** **Here are some layered assessments I have been working on. I offer students a chance to meet with me every day before school to get help on these assignments if needed. I will say the results on the summative after the first set of LAs was the best I have ever had! For the first time EVER….I do not have to re-teach drawing cumulative frequency graphs and using the graph to find percentiles. I don’t know if it has to do with the LAs or the fact that I had extra time in class to do more hands on class work with them.

**Measurement Topic 1.1: Displaying Distributions with Graphs **

__Level C: Part 1 – 65 points__

Assignment 1.1a/Pg. 7: 1.1-1.4, Pg.11: 1.5,1.6 (10 points)

Assignment 1.1b/Pg. 16:1.7-1.11 (10 points)

Assignment 1.1c/Pg. 22:1.12-1.15 (10 points)

Assignment 1.1d/Pg. 26:1.16-1.18 (5 points)

Assignment 1.1e/Pg. 31:1.19,1.20 and Pg.33:1.21 (5 points)

Go to __https://oli.web.cmu.edu/jcourse/workbook/activity/page?context=5cb56db080020ca601f3240001a6dc8b__ and answer all questions correctly. Turn in a snapshot of your results. (5 points)

Go to __http://www.datavis.ca/gallery/goosed-up.php__ and describe the mistakes shown on 4 of these “bad graphs.” (10 points)

Go to __http://www.stat.sc.edu/~west/javahtml/Histogram.html__ and describe how changing the bin widths effects the histogram. Then explain which bin width you think provides the best graph. (10 points)

First go to __https://oli.web.cmu.edu/jcourse/workbook/activity/page?context=5cb56ccd80020ca601a572a74272d974&view=frameset__ and work through the lesson. Then go to __https://oli.web.cmu.edu/jcourse/workbook/activity/page?context=5cb56cec80020ca600a4e897e0c2782d__ and use your calculator to examine the ages of Oscar Winners. Then answer the question, click on “submit and compare” and turn in a snap shot of your results. (10 points)

Go to : __http://app.gen.umn.edu/faculty_staff/delmas/gc_1454_course/distribution_files/distribution.html__ and examine the 15 examples of different shaped histograms. Then describe the differences of the 5 shapes. (10 points)

Go to __http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07-825200-8&chapter=12&lesson=1&&headerFile=4&state=na__ and take the self check quiz until you get 100%. Turn in a snapshot of your results. (5 points)

__Level B: Part 2 – 15 points__

Find an example of a “bad graph” from a newspaper, textbook or magazine. Describe the errors you see in your example and explain how to make your graph a “good example.” Submit your example and explanation. (15 points)

Use real world data and create an example of a bad graph. Describe the errors in your bad graph. Then re-draw the graph and make it a good example. Submit your bad and good example, explanation, along with your data and cited source. (15 points)

__Level A: Part 3 – 20 points__

Special Problem 1.1 – Find or collect a set of quantitative data. Next, draw (by hand) 2 appropriate graphical representations of your data. Then discuss the features of each graph. Explain which one of your graphs is more appropriate than the other. You must attach your raw data sheet to your work with source cited. (20 points)

Peanut Butter Article – You will write and turn in a newspaper article about peanut butter. Click on the link for more information. (20 points)

**Measurement Topic 1.2: Describing Distributions with Numbers**

__Level C: Part 1 – 65 points__

Assignment 1.2a/ Pg. 40: 1.31-1.35 (10 points)

Assignment 1.2b/Pg. 47: 1.36-1.39 (5 points)

Assignment 1.2c/Pg.52: 1.40-1.43 (10 points)

Assignment 1.2d/Pg.56: 1.44-1.46 (5 points)

Assignment 1.2e/Pg.59: 1.47-1.50 (10 points)

TI Boxplots and Histogram Worksheet. If you don’t want to store data in list WKND, you can use L_{1} instead. (10 points)

TI Yankees vs. Mets Worksheet. If you don’t want to store data in YSALS and MSALS, you can use L_{1 }and L_{2}. (10 points)

Go to __https://oli.web.cmu.edu/jcourse/workbook/activity/page?context=5cb56ccd80020ca601a572a74272d974&view=frameset__ complete the lesson and both “Learn by Doing” worksheets. Turn in a copy of both worksheets. (10 points)

Go to __http://www.onlinemathlearning.com/mean-worksheets.html__ complete the online worksheet with 100% accuracy. Turn in a printed copy of your results. (5 points)

Go to __http://www.onlinemathlearning.com/mean-worksheets-2.html__ complete the online worksheet with 100% accuracy. Turn in a printed copy of your results. (5 points)

Go to __http://www.onlinemathlearning.com/mean-worksheets-3.html__ complete the online worksheet with 100% accuracy. Turn in a printed copy of your results. (5 points)

Go to __http://media.emgames.com/emgames/demosite/playdemo.html?activity=M5A006&activitytype=dcr&level=3__ and play the Landmark Shark Game until you have earned at least 300 points. Submit a copy of your score sheets. (10 points)

__Level B: Part 2 – 15 points__

Special Problem 1A: Gabalot High Phone Calls (15 points)

Special Problem 1A: Study Habit and Attitudes (15 points)

__Level A: Part 3 – 20 points__

Special Problem 1B: Did Mr. Starnes Stack His Class? (20 points)

Find or collect at least 30 pieces of quantitative data and complete a full analysis of your data set. Include reasons why you chose to use a particular measure of center and spread in your analysis. Then explain how your numerical analysis would change if you added a very large outlier. (20 points)

** **

**Measurement Topic 2.0: Normal Distribution**

__Level C: Part 1 – 65 points__

Assignment 2.1a/Pg. 84:2.4, Pg. 89: 2.6-2.9 (10 points)

Assignment 2.1b/Pg. 90: 2.12-2.15 (10 points)

Assignment 2.2a/Pg. 103:2.21-2.25 (10 points)

Assignment 2.2b/Pg.109: 2.28-2.33 (10 points)

Applying the Concepts 6-1 worksheet (15 points)

Applying the Concepts 6-2 worksheet (5 points)

Sports and Leisure worksheet (10 points)

Go to __http://www.wisc-online.com/objects/ViewObject.aspx?ID=TMH2102__ and complete the lesson on “The Normal Distribution and Empirical Rule.” Write down every problem you are asked to do with the correct answer. (10 points)

Go to __http://www.oswego.edu/~srp/stats/normal_wk_4.htm__ and complete the problems. Show all work! (5 points)

__Level B: Part 2 – 15 points__

Statistics Today: What is Normal? (15 points)

Normal Distribution Crossword Puzzle (15 points)

__Level A: Part 3 – 20 points__

Are M&M’s “Normal” or Just “Plain”? Activity (20 points)

Find a real world example of a normal distribution and create a worksheet with an answer key. Include problems that use the Empirical Rule and Standardized Scores. Make the worksheet fun and engaging using graphics, etc. (20 points)

Many of my students are frustrated when setting up problems. They say “I don’t know how to do this.” For many it is true that they never learned **“how to”** follow a logical step-by-step process. Sometimes we just think by the time they reach high school they should know how to organize their thoughts. But, the fact is, they do not. We need to help our students organize their thoughts across the curricula and relieve some of their frustrations.

**The Jane Schaffer Writing Model** is one method of presenting organized thoughts that lead to a solution or conclusion. This model is not limited to writing English essays. It can easily be applied to all curricula.

I use this process in my math classes for several reasons. It reinforces what is being used in other disciplines in our school. It fits nicely into our school literacy plan. This method is reinforced by the other departments and provides students with a consistent path to follow. It gives my students additional practice in organizing their thoughts, especially about geometry proofs. And, it gives me my writing sample that I am required to give to my curriculum director each quarter. Students have told me that it helps them. Students appreciate knowing what is expected. And the list of reasons goes on.

This example is simplistic. But, the model guides the students to what is expected when writing an explanation of their work. The same process applies when writing 2-column proofs, paragraph proofs that are more complicated and just about any written work. This process does not have to be complicated. KIS (KEEP IT SIMPLE).

In the standards based tiered assessment, most solutions require “why” answers and all are justifiable. The “A” and “B” sets usually require detailed explanations of the student’s reasoning. The Schaffer Writing Model helps the student present these solutions in a readable and organized way. Of course, there are many other models. Our school’s choice, as our standard, has been the Jane Schaffer Model. This standard process is easily applied to the tiered assessment format.

Note that the **green** words are all part of the math vernacular. We, too often, assume that these are a part of the students’ vocabulary. Productive discussion about real world math requires a good math vocabulary. We need to teach and reinforce the academic vocabulary every day.

____________________________________________________________________________________

A simple example: Read the problem. Sketch what you see from the problem. Create a logical step-by-step solution to justify your final answer to the problem. Can you think of any place in the real world where this situation might apply? There is a plethora of examples.

Two **parallel** **lines**, **line **l and **line** m, are cut by a **transversal **t. The **angles** formed at the **intersection** of **line** l and **line** t are **labeled** **angles **1, 2, 3 and 4 beginning in the **top left quadrant** of the **intersection** and **progressing** **clockwise** around the **intersection**. The **angles** formed by the **intersection** of **line** m and **line **t are **labeled** angles 5, 6, 7 and 8 beginning in the **top left** **quadrant** of the **intersection** and **progressing** **clockwise** around the **intersection**.

The **measure** of **angle** 1 is (2x – 3)^{0}. The **measure** of **angle** 5 is **13 ^{0}**. What is the

__Make a sketch. Justify your answer.__

Teaching for literacy

- Reading the words with understanding.
- Making sure the vocabulary is understood.
- Accurately sketching or drawing from what is read. Following written direction and visualize.
- Applying the given data to a solution process in logical order.
- Justifying the process and solution by standard academic writing.

_________________________________________________________________________________________

**Basic math version of the Schaffer Writing Model**

**Postulates**, **theorems**, **corollaries**, **definitions** and **properties** will be used to find the **value** of x and the **measure** of **angle** 5.

**Topic** sentence

Step 1:** Given**: Line l || Line m, m L 1 = (2x – 3)^{0} and m L 5 = 13^{0} **Concrete data**

Step 2: 2x – 3 = 13 **Commentary**

Step 3: 2x = 13 + 3 “

Step 4: 2x = 16 “

Step 5: x = 8 Concluding sentence 1

Step 6: m L 5 = 13^{0} **Corresponding angle** are **congruent **Concluding sentence 2

** Corresponding angles postulate**

By paragraph

By using postulates, theorems, corollaries, definitions and properties we can find the value of a variable (x) and determine the measure of an angle (angle 5). From the example problem, we are given that line l is parallel to line m, line t transverses line l and line m, the measure of angle 1 is 2 times the variable x minus 3 and the measure of angle 5 is 13. We can apply the parallel lines transversal postulates and theorems. Since angle 1 and angle 5 are corresponding angles and by postulate are congruent we can write 2x – 3 = 13. Using the addition property of equality we then write an equation 2x = 16 (add 3 to both sides). We use the division property of equality to divide both sides by 2. And, by corresponding angles postulate, angle 5 is congruent to angle 1, and therefore their measures are equal. We can conclude that x = 8. The resulting measure of angle 1 is 13.

_____________________________________________________________________________________

**TS **- By using postulates, theorems, corollaries, definitions and properties we can find the value of a variable (x) and determine the measure of an angle (angle 5).

**CD** - From the example problem, we are given that line l is parallel to line m, line t transverses line l and line m, the measure of angle 1 is 2 times the variable x minus 3 and the measure of angle 5 is 13.

**CM** - We can apply the parallel lines transversal postulates and theorems. Since angle 1 and angle 5 are corresponding angles and by postulate are congruent we can write an equation 2x – 3 = 13. Using the addition property of equality we then write 2x = 16 (add 3 to both sides). We use the division property of equality to divide both sides by 2. And, by corresponding angles postulate, angle 5 is congruent to angle 1, and therefore their measures are equal.

**CS** - We can conclude that x = 8. The resulting measure of angle 1 is 13.

While visiting Melissa Gollegly’s English class, I was so impressed with the level of student engagement as they worked on a writing assignment titled, “This I Believe.” The rubric that she used indicated various levels of the writing process proficiency. Among those listed were:

4. Meeting

3. Approaching

2. Beginning

1. Confused

I witnessed students who I have previously seen appearing disinterested, disengaged, or disconnected becoming involved in the act of collaboration, the writing process, and making improvements or adjustments to their interactive notebooks. While I am sharing my observations with you, I must add that what impressed me even more is Melissa’s relentless pursuit of “learning for all students” which is indicated by the following message posted on her assignment.

“If you score a 1, you will be responsible for meeting with me for 10 minutes either before school, after school, or during second lunch. This is absolutely not a punishment. If you scored a 1, you need additional help in order to succeed with this assignment and probably others. I want you to succeed. If you do not meet with me within 1 school week, I will help you by setting up an appointment with your parents. I agree, this sounds like a punishment. However, if you score a 1 on any assessment this year, not only do you fail the class, but I failed you as your teacher. So, we just have to work together a little more. J Good luck and enjoy this assignment.”