Download Number theory Quiz Study guide.pub

Math€Quiz€on€Wednesday,€January€11th€
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This quiz will cover topics relating to factors and multiples, as well as prime,
composite and square numbers. You should study and understand the following
concepts:
•Vocabulary:
Vocabulary:
product, factor, multiple, square number, prime number,
composite number (Look in your notebook glossary!!)
Differences between prime and composite numbers and special characteristics of a square number
•
Be able to list the factors of numbers 1-100, using strategies such as factor rainbows, factor t-charts, and your knowledge of divisibility rules
•
•
Be able to list the first 5 to 6 multiples of numbers 1-12
Be able to use clues about a number’s characteristics to determine what
the mystery number might be
•
How can you study for this quiz?
From now until Wednesday, you should review all the pages related to the topics above in your math interactive notebooks. Use the flip book pages to quiz
yourself. References like your multiplication table, factor t-charts through 100
and our Eratosthenes’ Sieve investigation will be helpful to review. Ask Mrs.
Nunez if you have questions!
Flip this sheet over for some helpful hints to review and study!
Helpful Hints to Remember...
Factors and Multiples:
• All whole numbers have factors of one and itself.
itself
•
All even numbers have a factor of two – and all even numbers are multiples
of two (you can see this by skip counting by 2)
•
When listing factors, it’s best to start with the number 1,
1 then work your way
up to the next digit, until you see any repeated factors. List them like this:
• Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
•
One way to find multiples of a number is to skip count by that number.
number Example: Multiples of 4 are 4, 8, 12, 16, 20, 24…
•
Multiples are not always listed in order. Example: 54, 36, 9, 27, 63, and 18
are all multiples of 9.
Prime, Composite, and Square Numbers
• Prime numbers have two and ONLY two factors – one and the number itself. Composite numbers must have MORE than two factors.
•
Some odd numbers are prime – but not ALL of them.
them Don’t be fooled!
•
The number 1 is the only number that is neither prime nor composite. It
only has one factor!
•
Just because the number 2 is even, this does not mean it is composite –
check the factors – there are only 2! (1 x 2)
•
When thinking of square numbers, picture the kind of array the number
would make – it’s a perfect square!
square Examples: 4 x 4 = 16, 7 x 7 = 49
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Name:€____________________________€Date:€___________€
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Extra€Practice€for€Number€Theory€Quiz€
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Complete the following problems as homework tonight to help you prepare for tomorrow’s quiz!
1. STUDY the definitions of our key math terms from this unit (prime, composite, product,
factor, multiple, square number).
2. Using factor rainbows or t-charts, determine ALL the factors of the following numbers.
Record them in an ordered list, from least to greatest.
25:
48:
89:
3. List the first five multiples of each number below:
7:
8:
4. Look at each set of numbers below. Determine what factors the set of numbers have in
common.
Example: 45, 65, 25, 10 —> These all share the factors of 1 and 5 (or they are all
multiples of 1 and 5).
12, 18, 27:
16, 28, 48:
5. Solve the following What Number am I? riddle:
• I am a 3-digit odd number.
• My hundreds digit is the only even prime number.
• If you multiply my tens digit and my ones digit together, the product is a square
number between 16 and 35.
• If you add my tens digit and my ones digit together, the sum is 10.
What number am I?
______________