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Answers and Explanations to Fill in Missing Numbers Exercise
Questions
- 1, 2, 4, x, 16, 32, 64
- 30, 23, x, 9
- 84, x, 66, 57
- 63, 61, 59, x
- 32, 40, 24, 16, 24, x, 8
- 1, 2, 6, 24, x
- x, 12, 18, 10, 6, 14, 5, 0, 10 (this one is very difficult, break it into three parts to find pattern)
- 8, 25, 52, 89, x
Answers
- 1, 2, 4, 8, 16, 32, 64 (pattern is next number is double of previous number)
- 30, 23, 16, 9 (difference of 7 between each number)
- 84, 75, 66, 57 (difference of 9 between each number)
- 63, 61, 59, 57 (difference of 2 between each number)
- 32, 40, 24, 16, 24, 8, 8
Group A: 32, 40, 24, 16
Group B: 16, 24, x, 8
What are the similarities in pattern? I see that 32 is double of 16 in Group A. And 16 is double of 8 in Group B. 40 is 8 more than 32 in Group A. 24 is 8 more than 32 in group B. So if 40 is 16 more than 24 in Group A, then 24 must be 16 more than x in Group B. 24-16 = 8.
- 1, 2, 6, 24, 120 (pattern is 1×2 = second number, 2×3=third number, 6×4=fourth number, 24×5=fifth number, 120)
- x, 12, 18, 10, 6, 14, 5, 0, 10 (this one is very difficult, break it into three parts to find pattern)
Again, break sequence into parts. Which group doesn’t make sense? For me, it’s 5,0,10 sequence that’s odd. Now figure out the relationship between numbers in this sequence. I see 5-5=second number and 5+5=third number. Let’s see if this works with other groups. So,
10, 6, 14. Hmmm, 10-10 doesn’t work. Let’s still try to get to six using subtraction, 10-4=6, the second number. And 10+4=14, the third number! New theory, the first group will be subtracting and adding by 3. Let’s try:
15, 12, 18
15-3=12. And 15+3=18!
- 8, 25, 52, 89, 136
Difference between 8 and 25 is 17.
Difference between 25 and 52 is 27
Difference between 52 and 89 is 37
Difference between 89 and 136 is 47.
Key takeaways:
- Break difficult math problems into parts and then play with it.
- To develop your intuition for patterns, practice basic arithmetic drills we provide in the first few lessons.
Make your own missing number problems.
Notice we often ask students to make their own questions? This not only trains them to be responsible for their own educations, it forces them to think about education from a teacher’s point of view. It’s training them to see the world from different perspectives.
Make 10 of your own problems. Example:
- 2, 100, 5, 103, x, 106
(answer is 8, pattern is difference of 3 between every other number).
Scrabble Anagram Drill
- P, N, O, I, A, S, Y
Make 5 words with the above seven letters. Words must contain at least 3 letters. Those of you with advanced verbal skills, bump it up to at least 4 letters.
Example: soapy
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