Study Guide for Unit 2 – Multiplication with Whole Numbers
NOTE: I will provide a hard-copy of the answer sheet after you show me that you have worked
on this study guide. Also, you may practice for this upcoming unit test by practicing the
following on IXL (please see me if you don’t know your password): Fourth Grade D5, D6, D8, D9,
D10, D11, D12, D17, D18, M7, A6 and maybe: A2, D7
I.
Understand Unit Vocabulary (Note that you need to write one of these words twice.)
Product
Rounding
Partial products
Estimate
Factor
Square units
Array
Area
Distributive property
Algebraic notation method
Fill in the blank to match the definition and example:
1. A/an _________________________________ is an arrangement of objects, symbols, or
numbers in rows and columns.
2.
A/an ________________________________(rhymes with “get”) is a number close to an exact
amount (noun). When you _____________________________ (rhymes with “gate” ) you try
to find out about how many or how much.
3. When you find the ten, hundred, thousand, etc. that a number is closest to, you are
_______________________________.
Example: 4,273 to the nearest 10 is 4,270
4,273 to the nearest 100 is 4,300.
4,273 to the nearest 1,000 is 4,000.
4. A __________________ is the answer to a multiplication problem.
Example: 4 x 7 = 28
5.
The product of the ones, tens, or hundreds, etc. of a multiplication problem. It is just PART of
the solution to the multiplication problem.
24
X 12
48
So, 48 and 240 are “__________________________.”
+ 240
288
6. And 7. _____________________________ is the number of ______________________that
cover a figure.
10 units
3 units
8. A ________________________________ is one of two or more numbers that are multiplied
together to find a product.
4 X 7 = 28
9. The _________________________________________ shows that you can multiply a sum by
a number, OR multiply each addend by a number and add the products and the result is THE
SAME!
Multiplying a sum by a number
Multiplying each addend by a number
and adding the products:
3 X (2 + 4)
=
3X
=
6
+ 12
=
18
YES! There are two ways to get the
18
6
(3 X 2) + (3 X 4)
same answer!
10. The ___________________________________________________________ is a strategy
based on the Distributive Property. In a multiplication equation, you take one of the factors and
decompose it (write it in expanded notation). This makes simpler multiplication expressions.
Example:
a. The equation is:
b. Decompose (expand) the 28:
c. Use the distributive property to make
simpler multiplication problems:
d. Solve what is in parentheses:
e. Solve by finding the sum:
II.
9 X 28 = ?
9 X (20 + 8) = ?
(9 X 20) + (9 X 8) = ?
180
180
+ 72 = ?
+ 72 = 252
Know the steps for solving multiplication problems like 20 X 30 or 50 X 70 or 80 X 40 by
first factoring the tens.
Study this example, then try it on your own.
Here is the problem:
20
X 30
= ?
Factor the tens:
(2 X 10) X ( 3 X 10) = ?
The commutative property and the
associative property allows you to rearrange
like this:
Simplify (solve what’s in parentheses):
Multiply and find the product:
(2 X 3) X (10 X 10) = ?
6
6
X 100
X 100
Here is the problem:
Factor the tens:
The commutative property and the
associative property allows you to rearrange
like this:
Simplify (solve what’s in parentheses):
Multiply and find the product:
50
X
70
= ?
Here is the problem:
Factor the tens:
The commutative property and the
associative property allows you to rearrange
like this:
Simplify (solve what’s in parentheses):
Multiply and find the product:
80
X
40
= ?
=?
= 600
III.
Be able to use mental math to solve problems such as these (be careful, there may not be a
pattern happening!):
3 x 6 = _______________
3 X 60 = ____________________
30 X 60 = _______________________
3 X 600 = _________________________
3 X 6,000 = ________________________
IV.
Be able to solve, using any method:
One digit by two digit problems like:
4 X 79 =
5 X 61 =
One digit by three digit problems like:
4 X 302 =
8 X 153 =
One digit by four digit problems like:
5 X 4,312 =
4 X 8,261 =
Two digit by two digit problems like:
18 X 40 =
V.
Estimate products and
solve for exact answer by:
a. Rounding factors for estimate
b. Multiplying for exact answer
VI.
Solve word problems such as:
13 X 43 =
EXAMPLE
32 X 7
30 X 7 = 210
32 X 7 = 224
EXAMPLE
48 X 32
50 X 30 = 1,500
48 X 32 = 1,536
a. Eight fourth grade classes were collecting Box Tops for Education. Each class collected
the same amount – 328 Box Tops per class! How many Box Tops did the fourth grade
collect altogether?
b. Mary’s bedroom is exactly 9 feet long and 14 feet wide. Her brother’s room is HUGE! It
is 25 feet long and 32 feet wide! If Mary and her brother want to buy square foot tiles to
cover BOTH their floors, how many tiles will they need altogether?