Patterns and Operations Workbook
Standard: 3.OA.9 Level 1: Basic ★☆☆
Patterns and Operations
Progressive practice with mental math, fact extensions, and Frames-and-Arrows
Name:
Date:
A Fill in the Unit Box. Then solve using mental math patterns.
Write an object in the Unit box (e.g., apples, points, stickers). Notice how each answer changes as you add tens and hundreds.
Unit
1 Addition Patterns
a. 3 + = 12
b. 30 + = 120
c. 300 + = 1,200
2 Subtraction Patterns
a. 17 − 8 =
b. 27 − 8 =
c. 57 − 8 =
B Frames-and-Arrows: Fill in the missing numbers or rule.
Follow each curved arrow to apply the rule in order from left to right.
3 Apply the subtract 10 rule:
Rule
− 10
74
54
24
4 Apply the add 5 rule:
Rule
+ 5
35
40
50
? Reflection Question:
In exercise 2, why does every answer end in the digit 9? Explain briefly:
Math Practice Workbook • Grade 3 Page 1 of 3
Standard: 3.OA.9 Level 2: Intermediate ★★☆
Patterns and Operations
Discovering the rule, missing addends, and extended number chains
Name:
Date:
C Fill in the Unit Box. Find each missing value using patterns.
Pay close attention to where the blank line is: solve for the missing addend or difference.
Unit
5 Find the Missing Number
a. + 6 = 15
b. + 60 = 150
c. 900 + = 1,500
6 Subtracting Tens
a. 130 − 40 =
b. 230 − 40 =
c. 630 − 40 =
D Frames-and-Arrows: Find the rule or complete the missing frames.
In exercise 7 the rule box is blank: discover it by comparing consecutive numbers.
7 Discover the rule and fill in the final frames:
Rule?
45
65
85
8 Apply the subtract 25 rule:
Rule
− 25
175
125
75
★ Reasoning Word Problem:
Mateo saves money following a fixed rule each week. If he began with $40 and has $100 in Week 4, what is his weekly savings rule?
Mateo's Rule:
Math Practice Workbook • Grade 3 Page 2 of 3
Standard: 3.OA.9 Level 3: Challenge ★★★
Patterns and Operations
Inverse operations, two-way frames, and multi-step chains
Name:
Date:
E Fill in the Unit Box. Use inverse operations and fact families.
Use the relationship between addition and subtraction to solve for larger values quickly.
Unit
9 Inverse Relationships
a. 45 + = 100 → 100 − 45 =
b. 450 + = 1,000 → 1,000 − 450 =
c. 4,500 + = 10,000 → 10,000 − 4,500 =
10 Strategy Subtraction
a. 92 − 15 =
b. 192 − 15 =
c. 492 − 15 =
F Frames-and-Arrows High Challenge.
Watch out! Some starting frames are blank. Remember: to work backward, use the opposite operation.
11 Fixed rule + 15 (deduce the starting number and final frames):
Rule
+ 15
60
75
105
12 Discover the decreasing rule and complete both endpoints:
Rule?
210
180
120
Bonus Challenge Two-Step Alternating Pattern:
Observe the sequence: 6 → 12 → 10 → 20 → 18 → [ _____ ] → [ _____ ]
Next 2 numbers:
Explain the two rules:
Math Practice Workbook • Grade 3 Page 3 of 3
