Download MATH TOPIC 1 TEST: REVIEW PACKET

Mrs. Marshall & Mr. Liberato’s Math Class Study Guide
MATH TOPIC 1 TEST: REVIEW PACKET
Directions: This packet covers ALL of Topic 1. Take a lesson or two a night and review. Do not
try to study it all in one night. The packet provides MANY examples of each lesson and some
for you to try as well. You should complete EVERY “You Try It” section – do a little each
night.
Vocabulary
Dividend – The number that is divided. Example: 32 ÷ 4 = 8.
32 is the dividend
Divisor - The number by which another number is divided.
Example: 32 ÷ 4 = 8.
4 is the divisor
Quotient – The answer to a division problem
Example:
32 ÷ 4 = 8.
8 is the quotient.
Fact Family - A group of related facts using the same set of numbers.
Example: 2 x 5 = 10
5 x 2 = 10
10 ÷ 5 = 2
10 ÷ 2 = 5
2, 5,
10
LESSON 1-1: “Meanings of Multiplication”
Array: A way of displaying objects in equal rows and columns.
Example:
The multiplication
sentence for this array is
3 x 6 because there are 3
groups of 6
The multiplication sentence for this
array is 2 x 4 because there are 2
groups of 4
Factor: The numbers multiplied together to find the product.
Example:
8 x 2 = 16
(8 and 2 are both the factors)
6 x 9 = 54
(6 and 9 are both the factors)
Product: The answer to a multiplication problem
Example:
9 x 4 = 36
(36 is the product)
Repeated Addition: A way of writing a multiplication problem into an addition problem.
Example:
3 x 9 = 27 (think of this as 3 groups of 9)
Repeated Addition= 9 + 9 + 9 = 27
6 x 2 = 12 (think of this as 6 groups of 2)
Repeated Addition= 2 + 2 + 2 + 2 + 2 + 2 = 12
You Try It:
1.
What is the multiplication sentence for this repeated addition sentence?
4 + 4 + 4 = 12
2.
What is the repeated addition sentence for this multiplication problem?
9 x 4 = 36
LESSON 1-2 & 1-5:
“Patterns for Facts”; “Problem Solving: Look for a Pattern”
Multiple: The product of any two whole numbers.
Example:
Multiples of 2 are the products in bold.
2x1=2
2x2=4
2x3=6
2x4=8
2 x 5 = 10
2 x 6 = 12
(The Multiples of 2 are the products).
Quick Tip: When looking at multiples of two, the ones digit is always even
When multiplying you can SKIP COUNT. This means counting up by the specific number:
Example: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
Example: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
You Try It:
What are the multiples of 6 up to 6 x 10?
1.
What comes next in the sequence:
18, 27, 36, _____
5, 10, 15, ______
LESSON 1-3:
“Multiplication Properties”
Commutative Property of Multiplication: Numbers can be multiplied in any order and the product
remains the same.
Example:
7x2=2x7
9x3=3x9
Identity Property of Multiplication: The product of any number and 1 is the number.
Example:
7x1=7
3x1=3
Zero Property of Multiplication: The product of any number and 0 is zero.
Example:
6x0=0
5x0=0
You Try It: Name the Property being used and give another example of each.
1.
9,000,000 x 0 = 0
Property:
Give another example:
2. 15 x 1 = 15
Property:
Give another example:
3. 4 x 8 = 8 x 4
Property:
Lesson 1-4 Distributive Property: Breaking apart problems into 2 simpler problems.
Example:
4 x 32
STEP 1: We can break apart 32 into an easier addition problem (30 + 2)
STEP 2: Multiply 4 by each of the numbers INSIDE the parentheses=
(4 x 30) + (4 x 2)
STEP 3: Add both of the parentheses together
(120) + (8) = 128
You Try It:
9 x 22
LESSON 1-6 & 1-7: “Meanings of Division” & “Relating Multiplication and Division”
You can use multiplication to help you solve division problems. You can also use division to help you
solve multiplication problems. Fact Families are very helpful for this.
Fact Family - A group of related facts using the same set of numbers.
Example: 2 x 5 = 10
5 x 2 = 10
10 ÷ 5 = 2
10 ÷ 2 = 5
2, 5, 10
Example:
6 x 6 = 36
6,
36 ÷ 6 = 6
6,
36
You only need to write 2 number sentences for this fact because two of your factors are
the same.
LESSON 1-8:
“Special Quotients”
Any number divided by itself is 1.
o Example: 8 /8 = 1
Zero divided by any number is zero.
o Example: 0 / 5 = 0
You cannot divide by 0.
o There is no such number.
You will need to solve problems like these. Compare. Use >, <, or = for each
6÷6
3÷3
7 ÷7
7÷7
0÷4
0÷9
0 ÷ 11
0 ÷ 15
LESSON 1-10:
.
“Problem Solving: Draw a picture and write an equation”
Bar Diagrams can help us to solve multiplication and division problems.
Example:
There are 10 students in each row at the assembly. There are 8 rows of students. Which
number sentence shows the total number of students?
-------------------------------------------- ? (Total students) -----------------------10
10
A.
B.
C.
D.
10
5 x 6= 30
8 x 10 = 80
8 x 8 = 64
10 x 10 = 100
10
10
10
10
10
You Try It:
Carmen’s recipe calls for three times as many carrots as peas. If Carmen uses 2 cups of peas,
how many cups of carrots will she use?
----- ? (# of carrots in all) ---2
2
2
Multiplication Sentence: ________ x ________ = _________
Practice some word problems....
I am going shopping for 10 students who want sandwiches. Each sandwich needs 2 pieces of cheese. How
many pieces of cheese should I buy?
Jimmy has 5 pairs of shoes. How many total shoes does Jimmy have?
5 students want to buy 2 brand new shirts each. How many shirts will they buy altogether?
Using Bar Graphs with Division
A classroom has 26 chairs. The teacher wants to arrange the chairs in 4 rows. Write a number sentence
that shows how many desks the teacher can have in each row if each row has the same number of chairs?
26
? chairs
chairs