Eight Expert Slides
8
16
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32
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48
56
64
72
80
800
888
1000
108
8
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48
Secret Agent Mission
THE RULE OF EIGHT
Cracking the code of large numbers using divisibility shortcuts.
Mission Briefing
Review: The Rule of 2
If the number is even (ends in 0, 2, 4, 6, 8).
Review: The Rule of 4
If the last two digits are divisible by 4.
Agent Inquiry:
If 2 relies on the last digit,
and 4 relies on the last two...
What is your prediction for the Rule of 8?
Surveillance Footage
Embedded media
Watch closely for the "Last Three Digits" strategy.
THE MASTER
RULE OF 8
1
The number formed by the last three digits is divisible by 8.
OR
2
The last three digits are all zeros (000).
Why does it work?
Think about the place value of large numbers...
1,000 ÷ 8 = 125
Since 1,000 is divisible by 8, any multiple of 1,000 is ALSO divisible by 8! (2k, 5k, 100k...)
Agent Intel:
In the number 16,248:
We KNOW the 16,000 part is divisible by 8 because it's multiples of 1,000.
We only need to check the remaining 248!
Field Test: Divisible by 8?
Number Alpha
4,000
HINT: Look at the last 3 digits!
Number Beta
12,168
Is 168 divisible by 8?
Discuss with your partner. Ready to reveal?
Mission: Divisibility Sort
Step 1: CUT
Carefully cut out the number cards from your mission sheet.
Step 2: ANALYZE
Apply the Rule of 8 to each card. Use your "scratch pad" to check the last 3 digits.
Step 3: SORT
Glue the cards into the correct zones on your sorting mat.
Remember: One digit off means the whole mission fails! Check your work twice.
DEBRIEFING
Final Reflection Question:
"Why is the divisibility rule for 8 often harder to use than the rules for 2 or 5?"
Mission Accomplished
Codebreaker Sorting Kit
Codebreaker Sorting Mat
Mission: Identify the divisibility of number sequences.
Agent:
Date:
DIVISIBLE BY 8
Verification required for each entry
NOT DIVISIBLE BY 8
Anomaly detected in these sequences
Agent Scratch Pad: Division Checks
Confidential Research Area - Show all work
Mission Cards: Evidence Set
Cut along the dotted lines and sort into the zones on Page 1.
CODE: 001
5,000
CODE: 002
12,016
CODE: 003
1,105
CODE: 004
2,240
CODE: 005
8,004
CODE: 006
116,080
CODE: 007
45,128
CODE: 008
7,422
CODE: 009
9,888
CODE: 010
2,010
CODE: 011
24,000
CODE: 012
5,012
End of Evidence File // Secure all components before glueing
Mission Intel Teacher Guide
Internal Agency Use Only
Mission Intel Teacher Guide
Lesson: The Rule of Eight
Mission Objective
Students will identify and use the divisibility rule for 8 (last three digits) to categorize large numbers, understanding the conceptual link between 1,000 and divisibility by 8.
Equipment List
- • Eight Expert Slides (Digital)
- • Codebreaker Sorting Kit (1 per student)
- • Scissors & Glue Sticks
- • Scratch paper / Notebooks
Mission Timeline
05
Minutes
Warm-up: The Pattern Search
Use the slides to review the rules for 2 and 4. Challenge students to predict the rule for 8 based on the "doubling" pattern (2 = last digit, 4 = last 2 digits, 8 = ?).
10
Minutes
Surveillance: Video Analysis
Watch the YouTube video. Pause at the time-stamps noted in the slides to check for understanding. Key Discussion: Why is 1,000 the "Magic Number"? (1000 ÷ 8 = 125). Explain that any number ending in 000 is automatically divisible by 8.
20
Minutes
Field Work: Codebreaker Sort
Students work independently or in pairs to cut and sort the 12 evidence cards. Encourage them to use the "Scratch Pad" area to divide the last three digits of numbers they aren't sure about.
10
Minutes
Debrief: Mission Reflection
Discuss the reflection question: "Why is the rule for 8 harder than 2 or 5?" Help students articulate that dividing a 3-digit number by 8 often requires mental math or scratch work, whereas rules for 2 and 5 are visual checks only.
Master Decryption Key
Divisible by 8
- 5,000 (000 rule)
- 12,016 (016 ÷ 8 = 2)
- 2,240 (240 ÷ 8 = 30)
- 116,080 (080 ÷ 8 = 10)
- 45,128 (128 ÷ 8 = 16)
- 9,888 (888 ÷ 8 = 111)
- 24,000 (000 rule)
Not Divisible
- 1,105 (Odd number)
- 8,004 (4 ÷ 8 R 4)
- 7,422 (Ends in 22)
- 2,010 (Ends in 10)
- 5,012 (12 ÷ 8 R 4)
Agent Training Tips
Common Pitfalls
Watch for students who check only the last digit (Rule of 2) or the last two digits (Rule of 4). Remind them that 8 requires a "deeper scan" of three digits.
Differentiation: Level Up
For advanced agents, ask if there is a Rule of 16. (Following the pattern, it would be the last four digits!)
