Place Value Guided Worksheet Lesson 1 Guided Notes Number Navigators Sequence
Place Value Guided Notes
Explore how our base-ten number system grows and shrinks.
Name:
Date:
1
Core Concept: The 10× Pattern
1. Single Unit
1
One individual piece.
2. Ten Rod
10
10 units grouped together.
3. Hundred Flat
100
10 rods grouped together.
Golden Rule: Every place value to the left is
times greater than the place to its right.
Every place value to the right is
of the place to its left.
2
Guided Chart: The Place Value House
Follow along as your teacher places the digits for 4,372.5.
Thousands Hundreds Tens Ones . Tenths 4 3 7 2 . 5 Worth: 4,000 Worth: 300 Worth: 70 Worth: 2 Worth: 0.5
3
Together Check: Try With Your Class
Look at the number: 5,816.3
What is the place of the 8?
What is the value of the 8?
What is the place of the 3?
What is the value of the 3?
Lesson 1: Place Value Guided Notes Page 1 of 2 • Continue to Page 2
Decomposing & Expanded Form
Lesson 1 Guided Notes • Page 2
4
Decomposing Numbers Step-by-Step
Break apart each number by its place value components.
Example: 2,648
2 Thousands = 2,000
6 Hundreds = 600
4 Tens = 40
8 Ones = 8
Guided Practice: 4,195
4 Thousands = ___
1 Hundred = ___
9 Tens = ___
5 Ones = ___
5
Connecting to Expanded Form
Expanded form writes the sum of each digit's total value.
A. Write in expanded form: 6,374
___ + ___ + ___ + ___
B. What happens when a digit is 0? Write: 8,042
___ + ___ + ___
C. Combine back into standard form: 5,000 + 700 + 30 + 9
6
Partner Discussion & Summary
Explain to your partner:
How is the 4 in 400 different from the 4 in 40?
Lesson 1: Place Value Guided Notes Page 2 of 2 • Ready for Practice Worksheet
Place Value Power Worksheet Lesson 1 Independent Practice Number Navigators Sequence
Place Value Power Practice
Break down numbers into their true values using the base-ten code.
Name:
Date:
Place Value Anchor: Each position is worth 10 times the place to its right! For example, in 4,520, the digit 5 is in the hundreds place, so its value is 500.
1
Place Value House: Place Each Digit
Write each digit of the number into its correct column.
Number Thousands (1,000) Hundreds (100) Tens (10) Ones (1) Tenths (0.1) 3,492 3 4 9 2 — 6,108 — 854.7 — 2,075.3
2
Value Detective: What is the Digit Worth?
Identify the place and actual value of the underlined digit.
Problem A 7,482
Place name:
Total value:
Problem B 9,125
Place name:
Total value:
Problem C 382.6
Place name:
Total value:
Problem D 651.4
Place name:
Total value:
Lesson 1: Place Value Power Page 1 of 2 • Continue to Page 2
Expanded Form & Mystery Clues
Lesson 1 • Page 2
3
Expanded Form Breakdown
Write each number in expanded form by adding the values of all digits.
Example: 4,625 4,000 + 600 + 20 + 5
1. Expand: 5,831
___ + ___ + ___ + ___
2. Expand: 7,064
___ + ___ + ___
3. Combine into standard number: 3,000 + 900 + 40 + 8
4
Math Detective: Crack the Mystery Code
Read the clues and determine the 4-digit mystery number.
The digit in the thousands place is an odd number greater than 6: 7
The digit in the hundreds place has a value of 200.
The digit in the tens place is 5 less than the thousands digit.
The digit in the ones place is 9.
What is the mystery number?
5
Navigator Reflection
Place Value Power Teacher Guide Teacher Guide & Key Number Navigators • Lesson 1
Place Value Power Teacher Guide
Pacing guide, targeted intervention prompts, and complete student answer key.
Target: 6th Grade Below Proficiency
Suggested Pacing
10 min: Guided Notes Part 1 & 2 (10× pattern & chart).
15 min: Guided Practice Part 3 & 4 (decomposing).
15 min: Independent Practice Worksheet (house & riddles).
5 min: Reflection synthesis & exit check.
Common Misconception
Students often confuse a digit's face value with its place value (e.g., saying the 4 in 4,520 is worth "4"). Prompt them: "If you had that many dollars, would you have $4 or $4,000?"
✓
Worksheet Answer Key
Part 1 & 2: Place Value House & Value Detective
6,108: Th: 6 | H: 1 | T: 0 | O: 8 | Tenths: —
854.7: Th: — | H: 8 | T: 5 | O: 4 | Tenths: 7
2,075.3: Th: 2 | H: 0 | T: 7 | O: 5 | Tenths: 3
A. 7,482: Hundreds place = 400
B. 9,125: Thousands place = 9,000
C. 382.6: Ones place = 2
D. 651.4: Tenths place = 0.4
Part 3 & 4: Expanded Form & Mystery Clues
1. 5,831: 5,000 + 800 + 30 + 1
2. 7,064: 7,000 + 60 + 4 (hundreds is 0)
3. Standard: 3,948
Mystery Number Solution: Thousands = 7, Hundreds = 2, Tens = 2 (7 - 5), Ones = 9 ➔ 7,229
Targeted Questioning Prompts
"When we multiply by 10, what happens to the position of each digit? Why does the decimal point seem to stay put while digits shift?"
Number Navigators Facilitator Materials Lesson 1 Teacher Reference • Page 1 of 1
Number Line Guided Worksheet Lesson 2 Guided Notes Number Navigators Sequence
Number Line Guided Notes
Master landmark benchmarks, open lines, and spatial number sense.
Name:
Date:
1
Landmark Benchmarks: 0, Half (0.5), and 1.0
Before placing any number, always identify your midpoint first!
0
Starting Line
0.5 (Halfway)
Middle Benchmark
1.0
One Whole
Numbers less than 0.5:
Live on the LEFT side (closer to 0). Example: 0.2
Numbers greater than 0.5:
Live on the RIGHT side (closer to 1). Example: 0.8
2
Open Number Line: Friendly Jumps
Break difficult calculations into comfortable chunks of tens and ones.
Teacher Model: Solve 28 + 35 Break 35 into: +20, then +10, then +5
+20 jump +10 jump +5 jump
28 48 58 63 ★
3
Guided Try: Make Your Own Jumps
Solve 45 + 27 by jumping on the open line below:
45
List your jumps: +____, +____, +____
Total:
Lesson 2: Number Line Guided Notes Page 1 of 2 • Continue to Page 2
Decimal Estimation & Number Sense
Lesson 2 Guided Notes • Page 2
4
Zoom In: Counting by Tenths
Between 0 and 1, there are 10 equal parts called tenths.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
5
Estimating Mystery Positions
Follow the clue steps to estimate the position of mystery mark M.
M
0 0.5 1.0
Step 1: Is point M greater than or less than 0.5?
Step 2: Is point M closer to 0.5 or closer to 1.0?
Step 3: Best estimate for M (e.g. 0.7, 0.75, 0.8):
6
Navigator Strategy Reflection
Why is having a number line in your head helpful when comparing decimals?
Lesson 2: Number Line Guided Notes Page 2 of 2 • Ready for Practice Worksheet
Number Line Navigator Worksheet Lesson 2 Independent Practice Number Navigators Sequence
Number Line Navigator Practice
Plot positions, use landmark benchmarks, and make friendly jumps.
Name:
Date:
Navigator Rule of Thumb: Always spot your midpoint first! On a line from 0 to 1, the middle is 0.5. Values smaller than 0.5 go left; values greater than 0.5 go right.
1
Benchmark Anchors: Place the Target Points
Draw a dot and label the given number on each number line.
A. Plot point: 0.3 Hint: Is it less than or greater than 0.5?
0 0.5 1.0
B. Plot point: 0.75 Hint: Halfway between 0.5 and 1.0
0 0.5 1.0
2
Open Number Line: Friendly Jumps
Show your friendly hops to solve each calculation.
Problem 1: Solve 34 + 28 Break 28 into +20 and +8
34
Final landing spot:
Problem 2: Solve 72 - 35 Jump backwards: -30, then -2, then -3
72
Final landing spot:
Lesson 2: Number Line Navigators Page 1 of 2 • Continue to Page 2
Mystery Points & Relative Ordering
Lesson 2 • Page 2
3
Mystery Marker: What Number is Marked?
Examine where each letter points and estimate its decimal or whole value.
Line A: Range 0 to 10
P
Q
0 5 10
Estimated value of Point P:
Estimated value of Point Q:
Line B: Range 0 to 1
R
S
0 0.5 1.0
Estimated value of Point R:
Estimated value of Point S:
4
Compare Using Benchmarks
Write <, >, or = in the circle. Use 0.5 as your mental landmark.
0.42
0.50
0.8
0.65
0.3
0.19
5
Navigator Strategy Check
A classmate says 0.08 is greater than 0.2 because 8 is bigger than 2. How would you use a number line to prove them wrong?
Lesson 2: Number Line Navigators Page 2 of 2 • Mastery Complete
Number Line Navigator Teacher Guide Teacher Guide & Key Number Navigators • Lesson 2
Number Line Navigator Teacher Guide
Pacing guide, targeted intervention prompts, and complete student answer key.
Target: 6th Grade Below Proficiency
Suggested Pacing
10 min: Guided Notes Part 1 (0, 0.5, 1 benchmarks).
15 min: Guided Notes Part 2 & 3 (frog jumps & zoom).
15 min: Independent Practice Worksheet (plotting & comparing).
5 min: Misconception discussion & debrief.
Common Misconception
Students frequently misjudge decimals like 0.08 vs. 0.2, thinking "8 is bigger than 2." Use tenths grids or the number line to remind students that 0.2 is 2 tenths (0.20) while 0.08 is less than one single tenth.
✓
Worksheet Answer Key
Part 1 & 2: Benchmark Anchors & Frog Jumps
Item A (0.3): Point plotted just under halfway between 0 and 0.5 (left of midpoint).
Item B (0.75): Point plotted precisely midway between 0.5 and 1.0 (right of midpoint).
Problem 1 (34 + 28): 34 + 20 = 54, then 54 + 6 = 60, then 60 + 2 = 62
Problem 2 (72 - 35): 72 - 30 = 42, then 42 - 2 = 40, then 40 - 3 = 37
Part 3 & 4: Mystery Locations & Comparisons
Line A: Point P ≈ 2 (accept 1.8–2.2); Point Q ≈ 7 (accept 6.8–7.3)
Line B: Point R ≈ 0.4 (accept 0.38–0.42); Point S ≈ 0.9 (accept 0.88–0.92)
Comparisons: 0.42 < 0.50 | 0.8 > 0.65 | 0.3 > 0.19
Targeted Questioning Prompts
"How does finding 0.5 first make placing any decimal between 0 and 1 twice as easy?"
Number Navigators Facilitator Materials Lesson 2 Teacher Reference • Page 1 of 1
Area Model Guided Worksheet Lesson 3 Guided Notes Number Navigators Sequence
Area Model Guided Notes
Multiply multi-digit numbers with visual rectangles and partial products.
Name:
Date:
1
Step 1: The Blueprint Split
Instead of multiplying hard numbers all at once, split both numbers into tens and ones:
Split first factor:
24 = 20 + 4
(2 tens and 4 ones)
Split second factor:
16 = 10 + 6
(1 ten and 6 ones)
2
Step 2: Fill the Four Rooms
Multiply each side dimension to find the area of each individual room.
20
4
10 6
20 × 10 200
4 × 10 40
20 × 6 120
4 × 6 24
Step 3: Add Up
200
+ 120
+ 40
+ 24
384
3
Guided Check: Solve 25 × 13 Together
Decompose: 25 = 20 + 5 and 13 = 10 + 3 Multiply the 4 rooms:
20 × 10 = ___
5 × 10 = ___
20 × 3 = ___
5 × 3 = ___
Lesson 3: Area Model Guided Notes Page 1 of 2 • Continue to Page 2
Guided 2×2 Practice & Zero Shortcuts
Lesson 3 Guided Notes • Page 2
4
Tens × Tens Strategy Reminder
Notice how multiplying tens by tens connects back to Lesson 1's place value shifts.
30 × 10 = 300 ➔ (3 tens × 1 ten = 3 hundreds)
40 × 20 = 800 ➔ (4 × 2 = 8, then two zeros for tens × tens)
5
Blueprint Walkthrough: Solve 34 × 21
Label all four outer edges, calculate the room areas, and add.
30
4
20 1
30 × 20 =
4 × 20 =
30 × 1 =
4 × 1 =
Add 4 Rooms
Total:
6
Navigator Strategy Reflection
Why does splitting numbers into tens and ones prevent common multiplication mistakes?
Lesson 3: Area Model Guided Notes Page 2 of 2 • Ready for Practice Worksheet
Area Model Adventurers Worksheet Lesson 3 Independent Practice Number Navigators Sequence
Area Model Adventurers Practice
Split numbers into tens and ones to conquer 2-digit multiplication.
Name:
Date:
3-Step Navigator Method: 1) Split each number into tens and ones. 2) Multiply each row by each column to fill the 4 rooms. 3) Add all 4 room totals together!
1
Guided Mission: Solve 26 × 14
Decompose: 26 = 20 + 6 and 14 = 10 + 4 Fill each room:
20
6
10 4
20 × 10 = 200
6 × 10 = 60
20 × 4 = 80
6 × 4 = 24
Add 4 Rooms
200
+ 80
+ 60
+ 24
364
2
Practice Room: Solve 35 × 18
Decompose: 35 = 30 + 5 and 18 = 10 + 8 Calculate each box:
30
5
10 8
30 × 10
5 × 10
30 × 8
5 × 8
Add Partial Products
Lesson 3: Area Model Adventurers Page 1 of 2 • Continue to Page 2
Independent Models & Real-World Application
Lesson 3 • Page 2
3
Independent Challenge: Solve 43 × 25
Decompose both numbers, label the dimensions, and calculate all 4 partial products.
Draw & label your 2×2 box:
Stack & Add:
Final:
4
Navigator Mission: The School Garden
The 6th-grade math club is building a rectangular pollinator garden.
The garden measures 22 feet long and 15 feet wide.
What is the total area of the garden in square feet?
Area Model Work Space:
Addition Work Space:
Total Area:
5
Sequence Reflection
How did knowing place value (Lesson 1) help you multiply tens and ones in the area model?
Lesson 3: Area Model Adventurers Page 2 of 2 • Sequence Complete
Area Model Adventurers Teacher Guide Teacher Guide & Key Number Navigators • Lesson 3
Area Model Adventurers Teacher Guide
Pacing guide, targeted intervention prompts, and complete student answer key.
Target: 6th Grade Below Proficiency
Suggested Pacing
10 min: Guided Notes Part 1 & 2 (blueprint split & 4 rooms).
15 min: Guided Notes Part 4 & 5 (tens × tens walkthrough).
15 min: Independent Practice Worksheet (boxes & story problem).
5 min: Sequence wrap-up reflection & celebration.
Common Misconception
When multiplying tens by tens (e.g., 30 × 10), students frequently record 30 or 40 instead of 300. Remind them of the Lesson 1 rule: "3 tens multiplied by 10 shifts one place value left to become 3 hundreds (300)."
✓
Worksheet Answer Key
Problem 1 & 2: Guided & Practice Rooms
Problem 1 (26 × 14): 200 + 80 + 60 + 24 = 364
Problem 2 (35 × 18):
• Top-left: 30 × 10 = 300 | Top-right: 5 × 10 = 50
• Bottom-left: 30 × 8 = 240 | Bottom-right: 5 × 8 = 40
• Total sum: 300 + 240 + 50 + 40 = 630
Problem 3 & 4: Independent Challenge & Story Problem
Problem 3 (43 × 25): Split (40 + 3) × (20 + 5)
• Rooms: 40×20 = 800, 3×20 = 60, 40×5 = 200, 3×5 = 15
• Total: 800 + 200 + 60 + 15 = 1,075
Problem 4 (Garden: 22 ft × 15 ft):
• Rooms: 20×10 = 200, 2×10 = 20, 20×5 = 100, 2×5 = 10
• Total Area: 200 + 100 + 20 + 10 = 330 sq ft
Targeted Questioning Prompts
"How does multiplying four small numbers feel compared to doing long multiplication on paper? Why does the area model prevent carrying errors?"
Number Navigators Facilitator Materials Lesson 3 Teacher Reference • Page 1 of 1
