What, Letters in Math?

Working with Variables

Before Reading

I. Motivation: (Have the students do the warm-up activity on page 152.) "What did the mice say about the elephant? To answer the question, find this sum on your calculator: 3097119 + 3088015. Now turn your calculator upside down and read the words. Digits on your calculator can form letters. Punch in each digit, then turn the calculator upside down to see what letter is formed. There are letters in math!"

II. Prior Knowledge: "How many of you know of a time you have used a symbol? (I predict they will be a little lost at this time.) I bet you use symbols every day. When you went to the bathroom before lunch to wash your hands, how did you know what bathroom to go into? You knew because of the symbol of the male or female on the door. They really are not people, but they represent males and females. Let's take a couple of minutes and I will have you draw down four examples of symbols that you see almost every day, in the school or anywhere else."

This would be an example of male and female signs.

from http://www.cdc.gov

This would be an example of a rail road crossing.

from http://www.free-graphics.com

III. Purpose: "Why did we just look at these symbols and their meanings?" (I really don't expect an answer yet because we have not yet used letters or variables.) "In math, letters and symbols are used everyday to express somthing else. These are called variables. In the rail road crossing example, we do not know how many tracks are going to be in front of us, all we know is that there is going to be some kind of railroad crossing. It varies. We will read the story on the first two pages of section 5-1 for some more information on variables." This text is an expository text with an enumeritive/listing structure. It goes through steps to show why variables are needed.

During Reading

Carter, et al. (1992). Pre-algebra. Cincinnati, OH: South-Western. p. 152-155.

"Question: What did the mice say about the elephant? To answer the question, find this sum on your calculator: 3097119 + 3088015. Turn your calculator upside down and read the words. Digits on your calculator can form letters. Punch in each digit, then turn the calculator upside down to see what letter is formed." 8.3

"When evaluating a variable expression you must be told what value to use for the variable. Then substitute that value into the expression and evaluate using the correct order of operations. A variable expression will change when the value of the variable changes." 11.6

Differentiated Text: To help the not so mathematically gifted.

Flesch – Kincaid Grade Level 7.6 "When figuring out a variable sentence, the variable values must be given. The numbers should be given to be put in place of the variable. Then put the number in instead of the letter, and then solve. When the number changes for a variable, the answer should change also." This says exactly what the example says with the 11.6 reading level. When I make it more simple, it makes it so every body in class can follow along.

Readability: Using the Flesh-Kinkaid, the readability level is 9.95.

Readability is not really an efficient way to evaluate any text. It basically takes into account the size of words and length of sentences in a certain text. Also, it is only applied to select samples of the certain text. There are some redeeming qualities about readibility, because obviously a piece of text that is written for a first grader will not score higher than second or third grade and text that is written for high school won't score down in the third grade level. The level is normally pretty accurate, it is just not exactly what is to be expected. The fact is that readability is not that good, but this piece of text gets a 9.95 Flesch-Kinkaid readability level, which is about what is expected since this text is designed for grades 8 or 9, and is also towards the middle and end of the text.

IV. Text Structure: Expository, enumerative/listing

• list of connected information
• outlining series of steps

V. Vocabulary:

• Variable: a letter that represents a number or numbers.
• Substitute: to put in place of.
• Evaluate: to find the value.

VI. Strategy Instructions: Structured Notes: "We are going to use structured notes again today. Remember, this will be a very good source to go back to and use as a study guide for the next test, as long as it is done correctly. This will be your writing to learn activity."

Steps:

1. Prepare Paper: Fold the left side of the notebook paper over the pink line. Trace a line where the end of the left side of the paper is.

2. Record: Write the math problem on the big side of the paper. On the left side, write the reason each step was made.

3. Questions: Formulate questions from the text or notes. Place the notes in the left column.

4. Recite: With the left hand side covered:

Look at the steps the problem taken for the problem.

Tell what was done.

Tell why it was done.

5. Reflect: Ask "Did all of those steps make sense? How were they applied?"

6. Review: Spend some time every week reviewing these notes.

7. Summarize: Summarize the main ideas.

Pramann, Nicole. "Structured Notes" (February 2006)

Model:

"I am going to model an example just in case you students have forgetten how to write structured notes."

Click here to view the example.

Guided Practice:

"I will now walk around the room while everyone goes through examples 2 and 3 on page 154. If you have any questions, please raise your hand and I will come to rescue you." Have the students do the examples 2 and 3 on page 154. I will go around and make sure they are doing it correctly.

Click here to view the example.

VII. Content: "Now I will have you do problems 8 and 13 on page 155. Be sure to use our structured notes strategy so you can use these next week to study for our test in two Fridays from now." The examples should look similarly to this model.

After Reading

VIII. Questioning:

"Remember doing our QAR questions class? We are going to do a couple more to finish up this amazing lesson."

"What does a variable expression mean?" The answer is a phrase that uses a variable. For example, 7(x + 5). This answer is a think and search because it never really says what a variable expression is, it only says what a variable is.

"What are some signals that you have heard that can be thought of that are variables? For example, many ding ding dings by a train crossing stands for 'LOOK OUT, A TRAIN IS COMING.' " This would be a on your own because the students have to think of some time that they have seen or heard something that represents something else. An example would be a storm siren, a train horn, or an alarm for a school or job. They all sound similar, however they represent different things.

"When will the value of a variable expression change?" This is a right there question because the answer is right there on page 153. The answer is when value of the variable changes.

IX. Writing to Learn Activity: The writing activity was up in the reading strategy. They basically re-wrote the whole section worth of examples into their structured notes, but in a form so they would be able to use them to study.

X. Closure: "Your assignment for Wednesday will be 1- 23 on pages 154 and 155. You have already done two of them. I want numbers 15, 16, and 17 done with structured notes. I will collect everyone's structured notes on Friday to make sure everyone has done them." I will explain each section of the homework, emphasizing the problems that will use the vocab words such as evaluate and substitute. I will then give them their assignment. "For extra credit, if you can make a riddle like the elephant and mouse example, you will be rewarded with a bite size snickers bar, unless you don't like peanuts or chocolate, then you are going to get a cracker or something I have laying around. Have a good day."