Tenfold Territory Teacher Guide LAT: 34.0522° N
LONG: 118.2437° W (CA CCSS)
GRID SEC: I-A
SCALE: 10:1
Number Cartography • Day 1
Tenfold Territory Guide
CCSS 4.NBT.1
Sadlier-Oxford Ch. 1-1
Focus: 10x Place Value Shift
Target: Whole Numbers < 1M
Time: 60 Minutes
Materials: PV Disks, Base-10 Blocks
Cartographic Objective
Students will demonstrate that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right, using base-ten models and value tables.
Instructional Sequence
1 Launch: The Great Magnification (10 mins)
Show students 1 dollar bill and 1 ten-dollar bill. Ask: "How many ones compile into a ten?" Introduce the mapmaking lens: zoom in/out by factor of 10. Draw a "1" in the ones place on the board. Shift it to the tens place. Ask what changed.
2 Guided Charting: Tenfold Hops (20 mins)
Model writing 4,444 on a Place Value Chart. Guide students to notice that while the digit "4" is identical, its value depends on its territory."How does the value of the 4 in the hundreds place compare to the 4 in the tens place?" Write: 400 = 40 × 10 .
3 Independent Mapping: Digging Deep (20 mins)
Distribute Tenfold Territory Worksheet . Have students work independently or in pairs on the "Territory Zoom-In" problems. Walk around and look for students who struggle to transition from models to numeric equations.
4 Debrief & Exit Expedition (10 mins)
Ask: "If a map scale says 1 inch represents 10 miles, what do 10 inches represent?" Connect to place value hops. Administer Tenfold Territory Exit Ticket .
Map Legend (Vocab)
Digit The symbols 0-9 used to write any number.Place Value The value of where a digit sits in a number.Tenfold (×10) Multiplied by ten; shifted one place to the left.
Navigation Hazards
The "Add a Zero" Rule: Students often mechanically add a zero without realizing they are scaling the value by 10. Emphasize that the entire digit shifts places, magnifying its underlying scale.
Guiding Prompts
"If we look at 3,300, is the first 3 ten times larger than the second 3? Why or why not?"
"How does our place value grid help us navigate changes when multiplying by 10?"
Sadlier Chapter Alignment: Designed to support Ch. 1, Lesson 1-1. Extends the textbook's visual representations by explicitly framing the movement across places as "mapping coordinates."
CALIFORNIA DEPARTMENT OF EDUCATION • MATHEMATICS FRAMEWORK PAGE 1 OF 1
Tenfold Territory Worksheet LAT: 34.0522° N
LONG: 118.2437° W (CA CCSS)
Student Map Packet
Tenfold Territory Worksheet
Mission 1.1
Date: ____________
PIONEER NAME: _________________________________
CREW NO: _____
Place Value Navigation Key
As you travel one territory to the left on your map, the value becomes 10 times greater (multiplied by 10).
Hundred Thousands 100,000
Ten Thousands 10,000
Thousands 1,000
Hundreds 100
Tens 10
Ones 1
[10,000] ← (×10) ← [1,000] [1,000] ← (×10) ← [100] [100] ← (×10) ← [10]
A Territory Zoom-In: Comparing Digits
Analyze the numbers below. Use the values of the underlined digits to answer the questions.
4,450 and 4,450
1. What is the value of the underlined 4 in 4,450? ___________
2. What is the value of the underlined 5 in 4,450? ___________
3. The value of the 4 in the hundreds place is _______ times the value of the 5 in the tens place.
8,888 and 8,888
4. The underlined 8 on the left sits in the ________________________ place.
5. The underlined 8 on the right sits in the ________________________ place.
6. Write an equation showing how many times larger the left 8 is than the right 8: _____________________
B Scaling the Coordinates
Fill in the blank spaces in our cartographer logs to balance the scales.
7. 5,000 = 500 × _______
8. 20,000 = 2,000 × _______
9. 900 = 90 × _______
10. 10 × 40 = _______
11. 10 × 6,000 = _______
12. 10 × 10,000 = _______
C Field Expedition: Show Your Work
A map maker is drawing a coordinate system. She marks a mountain at point 3,000 . She wants to mark a tower that is 10 times further away. At what number should she mark the tower? Explain your mathematical map route below.
PIONEER WORKSPACE & EXPLANATION
CA COMMON CORE STANDARD 4.NBT.1 LEVEL: BRONZE CARTOGRAPHER
Tenfold Territory Exit Ticket Formative Assessment
Tenfold Territory Exit Ticket
Ticket A CCSS 4.NBT.1
NAME: ________________________
DATE: ____________
1. Look at the number below. Identify the value of each underlined digit:
7,772
Value of underlined 7: _______________
Value of underlined 7: _______________
2. Complete the statement to explain the relationship between these two digits:
The value of the 7 in the hundreds place is _______ times the value of the 7 in the tens place because shifting one place to the left multiplies the value by _______.
3. Write a standard form equation to represent this scale shift:
700 = _______ × 10
CUT ALONG DOTS TO SEPARATE TICKETS
Formative Assessment
Tenfold Territory Exit Ticket
Ticket B CCSS 4.NBT.1
NAME: ________________________
DATE: ____________
1. Look at the number below. Identify the value of each underlined digit:
7,772
Value of underlined 7: _______________
Value of underlined 7: _______________
2. Complete the statement to explain the relationship between these two digits:
The value of the 7 in the hundreds place is _______ times the value of the 7 in the tens place because shifting one place to the left multiplies the value by _______.
3. Write a standard form equation to represent this scale shift:
700 = _______ × 10
Millions Map Teacher Guide LAT: 34.0522° N
LONG: 118.2437° W (CA CCSS)
GRID SEC: I-B
SCALE: 1,000,000:1
Number Cartography • Day 2
Millions Map Guide
CCSS 4.NBT.2
Sadlier-Oxford Ch. 1-2
Focus: Reading & Writing to Millions
Target: Numbers < 10,000,000
Time: 60 Minutes
Materials: Millions Charts, Dice
Cartographic Objective
Students will identify the place and value of any digit up to the millions place and read and write these multi-digit numbers using proper comma separations.
Instructional Sequence
1 Launch: Entering the Million Mile (10 mins)
Begin with a number in the hundred thousands: 999,999. Ask: "What happens when we add 1?" Guide students to see that the standard 6-digit territory overflows into a brand-new continent: the Millions. Introduce commas as boundary gates.
2 Guided Mapping: Comma Gateways (20 mins)
Draw a 7-digit blank template with comma separators on the board: _,___,___ . Explain that commas separate periods (Thousands Period, Units Period). Write 4,258,103 . Practice reading it together, pausing at the commas: "4 million... 258 thousand... 103." Point to the '2' and ask for its place versus its value (Hundred Thousands vs. 200,000).
3 Independent Mapping: Charting Oceans (20 mins)
Distribute Millions Map Worksheet . Walk around guiding students to insert commas starting from the ones place, counting three spots to the left for each comma. Provide support on zero placeholders (e.g., 3,005,120).
4 Debrief & Exit Expedition (10 mins)
Ask: "Why are comma boundary gates essential when drawing large numbers?" Distribute Millions Map Exit Ticket to gauge mastery of 7-digit digit valuation.
Map Legend (Vocab)
Period A group of three places on a place value chart, separated by commas (Millions, Thousands, Units).Place vs. Value Place is the location (e.g., millions); Value is the worth of the digit (e.g., 4,000,000).Standard Form A way to write numbers using digits and commas (e.g., 6,432,019).
Navigation Hazards
The "Zero Trap": When writing standard form numbers with missing place values (e.g., "four million, twelve thousand, six"), students often write 4,12,6 instead of
Millions Map Worksheet LAT: 34.0522° N
LONG: 118.2437° W (CA CCSS)
Student Map Packet
Millions Map Worksheet
Mission 1.2
Date: ____________
PIONEER NAME: _________________________________
CREW NO: _____
The Comma Gateways Chart
Commas act as boundary gates that separate different number periods. Always count three places from the right to install a gateway.
Millions Period
Thousands Period
Ones Period
Millions 1,000,000
Hundred-Th. 100,000
Ten-Th. 10,000
Thousands 1,000
Hundreds 100
Tens 10
Ones 1
A Installing Comma Gates
Read each number. Insert commas to separate the periods correctly, then write the standard form number on the line.
1. 4325190
Answer: _________________
2. 8003125
Answer: _________________
3. 604100
Answer: _________________
4. 1925341
Answer: _________________
B Place and Value Coordinates
Identify the place (location name) and value (worth) of the underlined digit.
Target Number Place of Underlined Digit Value of Underlined Digit 4,812,900 ____________________________ ____________________________ 2,050,432 ____________________________ ____________________________ 7,910,045 ____________________________ ____________________________
C The Great Cartography Challenge
A surveyor recorded the population of California's largest city as 3,898,747 . He made an error and swapped the value of the digit in the millions place with the digit in the thousands place. Write the incorrect number he produced below. Show your place-value chart work.
SURVEYOR WORKSPACE & CORRECTED NUMBER
CA COMMON CORE STANDARD 4.NBT.2 LEVEL: SILVER CARTOGRAPHER
Millions Map Exit Ticket Formative Assessment
Millions Map Exit Ticket
Ticket A CCSS 4.NBT.2
NAME: ________________________
DATE: ____________
1. Install comma gateways into this population coordinate and write it in standard form:
3058914
Standard Form: ___________________________
2. Examine the number 4,129,568 . Tell the place and value of the underlined digit:
A. Place of 4: ________________________
B. Value of 4: ________________________
3. Write a 7-digit number with a 3 in the millions place and a 0 in the ten-thousands place:
____ , ____ ____ ____ , ____ ____ ____
CUT ALONG DOTS TO SEPARATE TICKETS
Formative Assessment
Millions Map Exit Ticket
Ticket B CCSS 4.NBT.2
NAME: ________________________
DATE: ____________
1. Install comma gateways into this population coordinate and write it in standard form:
3058914
Standard Form: ___________________________
2. Examine the number 4,129,568 . Tell the place and value of the underlined digit:
A. Place of 4: ________________________
B. Value of 4: ________________________
3. Write a 7-digit number with a 3 in the millions place and a 0 in the ten-thousands place:
____ , ____ ____ ____ , ____ ____ ____
Triple Forms Teacher Guide LAT: 34.0522° N
LONG: 118.2437° W (CA CCSS)
GRID SEC: I-C
SCALE: 3-WAY VIEW
Number Cartography • Day 3
Triple Forms Guide
CCSS 4.NBT.2
Sadlier-Oxford Ch. 1-3
Focus: Standard, Expanded, Word Forms
Target: Inter-form Translation < 10M
Time: 60 Minutes
Materials: Number Translation Wheels
Cartographic Objective
Students will fluidly write multi-digit whole numbers up to the millions place in standard, expanded, and word forms , and translate between them.
Instructional Sequence
1 Launch: Three Cartographer Views (10 mins)
Explain that a cartographer can draw a mountain (Standard), list its physical layers (Expanded), or say its name aloud (Word). Display 43,205 on the board. Expand it: 40,000 + 3,000 + 200 + 5 . Read it: "Forty-three thousand, two hundred five."
2 Guided Charting: Translating Lands (20 mins)
Analyze a millions-level number: 3,450,012 . Write expanded form on the board. Make sure to point out that we do not write + 0 for missing place values, but we still read them properly in word form. Pause at commas. Word form: "Three million, four hundred fifty thousand, twelve." (Note: no "and" because "and" represents decimals).
3 Independent Mapping: Multi-form Logs (20 mins)
Distribute Triple Forms Worksheet . Circulate to monitor how students write Expanded Form when there are multiple interior zeroes. Guide students to check their standard form by stacking and adding expanded values vertically.
4 Debrief & Exit Expedition (10 mins)
Review: "When we write word form, why do we use a hyphen in twenty-five but not in four hundred?" (Hyphenate two-digit numbers 21-99). Administer Triple Forms Exit Ticket .
Map Legend (Vocab)
Expanded Form Writing a number to show the sum of the value of each digit (e.g., 5,000 + 400 + 2).Word Form Writing a number using words to represent how it is read (e.g., five thousand, four hundred two).Hyphen Rule Use hyphens for compound numbers from twenty-one to ninety-nine.
Navigation Hazards
The "And" Decimals Bug: Students frequently write "four hundred and twelve". Reiterate that in mathematics, the word "and" is reserved exclusively for decimal points. Keep the whole-number word form clean of "and".
Triple Forms Worksheet LAT: 34.0522° N
LONG: 118.2437° W (CA CCSS)
Student Map Packet
Triple Forms Worksheet
Mission 1.3
Date: ____________
PIONEER NAME: _________________________________
CREW NO: _____
The Tri-View Charting Rule
Every point on a number map has 3 views: Standard (digits), Expanded (sum of parts), and Word (spoken words). Do not write "and" for whole numbers.
Standard 4,302
A Expanding the Territories (Expanded Form)
Convert these standard coordinates into their expanded, additive formats.
540,129
Answer: __________________________________________________________________
2,058,011
Answer: __________________________________________________________________
B Spelling the Coordinate Names (Word Form)
Spell the name of the standard coordinates. Remember the hyphen rule for digits from 21 to 99.
3. 3,500,240
Answer: _________________________________________________________________________________________
4. 1,029,607
Answer: _________________________________________________________________________________________
C Rebuilding the Map Coordinates (Standard Form)
Read the expanded or word forms and assemble them into standard, comma-separated digits.
5. 4,000,000 + 200,000 + 50,000 + 8,000 + 900 + 3
Standard Form: ___________________________
6. Seven million, sixty-one thousand, four hundred eighty-two
Standard Form: ___________________________
D Double-Check Alignment
A rookie cartographer wrote the word form "six million, forty thousand, eight" as standard form 6,40,800 . Identify the rookie's error and write the correct standard form in your workspace.
PIONEER WORKSPACE & WRITTEN PROOF
CA COMMON CORE STANDARD 4.NBT.2 LEVEL: GOLD CARTOGRAPHER
Triple Forms Exit Ticket Formative Assessment
Triple Forms Exit Ticket
Ticket A CCSS 4.NBT.2
NAME: ________________________
DATE: ____________
1. Convert this coordinate to Expanded Form :
4,092,305
Answer: __________________________________________________________________
2. Convert this coordinate to Word Form :
65,210
Answer: __________________________________________________________________
3. Write this coordinate name in Standard Form :
"Three million, five hundred twelve thousand, forty-two"
Standard Form: ___________________________
CUT ALONG DOTS TO SEPARATE TICKETS
Formative Assessment
Triple Forms Exit Ticket
Ticket B CCSS 4.NBT.2
NAME: ________________________
DATE: ____________
1. Convert this coordinate to Expanded Form :
4,092,305
Answer: __________________________________________________________________
2. Convert this coordinate to Word Form :
65,210
Answer: __________________________________________________________________
3. Write this coordinate name in Standard Form :
"Three million, five hundred twelve thousand, forty-two"
Standard Form: ___________________________
Comparing Peaks Teacher Guide LAT: 34.0522° N
LONG: 118.2437° W (CA CCSS)
GRID SEC: I-D
SCALE: HIGHEST PEAK
Number Cartography • Day 4
Comparing Peaks Guide
CCSS 4.NBT.2
Sadlier-Oxford Ch. 1-4
Focus: Comparing Large Numbers
Target: >, <, = Symbols to Millions
Time: 60 Minutes
Materials: Elevation Cards, PV Charts
Cartographic Objective
Students will compare two multi-digit whole numbers up to the millions place by aligning corresponding place values from left to right, using >, <, and = symbols to record results.
Instructional Sequence
1 Launch: Measuring Mountain Peaks (10 mins)
Show coordinates or elevation heights of two real California peaks: Mt. Whitney (14,505 ft ) and Mt. Williamson (14,379 ft ). Ask: "How can we mathematically prove which is higher?" Introduce aligning numbers by their place values.
2 Guided Charting: Scanning Left to Right (20 mins)
Draw two numbers stacked vertically on a place value chart:3,452,190 vs 3,458,012 . Explain the left-to-right rule: Start at the greatest place (Millions). Since both have a 3, move right to the Hundred-Thousands. Both have a 4. Continue until the digits differ (Thousands: 2 < 8 ). Write 3,452,190 < 3,458,012 .
3 Independent Mapping: Mountain Showdowns (20 mins)
Distribute Comparing Peaks Worksheet . Walk around. Monitor if students are drawing placeholder alignment lines. Remind them to align commas to ensure they aren't comparing a ten-thousands place to a thousands place.
4 Debrief & Exit Expedition (10 mins)
Give a prompt: "Why can a number with fewer digits never be greater than a number with more digits?" Connect to the largest place value. Administer Comparing Peaks Exit Ticket .
Map Legend (Vocab)
Compare To examine differences in value and decide if one number is greater than, less than, or equal to another.Greater Than (>) Symbol showing the first number has a larger value than the second.Less Than (<) Symbol showing the first number has a smaller value than the second.
Navigation Hazards
Right-to-Left Scanning: Students often instinctively compare digits starting from the ones place because they are used to adding/subtracting from right to left. Teach them to start comparing like a book: left to right.
Comparing Peaks Worksheet LAT: 34.0522° N
LONG: 118.2437° W (CA CCSS)
Student Map Packet
Comparing Peaks Worksheet
Mission 1.4
Date: ____________
PIONEER NAME: _________________________________
CREW NO: _____
The Left-to-Right Peak Scanner
To compare peaks, stack numbers vertically and align commas. Begin scanning from the greatest place value on the left . Stop at the first place where digits differ.
Peak A: 1,452,900
Peak B: 1,458,120
1,452,900 1,458,120
2 < 8, so Peak A < Peak B
A Peak Face-Off
Compare these peak elevations using >, <, or = symbols in the circles.
1. 43,510 ? 43,501
2. 290,145 ? 209,999
3. 4,102,568 ? 4,120,568
4. 6,005,120 ? 6,005,120
B Elevation Logs
Look at the elevations of different peaks and answer the comparisons.
Peak Name Elevation (ft) Period Coordinates Mount Shasta 14,179 Fourteen thousand, one hundred seventy-nine Mount Whitney 14,505 Fourteen thousand, five hundred five Mount Ritter 13,143 Thirteen thousand, one hundred forty-three
5. Compare Mount Shasta's elevation to Mount Whitney's:
14,179 _____ 14,505
6. Which peak in our table has the lowest elevation?
Peak: _________________
C Sorting the Elevations
Arrange these numbers in order from least to greatest.
3,405,120 • 3,045,999 • 3,450,120
Least: ___________ < Middle: ___________ < Greatest: ___________
D Cartographer's Logic
Leo says: "432,019 is greater than 1,005,120 because 4 is greater than 1." Explain Leo's error using place-value logic. Draw a stacking proof diagram in your workspace.
PIONEER WORKSPACE & WRITTEN PROOF
CA COMMON CORE STANDARD 4.NBT.2 LEVEL: PLATINUM CARTOGRAPHER
Comparing Peaks Exit Ticket Formative Assessment
Comparing Peaks Exit Ticket
Ticket A CCSS 4.NBT.2
NAME: ________________________
DATE: ____________
1. Compare these coordinate numbers using >, <, or = in the spaces:
A. 345,190 _____ 345,901
B. 2,045,618 _____ 2,045,618
C. 1,999,999 _____ 2,000,000
D. 75,120 _____ 7,512
2. Arrange the peak heights in order from greatest to least :
4,505 ft • 4,179 ft • 4,812 ft
___________ > ___________ > ___________
3. Write a comparison statement where a 6-digit number is greater than a 5-digit number :
___________ > ___________
CUT ALONG DOTS TO SEPARATE TICKETS
Formative Assessment
Comparing Peaks Exit Ticket
Ticket B CCSS 4.NBT.2
NAME: ________________________
DATE: ____________
1. Compare these coordinate numbers using >, <, or = in the spaces:
A. 345,190 _____ 345,901
B. 2,045,618 _____ 2,045,618
C. 1,999,999 _____ 2,000,000
D. 75,120 _____ 7,512
2. Arrange the peak heights in order from greatest to least :
4,505 ft • 4,179 ft • 4,812 ft
___________ > ___________ > ___________
3. Write a comparison statement where a 6-digit number is greater than a 5-digit number :
___________ > ___________
