Happy Holidays!!

Today's classes were shortened for a holiday music assembly. We spent most of the class period reviewing the Barbie Bungee Jumping questions that were turned in on Thursday.

Tonight's Homework: None. Enjoy the break from school, and be sure to do something nice for others over the vacation. If you travel, be sure to do so safely, so I'll see you in class on January 8th. Remember, there is an extra credit report due on January 10th, should you find yourself bored over the vacation.

Quiz Taken in Class Today

Well, sometimes the best plans in the world have to be changed, and that’s what happened today. Disruptions to today’s class caused me to change today’s chapter test to a quiz, as class time was shortened. We will take a combined chapter 4 and 5 test in mid-January.

Tonight’s Homework: None! I guess we’re starting our vacation a little early!

Allie and Rachel: This quiz is over the things you'd expect. Be sure to contact me when you get back into town if you want to take it before school resumes.

Analyzing Bungee Jumping Data

We went over key ideas that will be covered on tomorrow's test. These include:
•Writing equations in standard form (Ax + By = C)
•Writing equations in slope-intercept form (y = mx + b)
•Determining the slope of a line from its equation (m)
•Determining the y-intercept of a line from its equation (0, b)
•Determining the x intercept of a line from its equation (x, 0)
•Writing the equation of a line given the slope and a point
•Writing an equation parallel to a given equation (same slope)
•Writing an equation perpendicular to a given equation (negative reciprocal of the given slope)

The test will be given over two days, so you won't feel the pressure as much. Be sure to study.

Tonight's Homework: Finish the yellow worksheet (both sides) for tomorrow. Be sure to include complete answers to the Barbie Bungee Jumping activity.

Barbie Bungee Jumping ala Rubber Bands

After reviewing last night's homework, students spent the bulk of the class period collecting data for the bungee jumping event. The sixth grade locker area was where we staged this event, and students were climbing on top of the lockers to get high enough to allow the Barbies to dive with longer bungee cords. All in all, this was a very fun class period for all!

Tonight's Homework: Page 267 ( 9 - 34, all). Be reminded that the test over chapters 4 and part of 5 will be given on Thursday, December 20th. Start studying now!

Equations for Parallel Lines and Perpendicular Lines

Parallel lines have the same slope, but different y-intercepts (see page 242). Perpendicular lines are lines whose slopes are the negative reciprocals of each other, like -3 and 1/3. (See the challenge problem on page 246.)

Tonight's Homework: Page 246 ( 74 - 77 ) and Page 291 ( only 7 ).

Direct Variations

Now that we understand that slope is a way to report the rate of change, I have chosen to return to the section that deals with direct variation. Direct variation means that the rate of change is constant. (As x changes, so does y.) The point of this lesson is that direct variation gives you the slope of a line that passes through the origin.

Tonight's Homework: Lesson 4.5 ( 15 - 31 and 44 - 63 )

P.S. Maddy, thanks for the packet of work. It was a nice surprise!

Linear Equations a la Spreadsheet

Students received quiz results today. Many did well, although carelessness resulted in lost points, especially surrounding how to report the value of the y-intercept. We spent time using the handhelds to determine the slopes, y-intercepts and equations of lines when given different information.

Tonight's Homework: Lesson 5.3 ( 66 - 76 and 1-13, but not #7). Also, complete the front side of worksheet 5 for class tomorrow.

Note: You are welcome to come in early on Thursday to use the handhelds or to get extra help. Just knock on the window anytime after 7:45 a.m.

Writing Linear Equations When Given Just Two Points

Well, today's plan had to be altered a bit because all of you took more time on the quiz than I had expected (which is, of course, a GREAT thing!). Soooo, instead of working with the handhelds, we will practice writing equations for lines when given just two points on the line. To do this, find the slope, and then plug in the x and y values of one of the points into the equation with the slope to determine the y intercept. Once you have this, you will be able to plug in the values of m and b into the slope-intercept equation. ¡Voila!

Tonight's Homework: Lesson 5.3 ( 21 - 43 odd). Be sure to show your work.

Determining the Equation of a Line from a Point and the Slope

Students reviewed the method of determining the slope of a line when given two points on the line. Next, we talked about how we can determine the equation of a line when given both the slope and one of the points on the line. Students practiced this technique, and then got started on tonight's homework. Hopes for using the handhelds were dashed--perhaps tomorrow we'll be able to use them.

Tonight's Homework: Lesson 5.1 (12 - 29 all) and just the spreadsheet formula for the intercept for Graphing Worksheet 5.

P.S. Hi, Maddy! You are missed . . . a lot!!! Take care of yourself.

Determining Intercepts and Slope

Today's lesson combines major points from lessons 4.3 and 4.4. Recall that you need only 2 points to graph a line. Knowing the x and y intercepts can make this an easy task. If the equation is in standard form ( ax + by = c ), then you can replace the x with a 0 to find the y intercept. Similarly, replacing y with a zero and solving the equation for x will give you the x intercept. If you know the coordinates of two points on a particular line, you can determine the slope of that line by using the formula m = ( y2 - y1 )/( x2 - x1 ). See lesson 4.4 for more information about the format of this formula, as it is hard to type it correctly on this blog.

Tonight's Homework: Lesson 4.3 ( 17 - 32, FCO and 35 - 40 ) and Lesson 4.4 ( calculate the slope for 20 - 34, even ). You don't have to graph the problems for lesson 4.4.

Visualizing Positive and Negative Slopes with . . . Licorice and Cups!

We revisited our data from the "Stacking Cups" activity we started earlier in the week, and recognized patterns in each of the sets of data. Students then realized that deriving the formula for the nth term is relatively simple.

We collected more data from ingesting a piece of licorice, one bite at a time. Hopefully, students will be able to write a formula to describe the rate of change related to eating the licorice.

Tonight's Homework: Page 239 ( 44 - 63 all )

Using the Slope-Intercept Form of an Equation to Graph Lines

My hope for today's lesson is to introduce students to a quick way to graph lines from equations that are written in slope-intercept form. Of course, students must be able to manipulate formulae so they are written in this form before they can graph!

Tonight's Homework: Lesson 4.6 ( 13 - 21, 22 - 43, FCO and 78 - 89 FCO ).

Stacking Cups and Measuring Them

To help students get a better understanding of how linear equations relate to common day items, we stacked a variety of cups and looked for patterns in the data we collected. The data was turned into a line graph, and students were challenged to come up with a formula to describe the relationship.

Tonight's Homework: Worksheet 3 from the Palm unit and the Stacking Cups worksheet.