Double Duty Digits Lesson Plan
Grade 1 - 2 Math • Place Value
Double Duty Digits Lesson Plan
Representing 2-Digit Numbers in 2 Different Ways Using Tens and Ones Drawings
50–60 Minutes
CCSS 1.NBT.B.2 • 2.NBT.A.1
Lesson Objective
Students will represent any 2-digit number in at least two different combinations of tens and ones using standard quick-draws (rods and dots) and prove the total values remain equal.
Core Concept
Flexible decomposing: 1 ten rod has the exact same value as 10 ones cubes (1 ten = 10 ones). "Trading" a ten doesn't change the number's total.
Materials Needed
- • Base-ten blocks (rods & unit cubes)
- • Double Duty Digits practice sheet
- • Whiteboards & dry erase markers
Standard Math "Quick-Draw" Conventions for Students
Ten Rod: Draw a straight vertical line (|) → Value = 10
Ones Cube: Draw a neat circle or dot (•) → Value = 1
Keep dots grouped in 5-frames for quick counting!
1 Phase 1: Spark & Hook — The Candy Shop Dilemma (10 mins) Concrete Inquiry
Scenario: Present two gift bags labeled with the number 34. Bag A holds 3 rolls of 10 candies and 4 loose pieces. Bag B holds 2 rolls of 10 candies and 14 loose pieces.
Guiding Prompt: "Maya says Bag B has more candy because there are 14 loose candies. Leo says they have the exact same amount. Who is correct? How can we prove it?"
Key Takeaway: Count Bag A (10, 20, 30... 31, 32, 33, 34). Count Bag B (10, 20... + 14 = 34). Unpack one roll into 10 loose pieces to show physical equivalence.
2 Phase 2: Teacher Modeling — Quick-Draw "Unpacking" (15 mins) Representational Modeling
Target number: 42. Draw on the board using two parallel boxes side by side:
Way 1: Standard Form
Draw 4 sticks and 2 dots: | | | | • •
Value sentence: 4 tens + 2 ones = 40 + 2 = 42
Way 2: Decomposed / Traded Form
Cross out 1 stick and replace with 10 dots: | | | ••••• ••••• ••
Value sentence: 3 tens + 12 ones = 30 + 12 = 42
Teacher Think-Aloud Script: "Notice how my total did not change! I didn't add any new candy or throw any away. I simply took one ten rod and 'unpacked' or traded it into 10 separate ones."
Tens and Ones Remix • Instructional Guide Page 1 of 2
Guided Delivery & Assessment Strategies
Discourse prompts, targeted interventions, and mastery look-fors
Implementation Guide
3 Phase 3: Guided Practice & Partner Quick-Draw (15 mins) Active Engagement
Call out target number 25. Student pairs work on personal dry-erase boards:
- Partner A draws Way 1 (Standard: 2 tens, 5 ones).
- Partner B draws Way 2 (Traded: 1 ten, 15 ones).
- Partners swap boards and count each other's drawings by tens and ones to verify both equal 25.
- Repeat with challenge number 50 (5 tens 0 ones OR 4 tens 10 ones).
4 Phase 4: Independent Practice on Worksheet (15 mins) Student Application
Distribute the Double Duty Digits Practice Sheet. Students solve structured representations for 2-digit numbers, draw quick-picks, fill in place value equations, and complete an error-analysis reasoning problem. Circulate with targeted rubric checks.
Math Discourse & Sentence Stems
Prompting Questions:
• "What happened to the ten rod when we traded it?"
• "How can two drawings look different but have the same total?"
Student Response Stems:
• "I unpacked 1 ten into 10 ones, so now I have..."
• "The total is still ___ because 1 ten is equal to 10 ones."
Common Misconceptions & Diagnostic Interventions
| Misconception | Teacher Diagnostic / Corrective Move |
|---|
| Adds 10 ones without removing a ten rod | Have the student place physical blocks on their drawing. physically remove 1 rod before sliding in 10 unit cubes: "Fair trade: you can't get 10 ones for free!" |
| Believes the number value has increased | Guide choral skip-counting. Count Way 1: "10, 20, 30, 31, 32". Count Way 2: "10, 20, and count up 12 ones: 32!" Highlight that both equal 32. |
| Disorganized dot drawings lead to counting errors | Enforce drawing dots in paired columns of 5 (ten-frame style) so students can immediately see full groups of 5 and 10 without losing count. |
Exit Ticket Quick Rubric (Look-Fors) Check student worksheet Problem 4
Emerging (1)
Draws identical representations or creates combinations that do not total the target number.
Developing (2)
Draws both forms accurately but struggles to articulate or write the matching number sentences.
Proficient (3)
Accurately draws standard and traded forms, labels tens/ones correctly, and explains equivalence.
Tens and Ones Remix • Instructional Guide Page 2 of 2
Double Duty Digits Worksheet
Double Duty Digits
Show 2-Digit Numbers in 2 Different Ways!
Name:
Date:
Quick-Draw Code:
1 Line = 1 Ten (10)
1 Dot = 1 One (1)
Remember: 1 Ten = 10 Ones
Look & Learn Example Target Number: 24
Way 1: Standard Way
| | • • • •
2 tens + 4 ones 20 + 4 = 24
Way 2: Trade 1 Ten for 10 Ones
| ••••• ••••• ••••
1 ten + 14 ones 10 + 14 = 24
Directions: Represent each number in two different ways using quick-draw lines (|) and dots (•). Then fill in the blanks.
1 Show 35
Draw lines (|) and dots (•)
Way 1
______ tens and ______ ones
______ + ______ = 35
Way 2 (A Different Way)
______ tens and ______ ones
______ + ______ = 35
2 Show 42
Draw lines (|) and dots (•)
Way 1
______ tens and ______ ones
______ + ______ = 42
Way 2 (A Different Way)
______ tens and ______ ones
______ + ______ = 42
Double Duty Digits • Student Practice Page 1 of 2
Double Duty Digits • Continued Practice
Name:
3 Show 56
Draw lines (|) and dots (•)
Way 1
______ tens and ______ ones
______ + ______ = 56
Way 2 (A Different Way)
______ tens and ______ ones
______ + ______ = 56
4 Show 30 Think: What if there are 0 ones?
Draw lines (|) and dots (•)
Way 1
______ tens and ______ ones
______ + ______ = 30
Way 2 (A Different Way)
______ tens and ______ ones
______ + ______ = 30
5 Math Detective: Who Is Correct?
Sam says:
“I can draw the number 41 with 3 tens and 11 ones.”
Kayla says:
“No, you can only make 41 with 4 tens and 1 one!”
Who is correct? Circle one:
Sam Kayla
Draw quick-draws to prove it:
Explain your thinking:
Double Duty Digits • Student Practice Page 2 of 2
Double Duty Digits Answer Key
Teacher Reference
Double Duty Digits • Answer Key
Worked visual solutions and acceptable alternate representations (Pages 1 & 2)
Answer Key
Grading Note on "Way 2": Students most commonly trade 1 ten for 10 ones. However, any mathematically equivalent combination (e.g., trading 2 tens for 20 ones) is fully correct as long as the drawing and equations match!
1 Number: 35
Sample Solutions
Way 1: Standard Form
| | |
• • • • •
3 tens and 5 ones
30 + 5 = 35
Way 2: Traded 1 Ten (Most Common)
| |
••••• ••••• •••••
2 tens and 15 ones
20 + 15 = 35
*Also accept: 1 ten & 25 ones (10 + 25 = 35) or 0 tens & 35 ones (0 + 35 = 35).
2 Number: 42
Sample Solutions
Way 1: Standard Form
| | | |
• •
4 tens and 2 ones
40 + 2 = 42
Way 2: Traded 1 Ten
| | |
••••• ••••• ••
3 tens and 12 ones
30 + 12 = 42
*Also accept: 2 tens & 22 ones (20 + 22 = 42) or 1 ten & 32 ones (10 + 32 = 42).
Double Duty Digits • Teacher Answer Key Page 1 of 2
Double Duty Digits Answer Key • Problems 3, 4 & 5
Scoring & Reasoning
3 Number: 56
Way 1: Standard • Way 2: Decomposed
Way 1 (Standard)
| | | | | ••••• •
5 tens and 6 ones • 50 + 6 = 56
Way 2 (Traded 1 Ten)
| | | | ••••• ••••• ••••• •
4 tens and 16 ones • 40 + 16 = 56
4 Number: 30 (Zero Ones)
Key Milestone Problem
Way 1 (Standard)
| | | (no dots)
3 tens and 0 ones • 30 + 0 = 30
Way 2 (Traded 1 Ten)
| | ••••• •••••
2 tens and 10 ones • 20 + 10 = 30
5 Problem 5 Solution & Scoring Rubric
Correct Choice: Sam
Circled Answer: Sam ✓ Kayla
Sample Student Drawing:
| | | ••••• ••••• •
