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📄 Sheet #1•10 Problems

PanMaths.comArithmetic Patterns in Tables Worksheets • Worksheet #1

Name: __________________________

Date: _____________ Period: ____

Score: _____ / 10

1.Function Table

Rule: Multiply by 4

Input	Output
2	8
3	12
5	20
7	?

Answer:

2.Function Table

Rule: Add 6

Input	Output
4	10
7	13
9	15
12	?

Answer:

3.Arithmetic Pattern

Look at the row of 5s in a multiplication table: 5, 10, 15, 20, 25... What do all multiples of 5 end with in their ones place?

A) 0 or 5B) Only 5C) Even numbersD) 1, 3, or 5

Answer:

4.Function Table

Rule: Multiply by 3

Input	Output
3	9
6	18
8	24
?	30

Answer:

5.Arithmetic Pattern

When you multiply any whole number by an even number (such as 2, 4, 6), is the product always even or always odd?

A) Always EvenB) Always OddC) Sometimes EvenD) Depends on input

Answer:

6.Function Table

Rule: Multiply by 8

Input	Output
2	16
4	32
5	40
7	?

Answer:

7.Function Table

Rule: Subtract 7

Input	Output
15	8
20	13
25	18
32	?

Answer:

8.Arithmetic Pattern

When you add two odd numbers together (such as 3 + 5 or 7 + 9), is the sum always even or odd?

A) Always EvenB) Always OddC) Depends on numbersD) Always Prime

Answer:

9.Function Table

Rule: Multiply by 6

Input	Output
3	18
5	30
6	36
9	?

Answer:

10.Arithmetic Pattern

In an addition table, what happens to the sum if one addend increases by 1 while the other stays the same?

A) Sum increases by 1B) Sum doublesC) Sum stays the sameD) Sum decreases by 1

Answer:

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PanMaths.comAnswer Key & Worked Solutions • Worksheet #1

Answer Key

Total Problems: 10

1.Function Table

Rule: Multiply by 4

Input	Output
2	8
3	12
5	20
7	28

Answer:28

4. Missing Value = 28 ✅

2.Function Table

Rule: Add 6

Input	Output
4	10
7	13
9	15
12	18

Answer:18

4. Missing Value = 18 ✅

3.Arithmetic Pattern

Look at the row of 5s in a multiplication table: 5, 10, 15, 20, 25... What do all multiples of 5 end with in their ones place?

A) 0 or 5B) Only 5C) Even numbersD) 1, 3, or 5

Answer:0 or 5

2. Property / Rule: 0 or 5 ✅

4.Function Table

Rule: Multiply by 3

Input	Output
3	9
6	18
8	24
10	30

Answer:10

4. Missing Value = 10 ✅

5.Arithmetic Pattern

When you multiply any whole number by an even number (such as 2, 4, 6), is the product always even or always odd?

A) Always EvenB) Always OddC) Sometimes EvenD) Depends on input

Answer:Always Even

2. Property / Rule: Always Even ✅

6.Function Table

Rule: Multiply by 8

Input	Output
2	16
4	32
5	40
7	56

Answer:56

4. Missing Value = 56 ✅

7.Function Table

Rule: Subtract 7

Input	Output
15	8
20	13
25	18
32	25

Answer:25

4. Missing Value = 25 ✅

8.Arithmetic Pattern

When you add two odd numbers together (such as 3 + 5 or 7 + 9), is the sum always even or odd?

A) Always EvenB) Always OddC) Depends on numbersD) Always Prime

Answer:Always Even

2. Property / Rule: Always Even ✅

9.Function Table

Rule: Multiply by 6

Input	Output
3	18
5	30
6	36
9	54

Answer:54

4. Missing Value = 54 ✅

10.Arithmetic Pattern

In an addition table, what happens to the sum if one addend increases by 1 while the other stays the same?

A) Sum increases by 1B) Sum doublesC) Sum stays the sameD) Sum decreases by 1

Answer:Sum increases by 1

2. Property / Rule: Sum increases by 1 ✅

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Worksheet Info

Categorygrade-3

Grade LevelGrade 3

DifficultyEasy, Medium, Hard, Sprint

Time5-10 min

CCSS CodeCCSS.MATH.CONTENT.3.OA.D.9

Skills Practiced

✓ Arithmetic Patterns in Tables

Key Strategies

🔍 Step 1: Compare Input to Output: Observe whether output values are getting larger (addition or multiplication) or smaller (subtraction or division) compared to input numbers.
📏 Step 2: Test the Rule Across Multiple Rows: Check your hypothesized rule against at least two given input-output pairs to confirm it applies universally across every row in the table.
🔢 Step 3: Apply Rule to Find the Missing Value: If the output is missing, apply the forward operation (e.g., input × 4 = output). If the input is missing, apply the inverse operation (output ÷ 4 = input).
💡 Step 4: Explain Number Properties: Recognize foundational algebraic patterns: even × even = even, odd × odd = odd, even × odd = even, and multiples of 5 always end in 0 or 5.

Related Worksheets

📄 Multiplication Tables 0 to 5View →📄 Multiplication Tables 6 to 10View →📄 Commutative Property of MultiplicationView →📄 Associative Property of MultiplicationView →📄 Distributive Property GridView →📄 Division Facts as Inverse MultiplicationView →

📜 Standard: CCSS.MATH.CONTENT.3.OA.D.9🔗 CCSS.MATH.CONTENT.3.OA.C.7🔗 CCSS.MATH.CONTENT.3.OA.D.8

Mastering Arithmetic Patterns in Tables: Core Concepts & Mental Models

Arithmetic patterns are predictable numerical relationships that repeat according to consistent mathematical rules. In Grade 3, students discover patterns across addition and multiplication tables—such as noticing that every number multiplied by an even number yields an even product, or that adding two odd numbers always results in an even sum. Students learn to decipher input-output function tables by analyzing row pairs to discover the underlying operation rule and apply it to find missing values.

Worked Example & SolutionTeacher Step-by-Step Method

📝 Problem: In an input-output table, input 2 produces output 8, input 3 produces output 12, and input 5 produces output 20. What output corresponds to input 7?

Worked Solution: Step 1: Compare input and output: 2 × 4 = 8, 3 × 4 = 12, 5 × 4 = 20. Step 2: The universal rule is 'Multiply by 4'. Step 3: Apply to input 7: 7 × 4 = 28. Output is 28.

💡 Essential Strategies for Arithmetic Patterns in Tables

🔍 Step 1: Compare Input to Output

Observe whether output values are getting larger (addition or multiplication) or smaller (subtraction or division) compared to input numbers.

📏 Step 2: Test the Rule Across Multiple Rows

Check your hypothesized rule against at least two given input-output pairs to confirm it applies universally across every row in the table.

🔢 Step 3: Apply Rule to Find the Missing Value

If the output is missing, apply the forward operation (e.g., input × 4 = output). If the input is missing, apply the inverse operation (output ÷ 4 = input).

💡 Step 4: Explain Number Properties

Recognize foundational algebraic patterns: even × even = even, odd × odd = odd, even × odd = even, and multiples of 5 always end in 0 or 5.

📖 Key Mathematical Vocabulary

Arithmetic Pattern

A regular, repeating sequence of numbers formed by following a specific mathematical rule.

Input-Output Table

A two-column table displaying pairs of numbers where the output is determined by applying a consistent rule to the input.

Function Rule

The mathematical operation (such as 'Multiply by 6' or 'Add 8') that links input to output.

Parity (Even / Odd)

The mathematical property of an integer being either divisible by 2 (even) or not divisible by 2 (odd).

❓ Frequently Asked Questions

How do you solve a arithmetic patterns in tables problem step by step?

Here is a worked example: "In an input-output table, input 2 produces output 8, input 3 produces output 12, and input 5 produces output 20. What output corresponds to input 7?". Solution: Step 1: Compare input and output: 2 × 4 = 8, 3 × 4 = 12, 5 × 4 = 20. Step 2: The universal rule is 'Multiply by 4'. Step 3: Apply to input 7: 7 × 4 = 28. Output is 28.

What is the core learning objective for arithmetic patterns in tables?

Identify arithmetic patterns (including patterns in addition tables or multiplication tables), and explain them using properties of operations; determine input-output function rules and calculate missing values. This directly aligns with Common Core Standard CCSS.MATH.CONTENT.3.OA.D.9.

How does the unlimited arithmetic patterns in tables worksheet generator work?

Every click of 'Generate New Worksheet' creates a completely fresh set of arithmetic patterns in tables problems with unique numbers. No two worksheets are ever the same — perfect for daily practice, homework variety, and preventing student copying. You can also customize the problem count (6, 8, 10, 12, 15, or 20 problems per sheet).

Are these arithmetic patterns in tables worksheets free to print with answer keys?

Yes! Every single worksheet on PanMaths is 100% free with no sign-up needed. Each sheet includes a dedicated Answer Key on Page 2 with step-by-step intermediate evaluation lines for 1-minute grading.