Number Power Practice Packet Grade 3 Mathematics • Place Value Mastery
Number Power Practice
Name:
Date:
Standard 3.NS.1: Represent whole numbers up to 10,000 in standard, expanded, word, or model form.
Page 1 of 3
Level 1 • Basic Base-Ten Block Model to Forms
Look at the base-ten blocks below. Write the number in standard, expanded, and word form.
100
100
100
100
4 Hundreds
6 Tens
3 Ones
Standard:
Expanded:
Word:
Level 2 • Developing 4-Digit Number with Zero Placeholders
Consider the 4-digit number 4,078 . Complete each statement below:
Value of digit 4 :
Value of digit 7 :
Meaning of 0 :
Expanded Form:
Word Form:
Level 3 • Proficient Regrouping Decomposed Place Values
Elena built a number using place-value disks: 5 thousands, 14 hundreds, 6 tens, and 17 ones .
A. Standard Form:
B. Expanded Form:
C. Word Form:
Explain how 14 hundreds and 17 ones were regrouped:
Level 4 • Challenge Equivalence Detective & Error Analysis
Circle ALL statements equivalent to 7,420 :
A 7 thousands + 42 tens
B 74 hundreds + 20 ones
C 70 hundreds + 4 tens + 20 ones
D 7,000 + 300 + 120
Choose one incorrect option above and explain why it is NOT equal to 7,420:
Place Value Power • Practice Packet Page 1 • Standard 3.NS.1
Grade 3 Mathematics • Rounding Reasoning
Rounding to Nearest Ten
Name:
Date:
Standard 3.NS.6: Identify benchmark values, plot on number lines, and justify rounding to nearest ten.
Page 2 of 3
Level 1 • Basic Benchmark Tens & Midpoint on a Number Line
Round the number 43 to the nearest ten using the number line.
40 45 (Halfway) 50
Mark a dot (•) where 43 is located.
Benchmark Tens: &
Closer Ten:
43 rounded to nearest 10:
Level 2 • Developing The Midpoint Rule (Rounding 5s)
Both 64 and 65 fall between benchmark tens 60 and 70 . Round each number:
A. Round 64:
Why? The ones digit (4) is (circle):
B. Round 65:
Rule: When a number is exactly at the midpoint (5 in ones place), we round (circle):
Level 3 • Proficient 1-Digit Numbers & Near-Century Numbers
Determine the benchmark tens and rounded values for the special cases below:
Case 1: The 1-Digit Number 8
• Two benchmark tens: and
• Halfway value:
• 8 rounded to nearest ten:
Case 2: The 2-Digit Number 97
• Two benchmark tens: and
• Halfway value:
• 97 rounded to nearest ten:
Level 4 • Challenge Reverse Rounding & Solution Sets
Mystery Number Challenge: An unknown whole number n rounds to 80 when rounded to the nearest ten.
A. List ALL numbers that round to 80:
Smallest: Largest:
B. Boundary Justification: Explain why 74 and 85 do NOT round to 80:
Place Value Power • Practice Packet Page 2 • Standard 3.NS.6
Grade 3 Mathematics • Algebraic Word Problems
Word Problems & Unknowns
Name:
Date:
Standard 3.CA.2: Solve real-world problems with unknown results, totals, or differences using models & equations.
Page 3 of 3
Level 1 • Basic Join Structure • Result Unknown
The orchard picked 245 bushels of Honeycrisp apples on Saturday and 188 bushels of Gala apples on Sunday. How many bushels did they pick altogether?
Bar Model / Tape Diagram:
Equation with Symbol (□):
Final Answer:
They picked bushels.
Level 2 • Developing Part-Part-Whole Structure • Unknown Part
Maple Elementary has 512 students. If 268 students eat hot lunch, and the rest bring lunch from home, how many students bring lunch from home?
Part-Part-Whole Bar Model:
Total: 512 Students
Hot: 268
Home: ?
Equation with Symbol (□ or n):
Final Answer:
students bring lunch.
Level 3 • Proficient Comparison Structure • Unknown Difference
During a food drive, Room 14 collected 425 cans. Room 16 collected 289 cans. How many more cans did Room 14 collect than Room 16?
Comparison Bar Model:
Equation with Variable (d):
Final Answer:
Difference: cans.
Level 4 • Challenge Multi-Step Algebraic Structure • Unknown Change
A bakery started with 140 croissants. The baker baked another batch (c ). Customers bought 85 croissants. At closing time, 195 croissants remained.
A. Equation using symbol c:
B. Value of unknown c:
Baked: croissants.
Show step-by-step calculations:
Place Value Power • Practice Packet Page 3 • Standard 3.CA.2
Number Power Answer Key Teacher Solutions & Scoring Guide
Number Power Answer Key
TEACHER COPY
Standard 3.NS.1: Number Representations up to 10,000 • Solution & Diagnostic Notes
Key • Page 1
Level 1 • Basic Key Base-Ten Blocks (4 Hundreds, 6 Tens, 3 Ones)
Standard: 463
Expanded: 400 + 60 + 3
Word Form: four hundred sixty-three
Teaching Note: Remind students to hyphenate tens and ones compound words (sixty-three). Do NOT accept "four hundred AND sixty-three" as "and" represents a decimal point.
Level 2 • Developing Key Number with Zero Placeholder: 4,078
Value of 4: 4,000
Value of 7: 70
Meaning of 0: 0 hundreds (placeholder)
Expanded: 4,000 + 70 + 8 (or 4,000 + 0 + 70 + 8)
Word Form: four thousand, seventy-eight
Level 3 • Proficient Key Regrouping: 5 thousands, 14 hundreds, 6 tens, 17 ones
A. Standard Form:
6,477
B. Expanded Form:
6,000 + 400 + 70 + 7
C. Word Form:
six thousand, four hundred seventy-seven
Explanation Guide: 17 ones = 1 ten + 7 ones (tens: 6 + 1 = 7). 14 hundreds = 1 thousand + 4 hundreds (thousands: 5 + 1 = 6). Total = 6,477.
Level 4 • Challenge Key Equivalence Detective: Target 7,420
✓ A. 7,000 + 420 = 7,420 (CORRECT - Circle)
✓ B. 7,400 + 20 = 7,420 (CORRECT - Circle)
✗ C. 7,000 + 40 + 20 = 7,060 (INCORRECT - Do Not Circle)
✓ D. 7,000 + 300 + 120 = 7,420 (CORRECT - Circle)
Error Analysis for C: Option C is false because 70 hundreds = 7,000, but 4 tens (40) plus 20 ones (20) makes only 60, giving 7,060 instead of 7,420.
Place Value Power • Answer Key & Rubric Page 1 • Standard 3.NS.1
Teacher Solutions & Scoring Guide
Rounding Answer Key
TEACHER COPY
Standard 3.NS.6: Rounding to Nearest Ten • Solution & Diagnostic Notes
Key • Page 2
Level 1 • Basic Key Benchmark Tens for 43
Benchmark Tens: 40 and 50
Closer Ten: 40
43 rounded:
Targeted Skills Practice Sheet Grade 3 Mathematics • Targeted Skills Practice
Rounding & Problem Solving
Name:
Date:
Standard 3.NS.6: Identify benchmark tens, plot on number lines, and justify rounding to nearest ten.
Part 1 of 2
Level 1 • Basic Benchmark Endpoints & Distances
Round the number 28 to the nearest ten using the number line.
20 25 (Halfway) 30
Mark a point (•) where 28 belongs on the line.
Benchmark Tens: &
Closer Endpoint:
28 rounded to 10:
Level 2 • Developing Same Benchmarks, Different Directions (52 vs 57)
Both 52 and 57 lie between benchmark tens 50 and 60 . Complete each statement:
A. Round 52:
Distance to 50: | Distance to 60:
52 is closer to:
B. Round 57:
Distance to 50: | Distance to 60:
57 is closer to:
Level 3 • Proficient Single-Digit Rounding & Place Value Reasoning
Apply place-value logic to round each number to the nearest ten:
Number 1: Single-Digit 4
• Two benchmark tens: &
• Halfway point:
• 4 rounded to nearest ten:
Number 2: Two-Digit 86
• Two benchmark tens: &
• Halfway point:
• 86 rounded to nearest ten:
Level 4 • Challenge Real-World Estimation & Boundary Analysis
Coach Rivera orders practice jerseys for Team A (34 players) and Team B (36 players).
34 rounded to nearest 10:
36 rounded to nearest 10:
Both numbers are only 2 away from a ten, but they round to different values. Why?
Real-World Decision: If Coach Rivera rounds 34 down to order jerseys, what problem occurs?
Place Value Power • Targeted Practice Page 1 • Standard 3.NS.6
Grade 3 Mathematics • Targeted Skills Practice
Word Problems with Unknowns
Name:
Date:
Standard 3.CA.2: Solve word problems with unknown results, totals, or differences using models & equations.
Part 2 of 2
Level 1 • Basic Take Away Structure • Result Unknown
The school bookstore had 375 pencils. During the week, students purchased 142 pencils. How many pencils remain in the store?
Targeted Skills Answer Key Teacher Solutions & Scoring Guide
Targeted Skills Answer Key
TEACHER COPY
Standard 3.NS.6: Rounding to Nearest Ten • Solution & Diagnostic Notes
Key • Part 1
Level 1 • Basic Key Benchmark Tens for 28
Benchmark Tens: 20 and 30
Closer Endpoint: 30
28 rounded: 30
Verification: 28 is 8 units from 20 and only 2 units from 30. Since 2 < 8, 28 rounds to 30. On the number line, the point should be plotted between the midpoint 25 and 30.
Level 2 • Developing Key Comparing 52 and 57 (Midpoint 55)
A. 52 rounded: 50
Distance to 50: 2 | Distance to 60: 8
52 is closer to: 50 (rounds down).
B. 57 rounded: 60
Distance to 50: 7 | Distance to 60: 3
57 is closer to: 60 (rounds up).
Key Teaching Point: 52 is below the halfway mark 55, while 57 is above it. The midpoint separates which benchmark ten a number is closest to.
Level 3 • Proficient Key Single-Digit 4 & Place Value of 86
Case 1: Single-Digit 4
• Two benchmark tens: 0 and 10
• Halfway point: 5
• 4 rounded to nearest ten: 0
Case 2: Two-Digit 86
• Two benchmark tens: 80 and 90
• Halfway point: 85
• 86 rounded to nearest ten: 90
Place Value Rule: Look at the ones place. If the digit is 0, 1, 2, 3, or 4, keep the tens digit. If it is 5, 6, 7, 8, or 9, increase the tens digit by 1.
Level 4 • Challenge Key Real-World Jersey Ordering (34 & 36)
34 rounded: 30 | 36 rounded: 40
34 < 35 (rounds down to 30); 36 > 35 (rounds up to 40).
Why different? Both numbers are distance 2 from their nearest ten, but 34 is left of the midpoint 35, while 36 is right of 35.
Real-World Consequence: If Coach Rivera orders 30 jerseys for Team A, 4 players will NOT get a jersey! In situations involving people or supplies, rounding down causes a shortage, so rounding up to 40 is practically needed.
Place Value Power • Targeted Answer Key Page 1 • Standard 3.NS.6
Algebraic Word Problems Worksheet Grade 3 Mathematics • Algebraic Word Problems
Word Problem Quest Worksheet
Name:
Date:
Standard 3.CA.2: Solve real-world addition & subtraction problems with models and unknown-symbol equations.
Part 1 of 2
Level 1 • Basic Join Structure • Result Unknown
Problem 1: The Community Science Center welcomed 264 visitors on Friday and 358 visitors on Saturday. How many total visitors entered the science center over both days?
A. Draw a Join Tape Diagram:
Label both parts and bracket the total whole (□).
B. Equation with Unknown Symbol (□):
C. Vertical Work & Calculation:
Final Solution: visitors
Level 2 • Developing Part-Part-Whole Structure • Unknown Part
Problem 2: A nature reserve has a total of 530 native trees along its main trail. Park rangers counted 318 oak trees. The remaining trees are sugar maple trees (m ). How many sugar maple trees are along the trail?
A. Complete the Bar Model:
Total Whole: 530 Trees
Oak Trees: 318
Maple Trees: m
Write two related equations for this model:
B. Equation with Unknown Variable (m):
C. Vertical Work (Regrouping):
Final Solution: maple trees
Place Value Power • Word Problem Quest Page 1 • Standard 3.CA.2
Grade 3 Mathematics • Algebraic Word Problems
Comparative & Multi-Step Problems
Name:
Date:
Standard 3.CA.2: Comparison differences, unknown start structures, and multi-step story problems.
Part 2 of 2
Level 3 • Proficient Comparison Structure • Unknown Difference
Problem 3: During a recycling drive, the 3rd grade collected 614 plastic bottles. The 4th grade collected 479 plastic bottles. How many more bottles did the 3rd grade collect than the 4th grade?
A. Comparison Bar Model:
B. Equation with Difference (d):
C. Solution:
Difference: more bottles.
Level 4 • Advanced Take Away Structure • Unknown Start
Problem 4: An art supply store had a bin of colorful beads (b ). Teachers purchased 186 beads for a craft project. There were 345 beads left in the bin. How many beads were in the bin at the start?
Algebraic Word Problems Key Teacher Solutions & Scoring Guide
Word Problem Quest Key
TEACHER COPY
Standard 3.CA.2: Core Problem Structures (Join & Part-Part-Whole) • Solution Key
Key • Part 1
Level 1 • Basic Key Join Structure: 264 Friday + 358 Saturday
Problem 1 Overview: Joining two known parts to find an unknown total whole.
A. Model Illustration:
Total Whole: □ = 622 Visitors
Friday: 264
Saturday: 358
Both parts join to create the entire bar.
B. Equation with Unknown Symbol:
264 + 358 = □
C. Calculation Steps:
¹ ¹
2 6 4
+ 3 5 8
6 2 2
Final Answer: 622 visitors
Level 2 • Developing Key Part-Part-Whole: 530 Total − 318 Oak
Problem 2 Overview: Known whole and one known part; finding the missing part (maple trees m).
A. Completed Bar Model:
Total Whole: 530 Trees
Oak: 318
Maple: m = 212
Related Equations:
318 + m = 530 and 530 − 318 = m
B. Equation with Variable (m):
530 − 318 = m (or 318 + m = 530)
C. Calculation Steps:
² ¹⁰
5 3 0
− 3 1 8
2 1 2
Final Answer: 212 maple trees
Place Value Power • Word Problem Quest Key Page 1 • Standard 3.CA.2
Teacher Solutions & Scoring Guide
Comparative & Multi-Step Key
TEACHER COPY
Standard 3.CA.2: Comparison, Unknown Start, & Multi-Step Problems • Solutions
Key • Part 2
Level 3 • Proficient Key Comparison: 3rd Grade (614) vs 4th Grade (479)
A. Comparison Model Structure:
3rd Grade: 614 bottles
4th Grade: 479
d = 135
B. Equation & Calculation:
614 − 479 = d or 479 + d = 614
Calculation: 614 − 479 = 135
Difference: 135 more bottles
Level 4 • Advanced Key Take Away Unknown Start: b − 186 = 345
A. Equation & Solution:
b − 186 = 345 → b = 345 + 186
Calculation: 345 + 186 = 531
Started with: 531 beads
B. Conceptual Justification:
To find the whole starting quantity before anything was removed, we add the portion that was taken away back to the portion that was left over (Inverse Operation: 345 + 186 = 531).
