Solving Inequalities Days 3 & 4

Today will start with a test on Simplifying Expressions.
We will then work on GoMath! 7.3, Solving Two-Step Inequalities, as a class and in partners. We will continue this activity in class tomorrow.

Solving Inequalities Day 2

We will be using GoMath! for today's lesson.

Solving Inequalities: Day 1

Starter:

1. Find your new seat. Use the chart on the north wall, and make sure the number on your chair matches your number on the chart.
2. In your team, explain how to graph -6+-12 on a number line.
3. In your team, discuss why
   (-6)(-8)=(-1)(-1)(6)(8).
4. In your team, discuss how to simplify
   3(x+6)-(4x+18).

What You Ought to Know about Inequalities:

1. Solving inequalities is the same as solving equations unless the coefficient is negative, in which case the inequality symbol needs to be reversed.
2. Properties of operations, including their inverses, can be used to isolate and define independent variables.
   *"Inverse" means the same as "reverse," so the inverse of multiplication is division, the inverse of subtraction is addition, etc.
3. Coefficients show multiples of an independent variable.
4. Constants show invariable numbers: they do not change because they are not variable, and they are not related to variables.
   *"Variable" means it can change.
5. Independent variables are usually unknown or changeable values.
6. Dependent variables are defined by operations with constants, coefficients, and independent variables.
7. An open dot like this is used to graph inequalities that are greater than, >, or less than, <. It means the independent variable is not included in the answer.
8. A closed dot like thisis used to graph inequalities that are greater than or equal to, ≥, or less than or equal to, ≤. It means the independent variable is included in the answer.

What You've Got to Do

1. Extract inequalities from story problems and model with manipulatives.
2. Use manipulatives and mathematical writing to show how to solve inequalities.
3. Write equations and inequalities to represent real-world variable situations.
4. Solve equations and solve and graph inequalities that represent real-world variable situations.

Try This:

This should help you better understand how to simplify expressions. When you're finished, try making your own slideshow or video example to explain how to simplify a different expression.

Practice

Today, all students will have the opportunity to retake assessments and show how they have improved.
Before you start, you may want to practice these:

Adding Integers
Subtracting Integers
Multiplying Integers
Dividing Integers
Simplifying Complex Expressions

Test Retakes Today and Tomorrow

Today and tomorrow, students will have the opportunity to retake tests one last time before the end of the quarter.
Practice these sets to work on basic skills.

Simplifying Expressions with Pictures

Complete today's starter on paper as a team:


Here are a few examples of how to use pictures to help you simplify expressions:












Homework: Practice for 20 focused minutes. Draw pictures if necessary. Click here for practice cards.
If you'd like to use the Slides presentation to help you with the pictures, you can make a copy of this presentation for your own use.

7NS1 Overview for Parents and Students

I can translate word problems into equations and inequalities: part 2.

Starter:

1. Get a blue calculator and push 2nd, 0, 7, 1, 2.
2. On your calculator, push 2nd, 0, 7, 2, 2.
3. On your calculator, type -(-20) by pushing the red minus sign, the white minus sign, 2, 0, and enter. What do you notice?
4. Clear your calculator's memory: push 2nd, 0, 7, 1, 2
5. On your calculator, type 0- -4(5) by pushing the red minus sign, the white minus sign, 4, (, 5, ), and enter. What do you notice?
6. Detton said that 6-4(2x-9)+11 simplifies to 4x+-7. What mistakes did he make? Identify and correct his errors.

Retake yesterday's Two-Question Quiz. Then take today's Two-Question Quiz.

Instruction: Identify key-words that help us translate verbal scenarios to algebraic equations and inequalities. Use properties of operations to solve equations and inequalities.

Exercises: 

1. The area of a tennis court is 2,808 square feet. The court is 2x+6 feet long and 36 feet wide. How long is the tennis court? 
2. Jai and Lupe plan to rent a kayak. The rental is $12 for the first hour and $9 for each hour after that. If they have $50, how many hours can they use the kayak?
3. A company sets up a food booth and a game booth at the county fair. The fee for the food booth is $100 plus $5 per day. The fee for the game booth is $50 plus $7 per day. The company ran both booths for the same number of days and spent a total of $210. How many days did the company run the booths?

I can translate word problems into equations and inequalities.

Starter: On a piece of paper, practice using the Multiplicative Identity and other properties of operations to simplify the expression 4(-5+8m)-(m+10).



Two-Question Quiz: Use the Distributive Property to expand expressions. (Canvas)

Instruction: Identify key-words that help us translate verbal scenarios to algebraic equations and inequalities.
Use properties of operations to solve equations and inequalities.

Exercises: 

1. A box of pencils is divided into three batches of x pencils each. If 2 pencils are added to each batch, there are 21 pencils. How many pencils were in the box? Method 1, Method 2
2. The area of a tennis court is 2,808 square feet. The court is 2x+6 feet long and 36 feet wide. How long is the tennis court? 
3. Jai and Lupe plan to rent a kayak. The rental is $12 for the first hour and $9 for each hour after that. If they have $50, how many hours can they use the kayak?
4. A company sets up a food booth and a game booth at the county fair. The fee for the food booth is $100 plus $5 per day. The fee for the game booth is $50 plus $7 per day. The company ran both booths for the same number of days and spent a total of $210. How many days did the company run the booths?

Review or Test

Starter:

This isn't as tricky as it might seem. You're really just showing how the numbers can be paired up and moved around: you don't really know what the numbers are to be able to do that. You will need the additive inverse and the multiplicative identity, and most of the other properties we've used this week. 

1st, 2nd, 5th, 6th, and 7th periods will join the discussion 4th period started yesterday, exploring some of the mistakes made on the CFA and how to avoid them.

4th period may re-take the CFA, or they may get some more practice with properties of operations: we will decide as a class.

6th period will take the CFA.

Discuss, Practice, or Test

Starter: Work for 10 minutes to use properties of operations to simplify the expressions in this practice set:

From reviewing 4th period's responses to the CFA yesterday, I learned that students are doing really well with:

• Recognizing that coefficients cannot be added to constants.
• Using the Distributive Property to expand expressions.
• Combining like terms.

I've also learned that we need more practice with:

• Using the Multiplicative Identity to make sure we don't lose a negative symbol.
• Using the Multiplicative Identity in conjunction with the Additive Inverse.

1st, 2nd, 5th, and 7th periods will take the CFA today after correcting last night's homework.

4th period will participate in several Discussion Board conversations on Canvas to see what errors were made on the CFA and how to fix them on the retake.

6th period will spend an extra day practicing before taking the CFA on Friday.

Using Properties of Operations to Simplify Expression: Practice or Quiz

Starter: Complete the Canvas Assignment (in Assignments, not quizzes) 7EE1 Practice: Finishing Notes from 10/9/2018.

Homework tonight:

• Simplify: -6(-10+4x)
• Simplify: -9(7x-1)
• Add: -6(-10+4x)+-9(7x-1)
• Subtract: -6(-10+4x)- -9(7x-1)

1st, 2nd, 5th, 6th, and 7th periods:
Today in class, we will continue using properties of operations to simplify expressions. Students will work more independently today, and we will review last night's homework today. We will also show how to simplify -4n+4(1-3n).

*Please note that not every step we are taking to simplify expressions is absolutely necessary. Our main focus is on becoming familiar with properties of operations and where they are useful: if we use them when they aren't necessary, we are more likely to pay attention to them and use them when they are.

4th period will take the CFA today.

*CFAs are assessments that will be included on the end-of-term grade for all classes. All classes will take the CFA before the end of the day on Friday.

Using Properties of Operations to Simplify Expressions

Starter: Complete the Canvas assignment (in Assignments, not quizzes) 7EE1 Adding and Subtracting Expressions. Then re-take the Canvas practice quiz 7EE1 Simplifying Expressions.

Today's objective is to use properties of operations to simplify expressions. We'll use the name cards today to choose who gets to tell the next step in simplifying each of the following. Anything we don't finish in class will be homework. 

1. p+6+p-10
2. -3b+6b
3. -5n+7n
4. 8+9x+2x+1
5. -6x-3x
6. -4n+4(1-3n)
7. 6p-7(1+7p)

Apologies for the delayed posting: it's been a busy week. Videos or slides may be posted later to show the process students used to practice.

Review: Operations with Integers and Adding and Subtracting Expressions

Dear Guest Teacher,

Thank you for coming in today and helping my students. They are a great group of kids and have been very cooperative with me this year. My 6th period is a co-taught class, and my co-teacher is taking the lead today: please support the students in following the lesson she has planned.
I have a TA in each of my first three classes, not including advisory. They may work on homework for other classes or participate with the rest of the students by following the lesson.

Please review this document for important classroom information. The "Daily Plans" binder is currently on my desk. This binder contains instructions for Breakfast in the Classroom. Advisory needs to complete the Skill of the Month worksheet and then silently work on homework until the end of class.

For all other classes, use the directions below. Students do NOT use Chromebooks when a guest teacher is present: all of this will need to be projected and done as a whole class.

Starter: Click the Full-Screen icon and allow students to complete the activity. Please follow the time limits included on each slide.



After the starter, tell the students they will have a quiz tomorrow on today's lesson, then play this video for them to watch:

After the video, give the students about 30 seconds to discuss in their teams the answers to the practice problems. At the end of 30 seconds, call on one team to answer and ask the rest of the class if they agree or disagree with that answer and why. Enter the answer in the box and select "Check Answer" to see if they were correct. Come back to this page when you are finished. The practice problems can be found here.

Now have students watch this video to review and extend what they have just done:

Have students shout out the answers to this activity and when they are finished, come back to this page.

Finally, have students watch one more video. Once they finish, have them write their own complex expression to give to someone else in the class to simplify.

Students will not turn in any of their work today: they will have a quiz tomorrow.

Graded Assessment today: Adding and Subtracting Algebraic Expressions.

Work on these practice cards until given different instructions:

Before you take the test today, we will watch this video.
After we watch the video, get a BLUE CALCULATOR and take or re-take this quiz. You will not be able to answer any questions that you have previously answered.

Once you're finished, put your calculator away and resume working on the practice cards from the starter.

Learning from Level 1 Mistakes to Improve Level 2

Today, we will be talking about the results of our 2-Question Quiz and figuring out what errors in our thinking led us to incorrect solutions, and how we can reorganize our thinking to lead us to the correct answers.

The table shows actual answers given for this test question:
Add: (2a+8)+(4b+5).

1. Infer the thinking that led from the original expression to the simplified expression. Use ONLY numbers and operation symbols to share that thinking.
2. Identify the data in the table that shows the simplified form of (2a+8)+(4b+5).

1	68	16b	35b
10	98	19a	3t
14	9034	19ab	4b
17	-16a	19b	6a +13
18	(8a)+(9b)	19c	6a+9b
19	10(a) 9(b)	20a	6ab+13
20	10+9 =18	20b	8a 7b
22	10+9b	2a+4b+13	90a
27	10a+9b	2b/13	9a
36	13ab	3432r

The table shows actual answers given for this test question:
Subtract: 8m-(5+2m).

1. Infer the thinking that led from the original expression to the simplified expression. Use ONLY numbers and operation symbols to share that thinking.
2. Identify the data in the table that shows the simplified form of 8m-(5+2m).

-5	554	15m	6m(5)
-1	945	15m-	6m+-5
0	-1m	1m	6m+4m
1	-38m	1m or m	6m+5
5	-56m	2m	7(8)
10	1 m	3+6m	7+8=15
11	10+(-5)	37m	7m
12	10m	46m	8m-(5)+8m-(2m)
15	10m	5-6m	8m-5
18	10m/5	5+6m	8m-7m
21	10m+(-5)	56m	8m+-5+2m
24	10m5	5g	8m+5+2m
56	11m	5m	m
79	13m+2	6m	1m

Add, Subtract, Factor, and Expand Linear Expressions

Today's Utah Core Standard is:

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

Classroom expectation: Students will use content-specific vocabulary as they read algebraic expressions and write out the processes they use to add, subtract, factor, and expand those expressions.

Students will engage in learning and practice today by completing GoMath! Module 6 Lesson 1. This lesson supports what students have learned and practiced earlier in the week; the assignment may be accessed until 9 PM this evening: after that time, the teacher will review the data to determine which students need additional support.

The teacher will support student learning by working with small groups to review concepts that apply to this new topic but are still weak for many students (multiplying and dividing integers). In classes where more students are proficient in the previous standards taught, the teacher will support student learning by working in small groups with students who have already shown they need more support for the new topic. The teacher's goal with these small groups is to help them become peer tutoring groups that allow students to support each other in gaining proficiency.

Factoring and Expanding Linear Expressions

Essential Question: How can I use properties of operations to factor and expand linear expressions?

Lesson:

Today, we will use the Distributive Property to expand linear expressions. We will then reverse the process to factor linear expressions. Finally, you will take a 2-question Quiz to show what you’ve learned.

1. Remember the Distributive Property: a(b+c)=a(b)+a(c).
2. Substitute numbers and variables into the expression.
3. Expand the expression.
4. Reverse the Distributive Property: a(b)+a(c)=a(b+c)
5. Repeat #2-3.

After the lesson, we’ll review the Starter then take a 2-Question quiz.

Introduction to 7EE1: Adding and Subtracting Algebraic Expressions

Essential Question: How do I know what terms can be added to or subtracted from each other?

Use the seating chart on the north bulletin board (to the left of the door) to find your new seat.

Start today's lesson by completing the practice quiz 7EE1 Introduction: Properties of Operations. You must complete your own quiz, but you may work with your team, and you may use the pink poster on the north chalkboard.

We will then complete the practice quiz 7EE1 Introduction: Vocabulary as a class.

Once we're familiar with the terminology, we'll add, subtract, multiply, and divide simple expressions.


Finish today's lesson by taking this two-question quiz.