section 1.1 evaluating expressions substituting a given ...section 1.4 write equations and...

Ch 1 Expressions, Equations & Functions

Section 1.1 Evaluating Expressions

You will learn:

*How to evaluate expressions by substituting a given variable with a given numeric value and reducing

*What it means: to evaluate an expression, you are simply reducing or simplifying to find the answer for what is shown.

Let's look at some examples...


WRITE THESE DOWN!!!

Example 1: Evaluate the Expression when n = 3.

a.) 13n

b.) n 2

c.) 10 + n

d.) 9 n

(the basics...)


1. 5(c - d) 2. c2 - cd 5

Example 2: Evaluate when c = 15 and d = 10

(A little more difficult...)


Example 3: Evalute when m = 4, n = 7 and p = 10.

1. m + n + p 2. m2 - 3m

3. p - (5 + m) 4. 10p + n p

5. mn 6. p - n + m p n + p

(most difficult...)


Homework for Section 1.1

Worksheet: No Calculator until after setup

From Today, Can You:

Substitute a number in for a variable & reduce your answer


WarmUp

Evaluate for b = 2.

1. 8 + 15b 2. 3b2 + 124 4b


Section 1.2 Order of Operations

You will learn:

*How to simplify expressions using the correct order of operations

PEM/DA/S


Activity:

*You will each be given a set of 10 questions to simplify using the order of operations to complete in 10 minutes.

*In the next 10 minutes, you will get together in groups based off of the question set you received and

Compare your answers as a group

Make an answer key for your set of 10 questions

List the correct Order of Operations in your notebooks

****When done, show the teacher to get your assignment****



Worksheet on Order of Operations

No Calculator!!!



Rest of slides are extras not used


1.2 Using the Order of Operations

On your own, simplify the following.

1. 4 + 6 ÷ 2

2. 4(6 + 2)

3. 3 2 - 4 1

4. 2 - 1 + 4 ÷ 2


9 - 3 ⇒ (9 - 3)3 - 1 (3 - 1)

Examples.

1. 12 - 9 ÷ 3 + 7 2. 9 + 3 (6 - 3)4

3. 15 + 2 9 ÷ 3 - 4 4. 7 + 3 5 4


1. 8 + 2 ÷ 2 2. 2 4 - 6 ÷ 2 3. 15 - 5 4 ÷ 2

4. 2(1 + 3) 5. 3.4(5 ÷ 2 - 1) 6. 1 + 3(5 - 2)

7. 1 + 2 8. 1 + 3 9. 2 - 66 2(4 - 3) 2(1.5)


Section 1.3 Write Expressions

You will learn:

*How to translate verbal statements into math expressions and math expressions into verbal statements


Key Vocabulary to Remember:

Math Vocabulary Verbal phrase example Expression

Addition Sum, plus, total, more than, increased by

the sum of 2 and a number x

a number n plus 7

Subtraction Difference, less than, minus, decreased by

the difference of a number n and 6

a number y minus 5

Multiplication times, product, multiplied by, of

12 times a number y

one third of a number x

Division quotient, divided by,divided into

the quotient of a number k and 2


Examples 1: Translate each verbal phrase into an expression

a. 4 less than the quantity 6 times a number n

b. 3 times the sum of 7 and a number y

c. The difference of 22 and the square of a number m.


Example 2: Write an expression for the situation.

1. A piece of ribbon hfeet long is cut from a ribbon 8 feet long.

Write an expression for the length (in feet) of the remaining piece.

2. You work with 5 other people at an ice cream stand. All the workers put their tips into a jar and share the amount in the jar equally at the end of the day. Write an expression for each person's share (in dollars) of the tips.


Example 3: Find a unit rate.

***Conversion amounts can be found in your agendas!!!***

1. A car travels 120 miles in 2 hours. Find the unit rate in feet per second.



Worksheet 1.3

From Today, Can You: Translate verbal statements into math expressions and math expressions into verbal statements


Activity: Describing a pattern verbally and algebraically

*You will need graph paper and a pencil

Directions:

*Start with a square on graph paper.Then draw a unit square (square of the same size) against each side of the first square to form figure 1.

*Figure 2: Copy down figure 1 and add a unit square to each "arm" to form figure 2.

*Repeat the step of adding another unit square on the end of each arm of the current figure to form the next figure until you have 5 figures drawn.


Questions to Answer :

1. How is the figure number related to the number of times 4 is added in the numerical expression? Use your reasoning to conclude the number of squares in the 6th figure.

2. Describe how to calculate the number of squares in the nth figure.

3. Write an algebraic expression for the number of squares in the nth figure.

4. a. Write an algebraic expression for the number of squares in the nth figure of the pattern shown.

b. Explain why the expression n2 is not an appropriate answer to part (a). Create a pattern that can be described by the expression n2.


Section 1.4 Write Equations and Inequalities

What you will learn:

You will translate verbal sentences into equations and inequalities.

After translating, you will check for or find solutions.

How this is different:

Expressions are math statements without an equal sign that are seen in questions where we need to reduce or simplify to report our answers

Equations are math sentences that have an equal sign "=" in them. Equations are solved for a particular variable.


Symbol Meaning Associated Words

= is equal to the same as

< is less than fewer than

≤is less than

or equal to

at most, no more than

> is greater than more than

≥is greater than

or equal to

at least, no less than

A Chart for your notebook!!!


Example 1: Write equations or inequalities.

a. The difference of twice a number k and 8 is 12.

b. The product of 6 and a number n is at least 24.

c. A number y is no less than 5 and no more than 13.


Example 2: Check possible solutions.

Check whether 3 is a solution of the equation or inequality.

a. 8 2x = 2

b. 4x 5 = 6

c. 2w + 5 > 12

d. 5 + 3n ≤ 20

Substitution Work Solution? Yes or No?


Example 3: Use mental math to solve an equation.

*One of the hardest things about a problem can be to know what it is asking or how to think about it...

a. x + 4 = 10

b. 20 y = 8

c. 6n = 42

d. a = 95

What I am thinking: My Solution:

*This technique can be used with many of the problems in math.... Process what is beind asked and generalize it for types of problems to use later.


The last time you and 3 friends went to a mountain bike park, you had a coupon for $10 off and paid $17 for 4 tickets.

What is the regular price of four tickets?

If you pay the regular price this time and share it equally, how much does each person pay?

Example 4: Solve a multistep problem



Worksheet 1.4



Section 1.5 Use a Problem Solving Plan

SKIP


Section 1.6 Represent Functions as Rules and Tables

You will learn:

*To represent functions as tables and graphs.

Bridging the gap:

You have been working with equations and inequalities. Many equations and inequalities are functions. Knowing they are functions helps us describe the relationship between two variables.


Vocabulary to Know:

A function consists of:

A set called the domain containing numbers called inputs

and

A set call the range containing numbers called outputs.

Example 1: Identify the domain and range of the function.

Input 10 12 13 17

Output 19.99 23.99 25.99 33.98


Input 0 1 2 4

Output 5 2 2 1

The table above is one way to show a function, another way to show a function is through a mapping diagram as seen below.

0

1

2

4

1

2

5

Input Output

***This is a function because each input is paired with exactly one output***


Example 2: Tell whether each pair is a function.

a. b.0

5

10

2

3

4

5

Input Output

Input Output

0 0

1 2

4 8

6 12

Keep in mind: Each x must match exactly one y; however, a yvalue may be paired with more than one x and can still be a function.


Example 3: Make a table for the function.

The domain of a function y = 3x is 0, 2, 4, 5, 7 and 8.

Example 4: Write a rule for this function.

Input 0 1 4 6 10

Output 2 3 6 8 12


Example 5: Try on your own!!

Write a rule for the functions below.

a.

b.

Input 0 1 2 4

Output 5 6 7 9

4

8

2

6

24

8

16

32



Worksheet 1.6


Represent functions as tables and graphs??

Do you know that each x (input) must be paired exactly one y (output) in order to call a relationship a function??


Section 1.7 Represent Functions as Graphs

You will learn to:

Represent functions as graphs.

So that you can:

Describe a relationship between variables visually


Example 1: Graph a function.

Graph the function y = .5x with domain 0, 2, 4, 6 and 8.

Example 2: Given a table, graph the function and write a rule.

0 1 2 3 4

2 3 4 5 6


1 2 3 4 5 6 7 8 9

123456789

Example 3: Write a rule for the given graph and identify the domain and range.


x y

1 0

2 3

3 6

4 9

5 12

x y

0 0

4 1

8 2

12 3

16 4

Write a rule for the tables below.


Big Concept Recap on Functions:



*** This is the LAST section in Chapter 1!! ***

Coming Soon: Chapter 1 Test!!!!

From Today, can You:

Use a graph to represent a function?

Use an inputoutput table to write a rule for a function whose graph is given?

Worksheet 1.7

section 1.1 evaluating expressions substituting a given ...section 1.4 write equations and...

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