Cosmic Multipliers Slides
Starfleet Academy • Mission 4
Sector Z-3000
Cosmic Multipliers & Alien Math
Master multi-tentacle groupings, planetary arrays, laser partial products, and hyperspace fact fluency!
Equal Groups
Alien pods & arms
Array Grids
Rows × columns
Decompose
Break apart factors
Fact Fluency
Rapid cosmic hacks
Concept 01
What is a Multiple?
Cosmic Beacon Patterns
A multiple is the result of multiplying a number by any whole number (1, 2, 3, 4...). Think of it as an alien jump on a planetary runway!
Hopping by Sixes: Multiples of 6
Rule: \( 6 \times n \)
\( 6 \times 1 \)
6
Jump 1
\( 6 \times 2 \)
12
+6 more
\( 6 \times 3 \)
18
+6 more
\( 6 \times 4 \)
24
+6 more
\( 6 \times 5 \)
30
+6 more
\( 6 \times 6 \)
36
+6 more
Cadet Query: Is 42 a multiple of 6?
Yes! \( 6 \times 7 = 42 \)
Strategy 01
Equal Groups: Tentacle Power
Group Size × Number of Groups
Mission: 4 Octo-Aliens each have 7 plasma tentacles. How many tentacles in total?
\( 4 \times 7 = ? \)
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Alien Alpha
7 Tentacles
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Alien Beta
7 Tentacles
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Alien Gamma
7 Tentacles
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Alien Delta
7 Tentacles
Repeated Addition: 7 + 7 + 7 + 7 = 28
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4 groups of 7 = 28 Tentacles!
Strategy 02
Space Arrays & Commutative Power
Rotate the Grid, Same Total
An array organizes items in equal rows and columns. Turning an array shows that \( 3 \times 5 = 5 \times 3 \)!
3 Rows of 5 Space Pods
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\( 3 \times 5 = 15 \)
5 Rows of 3 Space Pods
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\( 5 \times 3 = 15 \)
Order doesn't change the product! Commutative Property of Multiplication
Strategy 03
Cargo Split: Distributive Property
Break Hard Facts into Friendly Facts
Alien Cargo Challenge: How do we quickly solve \( 7 \times 8 \)?
Split 8 into 5 + 3!
Height (Rows)
7
Alien Crates
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Part A (Friendly 5s) \( 7 \times 5 \)
35
Easy to count by fives!
Part B (Remaining 3s) \( 7 \times 3 \)
21
Quick triple of 7!
Combine Partial Products: 35 + 21
\( 7 \times 8 = 56 \)
Mission Solved!
Fluency Hacks
Hyperspace Speed Strategies
Fast Reasoning Over Memorizing
The Double-Double
To multiply by 4, double the number, then double it again!
\( 9 \times 4 = ? \)
Double 9 ➔ 18
Double 18 ➔ 36
\( 9 \times 4 = 36 \)
Ten Minus One
To multiply by 9, multiply by 10 and subtract 1 group!
\( 7 \times 9 = ? \)
\( 7 \times 10 = 70 \)
\( 70 - 7 = 63 \)
\( 7 \times 9 = 63 \)
Double & Half
Cut one factor in half, and double the other to make an easy mental problem!
\( 16 \times 5 = ? \)
Half of 16 ➔ 8
Double 5 ➔ 10
\( 8 \times 10 = 80 \)
Starfleet Rule: If you get stuck on a fact, build it from a nearby friendly fact (like 2s, 5s, or 10s)!
Mission 01
Alien Bio-Dome Colonies
Word Problem Exploration
Incoming Transmission:
On Planet Gliese, the research outpost has 6 bio-domes. Each dome houses 9 alien botanists. How many botanists are working across the entire outpost?
Step 1: Identify Groups
What are the groups and what is inside each group?
6 Groups (Domes)
9 Botanists per dome
Step 2: Choose Strategy
Use the 10-minus-1 speed hack!
\( 6 \times 10 = 60 \)
\( 60 - 6 = 54 \)
Step 3: State the Solution
Complete sentence with units:
54 Botanists
Total in the colony
Multiple Check: Is 54 a multiple of 6? A multiple of 9?
Both! \( 6 \times 9 = 54 \)
Mission 02
Hyperdrive Fuel Crystals
Two-Digit Multiplication Challenge
The starship needs fuel! There are 14 fuel containers. Each container holds 6 glowing dilithium crystals. How many crystals does Commander Xlar have?
Decompose 14 into Tens & Ones
\( 14 = 10 + 4 \)
Multiply each part by 6, then add the partial products!
Container Base (Tens)
\( 10 \times 6 \) crystals
60
Container Reserve (Ones)
\( 4 \times 6 \) crystals
24
Total Crystals: 60 + 24
\( 14 \times 6 = 84 \text{ Crystals} \)
Active Drill
Alien Fact Showdown
Think • Pair • Defend Your Strategy
Identify the product AND name the strategy you used to calculate it!
Target Alpha
\( 8 \times 6 \)
Strategy: Double-double-double or 5s + 1s
Product:
48
Target Beta
\( 12 \times 7 \)
Strategy: Break into \( (10 \times 7) + (2 \times 7) \)
Product:
84
Target Gamma
\( 9 \times 8 \)
Strategy: \( 10 \times 8 - 8 \) or finger trick
Product:
72
Target Delta
\( 7 \times 7 \)
Strategy: Square fact or \( (7 \times 5) + 14 \)
Product:
49
Turn to your co-pilot: Which strategy was fastest for you, and why?
Share 1 Strategy
Debrief
Your Galactic Math Toolkit
Mission Certified
1. Multiples
Skip count along planetary beacons: numbers resulting from multiplying by 1, 2, 3...
2. Groups & Arrays
Rows × columns or groups of tentacles. Commutative property means order flips freely.
3. Distributive
Split tough numbers into friendly anchors like 5s and 10s. Add partial products together.
4. Speed Hacks
Use double-double for 4s, 10-minus-1 for 9s, and halving/doubling for mental speed.
FINAL RIDDLE Alien Mothership Teleporter
"I am a multiple of 7 and a multiple of 4. I am less than 40. What number am I?"
Answer Code:
28
