Show your thinking in the box.
5 min
______ + 5 = 16 + 2
17 + ______ = 18 + 3
Draw place value disks to represent each number in two different ways.
1 hundred = 10 tens
1. Target Number: 120
Way 1 Draw disks
hundred + tens = 120
Way 2 (A Different Way!) Draw disks
hundreds + tens = 120
2. Target Number: 140
Way 1 Draw disks
hundred + tens = 140
Way 2 (A Different Way!) Draw disks
hundreds + tens = 140
Grade 2 Math • Two Different Ways Turn over to Page 2 →
Small Group Math
Show Numbers in Two Different Ways: Practice
Page 2
Name:
Date:
3. Target Number: 200 — Show 200 in two different ways.
Way 1 Draw disks
hundreds + tens = 200
Way 2 (A Different Way!) Draw disks
hundred + tens = 200
4. Target Number: 230 — Show 230 in two different ways.
Way 1 Draw disks
Disk Decomposers Exit Ticket
Exit Ticket
Show in Two Different Ways
2nd Grade • Day 2
Name:
Date:
1. Target Number: 130 — Draw disks to show 130 in two different ways.
Way 1 Draw disks
hundred + tens = 130
Way 2 (A Different Way!) Draw disks
hundreds + tens = 130
2. Target Number: 200 — Draw disks to show 200 in two different ways.
Way 1 Draw disks
hundreds + tens = 200
Way 2 (A Different Way!) Draw disks
hundred + tens = 200
How confident do you feel showing numbers in two different ways?
Circle how you feel today:
😃 I got this! 🤔 Still practicing 🙋 Need help
Grade 2 Math • Two Different Ways Scoring: ____ / 2 Points
