Increasing Patterns Lesson Plan Uncommon Schools
3rd Grade Math Inquiry: Unit 3, Day 9A • Increasing Patterns
Warm-Up / Do Now: Prior Knowledge Activation (5–10 min) Hook & Habit
Teacher Script / Board Display: Display two growing sequences side-by-side on the board:
Pattern A
3, 6, 9, 12, __?__
Pattern B
3, 6, 12, 24, __?__
Teacher Script: "Scholars, track both patterns. In both sequences, the terms are increasing—getting greater. But examine the jumps from 3 to 6, then 6 to 12. Are they growing the exact same way? Turn and tell your partner: what is happening to the value in Pattern A versus Pattern B?"
Key Scholar Takeaway: In Pattern A, we add 3 every jump (\(+3\)). In Pattern B, we double or multiply by 2 every jump (\(\times 2\)). Both increase, but addition adds a constant amount, while multiplication scales by a constant factor!
Direct Instruction / "I Do": Explicit Modeling (10–15 min) Stamp The Method
Teacher Model Problem: Identify the rule and 5th term for: 2, 4, 8, 16, ___
Step 1: Check Direction
Look at terms: 2, 4, 8, 16. Values are increasing. That immediately narrows our operations to Addition (+) or Multiplication (×).
Step 2: Test Jump 1 vs. 2
From 2 to 4: could be \(+2\) or \(\times 2\).
Step 3: Name & Extend
Rule must have Operation + Value: Multiply by 2. Extend to 5th term: \(16 \times 2 = \mathbf{32}\).
Critical Misconception Alert:
• Incomplete Rule: Scholars writing just "2" or "it grows by 2". Prompt: "Does it grow by adding 2 or multiplying by 2? Name both the operation and the value!"
• Single-Jump Assumption: Scholars see \(2 \rightarrow 4\) and quickly declare \(+2\) without verifying subsequent terms. Prompt: "Does adding 2 work from 4 to 8? You must test every term!"
Uncommon Schools • 3rd Grade Math Inquiry Unit 3: Day 9A Lesson Plan • Page 1 of 2
Unit 3, Day 9A • Instructional Delivery & Discourse Guided Practice to Independent Mastery
Guided Practice / "We Do" (10–15 min) Partner Turn & Talk
We Do Problem 1: Number Sequence
5, 9, 13, 17, ____, ____
Prompt: "What is the operation and value? Prove it on your whiteboards."
Stamp: Rule is Add 4 (+4). Next terms: 21, 25.
We Do Problem 2: Function Table
Stamp: Rule is Multiply by 4 (×4). Input \(\times 4 =\) Output.
Monitor-Discuss Cycles & Point-of-Error Matrix (15–20 min)
Point of Error
Aggressive Monitoring Prompts
Mini-Stamp
Point of Error 1: Scholar uses addition when pattern requires multiplication (e.g. seeing \(1, 3, 9\) and saying \(+2\)).
• "Does \(1 + 2 = 3\)? Yes. But does \(3 + 2 = 9\)? Check every jump!"
• "If addition didn't work across all terms, what other operation makes values increase?"
Rules must work for every pair of consecutive terms in the sequence.
Point of Error 2: Scholar forgets the operation and writes only a bare number (e.g., "Rule: 5").
• "Are we adding 5 or multiplying by 5? What is the mathematical operation?"
• "Write your rule frame: [Operation] [Value]."
A complete rule always contains both an operation and a value.
Independent Practice / "You Do" (15–20 min) • Tiered Task Architecture 5 Tiered Problems
Tiers 1 & 2: Core Sequences
• Additive patterns (e.g., \(4, 9, 14, 19, \dots\)).
Tier 3: Function Tables
• Finding relationship between Input & Output (e.g., \(\times 6\)). Scholars identify rule and fill missing table entries.
Tiers 4 & 5: Rigor & Analysis
• Real-world context (growing savings account).
Stamp It (Synthesis • 5 min):
"When terms increase, test Addition first. If the added amount isn't constant, test Multiplication. A valid rule applies to all terms and states both operation and value!"
Differentiation & Accommodations:
• Striving Support: Provide a hundred-chart and visual jump-arrows. Use sentence stem: "The terms increase, so I test ___ and ___. The rule is ___."
Uncommon Schools • 3rd Grade Math Inquiry Unit 3: Day 9A Lesson Plan • Page 2 of 2
Increasing Patterns Student Packet 3rd Grade Math Inquiry • Unit 3, Day 9A Student Packet
Increasing Pattern Rules (+ and ×)
Name: Date:
Do Now: Warm-Up (5 min) Find Rule & Next Term
Find the rule (operation and value) and next term for each sequence:
Pattern A:
3, 6, 9, 12,
Rule:
Pattern B:
3, 6, 12, 24,
Rule:
Guided Practice: Partner Try (10 min)
1. Complete the sequence and state the complete rule (Operation + Value):
5, 9, 13, 17, , Rule:
Show how you proved the rule across every term:
Independent Practice: Patterns & Tables Tiers 1–3
1. Identify the rule (operation and value), then find the next two terms:
4, 9, 14, 19, ,
Rule:
2. Identify the rule (operation and value), then find the next term:
1, 3, 9, 27,
Rule:
3. Complete the function table using the rule: Multiply by 6
Input
2
3
5
8
10
Output
12
18
Uncommon Schools • 3rd Grade Math Inquiry Unit 3: Day 9A Student Packet • Page 1 of 2
Unit 3, Day 9A • Independent Practice (Continued) Patterns & Input/Output Only
Problem 4: Determine the Input/Output Table Rule Tier 4
Find the rule for each function table and fill in the missing output values:
Table A:
Rule:
Table B:
Rule:
Problem 5: Rule Verification & Error Analysis Tier 5
Andre was asked to find the rule for this sequence: 2, 4, 8, 16, 32.
Is Andre's rule correct for all terms? What is the correct rule?
Exit Ticket: Day 1 Check (5 min) Mastery Check
1. Look at the sequence: 7, 12, 17, 22, 27
a. What is the rule? (Operation + Value):
b. What is the 6th term in this sequence?
2. Find the rule and complete the table:
Table Rule:
Uncommon Schools • 3rd Grade Math Inquiry Unit 3: Day 9A Student Packet • Page 2 of 2
Increasing Rules Anchor Chart Grade 3 Math Anchor Chart
PATTERN DETECTIVES: INCREASING RULES
How to Identify, Prove, and Extend Growing Patterns across Operations
OPERATIONS:
Golden Rule Every Pattern Rule MUST Have TWO Parts:
[ OPERATION ] + [ VALUE ]
The 3-Step Pattern Detective Protocol Follow In Order
1 Check Direction
Are the numbers getting greater from left to right?
Increasing \(\rightarrow\) Test + or ×
2 Test First Jump
Find what connects term 1 to term 2.
e.g., \(2 \rightarrow 6\) could be \(+4\) OR \(\times 3\)
3 Verify ALL Jumps
A valid rule MUST work across every single term!
Check jump 2 and jump 3!
Addition Pattern (+) Constant Step
Adds the exact same amount between each consecutive term:
+ 5+ 5+ 5+ 5
4 \(\rightarrow\) 9 \(\rightarrow\) 14 \(\rightarrow\) 19 \(\rightarrow\) 24
Stated Rule: Add 5 (+5)
Multiplication Pattern (×) Scaling Up
Multiplies each previous term by a constant factor:
× 2× 2× 2× 2
3 \(\rightarrow\) 6 \(\rightarrow\) 12 \(\rightarrow\) 24 \(\rightarrow\) 48
Stated Rule: Multiply by 2 (×2)
Input / Output Function Tables: Operation Across Columns Input \(\times 4 =\) Output
Input (\(x\))
Output (\(y\))
2
8
3
12
4
16
5
20
How to Read Function Tables:
• Ask: "What operation gets me from Input to Output in every row?"
• \(2 \times 4 = 8\), \(3 \times 4 = 12\), \(4 \times 4 = 16\)...
Rule: Multiply by 4 (×4)
Trap
Don't Get Trapped by the First Jump!
In the sequence 2, 4, 8, 16, jump 1 from 2 to 4 could be + 2 OR × 2.
If you guess + 2, look at jump 2: \(4 + 2 = 6 \neq 8\)! Always check jump 2 before writing your final rule!
Uncommon Schools • 3rd Grade Math Inquiry CCSS.MATH.CONTENT.3.OA.D.9 • Pattern Rules Anchor Chart
Increasing Patterns Practice Sheet Uncommon 3rd Grade Math Inquiry • Unit 3, Day 9A Extra At-Bats
Rule Assessment
Finding Pattern Rules: Addition & Multiplication
Part 1: Addition Rules — Patterns & Input/Output Tables (Problems 1–6)
Name: Date:
Part 1: Find the Addition Rule (Operation + Value) Draw jumps above each pattern
1. Find rule & extend sequence:
3, 10, 17, 24, ,
Rule:
2. Find rule & missing term:
8, 14, , 26, 32
Rule:
3. Find rule & extend sequence:
15, 19, 23, 27, ,
Rule:
4. Find rule & complete table:
Table Rule:
5. Find rule & extend sequence:
6, 14, 22, 30, ,
Rule:
6. Find rule & complete table:
Table Rule:
Uncommon Schools • 3rd Grade Math Inquiry Pattern Rules Assessment • Page 1 of 2
Finding Pattern Rules: Addition & Multiplication Part 2: Multiplication Rules (Problems 7–12)
Part 2: Find the Multiplication Rule (Operation + Value) Draw jumps above each pattern
7. Find rule & extend sequence:
2, 6, 18, 54, ,
Rule:
8. Find rule & extend sequence:
1, 2, 4, 8, ,
Rule:
9. Find rule & extend sequence:
5, 15, 45, 135, ,
Rule:
10. Find rule & complete table:
Table Rule:
11. Find rule & extend sequence:
3, 12, 48, 192, ,
Rule:
12. Find rule & complete table:
Table Rule:
Uncommon Schools • 3rd Grade Math Inquiry Pattern Rules Assessment • Page 2 of 2
Decreasing Patterns Lesson Plan Uncommon Schools
3rd Grade Math Inquiry: Unit 3, Day 9B • Decreasing Patterns
Warm-Up / Do Now: Prior Knowledge Activation (5–10 min) Hook & Habit
Teacher Script / Board Display: Display two shrinking sequences side-by-side:
Pattern A (Steady Countdown)
24, 20, 16, 12, __?__
Pattern B (Rapid Shrink)
24, 12, 6, 3, __?__
Teacher Script: "Scholars, look closely at both patterns. What direction are our numbers moving? They are decreasing—getting lesser! In Pattern A, we take away 4 each step. But look at Pattern B: 24 drops straight to 12, then to 6! What operation cuts numbers in half like that? Turn and whisper to your partner!"
Key Scholar Takeaway: In Pattern A, the terms decrease by constant subtraction (\(-4\)). In Pattern B, the terms decrease by division (\(\div 2\)). When numbers shrink rapidly by equal groups, we test division!
Direct Instruction / "I Do": Explicit Modeling (10–15 min) Stamp The Method
Teacher Model Problem: Identify the rule and 5th term for: 64, 32, 16, 8, ___
Step 1: Check Direction
Look at terms: 64, 32, 16, 8. Values are decreasing. Our only possible operations are Subtraction (−) or Division (÷).
Step 2: Test Subtraction vs. Division
First jump: \(64 - 32 = 32\).
Step 3: Name & Extend
Rule must have Operation + Value: Divide by 2. Extend to 5th term: \(8 \div 2 = \mathbf{4}\).
Critical Misconception Alert:
• Directional Reversal: Scholars read right-to-left and call it "Multiply by 2" or "Add 8". Prompt: "A sequence moves from left to right. Are the numbers getting larger or smaller? Name the decreasing operation!"
• First-Jump Confusion: Seeing \(64 \rightarrow 32\) and thinking the rule is "Subtract 32". Remind scholars: "You must prove the rule works on jump 2 and jump 3!"
Uncommon Schools • 3rd Grade Math Inquiry Unit 3: Day 9B Lesson Plan • Page 1 of 2
Unit 3, Day 9B • Instructional Delivery & Discourse Guided Practice to Independent Mastery
Guided Practice / "We Do" (10–15 min) Partner Turn & Talk
We Do Problem 1: Constant Subtraction
45, 39, 33, 27, ____, ____
Prompt: "Calculate each jump. Does the same subtraction apply to every term?"
Stamp: Rule is Subtract 6 (−6). Next terms: 21, 15.
We Do Problem 2: Function Table (Division)
Stamp: Rule is Divide by 10 (÷10). Input \(\div 10 =\) Output.
Monitor-Discuss Cycles & Point-of-Error Matrix (15–20 min)
Point of Error
Aggressive Monitoring Prompts
Mini-Stamp
Point of Error 1: Scholar uses subtraction for a division sequence (e.g. seeing \(80, 40, 20\) and saying \(-40\)).
• "Check jump 2: does \(40 - 40 = 20\)? No! What operation cuts 40 down to 20?"
• "When terms shrink by halves or equal parts, test division."
Subtraction must subtract the exact same number every single time.
Point of Error 2: Scholar states the inverse operation (e.g. looking at \(30, 25, 20\) and writing "Add 5").
• "Trace the numbers with your finger from left to right. Are they growing or shrinking?"
• "If they are shrinking, can the rule be addition? Use the correct operation!"
Decreasing sequences must use subtraction or division.
Independent Practice / "You Do" (15–20 min) • Tiered Task Architecture 5 Tiered Problems
Tiers 1 & 2: Core Sequences
• Subtraction patterns (e.g., \(54, 48, 42, 36, \dots\)).
Tier 3: Function Tables
• Dividing inputs by 5 or 8 (e.g., Input 40, 32, 24, 16 \(\rightarrow\) Output 5, 4, 3, 2). Complete missing values.
Tiers 4 & 5: Context & Critique
• Word context: Baker giving away cookies at constant rate vs equal division.
Stamp It (Synthesis • 5 min):
"When terms decrease, test Subtraction first. If the subtracted amount changes between jumps, test Division. Always track from left to right and include both operation and value!"
Differentiation & Accommodations:
• Striving Support: Use vertical number lines (descending elevator visual) and sentence stem: "The sequence decreases from left to right, so the operation is ___."
Uncommon Schools • 3rd Grade Math Inquiry Unit 3: Day 9B Lesson Plan • Page 2 of 2
Decreasing Patterns Student Packet 3rd Grade Math Inquiry • Unit 3, Day 9B Student Packet
Decreasing Pattern Rules (− and ÷)
Name: Date:
Do Now: Warm-Up (5 min) Activate Prior Knowledge
Look at the two decreasing patterns below. Find the next term and state what is happening to the numbers.
Pattern A (Steady Countdown):
24, 20, 16, 12,
What is the rule? (Operation + Value):
Pattern B (Rapid Shrink):
32, 16, 8, 4,
What is the rule? (Operation + Value):
Guided Practice: Partner Try (10 min)
1. Complete the sequence and state the complete rule:
45, 39, 33, 27, , Rule:
Show your calculations between each jump:
Independent Practice: Problem Set (Part 1) Tiers 1–3
1. Identify the rule (operation and value), then find the next two terms:
54, 48, 42, 36, ,
Rule:
2. Identify the rule (operation and value), then find the next term:
80, 40, 20, 10,
Rule:
3. Complete the function table using the rule: Divide by 5
Input (Total Counters)
50
35
25
15
5
Output (Equal Groups of 5)
10
7
Uncommon Schools • 3rd Grade Math Inquiry Unit 3: Day 9B Student Packet • Page 1 of 2
Unit 3, Day 9B • Independent Practice (Continued) Application & Mastery
Problem 4: Real-World Inventory Comparison Tier 4
A bakery starts the morning with shelves full of fresh muffins.
Shelf A (Count):
60, 54, 48, ,
What is Shelf A's rule?
Shelf B (Count):
64, 32, 16, ,
What is Shelf B's rule?
Which shelf drops to 4 muffins first? Explain your reasoning:
Problem 5: Error Analysis & Critique Tier 5
Marcus looks at this decreasing sequence: 24, 18, 12, 6.
Is Marcus correct? Why or why not? What is the correct rule?
Exit Ticket: Day 2 Check (5 min) Mastery Check
1. Look at the sequence: 45, 38, 31, 24
a. What is the rule? (Operation + Value):
b. What is the 5th term in this sequence?
2. A sequence starts at the number 64 and follows the rule Divide by 2. Write the first 4 terms of this sequence:
64, , ,
Show your work below:
Uncommon Schools • 3rd Grade Math Inquiry Unit 3: Day 9B Student Packet • Page 2 of 2
Decreasing Rules Anchor Chart Grade 3 Math Anchor Chart
PATTERN DETECTIVES: DECREASING RULES
How to Identify, Prove, and Extend Shrinking Patterns across Operations
OPERATIONS:
Direction Rule Always Track Numbers Left-to-Right \(\rightarrow\)
[ OPERATION ] + [ VALUE ]
The 3-Step Pattern Detective Protocol Follow In Order
1 Check Direction
Are the numbers getting lesser from left to right?
Decreasing \(\rightarrow\) Test − or ÷
2 Test Subtraction First
Check if the same amount is subtracted each jump.
\(50 - 8 = 42\), \(42 - 8 = 34\)
3 If Unequal, Test Division
If subtraction differences change, test equal sharing / groups!
\(80 \div 2 = 40\), \(40 \div 2 = 20\)
Subtraction Pattern (−) Steady Step-Down
Subtracts the exact same amount between each consecutive term:
− 6− 6− 6− 6
54 \(\rightarrow\) 48 \(\rightarrow\) 42 \(\rightarrow\) 36 \(\rightarrow\) 30
Stated Rule: Subtract 6 (−6)
Division Pattern (÷) Rapid Shrink
Divides each previous term by a constant divisor:
÷ 2÷ 2÷ 2÷ 2
64 \(\rightarrow\) 32 \(\rightarrow\) 16 \(\rightarrow\) 8 \(\rightarrow\) 4
Stated Rule: Divide by 2 (÷2)
Input / Output Function Tables: Division Across Columns Input \(\div 5 =\) Output
Input (Counters)
Output (Groups)
50
10
35
7
25
5
10
2
How to Read Decreasing Tables:
• Ask: "What operation reduces the Input to the Output in every row?"
• \(50 \div 5 = 10\), \(35 \div 5 = 7\), \(25 \div 5 = 5\)...
Rule: Divide by 5 (÷5)
Trap
Don't Get Trapped by Reading Backwards!
In the sequence 24, 18, 12, 6, some scholars read backwards and say "Add 6".
WRONG! Numbers move forward from left to right. Since 24 shrinks to 18, you are losing value. The rule is Subtract 6 (−6)!
Uncommon Schools • 3rd Grade Math Inquiry CCSS.MATH.CONTENT.3.OA.D.9 • Pattern Rules Anchor Chart
