Unit 1: Intro to Pre-Algebra
ANSWER KEY
The following unit includes:
Arithmetic Properties
Order of Operations
Distributive Property
Rational and Irrational Numbers
Thank you for purchasing my notebook!
Please don’t forget to rate me.
Get Connected
My Teachers Pay Teachers
Read My Blog
Click on the
buttons to
check out more
from me.
Visit My Pinterest
Watch My Videos
Email Me
Math in Demand
with
Teacher Notes: Provided in this file is the answer key for Unit 1. There
are a few things that you might find helpful:
(1) You can differentiate for your students by deciding to print the blank template or answer key. I like to use
direct instruction and have my students fill in the blank template. However, I accommodate any of my students that have difficulty writing by providing the answer key.
(2) If you feel that I left anything out, you can ALWAYS have students add any additional notes. Every teacher
likes to teach a concept differently than another.
(3) You can use colored paper when printing the cutouts. This makes it less for students to color and it still
makes the page look colorful! Also, have students color code important info with highlighters!! It looks great!
(4) You can print the interactive notebook at 90% to make it fit into a smaller composition notebook.
If you have any questions, please don’t hesitate to email me at [email protected]. Thank you so much!
Math in Demand
Unit 1 Checklist
(Intro to Pre-Algebra) As you go through the unit, check off the concepts that you have mastered. Leave the other ones unchecked so that you know which concepts you need to study before a test!
The following unit includes:
□ Arithmetic Properties
□ Order of Operations
□ Distributive Property
□ Rational and Irrational Numbers
©2016 Math in Demand
©2016 Math in Demand
Unit 1 Overview (Intro to Pre-Algebra)
Concepts(s):
Essential Questions:
Vocabulary:
Important Dates: Pre-Test: Post-Test: Vocabulary Quiz:
Scores: Pre-Test: Post-Test: Vocabulary Quiz:
Commutative Associative Distributive Property Additive Inverse
Order of Operations Parentheses Rationals Irrationals
What are the arithmetic properties? What is the importance of the order of operations? When do I use the distributive property? What is the difference between rational and irrational
numbers?
Arithmetic Properties
Order of Operations
Distributive Property
Rational and Irrational Numbers
This overview shows you important information that you will be learning throughout the
unit. Make sure to fill out important dates and scores!
Intro to Pre-Algebra (Arithmetic Properties)
Fill out the properties of real numbers table below. Let a, b, and c be real numbers.
Property Example
1.) Commutative Property of Addition
2.) Commutative Property of Multiplication
3.) Associative Property of Addition
4.) Associative Property of Multiplication
5.) Distributive Property
6.) Additive Identity Property
7.) Multiplicative Identity Property
8.) Additive Inverse Property
9.) Multiplicative Inverse Property
10.) Zero Property
I can ___________________
_______________________
©2016 Math in Demand
a + b = b + a
a ∙ b = b ∙ a
a ∙ (b ∙ c) = (a ∙ b) ∙ c
a + (b + c) = (a + b) + c
a ∙(b + c) = a∙b + a∙c
a + 0 = a
a∙1 = a
a + (-a) = 0
a∙(�) = 1
a∙0 = 0
8 + 2 = 2 + 8
3 ∙ 4 = 4 ∙ 3
8∙(1∙2) = (8∙1)∙2
2+(7+3) = (2+7)+3
4∙(3+6) = 4∙3 + 4∙6
8 + 0 = 8
5∙1 = 5
4 + (-4) = 0
4∙( ) = 1
9∙0 = 0
identify the arithmetic
properties.
Intro to Algebra (Arithmetic Properties)
1.) 6 + 0 = 6
Additive Identity Property
Reflection: I learned…
Determine the type of property shown below:
2.) -8 ∙12 = 12 ∙ -8
Commutative Property of Multiplication
3.) 9∙(5+3) = 9∙5 + 9∙3
Distributive Property
4.) 18 + 5 = 5 + 18
Commutative Property of Addition
5.) 3∙(4∙5) = (3∙4)∙5
Associative Property of Multiplication
6.) 7+(2+4) = (7+2)+4
Associative Property of Addition
7.) 3 + (-3) = 0
Additive Inverse Property
8.) 7∙(7) = 1
Multiplicative Inverse Property
©2016 Math in Demand
On a rating of 1-5, how comfortable are you with this concept?
(5 is the highest)
1 2 3 4 5
Intro to Algebra (Order of Operations)
What does order of operations mean?
I can ___________________
_______________________
Please Excuse My Dear Aunt Sally!
Glue “P” Here Glue “E” Here Glue “MD” Here Glue “AS” Here
Example:
15 + (8 + 4) ∙ 32 + 2 ∙ (10 - 3) + 8
(1) Parentheses first 15 + (12) ∙ 32 + 2 ∙ (7) + 8
(2) Exponents 15 + (12) ∙ 9 + 2 ∙ (7) + 8
(3) Multiplication and Division 15 + 108 + 14 + 8
(Left to Right)
(4) Addition and Subtraction 123 + 22
(Left to Right)
= 145
©2016 Math in Demand
use order of operations to
simplify and solve expressions.
Order of operations is a collection of rules that say which calculation comes first in an expression.
Parentheses Do everything
inside parentheses
first! ( ) �
Exponents Exponents
come second!
Multiplication and Division Multiply and Divide from
Left to Right!!
Addition and Subtraction
Add and Subtract from Left to Right!!
XzasQ `1
Directions: Cut out the following figures on the dotted lines. Glue the figures on the areas that say “Glue Here”.
Directions: Cut out the following figures on the dotted lines. Glue the figures on the areas that say “Glue Here”.
Directions: Cut out the following figures on the dotted lines. Glue the figures on the areas that say “Glue Here”.
©2016 Math in Demand
Intro to Algebra (Order of Operations)
Reflection: I learned…
1.) (8 - 2)2 – 4 ÷ 2 ∙ 3
(6)2 – 4 ÷ 4 ∙ 2
36 – 4 ÷ 4 ∙ 2
36 – 1 ∙ 2 = 36 – 2 = 34
2.) 8 x 5 x (7+4) + 0 x 6
8 x 5 x 11 + 0 x 6
440 + 0 = 440
3.) 43 – 6 ÷ 3 ∙ 2 + 5
64 – 6 ÷ 3 ∙ 2 + 5
64 – 2 ∙ 2 + 5
64 – 4 + 5 = 60 + 5 = 65
Answer
Answer
Answer
©2016 Math in Demand
On a rating of 1-5, how comfortable are you with this concept?
(5 is the highest)
1 2 3 4 5
34
440
65
-a(b-c) = -ab + ac
Intro to Algebra (Distributive Property)
What is the distributive property?
a(b+c) =
Use the distributive property to solve the following:
8(x+2) = 8x + 16
Now, what if we have a negative number outside of the parentheses and the operation is subtraction?
Use the distributive property to solve the following:
-5(x-4) = -5x + 20
©2016 Math in Demand
I can ___________________
_______________________
a(b+c) = ab + ac
“get rid” of parentheses by
using the distributive property.
The distributive property is used to simplify expressions by multiplying a single term by two or
more terms inside parentheses.
The distributive property states that: This means a times b
or a∙b
It is easy to make mistakes here! Remember to always look at signs! A negative multiplied by another
negative is a positive!!!
Intro to Algebra (Distributive Property)
Reflection: I learned…
1.) 12(x–4)
12x – 48
2.) -8(y+12)
-8y – 96
3.) -(x–11) -x + 11
©2016 Math in Demand
On a rating of 1-5, how comfortable are you with this concept?
(5 is the highest)
1 2 3 4 5
Intro to Algebra (Rationals and Irrationals)
Glue Here
Glue Here
Define and provide
examples!
Glue “Rational Numbers” Here
What are rational numbers?
Give some examples:
©2016 Math in Demand
I can ___________________
_______________________
distinguish between
rational and irrational numbers.
The real number system is made up of all the points on the number line. The real number system is used
every day. Numbers play an important part in the real world by assigning values and weighing variables. � √8
A real number that cannot be expressed as
a ratio of integers.
Examples: 2.1354…
A number that can be written as a ratio; includes terminating and repeating decimals.
√25 1.23 2.425425… -100
What is the real number system?
What is the importance of the
real number system?
Irrational Numbers
Natural Numbers
Whole Numbers
Glue “Natural Numbers” Here
What are natural numbers?
Give some examples:
Directions: Cut out the following figures on the dotted lines. Glue the figures on the areas that say “Glue Here”. Make sure to glue them in their proper location.
©2016 Math in Demand
Positive Integers
1, 2, 3, …
Integers
Glue “Whole Numbers” Here
What are whole numbers?
Give some examples:
Rational Numbers
Glue “Integers” Here
What are integers?
Give some examples:
©2016 Math in Demand
A number without fractions or decimals
0, 1, 2, 3, …
A number that is not a fraction; can be positive or negative
-2, -1, 0, 1, 2, …
V
Intro to Algebra (Rationals and Irrationals)
Determine if the following numbers are rational or irrational. Explain your reasoning.
3.45 √8 2.1414… √25 8.94731… �
Rational
Irrational
Reflection: I learned…
©2016 Math in Demand
On a rating of 1-5, how comfortable are you with this concept?
(5 is the highest)
1 2 3 4 5
3.45 2.1414… √25
√8 �
Terminating Decimal Fraction
(Rational divided by rational)
Repeating Decimal
Perfect Square
Non-perfect Square
Non-terminating Decimal and Non-
repeating
© 2016 Math in Demand. The download of my notebook includes a limited use license from Math in Demand. You may only use the resource for personal classroom use.
Hence,
1.) This purchase does not allow you to transfer it to others such as another teacher, school, or district.
2.) You may not sell my notebook.
3.) You may not place my notebook on the internet.
4.) You may not use any part of my notebook to sell or create your own.
Violating these terms is against the Digital Millennium Copyright Act (DMCA).
Credits
Media Icons by Grade ONEderful at: http://www.GradeONEderful.com
Graphics by: www.jessicasawyerdesign.etsy.com
https://www.teacherspayteachers.com/Store/Glitter-Meets-Glue-Designs
Font by: http://www.teacherspayteachers.com/Store/Courtney-Keimer