Unit 1: Intro to Pre-Algebra

ANSWER KEY

The following unit includes:

Arithmetic Properties

Order of Operations

Distributive Property

Rational and Irrational Numbers

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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.

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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

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