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