A New Year means a New Start

Happy Holidays Everyone,

It is getting close to the end of 2014 and the beginning of 2015. 2015 will be a big year for my 8th graders. This is the year you will enter high school but before you do we need to prepare you.

If you remember, last week you had a bell ringer asking you to write down your goals for 2015. Several of you wrote that you would like to do better in school. One of my goals for this next semester is to help prepare you for high school and if you are in 7th grade help you become more successful in your own learning.

I have big plans for next semester. Be prepared for a big change in the way I am "teaching."

My personal goal as a teacher for 2015 is to reach EVERY student. By reaching every student, I mean I hope to make sure every student learns the concepts and is not left behind. I want to help you learn how you learn best. This goes along with my change in the way I will be teaching. I understand students learn in different styles and at different paces. I am working on plans to allow each student to work on meeting goals at their own pace but in a certain time frame.

 I was so impressed with my 8th graders' project, I have decided each unit we will have an overall project will take the place of homework. Along with the projects, I will be having ticket out the doors to help me determine the level of understand each student is at.

Since all of you are my focus for 2015, I have a quick survey to help me learn what worked and what did not work for you in first semester. Click here for survey.



I am excited about this new year! I hope this break allows you to come back refreshed and ready to learn.


Have a Fantastic Break,
Mrs. Gilliam

8th Grade Math: Writing Linear Equations Tutorials

Happy Saturday Everyone,

Reminders:

• Pattern Projects Due Monday/Tuesday
• Quiz over Linear Equations on Wednesday/Thursday

We have been working on putting together all the parts of writing linear equations over the last month. We have looked at equations through patterns, real world examples, tables, and graphs.

Key Things to Remember:

• y = mx+b (is the base equation for all linear equations)
• m represents the rate of change/slope
• b represents the starting point and y-intercept.
• Slope is the steepness of a line. The rate of change of the line.
• Y-intercept is where the line crosses the y-axis.
• Slope and rate of change are found by finding the change in y divided by the change in x.

Tutorial Videos:

Writing Linear Equations from Tables

Writing Linear Equations from Graphs

Writing a Linear Equation from a Word Problem

Hope you find these videos helpful! We only have one more week before break. Keep giving 100% this week. If you need any help with your project, send me an email or message me on celly.

If you are missing a test, please complete this before break!

Have a Super Saturday,

Mrs. Gilliam

     

8th Grade: Introducing Relations and Functions

Did you miss Wednesday or Thursday this week? If you did, you missed a big day in our new unit. Please come see me in seminar or in the morning to get caught up.

On Wednesday and Thursday, we learned about relations and functions.

I started by asking everyone what comes to their mind when thinking of  the word,  "Relation."

The main idea that came to everyone's mind is relationships. When you think of the word relation, relationships should come to your mind.

A relation is a relationship between two variables. We will be primarily looking at the variables, x and y.

Then we discussed, the word "function." We decided the word function means something that works.

A function is a relation where each input has exactly one output. 

X-values are also known as domains, inputs, and independent variables.

Y-values are also known as ranges, outputs, and dependent variables.

Below are examples of relations, functions, and non-functions.

Graphs:

This graph is a relation and function.

This graph is a relation but not a function. The x-value, 0 has two y-values.

Tables:

This table is a relation and a function. Each x-value has only one y-value.

The first table is an example of a relation that is not a function. The x-value 4 has two y-values. The second table is a function. Each x-value has only one y-value, even though all y-values are the same. Remember we focus on the x-values.

Ordered Pairs:

All of the ordered pairs below are relations that function. 

Mapping Ordered Pairs: 

The mapping below shows a relation that is not a function.

Big Idea: Every function is a relation but not every relation is a function.

Have a Happy Snow Day,

Mrs. Gilliam

Class Dojo Point for Letting Me know the Correct Answer:

Is the following graph a function?

7th Graders and 8th Graders: Finding a Rate or Rate of Change Part 1

In 7th grade, we have been talking about different types of rates. We have discussed the meaning of unit rate and rate of change. 

Unit Rate: When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates.

Rate of Change: A ratio between a change in one variable relative to a corresponding change in another. Most often discussed with time and speed.

The reason I said both 7th and 8th graders for this post is because 8th graders will need to remember this idea for the upcoming unit. (You are not allowed to forget what you learned in 7th grade! It is a building block each year!)

We can find rate of change and unit rate in various ways. We can see it in a story, graph, table, pattern, or an equation. 

Above is a table showing temperature rising. Students may be asked the question what is the rate of change in this table and what does it mean.

First, I would start by defining the independent and dependent variables. 

Time = Independent = X 

Temperature = Dependent = Y

Next, I would look how is the table changing.... I have scratched out what I would with this problem below.

I could next say, I have a rate of change of 9 degrees every 3 hours. Some students may want to change this rate into a unit rate by saying the temperature increases 3 degrees every hour.

What are some other rates that are equivalent to the 9 degrees every 3 hours? (Classdojo point)

Next post will be finding it from a pattern, equation, and graph. 

Have a Great Sunday!

Mrs. Gilliam

7th and 8th Grade Parents: Why Retest?

A lot of parents and students ask the question "Why do we retest?"

I will start by saying, I have been on the fence with this issue but to me it all comes down to helping the students learn. In this post, I listed the reasons I believe in retesting students.

Reasons for Re-Testing

1. Some students need more time to process information. A retest allows students more time to process. It also allows students to gain further instruction on concepts they may be struggling with.

2. It allows students to learn from their mistakes. As students determine their misconceptions on test "A", synapses are firing causing information to be stored into memory.

     

Great Video on Growth Mindset (I am working on creating a growth mindset classroom.)

3. It allows students a second chance to prove to themselves that they can grow in their ability. It allows for teachers a chance to celebrate the student's successes, no matter how small.

                           

My main goal is to inspire students to get back up again when they have fallen down. 

Have a Wonderful Week,

Mrs. Gilliam

8th Graders: How to Study for Unit 2 Test

Happy Sunday Everyone,

Do not forget we are taking Unit 2 Test this week!

The best way to study for a test is to study a little each night before the test. Below I have listed some helpful tips, that can prepare you for the upcoming test.

1. Read over your notes in your notebook. Cover up the answers to the problems and rework them out.

2. Watch any of the following helpful videos. Work through each problem as the instructor works through the problem.

















3. Complete extra practice problems where you know the answer. Below I have listed some worksheets and sites you can use to practice.

Solving Equations Worksheet with Answers

Khan Academy Practice Problems: Variables on Both Sides

Khan Academy Distributive Property Practice

Word Problems Using Equations Practice Problems

Remember it is spirit week! Wear your pink tomorrow!

Have a Great Day,
Mrs. Gilliam

PS
One point on class dojo for any one that comments with the correct answer: 5(3x + 2) = 70

8th Grade: Patterns Practice

We have been looking at using patterns to write equations.

Below is the pattern we used last week. (All patterns from visualpatterns.org)

We start by thinking about what the next pattern will look like. 

Several students noticed each time it added 4 new blocks.

We then filled out the table like the one below.

You are then asked: What do you notice? What do you wonder?

On this table, you should notice you are adding 4 each stage.

You may wonder could my equation be y = n + 4

If you are wondering that, test out the equation. ALWAYS test out your equation.

Step 1:  y = 1 + 4  

             y = 5   (Correct amount of blocks for step 1)

Step 2: y = 2 + 4

            y = 6  (Not correct amount of blocks)

You should notice at step 2, this equation does not work.

Remember: We talked about the constant change being 4. Another way to think of adding 4 over and over again is to multiply by 4. 

Now I am wondering, could the equation be y = 4n. Let's test it out.

Step 1:  y = 4(1) 

             y = 4       (Not the correct amount of blocks)

Back to the drawing board.... or can we add on to this equation???

I would stop and think about how can I get the above equation to work for stage 1.

If I added a 1 to 4, that would give me the 5 I need.

y = 4n + 1   Lets, test it out............

Step 1: y = 4(1) + 1

            y = 5   (correct amount of blocks)

Step 2: y = 4(2) + 1

            y = 9 (correct amount of blocks)

Step 3: y = 4(3) + 1

            y = 13  (correct amount of blocks)

Now, we can find step 27.

Step 27: y = 4(27) + 1

              y = 109 blocks

Is this pattern proportional? How do we know? What would the graph look like?

Have a Great Night,

Mrs. Gilliam

8th Graders: Introduction to Variables on Both Sides of the Equation

On Wednesday and Thursday, we discussed the problem below:

Amber and Blake bought the same amount candy.

They both received the candy in a different way.

• Amber received 2 boxes with an unknown amount plus 4 candies in a bag.

• Blake received 1 box of an unknown amount plus 10 candies in a bag.

Write an equation and solve how many pieces of candy are in each box?

Several students started out by creating two expressions, one for Amber and one for Blake.

2x + 4       and 1x + 10

A few students decided to make an equation for each student.

C= 2x + 4              and            C= 1x + 10

C= the amount of candy in one box

We then discussed one of the most important words in the problem, SAME.

Everyone remembered, same meant an equal quantity.

We also decided if C=C then,

2x + 4 = 1x + 10

Next, we decided we needed to combine like terms but this time we had to take into account the equal sign being in between the variables.

We remembered the golden rule for equations, when crossing the equal sign we must complete the inverse operation. Below is how we finished solving it.

Finally, we discussed how do we know if this makes sense. Several students suggested plugging in 6 to each of the expressions/equations above to see if the students received the same amount of candy.

They both received 16 candies. We can say x = 6 is correct because Amber received 16 and Blake received 16 or you can say because 16=16

We will continue working on solving real world problems and equations with variables on both sides of the equal sign tomorrow. We are testing on Unit 2, next Monday and Tuesday.

Have a Great Night,

Mrs. Gilliam

GO LJHS Volleyball! Beat WJHS!

7th Graders: How to Study for the Unit 2 Test

Good Morning Parents and Students,

I have decided to start a blog for the class to help the parents that are struggling with Edline. My goal is to use this blog as a one-stop spot to get a better idea of what we are doing in class and how you can support your child. I want my classroom to be transparent as if you were sitting in the classroom with your child. If I make grammatical errors or misspell words, it is more than likely due to me rushing.

How to Study for the Unit 2 Test:

1. Review your notes from your math notebook.

2. Work extra practice problems like the ones found here (multiplying and dividing integers), and here (lots of worksheets with answers to check) On the second link, you can also click dividing fractions and decimals or any of the links on the side that is fractions and decimals.

3. Watch tutorial videos online and work through the problems with them:

Multiplying Fractions: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-fractions-decimals/cc-7th-mult-div-frac/v/multiplying-negative-and-positive-fractions

Multiplying Mixed Numbers: https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/mixed-number-mult-div-pre-alg/v/multiplying-mixed-numbers

Dividing Fractions: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-fractions-decimals/cc-7th-mult-div-frac/v/examples-of-dividing-negative-fractions

Converting Fractions to Decimals: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-fractions-decimals/cc-7th-fracs-to-decimals/v/converting-fractions-to-decimals-example

Multiplying Decimals: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6th-multiplying-decimals/v/multiplying-decimals

Dividing Decimals: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6th-div-decimals/v/dividing-decimals

Multiplying Decimal WP: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6th-multiplying-decimals/v/mulitplyling-decimals-3

Great Resource for Extra Practice: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations

Reminder: We are only looking at rational numbers (no exponents).

As you can tell I used Khan Academy for all of these. Khan Academy is a great resource to give students the ability to practice problems with a saftey net (the hints).

4. Come in for a last minute study session Monday morning at 7:30.

The students have been working really hard on this unit. If they take their time and remember the rules, they will do great on this test.


Have a Great Day,
Mrs. Gilliam