What's Collinear Mean?

We determined the word collinear has to do with lines and linear functions. More precisely, the word collinear was used today to describe points that fall on the same line. If points are collinear, then the slope of the segment connecting any two of the points will be a constant. We spent some time in class today working with sets of 3 points. We found the slope between groups of 2 of the points, and compared results to determine if the points were collinear.

Tonight's Homework: Big Book page 330 (1 - 7, all, but not #5). Enjoy the long weekend, but be sure to start preparing for concept tests 7 and 8, which will be given next week. (CT 7 on Wednesday, and CT 8 on Friday)

Reviewing Linear Functions

We played a game using groups of 4 to review key concepts that we've covered over the last 3 weeks in algebra. Students especially liked the blue preprinted grids that I distributed to the groups for use during the activity.

Tonight's Homework: Be sure to have the practice test for Concept Test 8 done and ready to review in class on Thursday. The test will be given on Friday, February 4th. In addition, if you didn't complete last night's homework, please do so tonight.

Direct Variation and Inverse Functions

We looked at two special kinds of functions today. The first type was the direct variation, which can be written as y = mx or y = kx. Students recognized these equations as special forms of the slope-intercept equation, where b = 0. These lines can have positive or negative correlation, and always pass through the origin.

The second special function in the inverse function. The equation takes the form xy = k, where k is a constant. The graph for these types of equations is not a line, but a pair of interesting curves that never really touch or cross the x and y axes. The word "asymptote" was introduced to students.

Tonight's Homework: Big Book p. 281-283 (1 - 4 and 10 - 18)

Standard vs. Slope-Intercept Forms of Linear Equations

Students reviewed the two basic forms for linear equations. The standard form of an equation is useful when trying to set up story problems or looking for the x and y-intercepts of a line. Slope-intercept form allows you to plot a point (the y-intercept) and then use the slope to draw the line. Students were given about 30 minutes to get started on their homework and/or check in with me about missing work and tests.

Tonight's Homework: Complete the practice test for Concept 7, and do both sides of the Linear Equation Worksheet that you started in class.

Equations of Perpendicular Lines

Today, we talked about perpendicular lines. We noted that the lines have to have opposite slopes (one line has a positive slope, while the other has a negative slope). We aksi noted that the products of the two slopes must be -1. Using the same process as we did to find equations of parallel lines, we did several examples in class, making sure everyone was able to complete each of the different steps of the process (identify the new slope, plug in the point of intersection, solve for b, and then write the new equation with the newly found values).

Tonight's Homework: Continue working on the practice test for Concept 7. It is due on Tuesday. Do all problems on both sides of the purple "Clicker Quiz" worksheet. In the home book, do page 203 (19 - 39, odd and 40).

Writing Equations for Parallel Lines

Today, we talked about parallel lines. We noted that parallel lines never cross, meaning that they each have the same slope. @e did several examples in class, making sure everyone was able to complete each of the different steps of the process (identify the new slope, plug in the point that's on the new line, solve for b, and then write the new equation with the newly found values).

Tonight's Homework: Work on the practice test for Concept 7. It is due on Tuesday. In the home book, do page 203 (1 - 18, all).

Reviewing the Slope-Intercept Form of an Equation

Today's classes were shortened so students could attend a special assembly in the afternoon. We reviewed this week's work, and then went over the directions for tonight's homework.

Tonight's Homework: Complete the word search and graphing worksheets. (Be sure to do the back side of the white worksheet!)

Analyzing the Slope-Intercept Equation, Part 2

Students used the handheld computers again today to look at how changing the "b" value of the slope-intercept formula alters the position of a line on the coordinate grid.

Tonight's Homework: Complete the summary for today's in-class assignment, if you did not do so in class today. Read pages 161-164 in the Home Book. Do pages 165-166(1=9 and 22-26). Neither of these assignments will be accepted late.

Analyzing the Slope-Intercept Equation, Part 1

Students used the handheld computers today to look at how changing the "m" value of the slope-intercept formula alters the position of a line on the coordinate grid.

Tonight's Homework: Read pages 174-176 in the Home Book. Do page 177(3-48, only the problems divisible by 3). This assignment will not be accepted late.

Notes: No resource tomorrow. If you missed class today, please plan to stay after school on Thursday or come in during lunch time to complete the palm activity.

Championship Game Day

Today, we looked at the two forms of a line: standard form and slope-intercept form. We looked at how each line can help us quickly graph a line. Briefly, here are the main points of our discussion:

Standard Form of the Equation: Use this to determine the x- and y-intercepts of the line. Graph these two points and you have the line.

Slope-Intercept Form of the Equation: Plot the y-intercept. Then, using the slope, find one or two more points that will be on the line by going up and over. Draw the line.

Tonight's Homework: None, since most of you will be watching the BCS Championship ball game tonight. Go Ducks! More importantly, let's hope it's a close, injury-free game!

Standard Form of an Equation

We've done a lot of work with equations of lines this week, and all have followed the form of y=mx + b, which is called the slope-intercept form of a linear equation. Today we talked about how to write an equation in standard form. Equations written in standard form look like this: Ax + By = C, where A is a whole number (positive, no decimal or fraction), and B and C are integers.

Tonight's Homework: Complete the three problems you received in class today. Be sure to answer all parts of each question.

Putting Everything Together

Today we took some time to put things together. We've looked at data that shows a positive correlation (stacking cups) and data that shows a negative correlation (drinking from a glass and eating a red vine). We've determined intercept values and discussed why these types of data are discrete rather than continuous. We've looked at why the data only spans Quadrant 1, and can now draw lines of best fit. We've seen that the patterns of change (rate of change) relate to the slope of the line.

We took some time today to write equations to describe the patterns for stacking cups and drinking a liquid. Because student data is somewhat individualized, students came up with different, but similar types of equations. We compared these, and then wrote about our findings.

Tonight's Homework: Complete anything you did not get done in class. (Most students left with very little homework for tonight.)

Really? She Told Me to Drink My Homework!

We tested our cup stacking predictions by actually measuring the height of stacks of 15 cups of various types. Many students found their predictions to be fairly close to the actual results, while others were pretty far off. We talked about what on the cup was causing the stack height to change (lip or taped part) and what was constant (the "excess" or body). We talked about the formula for how to predict the stack height, regardless of how many cups were in the stack.


Tonight's Homework: There are two parts to tonight's assignment. First, determine the formula for the stack height of each of the different types of cups we measured in class. Be sure to include both the lip and the "excess" numbers in your formula. (Most students finished this in class today.)

Part Two will be done at home. Using a cylindrical glass, fill it with your favorite beverage. Measure the height of the liquid, and then take a drink. Measure the height of the remaining liquid. Repeat this procedure until all of the liquid is gone. Create a well-labeled data table. Graph the data. Include the line of best fit for each cup. Determine the rate of change for each of the different types of cups. Summarize your results. Discuss things like:
•what are the y and x intercepts, and what do they represent:
•is this data continuous or discrete? How should it be shown on the graph (solid or dotted line)? Why?
•What is the rate of change for each type of cup?
•What is the formula that describes the height of the liquid based on the number of sips taken.

Happy New Year!

Students returned to class today, after a long holiday break. We'll have 4 day weeks for the entire month of January, due to holidays, furlough days and midterm grading.

Today, students spent time gathering data about the height of stacks of cups. We used 6 different types of cups during class, and students determined the height of stacks from 1 to 8 cups tall. Data from different groups was shared. This information will be used to complete tonight's homework.

Tonight's Homework: Graph the data you collected in class today. Include the line of best fit for each cup. Determine the rate of change for each of the different types of cups. Predict how tall a stack of 15 cups would be, using the data you've collected. Summarize your results. Discuss things like:
•what are the y and x intercepts, and what do they represent?
•is this data continuous or discrete? How should it be shown on the graph (solid or dotted line)? Why?
•What is the rate of change for each type of cup?