Frosty Operations Slides Grade 3 Virtual Math Expedition
Frosty Fact Families
Conquering multiplication and division within 100 using inverse operations and blizzard-proof number strategies.
Strategy: Inverse Operations (\(a \times b = c \iff c \div b = a\))
Winter Quest • Day 1
Virtual Expedition Norms
Ready to Explore
Expedition Log
Keep your paper and pencil ready to record fact families and show thinking.
Chat Snowstorm
Type your answers in the chat only when the snowflake icon signals it is time.
Inverse Thinking
Whenever you see division, immediately ask: "What multiplication fact helps me?"
Goal today: Fluently solve multiplication and division problems within 100 without counting on fingers!
Spiral Warm-Up: Avalanche Rush
Part 1 • Rapid Recall
1
Tens Pattern
\(10 \times 7 = \mathbf{?}\)
7 tens
2
Fives Landmark
\(5 \times 8 = \mathbf{?}\)
Half of 10×8
3
Sharing Equal Piles
\(24 \div 3 = \mathbf{?}\)
3 × ? = 24
4
Missing Factor
\(\mathbf{?} \times 4 = 36\)
36 ÷ 4
Waterfall Chat Prompt: Solve #3 and #4. Type your answers, but wait for the countdown!
3 • 2 • 1 • POST!
Warm-Up: True or Flurry False?
Spiral Reasoning
A
\(6 \times 8 = 8 \times 6\)
Does the order of factors change the total product? (Commutative Property)
TRUE (Both = 48)
B
\(40 \div 5 = 5 \div 40\)
Can we switch the dividend and divisor and get the same answer?
FALSE (Order Matters!)
C
If \(9 \times 4 = 36\), then \(36 \div 9 = 4\)
Are multiplication and division inverse operations that undo each other?
TRUE (Fact Family!)
Key Rule: In multiplication, factors can swap. In division, you always start with the total!
The Inverse Frost Connection
Core Strategy
Total (Product)
40
8
×
5
Opposite Directions
Multiplication combines equal groups to build a total.
Multiplication Facts
\(8 \times 5 = 40\)
\(5 \times 8 = 40\)
Division Facts
\(40 \div 5 = 8\)
\(40 \div 8 = 5\)
Power Move: When you see \(40 \div 5\), ask yourself: "5 times what equals 40?"
Standard 3.OA.C.7 • Fluently multiply and divide using the relationship between operations
Strategy 1: Fact Family Snow Cabins
Numbers 7, 9, 63
Cabin Roof (Product)
63
Cabin Pillars (Factors)
7
9
Every Cabin Holds 4 Equations:
Multiply: \(7 \times 9 = 63\)
Turnaround: \(9 \times 7 = 63\)
Divide by 7: \(63 \div 7 = 9\)
Divide by 9: \(63 \div 9 = 7\)
If a test or problem asks: \(63 \div 9 = \mathbf{?}\), you can instantly turn it around: \(9 \times \mathbf{?} = 63\)!
Virtual Volunteer: Who can read the 4 equations for the numbers 6, 8, 48 ?
Unmute or Raise Hand
Strategy 2: Break Apart on the Ice
Distributive Property
Step 1: Tackle Tough Multiplication
Solve \(7 \times 8\) by breaking 7 into \(5 + 2\)
\(5 \times 8\) (Friendly 5s fact): 40
\(2 \times 8\) (Doubles fact): 16
Combine parts: \(40 + 16\): 56
Conclusion: \(7 \times 8 = 56\)
Step 2: The Inverse Division Leap
Now solve \(56 \div 8 = \mathbf{?}\)
You do not need to count backwards by 8 fifty-six times!
Because you broke apart and proved that \(7 \times 8 = 56\) , you automatically know:
\(56 \div 8 = 7\)
Mastering known facts unlocks division in seconds!
Use friendly chunks (5s, 2s, 10s) to build up products, then reverse for division!
Guided Practice: Snowflake Chambers
Let's Try Together
Chamber 1
\(6 \times \mathbf{?} = 42\)
Think: \(42 \div 6 = \mathbf{?}\)
Friendly clue: \(6 \times 5 = 30\), so add two more 6s!
Answer: ? = 7
Chamber 2
\(72 \div 9 = \mathbf{?}\)
Think: \(9 \times \mathbf{?} = 72\)
Friendly clue: \(9 \times 8 = 72\)
Answer: ? = 8
Chamber 3
\(48 \div 6 = \mathbf{?}\)
Think: \(6 \times \mathbf{?} = 48\)
Friendly clue: 6 and 8 went on a date... 48!
Answer: ? = 8
Whiteboard / Chat Challenge: Which chamber was easiest? What multiplication fact popped into your head first?
Share Thoughts
Glacier Gauntlet: Problem Set
Solo Work Time
Problem 1: Penguin Feeding
A colony has 54 fish shared equally among 6 penguins . How many fish does each penguin receive?
Equation: \(54 \div 6 = \mathbf{?}\) | Related: \(6 \times \mathbf{?} = 54\)
Problem 2: Sled Dogs
There are 4 husky sled teams , with 9 dogs on each team. How many sled dogs are there in all?
Equation: \(4 \times 9 = \mathbf{?}\) | Related: \(36 \div 4 = \mathbf{?}\)
Problem 3: Igloo Blocks
Builders need 64 ice blocks . If each wall row needs 8 blocks , how many rows can they build?
Equation: \(64 \div 8 = \mathbf{?}\) | Related: \(8 \times \mathbf{?} = 64\)
Problem 4: Blizzard Lightning Facts
Solve both facts using their shared inverse relationship:
A) \(7 \times 7 = \mathbf{?}\) B) \(49 \div 7 = \mathbf{?}\)
You have 4 minutes on your expedition sheet. Show both multiplication and division!
Silent Focus Mode
Spot the Slip: Frosty's Blunder
Critical Thinking
☃️
Frosty's Written Work
Look closely at what Frosty wrote:
"I know that \(6 \times 7 = 42\)." (Correct!)
"So, that means \(42 \div 6 = 8\)!"
Frosty says: "Multiplication and division are related, so 42 divided by 6 has to be 8!"
Detective Questions
What mistake did Frosty make with his fact family members?
If you test \(6 \times 8\), what is the actual product?
What is the real fact family that connects 42 and 6?
The Fix:
\(42 \div 6 = 7\) because \(6 \times 7 = 42\)!
Fact families can only use their 3 family members!
Fact family numbers are locked together: {6, 7, 42}. No outside numbers allowed!
Exit Ticket: Arctic Checkpoint
Individual Formative Check
Q1
Related Fact
Solve: \(45 \div 5 = \mathbf{?}\)
Write down the multiplication fact you used to find the quotient.
5 × ? = 45
Q2
Fact Family Set
Look at the three numbers: 8, 9, 72 .
Write both division facts that belong to this family on your sheet or in private message.
72 ÷ 8 = ? | 72 ÷ 9 = ?
Q3
Word Problem
An ice-skating coach distributes 32 skates in pairs of 2 .
How many skaters can receive skates? Write both a division and multiplication equation!
32 ÷ 2 = ? | ? × 2 = 32
Virtual Turn-In: Submit answers via private direct message to the teacher or on your digital exit slip.
3 Minutes
Expedition Complete!
You proved that division is never scary when you know your multiplication fact families!
Remember the Frosty Rule:
Whenever you face \(A \div B = \mathbf{?}\), flip it in your mind to \(B \times \mathbf{?} = A\)!
Great job today, arctic mathematicians! • See you on the next quest!
Frosty Operations Handout Frosty Operations Expedition Log
Multiplication & Division Within 100 • Inverse Strategies
Name:
Date:
Inverse Rule: Multiplication & division undo each other: if 8 × 5 = 40 , then 40 ÷ 5 = 8 !
Part 1: Spiral Warm-Up (Avalanche Rush) 4 Points
1. Tens Fact
\(10 \times 7 = \_\_\_\_\)
Think: 7 tens
2. Fives Fact
\(5 \times 8 = \_\_\_\_\)
Think: Half of 10×8
3. Equal Groups
\(24 \div 3 = \_\_\_\_\)
Think: \(3 \times \_ = 24\)
4. Missing Factor
\(\_\_\_\_ \times 4 = 36\)
Think: \(36 \div 4\)
Check True or False:
A. \(6 \times 8 = 8 \times 6\) (Commutative Property) [ ] TRUE [ ] FALSE
B. \(40 \div 5 = 5 \div 40\) (Can division swap order?) [ ] TRUE [ ] FALSE
C. If \(9 \times 4 = 36\), then \(36 \div 9 = 4\) [ ] TRUE [ ] FALSE
Part 2: Fact Family Snow Cabins Guided Practice
Modeled Cabin: {7, 9, 63}
63
7 × 9
\(7 \times 9 = 63\)
\(9 \times 7 = 63\)
\(63 \div 7 = 9\)
\(63 \div 9 = 7\)
Your Turn: Build Cabin {6, 8, 48}
48
6 × 8
\(6 \times 8 =\)
\(8 \times 6 =\)
\(48 \div 6 =\)
\(48 \div 8 =\)
Break-Apart Power Strategy: Solve \(7 \times 8\) to find \(56 \div 8\)
1. Friendly 5s:
2. Doubles 2s:
3. Combine & Invert:
Frosty Operations Expedition Log • Page 1 of 2 Continue to the Glacier Gauntlet on page 2 →
Part 3: Glacier Gauntlet Independent Practice
Standard 3.OA.C.7
1. Penguin Colony
A colony has 54 fish divided equally among 6 hungry penguins . How many fish does each penguin receive?
Division: \(54 \div 6 =\) _____
Related Fact: \(6 \times\) _____ \(= 54\)
Answer: fish
2. Sled Dog Teams
There are 4 sleds , and each sled is pulled by 9 huskies . How many dogs are in the race? Write both facts.
Multiplication: \(4 \times 9 =\) _____
Related Division: _____ \(\div 4 = 9\)
Answer: dogs
3. Igloo Ice Blocks
A builder has 64 ice blocks . Each row requires 8 blocks . How many rows can be built?
Think: \(8 \times \_\_\_ = 64\)
Equation: \(64 \div 8 =\) _____
Answer: rows
4. Fast Facts Inverse Match
Solve each problem using its inverse twin:
A) \(7 \times 7 = \_\_\_\_\) → \(49 \div 7 = \_\_\_\_\)
B) \(8 \times 4 = \_\_\_\_\) → \(32 \div 8 = \_\_\_\_\)
C) \(6 \times 7 = \_\_\_\_\) → \(42 \div 6 = \_\_\_\_\)
Part 4: Spot the Slip (Frosty's Error)
Frosty said: "I know that \(6 \times 7 = 42\). Therefore, \(42 \div 6 = 8\)!"
Explain why Frosty is incorrect and write the correct fact:
Part 5: Arctic Checkpoint (Exit Ticket) 3 Questions
1. Related Fact
\(45 \div 5 = \_\_\_\_\)
Multiplication fact used:
2. Fact Family Set
Numbers: 8, 9, 72
Write both division facts:
3. Word Problem
32 ice skates given in pairs of 2. How many skaters?
Division equation:
Total skaters:
Frosty Operations Expedition Log • Page 2 of 2 Turn in to teacher via chat screenshot or digital upload
Frosty Operations Teacher Guide Frosty Operations Facilitator Guide
Grade 3 Virtual Math • 3.OA.C.7 Fluency via Inverse Relationships
Duration: 45–50 Mins
Instructional Objective Students will fluently multiply and divide within 100 by leveraging the inverse relationship between operations (e.g., using \(8 \times 5 = 40\) to solve \(40 \div 5 = 8\)) and applying distributive decomposition for challenging single-digit factors.
Pacing Guide
• Warm-Up:8 mins • Instruction:12 mins • Guided Chunks:10 mins • Solo Gauntlet:10 mins • Exit Slip:8 mins
Virtual Classroom Protocols & Norms
Waterfall Chat: Students type their response but do NOT press Enter until you say "3-2-1 Avalanche!" This prevents premature echoing.
Digital Thumbs: Use emoji reactions (👍 / ❄️) to confirm readiness or signal agreement during the True/False Flurry review.
Private Direct Chat: For the Exit Ticket checkpoint, students DM answers directly to the host to ensure independent demonstration.
Slide-by-Slide Facilitation Script: Part 1
Slides 1–2 (Intro & Norms): "Welcome arctic mathematicians! Today we are braving the blizzard to master multiplication and division facts up to 100. Open your Expedition Log and confirm your camera/audio are set."
Slide 3 (Spiral Avalanche Rush): Have students solve #1 and #2 verbally or in the waterfall chat. Emphasize: "Notice how 10s and 5s give us friendly landmarks. For #3, what question can you ask yourself instead of counting out 24 items? Ask: '3 times what gives 24?'"
Slide 4 (True or Flurry False): Call on two students to unmute. "Why is \(6 \times 8 = 8 \times 6\) True, but \(40 \div 5 = 5 \div 40\) False? Prompt: When we divide, which number must come first? The total group quantity!"
Slides 5–6 (The Inverse Frost Connection & Cabins): Highlight the Mountain / Cabin visual model. "A fact family is like a locked cabin. The roof is the total (40). The two base poles are the equal groups (8 and 5). If someone asks you \(40 \div 8\), look at the other base pole—it has to be 5!"
Slide 7 (Break Apart on the Ice): Walk through distributive decomposition. "If \(7 \times 8\) feels icy, split 7 into \(5 + 2\). \(5 \times 8 = 40\); \(2 \times 8 = 16\); \(40 + 16 = 56\). Now, what is \(56 \div 8\)? Instantly 7!"
Anticipated Student Misconceptions
1. Division Commutativity Confusion: Students may think \(48 \div 6 = 6 \div 48\). Remind them that division starts with the whole pizza, not the slice.
2. Adding Instead of Multiplying Factors: In missing-factor sentences like \(\_ \times 4 = 36\), students might subtract 4. Prompt them: "Skip count by 4 to 36!"
Frosty Operations Facilitator Guide • Page 1 of 2 Turn to Page 2 for Practice Facilitation & Complete Answer Key →
Facilitation Part 2 & Master Answer Key
Standard 3.OA.C.7 Verification
Slide-by-Slide Script: Practice & Assessment (Slides 8–12)
Slide 8 (Snowflake Chambers): Run rapid fire. Ask: "In Chamber 2, who used the 9s pattern to find \(72 \div 9\)? What did 9 multiply by to reach 72?"
Slide 9 (Glacier Gauntlet Solo Work): Put on 4-minute soft background music. Students work independently on Page 2 of their expedition sheets.
Slide 10 (Spot the Slip): Group analysis. "Frosty mixed up his family members! \(6 \times 7 = 42\), so 42 divided by 6 is 7, not 8! If it were 8, the product would be 48."
Slides 11–12 (Exit Ticket & Wrap Up): Direct students to private message their answers or upload their sheet photo. Celebrate mastery and reinforce the core inverse takeaway.
Master Answer Key (Expedition Log & Slides) 100% Verified
Part 1: Spiral Warm-Up
• \(10 \times 7 = \mathbf{70}\)
• \(5 \times 8 = \mathbf{40}\)
• \(24 \div 3 = \mathbf{8}\) (since \(3 \times 8 = 24\))
• \(\mathbf{9} \times 4 = 36\) (since \(36 \div 4 = 9\))
• True/False: A is TRUE ; B is FALSE ; C is TRUE .
Part 2: Student Cabin {6, 8, 48}
• \(6 \times 8 = \mathbf{48}\) | \(8 \times 6 = \mathbf{48}\)
• \(48 \div 6 = \mathbf{8}\) | \(48 \div 8 = \mathbf{6}\)
Part 3: Glacier Gauntlet
• 1. Penguin: \(54 \div 6 = \mathbf{9}\) fish; Related: \(6 \times 9 = 54\).
• 2. Dogs: \(4 \times 9 = \mathbf{36}\) dogs; Related: \(36 \div 4 = 9\).
• 3. Igloo: \(64 \div 8 = \mathbf{8}\) rows; Related: \(8 \times 8 = 64\).
• 4. Fast Facts: A) \(49\) → \(7\); B) \(32\) → \(4\); C) \(42\) → \(7\).
Part 4: Spot the Slip
• Frosty used 8 instead of 7. \(6 \times 8 = 48\), not 42. The correct inverse statement is \(42 \div 6 = \mathbf{7}\).
Part 5: Exit Ticket
• Q1: \(45 \div 5 = \mathbf{9}\); Fact used: \(5 \times 9 = 45\) (or \(9 \times 5 = 45\)).
• Q2: \(72 \div 8 = \mathbf{9}\) and \(72 \div 9 = \mathbf{8}\).
• Q3: \(32 \div 2 = \mathbf{16}\) skaters (or \(16 \times 2 = 32\)).
Tiered Differentiation
Scaffold (Tier 2): Provide a printable 10×10 multiplication chart. Show students how to find the product inside the grid and follow rows/columns outwards to find quotients.
Extension (Tier 1): Challenge students to create a double-family blizzard cabin involving 3 factors, e.g., \((2 \times 3) \times 8 = 48\) and inverse division \(48 \div 6 = 8\).
Exit Ticket Assessment Rubric
3/3 Correct (Mastery): Ready for multi-step word problems involving multiplication and division.
2/3 Correct (Approaching): Minor slip on 2-digit quotients or turnaround facts; assign paired peer warm-up tomorrow.
0–1/3 Correct (Needs Support): Pull into 10-minute small group using physical counters and triangle fact flashcards.
Frosty Operations Facilitator Guide • Page 2 of 2 End of Virtual Lesson Documentation
