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Algebraic Thinking Part I Lesson Notes
Appendix 1
Warm-up: This is another practice with Order of Operations. Your students could use
their order of operation and integer foldables to help them complete the problems.
Encourage them to write out all of the steps, because they should not be doing these
problems in their head.
Essential Question: What is the difference between a prime and composite number?
Helpful Hints:
o Begin discussions about factors by posing the question “what two numbers can
you multiply to give you ___?” Always have them start with one and the number
and have them work their way up from there. It is hard for them to organize their
thoughts, so if they go through 1 then 2 then 3 and so on… it is easier. Also tell
them they can stop when they start to repeat a number.
o Have them come up with their own definitions for prime and composite numbers.
o Use the Examples on T949 to introduce factor trees. Be sure to have them circle
the prime numbers, so they know not to extend the branch from that number.
o The sequence on T951 is similar to the chart on student page 545, which helps
students develop a logical thought process.
o Have students make a prime and composite card to hold up when checking the
questions.
o You could assign odds on student page 548 to be completed with the list and
evens with the factor tree, so they have practice with both. After today, they can
choose the one method they prefer.
o Since students always need practice with integer rules, the Quick Check involves
integers. Challenge your students to get as many correct answers as they can in
one minute.
Good Questions to Ask:
o What is a prime number? Answer: A number that has only one set of factors: one
and itself
o What is a composite number? Answer: A number that has more than one set of
factors.
o Is your age prime or composite? Answer: Answers will vary
o What must you do when you get to a prime number in a factor tree? Answer:
Circle it and end that branch
o How do you know you have found all of the factors using the rainbow method?
Answer: Because the numbers start to repeat
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o Why is the number 1not prime or composite? Answer: Because it only has one
factor, 1
o Is every even number a composite number? Answer: No, 2 is prime because it
has only one set of factors; all other even numbers are composite
o How many prime numbers are between 1 and 10? Answer: 4 numbers: 2, 3, 5, 7
o How many composite numbers are between 1 and 10? Answer: 5 numbers: 4, 6,
8, 9, 10
o Are there more prime or composite numbers from 1 – 100? Answer: Composite,
because there are 74 composite numbers and 25 prime numbers
o Is every odd number a composite number? Answer: No, 1 is odd, but is neither
prime nor composite
o What are examples of odd, prime numbers? Answer: 3, 5, 7, 11, etc.
o What are examples of odd, prime numbers greater than 20? Answer: 23, 29, 31,
etc.
o How can divisibility rules help you determine whether large numbers are prime or
composite? Answer: if divisibility rules apply to large numbers, then the numbers
will not be prime because they have more than one set of factors