Multiplication Navigator Student Guide
Grade 3 Math Reference Guide
Multiplication Navigator
Name
Date
KEY VOCABULARY
Multiplication means adding equal groups together rapidly.
\( \text{Factor} \times \text{Factor} = \text{Product} \)
Factor Number of groups
Factor Amount in each group
Product The total answer
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Strategy 1: Equal Groups & Repeated Addition
When objects are sorted into groups with the same number in each, use repeated addition to multiply.
Group 1 (4)
Group 2 (4)
Group 3 (4)
Sentence: 3 groups of 4
Addition: \(4 + 4 + 4 = 12\)
Multiplication: \(3 \times 4 = 12\)
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Strategy 2: Arrays & Turnaround Facts
Commutative Property
An array organizes objects into straight Rows (across →) and Columns (up & down ↓).
3 Rows of 5 Columns
\(3 \times 5 = 15\)
Turn it sideways!
5 Rows of 3 Columns
\(5 \times 3 = 15\) The total product stays the exact same!
Try It: Show Your Thinking
Write and draw your solutions below
1. Draw equal groups for: \(4 \times 2\)
Draw 4 circles with 2 dots in each:
Repeated Addition: ____ + ____ + ____ + ____ = ____
2. Complete the array equation:
2 rows of 6 dots
Multiplication: ____ \(\times\) ____ = ____
Turnaround Fact: ____ \(\times\) ____ = ____
Rule to Remember: Equal groups must ALWAYS have the exact same amount in each group! Page 1 of 3
Toolkit Section 2
Skip Counting & Fact Strategies
Multiplication Navigator
3
Strategy 3: Skip-Counting Highways
Each hop = 1 group
Skip-counting connects counting patterns to facts. For \(4 \times 5\), count 4 hops of 5: 5 → 10 → 15 → 20!
2s
24681012141618 20
3s
369121518212427 30
5s
51015202530354045 50
10s
102030405060708090 100
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Strategy 4: Mental Math Power Rules
Zero Property \(\times 0 = 0\)
Any number times 0 is 0. 7 groups with 0 items equals 0!
\(8 \times 0 = 0\) | \(0 \times 12 = 0\)
Identity Property \(\times 1 = \text{itself}\)
Multiplying by 1 never changes the factor. 1 group of 9 is 9.
\(9 \times 1 = 9\) | \(1 \times 15 = 15\)
Doubles (\(\times 2\)) Double It!
Multiplying by 2 is adding the number to itself: \(7 + 7\).
\(7 \times 2 = 7 + 7 = \mathbf{14}\)
Double-Double (\(\times 4\)) Double Twice!
Double the factor, then double that answer to get \(\times 4\).
\(6 \times 4 \rightarrow 12 \rightarrow \mathbf{24}\)
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Strategy 5: Break-Apart Facts (Distributive)
Split into friendly 5s & 2s
Stuck on tricky facts like 7s? Split the big factor into easy chunks you already know!
Problem: Solve \(7 \times 6\)
1. Split 7 into 5 + 2: \( (5 \times 6) + (2 \times 6) \)
2. Solve parts: \(30 + 12 = 42\)
5 rows of 6 = 30
2 rows of 6 = 12
Strategy Practice: Write the answer and which strategy you used
\(5 \times 8 = \) ____
Strategy:
\(4 \times 7 = \) ____
Strategy:
\(11 \times 0 = \) ____
Strategy:
Speed Secret: Any number times 10 simply shifts up a place value: add a zero at the end! Page 2 of 3
Toolkit Section 3
Word Problem Detective
Multiplication Navigator
The 4-Step Blueprint for Multiplication Stories
1 Find the Clues Identify number of groups & amount in each.
2 Draw a Model Sketch equal groups, an array, or a bar model.
3 Write Equation \( \text{Groups} \times \text{Each} = \text{Product} \)
4 State the Answer Write a full sentence with the correct unit label!
Worked Mentor Example Study the Steps
“Maya baked 4 trays of blueberry muffins. Each tray holds 6 muffins. How many muffins did Maya bake in all?”
1. Clues & Quick Model • 4 groups (trays) • 6 in each group
[6] [6] [6] [6]
2. Equation Double-Double strategy:
\(4 \times 6 = 24\)
6 → 12 → 24
3. Labeled Answer
Maya baked 24 muffins in all.
Includes unit label!
Problem A: Dinosaur Stickers Show Your Work
Leo bought 5 packs of dinosaur stickers for his collection. There are 8 stickers in each pack. How many stickers does Leo have altogether?
Draw Your Model (Equal Groups or Array):
Multiplication Equation:
____ \(\times\) ____ = ____
Answer Sentence with Units:
Leo has _______________________________________
Problem B: School Sunflower Garden Show Your Work
The third-grade class planted a garden with 3 rows of sunflowers. They planted 9 sunflowers in each row. How many sunflowers are growing in the garden?
Draw Your Model (Equal Groups or Array):
Multiplication Equation:
____ \(\times\) ____ = ____
Answer Sentence with Units:
There are ______________________________________
My Multiplication Superpowers:
Equal Groups Arrays Skip-Counting Story Problems
Always re-read your story problem to verify your answer makes sense! Page 3 of 3
