Learning Objectives: SWBAT solve word problems developing and solving their own algebraic equations with fluency. Standards: CCLS: 7.EE.4a Solve word problems

Learning Objectives: SWBAT solve word problems developing and solving their own algebraic equations with fluency.

Standards: CCLS: 7.EE.4a Solve word problems leading to equations of the form px+q=r and p(x+q)=r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

Do Now: Let’s review our key words and strategies to help us solve a word problem!



We have spent the last two days reviewing solving word problems by using equations.

Now it’s your TURN!

Complete the following worksheet in class.



Solving Word Problems With Equations:

This is independent work.

Complete the two problems on your own to the best of your abilities.



Homework:

For homework, complete the following problem in your notebook.

Mary is going on vacation to the Bahamas. She has already paid $400 for the hotel and airfare. In addition, she has allotted herself x dollars per day for the remainder of the trip.a) Write an equation representing how much money Mary will spend on her trip in total. Let t=the total cost.b) If Mary’s vacation cost $800 in total and she was away for 4 days. How much money did she allow herself to spend per day?



Do Now:

Take out yesterday’s worksheet on problem solving. Let’s go over question 2.



Today…

We are continuing with Problem Solving.

In your packet, there are 4 word problems.

Use the class time to work independently and solve each one.



Homework:

For homework complete the “Solving Algebraic Equations” Worksheet.



Do Now: Solve the following Word Problem

Ms. Williams went to the store to buy raffle prizes for her classes. She went with $50. She bought 12 pieces of candy for the same price and a few small games for $30.

Write an equation representing the total cost of Ms. Williams’ purchases. Let t=total cost, let c=the cost of 1 piece of candy.

Solve to see how much money Ms. Williams has left if the candy cost $0.75 each.



Let’s Review:

What have we been doing the last few days?

Solving Word Problems Using Equations!!!

What are the steps we take to solve these word problems?

1. Read carefully2. Underline keywords3. Translate4. Solve5. Check



Today:

We are going to complete the task:

EXPRESS YOURSELF!!!(Do Not Misplace Your Packets,

We Will Finish Working with Them on Wednesday! They are also going to be hung up!!!)



Homework:

In your notebook match the following equations and word problems.

1. Mark is 6 times older than his daughter. If his daughter is 5, how old is Mark?

2. Justin can throw a football x yards. Bryan can throw a football two more yards than Justin. What is the sum that Justin and Bryan can throw a football?

3. Vanessa needs to do is pick up some oranges for her mom. She buys 5 oranges for the same price. If she spends $6 on oranges, how much was each one?

a) x + x + 2 = t

b) 6x = M

c) 5o = 6

Learning Objectives: SWBAT factor linear expressions with rational coefficients.

Standards: CCLS: 7.EE.1 Apply properties of operations as strategies to add, subtract, factor,and expand linear expressions with rational coefficients.

Do Now:

Let’s review the distributive property…

Translate and simplify the following expression:

3 times 6 less than a number



Let’s Review…In the Distributive property…we are giving out a number in order to make an expression easier to work with.

1. 5 times the sum of a number and 2

2. 8 times 7 less than a number.

3. 2 times a number and 3.



Now you try…

1. 4 times a number and 3

2. 6 times the sum of 5 and X.

3. 2 time the difference of 7 and a number.



Now…

What is the opposite of the distributive property?

FACTORING!!!!!

Factoring is the process of finding the factorsOR

Finding what to multiply together to get an expression!

Let’s take a look…



Example: factor 2y+6Both 2y and 6 have a common factor of 2:

2y is 2 × y 6 is 2 × 3

So you can factor the whole expression into:

2y+6 = 2(y+3)

So, 2y+6 has been "factored into" 2 and y+3



Let’s try together…1. 3x + 9

2. 7p – 14

3. 5a + 10 – 25b

4. 8f – 4t

5. 2c + 14



Now try on your own:1. 10x + 20

2. 9t - 18

3. 2w + 6y + 8

4. 6b – 12s

5. 4e + 20



Homework:

Complete the Factoring Worksheet.



Do Now:

Factor the Following Expression:

5t + 25 – 5bt



Yesterday…We learned all about FACTORING.

Today we are going to continue…

Let’s break into groups and work together to factor!



Group 1: Brandon, Sammy, Bryan and Natari

Blue Handbook Page 243Ms. N

Group 2: Carlos O., Carlos T., Mya, and Semion

IXL.com: Algebra SectionFactoring: AA.2 Factor out a monomial

Ms. Williams

You have 30 minutes to complete your work, then we will switch.

Let’s Get Started!!!



Homework:

Complete the Equations Worksheet.

Learning Objectives: SWBAT solve multi-step mathematical problems with rational number.

Standards: CCLS: 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers,fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers usingmental computation and estimation strategies.

Do Now:

Find the expression for the area of this rectangle:

What is the factor of the expression you got?

3x + 4x

2

Hint: A = LW



Let’s Review…

When solving a word problem we must:1. Translate2. Solve3. Check

However, word problems represent real life scenarios, so we may need other information as well.

How do we find the perimeter of a square or rectangle?

How do we find the area of a square or rectangle?



Let’s try to find the area together:

Let’s try to find the perimeter together:

3x + 8

10

3x

24 + x



Let’s step it up a notch…This rectangle is missing a corner, lets find expressions to represent its area and perimeter together.

3x - 2

7

x + 4

3



Now you try…

Complete the Worksheet: Area and Algebra



Homework:

What does each symbol mean?

>

<

=

<

>

Learning Objectives: SWBAT understand solving an inequality and write an inequality in the form of x>c or x<c.

Standards: CCLS: 6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Do Now:

What does each symbol mean?

>

<

=

<

>



What we’ve done…

We have been translating and solving equations.

Let’s Review:

A number less than 5 is 2.

2 times the sum of 3 and b is 10.

The quotient of 4 and a number is 2.



Where we’re going…

Today we are going to start working with inequalities…

Less Than

Greater Than

Equal to

Greater than OR Equal to

Less than OR Equal to



Let’s watch a Brain Pop video on Inequalities…

http://www.brainpop.com/math/dataanalysis/inequalities/



Let’s look at some key words for solving Inequalities…

> < > <

Is more

than

Is greater

than

Is larger

than

above

Is smaller

than

Is less than

Below

Minimum

At least

Is not less

than

Not smaller

than

Maximum

At most

Not more

than

Is not

greater

than


Standards: CCLS: 6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such

inequalities on number line diagrams.

Let’s try together…

3 less than a number is greater than 4

The sum of 6 and a number is less than 12.

The product of 5 and a number is greater than or equal to 25.

The quotient of 6 and a number is less than or equal to 3.

3 times the difference of 4 and a number is greater than 12.



Now try it own your own…

6 less than x is greater than 2.

4 times the difference of 6 and a number is greater than or equal to 12.

8 and a number are greater than 10.

The quotient of 6 and a number is less than or equal to 2.

The sum of 12 and a number is no more than 15.



Let’s try using only key words:

A number and 6 is above 9.

The sum of 4 and x is smaller than 10.

The quotient of a number and 10 is at least 5.

The product of 2 and as number is no more than 12.



Your turn…

12 and a number is more than 15.

7 less than a number is smaller than 3.

24 divided by X has a minimum of 3.

5 times X is not greater than 60.



Homework:

Explain the steps involved in solving this inequality:

8a + 2 < 24

Learning Objectives: SWBAT represent solutions of inequalities on a number line.

Standards: CCLS 6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Do Now: Solve the following inequality

A number and 4 is more than 12.



Let’s review:

What are the keywords for solving inequalities?

> < > <

Is more

than

Is greater

than

Is larger

than

above

Is smaller

than

Is less than

Below

Minimum

At least

Is not less

than

Not smaller

than

Maximum

At most

Not more

than

Is not

greater than



Let’s review:Now translate and solve these inequalities:

12 less than a number is at least 5

6 and a number is greater than 28

The quotient of 15 and a number is less than 3.

But what’s the next step?



Now we have to place the answer on a number line!Let’s take a look: x > 4

***Be Careful With The Dot***

(If the sign is < or > then the dot is open! If the sign is < or > then the dot is closed!)

3 4 5 6 7



Let’s try together…Graph the following:

x > 2

x < 6

x > 7

0 1 2 3-1

2 4 6 8 10

5 6 7 8 9



Now you try…Graph the following:

x > -1

x < 5

x < 8

*Pay attention to the dot*

0 1 2 3-1

2 4 6 8 10

5 6 7 8 9



Homework:

Complete the Inequalities Worksheet

Learning Objectives: SWBAT create a math reference book using foldables in order to remember the steps to solve word problems.

Standards: CCLS 6.EE.2,6.EE.3, 6.EE.5, 6.EE.8, 7.EE.1, 7.EE.2, 7.EE.4 Students use properties of operations to generate equivalent expressions. Students understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities are related. They also use variables to represent quantities in a real-world or mathematical problem and construct simple equations and inequalities to solve problems. The Mathematical Practices should be evident throughout instruction and connected to the content addressed in this unit. Students should engage in mathematical tasks that provide an opportunity to connect content and practices.

Do Now:

Write down our problem solving steps? Do you think we may need to add an additional step for solving inequalities?



Today we are going to review our problem solving skills and key words.

This will help us to solve word problems in the future.

We are going to do this by creating a:

Math Reference Book



Let’s do this together…

Follow the DIRECTIONS!

Learning Objectives: SWBAT graph the solution set and interpret it in the context of the problem.

Standards: CCLS 7.EE4b Solve word problems leading to inequalities of the form px + q > r or px + q <r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Do Now:

Translate, Solve and Graph the following Inequality.

The product of X and 4 plus 6 is at least 24.



Let’s Review…A number less than 4 is greater than 2.

Five times a number and 2 is 15 at most.



Now let’s try to apply this new knowledge to solving word problems!

What are the steps to solving word problems?1. Translate2. Solve3. Check

We’re going to use the same steps but add graphing our answers!



The NEW steps will be…

1. Translate

2. Solve

3. Graph

4. Check



Let’s Try Together…

Thomas received $14.00 for his birthday and a $5.00 i-tunes gift card. He wants to purchase songs for his IPod. How many $ 0.95 songs (s) can Thomas purchase if he uses his gift card and spends no more than the money he received? Find your solution by writing an inequality, then graph the inequality.



Now You Try…

The new sign regarding height requirements at the entrance of the Viper Roller Coaster ride at Darien Lake is shown below. Your friend meets the sign’s requirements. Write an algebraic inequality to show his height (h) and write a replacement sign in word form that could be used at the Viper’s Entrance. 48 49 50 51 52



Carlos O and Bryan are playing basketball against Sammy and Natari. Carlos and Bryan have scored x three-pointers and 6 baskets for 2 points each. Their total score is above Sammy and Natari’s 50 points. Write an inequality representing Carlos and Bryan’s points. Then solve to show how many three-pointers they must have thrown. Graph your answer on a number line.



Homework:

Your elementary school is having a fall carnival. Admission into the carnival is $3 and each game inside the carnival costs $0.25. Write an inequality that represents the possible number of games that can be played having $10. What is the maximum number of games that can be played?

Documents

Learning Objectives: SWBAT solve word problems developing and solving their own algebraic equations with fluency. Standards: CCLS: 7.EE.4a Solve word problems