Thursday, September 18, 2008

Math: Solving and graphing inequalities

You solve an inequality as if it were an equation!

For example, 2y + 5 < 13
- 5 -5
Subtract 5 from both sides, and you are left with:
2y < 8
Divide both sides by 2, and you are left with:
y < 4

Now since you still don’t have a definite answer, y could equal lots things, right? You show that by putting the answer on a number line.

What you add today is circle the number on the number line, and decide to fill it in or leave it open. Filled in means it can equal that number, open means it can’t, and you find that out from the inequality sign.

For example, y < 4 looks like <---------------------->

The left side is darker because of “less than” and the dot above the 4 is open because your value cannot equal 4.

If you had less than or equal to, you would have had to close the circle because y could be 4.

Reading: Questioning

We should get in the hang of asking questions when we read. We ask questions all the time. For example, almost everyday one of you asks me for permission to use the bathroom, and almost everyday, you ask your parent or guardian for something. Basically, you are already great at asking questions!

When we read, it helps us to be active readers when we ask meaningful questions about what we read. We should question character motivation, character actions, and character decision-making. Not only should we focus our question on the characters or on events in the characters' lives, but we should also begin thinking about the author.

Yes, the author made specific decisions about his characters, and we should think as much about the author's decision-making as we do about a character's decision-making. For example, we need to begin asking questions about author's purpose and author's craft. It would be helpful trying to understand why an author decides to use a specific point of view or why he uses specific language or words. Knowing this information might help us understand the book even better.

Reading: Visualizing

Active readers visualize what they read. Of course, it is easier to visualize books that have colorful and descriptive language than it is to measure a mathematics text book.

When we visualize what we read, we create images in our head based on what we are reading and based on our prior knowledge. Visualizing is like making a movie in our head of what we read.

Visualizing helps us to be engaged in what we are reading so that we better connect to what we read and so that we remember what we read.

Tuesday, September 16, 2008

Math: Translating Inequalities


Inequality: A mathematical sentence that compares the values of two expressions using an inequality symbol.-Solution of an inequality: Any value or values of a variable in the inequality that makses an inequality true.

Solution of an inequality: Any value or values of a variable in the inequality that makes an inequality true.

For example, if I had x > 3, I know that any number that is bigger than 3 will make my inequality true. 3.1, 4, 100, and 200 are all possible solutions of an inequality because if I plug them in for x, my inequality will be true.


There are four inequality symbols:

< = less than
> = greater than
≥ = greater than or equal to
≤ = less than or equal to

When we are translating inequalities, we think back to what we know already about translating verbal expressions into algebraic expressions.

We have to pay attention to key words. Here are some to remind you:

Increase = +(plus)
Decrease = - (minus)
Is = = (equals)
Sum +
Difference -
Product x
Quotient (divide)
More than +
Less than -
Twice (multiply by two)

When we are solving inequalties, there are key words that help us know what to do and what sign to use when we see them:

< = less than
> = greater than, more than
≥ = greater than or equal to, more than or equal to, no less than, at least
≤ = less than or equal to, no more than, at most

Let's try it:

Two times a number is less than eight.

We know that two times a number = 2x

Then, we are told that 2x is less than eight.

We plug in the less than sign, <, and then we have 2x <

Now, we have to put in the eight and then we are left with: 2x < 8.

Reading/Writing: Author's Purpose

All writers have a purpose. While writers are motivated to write for different reasons, they often have a specific purpose for their writing.

The three purposes are:
- to entertain
- to persuade
- to inform

Today, in class, we read two pieces. We read a news article from NY Times about cheerleading injuries, and we read another short story from Sandra Cisneros.

The NY Times article was written to INFORM readers about the risks of cheerleading, especially for girls. The short story was written in a different way; it had more colorful language and evoked specific sentiments. The author wrote the piece to ENTERTAIN her readers, and she engaged our senses by painting a picture with her writing.

When writers write to persuade readers, they often present information to their readers to try to convince their readers to believe what they want their readers to believe. In that light, they try to present that information in an entertaining way. For example, advertisements are often considered writing pieces that try to persuade readers to buy a specific product.

For example, if you were running for a position like president, how will you try to campaign?
You would probably present information to your readers/voters about how wonderful you are, and you will use that information to show how amazing of a leader you’ll be. In other words, you are using the information to persuade others to vote for you.

Monday, September 15, 2008

Word Wall Words #1

Irate (adj)
Amiable (adj)
Peculiar (adj)
Preserve (verb)
Pursue (verb)

Reading: Making Connections to Text

It is important to make connections to the text that we read because it helps us be more engaged in our reading. Better readers are active readers, and it is important for us to get used to being active readers that connect to the the text we read.

When we relate to the text, the text seems more interesting because there is something about a situation or a character that reminds us of something in our own lives.

It ia also easier to remember what you read when you make connections to the text because you could think of your life and the character’s life and would be able to recall details easily.

Basically, reasons why connecting to text helps readers:

--It helps readers understand how characters feel and the motivation behind their actions.
--It helps readers have a clearer picture in their head as they read thus making the reader more engaged.
--It keeps the reader from becoming bored while reading.
--It sets a purpose for reading and keeps the reader focused.
--Readers can see how other readers connected to the reading.
--It forces readers to become actively involved.
--It helps readers remember what they have read and ask questions about the text.

There are three ways that we connect to text:

Text-to-self connections are highly personal connections that a reader makes between a piece of reading material and the reader’s own experiences or life. An example of a text-to-self connection might be, "This story reminds me of a vacation we took to my grandfather’s farm."

Text-to-world connections are the larger connections that a reader brings to a reading situation. We all have ideas about how the world works that goes far beyond our own personal experiences. We learn about things through television, movies, magazines, and newspapers.

Sometimes when reading, readers are reminded of other things that they have read, other books by the same author, stories from a similar genre, or perhaps on the same topic. These types of connections are text-to-text connections. Readers gain insight during reading by thinking about how the information they are reading connects to other familiar text. “This character has the same problem that I read about in a story last year,” would be an example of a text-to-text connection.