August 14, 2015
Problem 1.1
Focus Question: How can you find
all the factors (or divisors) of a
number?
Vocabulary to consider:
1. Divisor
2. Factor
3. Proper Factors
August 14, 2015
Launch-
What factors can you multiply to get a product of 10?
_____________________________
What numbers divide 10 evenly? ____________________
How are these two lists related? _________________
The Factor Game
August 14, 2015
Play the Factor Game several times with a partner.
A
1. How can you determine whether one number is a factor of
another number?
2. If you know a factor of a number, can you find another factor?
Explain.
3. Make a list of the factors of 18. Then make a list of the
divisors of 18. Are the factors of a number also divisors of the
number? Explain your reasoning.
August 14, 2015
B
Give an example of a number that has many factors. Then give
an example of a number that has few factors.
C How do you know when you have found all of the factors of a
number?
Explore-
Questions to consider with your
partner/group...
- Is it better to go first or second? Why?
- What is the best first move? Why?
- How do you know when the game is
over?
- How do you know when you have
found all the factors of a number?
August 14, 2015
Other things to consider...
- Is there a way to have all the numbers
circles on the game board?
- What is the fewest number of factors
that can be circles in a finished game?
- What is the worst first move? Is there
only on possibility?
Problem 1.2
Focus Question: What information
about a number can you find by
looking at its factors?
August 14, 2015
Vocabulary to consider:
4. composite number
5. prime number
Launch-
Is it better to go first or second? Why?
What is the best first move? Why?
How can you be sure you have found the
best first move?
How do you know when you have found all of
the factors of a number?
August 14, 2015
The Challenge
Let's find the point totals for every possible
first move for the Factor Game. We can look
for patterns and determine which moves are
good and which moves are bad. Can you
think of a way that we can organize our
work?
August 14, 2015
Summarize-
Let's use our organized data
to answer the questions on
page 11.
August 14, 2015
August 14, 2015
What do you think is a good strategy for
playing the Factor Game?
Cam's strategy: "Bigger numbers must have more
factors that smaller numbers, so I always try to circle
small numbers on my turn. That way my opponent
won't get very many points."
Liza's strategy: "Some numbers don't have any factors
except 1 and themselves. I try to choose those
numbers so my opponent gets only one point."