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1.9 – Chapter Review

Since the answers are in the back of the book for the review exercises, and knowing full well that kids are copying the answers from the back of the book with no attempt at them whatsoever, I made two worksheets to replace the problems in the book. I’m even thinking about using the book’s review as test problems.

On the first day I’ll give them the review for sections 1.1 to 1.4 and then collect them and grade them. I’ll return them the following day and collect them the next day. The students worked quite well on this assignment, but many did not finish in time. Because I had to be gone the next day, I prepared the answers in advance for the students to have.

On the second day I’ll give them the review for sections 1.6 and 1.7. I will go over these problems at the end of the day so that they have them to study from.

1.9 Chapter Review (Part 1)

1.9 Chapter Review (Part 2)

Chapter Objectives (those crossed out I did not focus on):

• 1.1 Bar Graphs and Dot Plots
  • Create a pictograph, bar graph, and dot plot of a data set
  • Calculate the minimum, maximum, and range of a data set
  • Interpret pictographs, bar graphs, and dot plots
  • Decide the appropriateness of bar graphs and dot plots for a given data set
• 1.2 Summarizing Data with Measures of Center
  • Calculate the mean, median, and mode of a data set, noting outliers
  • Enter data into calculator lists
  • Given a list of data, use a calculator to find the mean and the median
  • Compare and interpret the three measures of center
  • Explain the effects of outliers on the mean and the median
• 1.3 Five-Number Summaries and Box Plots
  • Calculate quartiles, interquartile range, and a five-number summary of a data set
  • Interpret box plots
  • Decide the appropriateness of a box plot for a given data set (the book only suggests that the wanting of each data value would make a box plot inappropriate)
  • Formally define outliers
• 1.4 Histograms and Stem-and-Leaf Plots
  • Create a histogram and a stem-and-leaf plot of a data set
  • Given a list of data, use a calculator to graph a histogram
  • Interpret histograms and stem-and-leaf plots
  • Decide the appropriateness of a histogram and a stem-and-leaf plot for a given data set
• 1.6 Two-Variable Data
  • On the coordinate plane, plot points with given coordinates, and determine the coordinates of plotted points.
  • Represent a two-variable data set with a scatter plot
  • Given a pair of calculator lists, plot points whose coordinates are in those lists
  • Interpret scatter plots
  • Learn and use vocabulary related to coordinates and graphs
• 1.7 Estimating
  • Use a scatter plot to compare estimates with actual values
  • Graph the equation y = , the linear parent function
  • Judge the overall accuracy of a set of estimates from a scatter plot and the graph of y = x.
  • Develop the graphing practices of scaling and plotting carefully and labeling the graph and axes.

1.8 – Using Matrices to Organize and Combine Data

We skipped this section because it isn’t part of the MN math standards.

1.7 – Estimating

Day 1:

Instead of doing the “Guesstimating” investigation in the book, I tried having the kids estimate ages of celebrities. Having twenty of them was a bit too much, although the kids did enjoy the exercise. I only did this in one class. For the last two classes, I did something else that didn’t take as long.

1.7 – Estimating Classwork (Celebrities)

Because it took so long, I had the students guess how many steps it would take, starting at the classroom door, to get to (with my steps):

1. the next classroom (5)
2. the front door of the school (47)
3. the cafeteria (72)
4. the commons area (179)
5. the media center (292)

In a previous class, I had the kids do this themselves. Because there are only five points, it does not take a long time to make a scatter plot (the downfall of the celebrities idea) and there is relatively much more time spent on analyzing y=x, over-estimates, and under-estimates.

I only assigned questions 2 and 3 which had to do with overestimating or underestimating.

In class, I put the estimate on the horizontal and the actual on the vertical. This seems logical to me, but the book has it the other way, so I’ll have to make sure that I’m following the textbook’s lead next time.

1.6 – Two Variable Data

Vocabulary:

• variable
• one-variable data
• two-variable data
• scatter plots
• coordinate plane
• origin
• quadrants
• coordinates
• ordered pair
• abscissa
• ordinate

Day 1:

After the quiz, I talked about the difference between one- and two-variable data. I put a dot plot up on the board that showed the number of televisions in different homes. I asked the students what the dots represented and then labeled each dot with a name – Abe, Bertha, Carlos, etc. Then I asked the students how many things do we know about each of these people (one). I then called this “one-variable statistics”.

I then talked about two variable statistics. What if we knew two things about each person – how could we show with one dot both pieces of information? Then I made a scatter plot.

Next, I gave them a list of the ages of husbands and wives at the time of marriage and we worked on graphing them on a two-dimensional plane. We worked on scaling and labeling. I made sure that they understood that each dot did not represent a person this time, but a couple. I called this “two-variable statistics”.

1.6 – Notes on Scatterplots

Day 2:

I continued working on the previous day’s work with the couple’s data. I talked about why we graph two variables at once – to see if there is a relationship between the data. I brought up positive, negative, and no relationship. I used Fathom files GrowingKids and BirthrateGNP.
Finally we did an exercise with positive and negative coordinates. (Second side of the previous day’s worksheet). I defined quadrants now, and made sure to ask the students what quadrant we were working on with the couples data.

I then assigned problems 1, 2, 4, and 9 – 11.

1.5 – Exploring a Conjecture

I am assigning this for extra credit and want their “research” on a poster.

1.4R – Review

In order to prepare the students for a quiz on sections 1.1 to 1.4, I had the students work on a review sheet during class. I did go over section 1.4 at the beginning of class as well.

The students have a very difficult time finding the median and quartiles when given a dot-plot. Some students cannot understand the dot-plot itself – they don’t see each dot as a person and the scale at the bottom as the number of keys. Also, the “at least” and “less than” still gets some kids.

1.4 – Review Worksheet

1.4 – Quiz (two forms)

1.4 – Quiz (makeup)

1.4 – Histograms and Stem-and-Leaf Plots

Vocab:

• histogram
• bins
• frequency

Investigation – Hand Spans

The math teacher that usually has the rulers was gone and I couldn’t locate them, so I had the kids find their heights in centimeters using a few meter sticks as they walked in the room. It doesn’t take long, to get the data, but I decided to make the histogram myself on the board because it takes too much time for some kids to create one. This way, I could do three histograms on the board. One with a proper scale and bin size, and two others with bin sizes that are too big or too small.

I then took the same data and made a stem-and-leaf plot under the document camera so that I could turn it 90 degrees and show that it is really equivalent to a histogram (for discrete data). We compared the histograms to the stem-and-leaf plots and talked about when one is preferable to the other.

In the afternoon, I did the histograms on the computer using Fathom. First I showed them a dot plot and a box plot for a quick review and then did the histogram. The only drawback is that I forgot to mention that “0-5″ means all numbers on the interval [0,5). But it is easy to change the bin widths and bring up why too many or too few bins makes for a bad histogram. They looked something like this. The horizontal histogram was created to show the students how it looks identical to the stem-and-leaf plot.

I then let them work on the section numbers 1, 2, 5, 7, 10, and 11.

1.3 – Five Number Summaries and Box Plots

First day:

I spent about 15 minutes going over homework from 1.2, then gave a quiz on sections 1.1 and 1.2, so I had about 15 minutes for the 1.3 lesson. I only went over the five-number summary using the very top of the worksheet here. I assigned questions 1 and 2 for homework since they did not include box plots.

I’ve found that circling the median (and min and max) makes finding quartile one and three more difficult. It is easier to draw a vertical line through or between two numbers. When circling the minimum (or max) some students don’t use those numbers to find Q1. And when circling two numbers for the median, the students don’t use them to calculate Q1.

1.3 – Five Number Summaries and Box Plots Notes

Second Day:

I passed out the quizzes from the previous day but because the grades were quite high, I did not spend time going over them. I did put a dot plot and a box and whisker plot of the grades up on the screen for the students to see.

I then went over questions 1 and 2 from the previous night’s homework.

Next, I almost finished doing the rest of the notes worksheet that I had passed out the day earlier. I spent a great deal of time explaining:

• where “quartiles” come from, showing them visually that the list of numbers is being cut into four equal sections.
• that each of the four sections of the box and whisker plot represent a quarter of the data in the list, and that “compact” parts mean that the data has little variance
• that it is easy to compare two different populations when using stacked box plots
• the IQR is like the range. The range is the difference between the max and min, the IQR is the difference between the first and third quartiles. I made note of this using brackets on my five-number summaries.
• the IQR shows up on the box-plot and the width of the box

I did not finish the last part – taking Michael Jordan out of the list of players and redoing the box plot for the 97 Bulls so I left that to them to do for homework.

Third Day:

They worked on numbers 3 – 5, 8, 10, and 11

Question 8 has the students make two box plots using the same scale but many accidentally draw two separate scales. When going over this homework, I will demonstrate why it is difficult to compare two populations using different scales using the following. It is downloadable as well, although Fathom files cannot be uploaded on WordPress :-(

1.3 Question 8 Printable pdf File

1.2 – Summarizing Data with Measures of Center

Vocab:

• measures of center (measure of central tendancy)
• mean
• median
• mode
• outliers

The penny investigation takes too much time, particularly the dot plot. There is a dot plot in the teacher materials that might help move things along. Also, since many students do not have graphing calculators at this point, step 7, which has them find the mean takes much too long. I focused on the median and the mode, using the worksheet that is attached. I did not assign homework after the lesson. On the second day, we did 1 – 3, 5, 7, 10, 11.

The penny data dot plot from this section is to be used again in section 1.3. However, I had given up on the penny data and wrote my own problem for section 1.3 that didn’t include their penny dot plot.

1.2 – Median and Mode Lesson

1.2 – Quiz

1.1 – Bar Graphs and Dot Plots

Definitions:

• pictograph
• data
• bar graph
• category
• dot plot
• spreads
• minimum
• maximum
• intervals
• range
• statistics

The investigation was good, although the dot plot took more time than I thought it would. There is a sample dot plot in the teaching materials that could be used instead. Some students had difficulty finding their pulse, although I found it helpful to tell them to find it and then keep their hands there until I said “Start” when it was time to begin counting.

The students had difficulty with question 5c which had them tell what would happen if we didn’t take our pulse rates for 15 seconds but instead took them for 60 seconds. More time talking about this is needed when having them multiply their number of pulses by four so that it is more understandable. Perhaps it would be beneficial to have half of the class count pulses for 15 seconds and the other half for a whole minute so that the differences show up on the dot plots.

The investigation took so long that I only gave questions 1 – 4 for homework on the first day. The second day we did 5, 6, 9, 10, 11 once we finished going over the homework. I also gave the students a practice quiz for section 1.1.

Algebra 01-1 Quiz

Pictographs (shown below) (Right click – “View Image” to see them in all their glory)