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MATH NEWS
Grade 4, Module 3, Topic F December 2013
OBJECTIVE OF TOPIC F
1
Find factor pairs for numbers to 100 and use
understanding of factors to define prime and composite.
2
Use division and the associative property to test for
factors and observe patterns.
3
Determine whether a whole number is a multiple of
another number.
4
Explore properties of prime and composite numbers to
100 using multiples.
4
th Grade Math
Module 3: Multi-Digit Multiplication and Division
Math Parent Letter
This document is created to give parents and students a
better understanding of the math concepts found in Eureka
Math (© 2013 Common Core, Inc.) that is also posted as the
Engage New York material which is taught in the
classroom. Module 3 of Eureka Math (Engage New York)
covers Multi-Digit Multiplication and Division. This
newsletter will discuss Module 3, Topic F.
Topic F. Reasoning with Divisibility
Words to know
ï‚· Factor ï‚· Composite Number
ï‚· Products ï‚· Prime Number
ï‚· Multiple ï‚· Associative Property
Things to remember!!!
The Commutative Property says you can swap numbers (or
change order) and still get the same answer.
1 x 6 = 6 and 6 x 1 = 6
Focus Area– Topic F
Reasoning with Divisibility
Identify Factors and Product
What are the two multiplication sentences that
represent the arrays above?
1 x 6 = 6 and 2 x 3 = 6
The same product is represented in both sentences.
What are the factors of 6? 1, 2, 3, 6
Look at the list of factors, draw an arrow to connect the
factor pairs.
Notice that 2 and 3 are the middle factor pair. We have
checked all numbers up to 2. There are no numbers
between 2 and 3, so we have found all factors of 6.
1 x 5 = 5
Find another factor pair for 5. 5 x 1 = 5
2, 3, and 4 are not factors of 5, so 5 has only one set of
factors. Numbers that have exactly two factors, 1 and
itself are called prime numbers. Numbers that have at
least one other factor beside 1 and itself are called
composite numbers.
Factors can also be written in a table.
27 35
1 27 1 35
5 7
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Use division to find factors of larger numbers.
How can one find out if 3 is a factor of 48? Divide 48 by 3.
What if there is a remainder?
If there is a remainder then 3 is not
a factor of 48.
3 is a factor of 48 because there
are no remainders when divided.
Use the associative property to find additional factors
Find the factors of 48.
Is 5 a factor of 48?
No, any number multiplied by 5 ends with a 0 or a 5.
Is 2 a factor of 48?
Yes, 2 is a factor of all even numbers.
Is 1 a factor of 48?
Yes, 1 is a factor of all numbers.
Is 3 a factor of 48?
Yes, we divided 48 by 3 and had no remainders.
Is 6 a factor of 48?
Yes, 6 x 8 = 48
Is this number sentence true?
48 = 6 x 8 = (2 x 3) x 8
Use the associative property to see that 2 and 3 are both
factors of 48. The associative property means that it does
not matter how you group numbers when you multiply.
2 x 3 = 6 Move the parentheses so that 3 is associated with
the 8 instead of the 2. 3 x 8 = 24 and 24 x 2 = 48
3 x 2 = 6 Move the parentheses so that 2 is associated with
the 8 instead of the 3. 2 x 8 = 16 and 16 x 3 = 48
What is a multiple?
Count by 3’s to 30.
0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
What pattern is being used when counting?
Add 3 to the number said
When we skip count by a whole-number, the numbers
said are called multiples.
How are multiples different from factors.
When listing factors, we listed them and were done,
multiples can go on forever.
Is 84 a multiple of 12?
Yes, 12 x 7 = 84 or count 12, 24, 36, 48, 60, 72, 84
Using the associative
property, since 3 x 4 = 12
we also know that 84 is
also a multiple of 3 and 4.
We also know that 3, 4, 8,
and 12 are also factors of 84.
4 x 6 = 4 x (2 x 3)
is the original problem
The associative property says
that when we are multiplying
all numbers together we can
multiply the numbers in any
order and still get the same
answer.
In the problem above, we can move our parentheses and
multiply 4 x 2 first then multiply the answer by 3.
4 x 2 = 8 and 8 x 3 = 24.
The commutative property states that you can swap
numbers over or change the order of the numbers and the
answer will remain the same, so 2 x 3 = 6 and 3 x 2 = 6.
We know that we can use the associative property next to
solve the problem.
