## Course Syllabus

Read over syllabus, share with parents, and return attached information form.

critical_thinking_syllabus_heidesch_2.pdf | |

File Size: | 368 kb |

File Type: |

critical_thinking_syllabus_return_info_form.pdf | |

File Size: | 88 kb |

File Type: |

## Fraction, Decimal, Percent, and Ratio Equivalents Sets A-D

In preparation for probability, we must review and examine rational numbers and the part to whole relationship that exists. Probability is a ratio comparing favorable outcomes to total outcomes of an event.

**involves examining fractions, decimals, and percents as three ways to represent the same amount. Using hundred grids, students can examine how the part to whole relationship is the same for equivalent fractions. When we simplify a fraction or rename it, the part to whole relationship does not change.**__Set A and B__**involves common fractions and their equivalent percents. Students should see a pattern through each fraction/percent family.**__Set C__**provides an array of different fractions, decimals, percents, and ratios. Students renamed the number given in its other three forms. Work must be shown for #3, 4, 6, 9, and 13. Students will demonstrate how to rename a fraction and ratio as a decimal, and how to find the simplest form of a fraction.**__Set D__ l1_fraction_decimal_percent_ratio_equivalents_sets_a-d.pdf | |

File Size: | 679 kb |

File Type: |

l1_fraction_decimal_percent_ratio_equivalents_sets_a-b_key.pdf | |

File Size: | 479 kb |

File Type: |

l1_fraction_decimal_percent_ratio_equivalents_sets_c-d_key.pdf | |

File Size: | 325 kb |

File Type: |

## Version 2 - Fraction, Decimal, Percent, and Ratio Equivalents Set D

l1_fraction_decimal_percent_ratio_equivalents_set_d_version_2.pdf | |

File Size: | 41 kb |

File Type: |

## Part to Whole Relationship

Different fractions were examined during warm-ups in an effort to understand how two fractions are equivalent, and how a number can be represented as a fraction, decimal, percent, and ratio.

l0_part_to_whole_1_2_to_5.pdf | |

File Size: | 187 kb |

File Type: |

l0_part_to_whole_2_7_to_8.pdf | |

File Size: | 196 kb |

File Type: |

l0_part_to_whole_3_17_to_20.pdf | |

File Size: | 192 kb |

File Type: |

l0_part_to_whole_4_8_to_12.pdf | |

File Size: | 195 kb |

File Type: |

## Choosing Cereal

l2_choosing_cereal.pdf | |

File Size: | 279 kb |

File Type: |

Students conducted 30 trials to represent the month of June for Kalvin and his breakfast dilemma.

__A1:____Coin Toss Results:__This table showed accumulated data - number of heads so far, fraction, of heads so far, and percent of heads so far. As each trial was completed, students would recalculate the number of heads, fraction, and percent so far. Students practiced renaming fractions as percents using the algorithm, divide the numerator by the denominator. "**assessed components of the table, headings, labels, properly completing the table. "**__Check 1__"__" assessed the ability to rename the fraction of heads as a percent using long division. Students were asked to divide to the thousandths place in order to round the decimal to the nearest one percent.__**Check 2**If students divide the numerator by the denominator, their quotient will be a number greater than one. This is impossible as one is equal to 100%. For example, if the fraction is 5/6, this means five of the coin tosses resulted in heads out of a total of six tosses or six days for the month of
June. 6/6 would mean each toss or 100% of the tosses resulted in heads. 6/6 is also equal to 1. 5/6 is less than 1, therefore, the decimal is less than 1 and the percent is less than 100%.

**A2: Line graph**completed using the data from the Coin Toss Results. Calculators were used to check and complete percentages.

**The results will vary between groups. But what all groups should see is that there is more variance in the data at the beginning of the 30 trials than there are towards the end. You should see a trend in the data where it gets closer and closer to 50% as each trial is completed. This is what you should see, but it's okay if it doesn't. Remember, experimental probability doesn't always reflect theoretical probability especially when the trials are few.**

__A3: As you add more data, what happens to the percent of tosses that are heads?__

**B1:**

**M****was completed and displayed showing the result of 30 tosses for each group. Each class and each group's data will vary. Some will have a high percentage of heads, others low, and some will be very close to 50%. Whether or not the experimental probability will reflect theoretical probability depends on the number of trials/experiments completed. Master charts for each class are posted below B2.**

__aster chart__B2: Class Percentage of Heads and Range of Data (percent)

**:**The percent of heads for the class can be achieved by dividing the total number of tosses for the class that were heads by the total number of trials completed by the class. Range is the difference between the largest and smallest data. We can represent range in two ways. "The range is (fill in the difference)" or "the range is from (fill in the highest data) to (fill in the lowest data)." For example, the range is from 70 to 33%. The range is 37%.## 1st Period - master chart

## 2nd Period - master chart

## 3rd Period - master chart

## 4th Period - master chart

## 5th Period - master chart

## 6th Period - master chart

B3: Scatter Plot (Class Data/Master Chart): Using class data from the Master Chart, students created a scatter plot where the y-axis represented percent of heads and the x-axis represented student groups. Here students get a visual of the range of their data in comparison to their peers. Unlike line graphs, scatter plots

**show change over time. It only shows a relationship between two elements. In this scenario, we are comparing the percentage of tosses that were heads achieved by each group. Therefore, the points are not connected. Examples of the scatter plot for each class are posted with C2: Line Graph of Running Total Table. Click on the image for your class and it should become enlarged.**__do not__B4: Which set of partners had data that would be considered outliers? An outlier is a number in a data set that is significantly smaller or larger than the other numbers. Sometimes there aren't any outliers, but data that lie on the furthest boundaries of the others.

**C1: Running Total Table:**

__The Law of Large Numbers__

**is introduced through the "Running Total Table" and cooresponding line plot. While there is a great deal of variation for a small number of trials, the percent of heads approaches 50% (the theoretical probability of a coin landing on heads) as a large number of trials are conducted.**

## 1st Period - Running Total Table

## 2nd Period - Running Total Table

## 3rd Period - Running Total Table

## 4th Period - Running Total Table

## 5th Period - Running Total Table

## 6th Period - Running Total Table

__C2: Line Graph of__**Let the y-axis represent percent of heads and the x-axis represent the total number of trials as the data accumulates. The x-axis values should begin at 30 and increase in multiples of 30: 30, 60, 90, 120, and so on.**

__Running Total Table:__## 1st Period - Graphs

## 2nd Period - Graphs

## 3rd Period - Graphs

## 4th Period - Graphs

## 5th Period - Graphs

## 6th Period - Graphs

C3: As your class adds more data, what happens to the percent of tosses that are heads? The percent of heads should approach 50%.

__C4: Using the data from all 6 classes, find the percent of all tosses that are heads. __ With even more data, the percent of heads should more closely approximate 50%, the theoretical probability of getting heads when tossing a coin.

D: Summarizng Questions. Use the data to answer the final questions on the task sheet. Think about which set of data is better for making a prediction and how there is a lot of variance with a small number of trials.

## Follow up on Choosing Cereal

This task involves a variety of open-ended questions involving experimental and theoretical probability, fair events, possible versus probable outcomes, making predictions using proportions/part to whole relationships, interpreting data from a table, organizing and finding all possible outcomes, and manipulating fractions. As we discuss the solutions in class, please add to and correct your solutions where necessary. Make sure to ask questions if you don't understand. Solutions will be posted after work is collected and checked.

l3_follow_up_choosing_cereal_task_sheet.pdf | |

File Size: | 924 kb |

File Type: |

## Quiz 1

## Tossing Paper Cups

Students examine what it means for outcomes to have an equally likely chance. In Choosing Cereal, the coin has two outcomes, heads or tails. In Tossing Paper Cups, the cup also has two outcomes, side or end. Will two outcomes of a given event always have the same chance as the other?

l4_tossing_paper_cups_task_sheet.pdf | |

File Size: | 275 kb |

File Type: |

Below are the master charts of each class. You will need this information to answer question C.

Below is an attachment of examples for explanations in Tossing Paper Cups. I hope it helps! Remember to do the following whenever you have to justify your answer:

**1. Introduce - Give the reader the context of the question. Use pronouns only after using the corresponding noun first. Your reader needs to know who "he," "it," and "they" are.**

**Rewording the question can be a good way to start.**

**2. Be Clear - Use complete sentences and don't abbreviate. Elaborate on your thoughts always. Don't assume the reader knows what you mean. Prove your understanding.**

**3. Use Facts - Use data or facts to support your reasoning.**

**4. Stay Focused - Make sure you are presenting ideas and information that pertain to the question or topic you are writing on. Otherwise, the reader gets confused.**

## Follow-up on Tossing Paper Cups

l5_follow_up_tossing_paper_cups_task_sheet.pdf | |

File Size: | 416 kb |

File Type: |

Sample explanations for Follow-up on Tossing Paper Cups are attached below. Remember to

**Introduce, Be Clear, Use Facts, and Stay on Point****!** l5_follow-uptossing_paper_cups_modeling_writing.pdf | |

File Size: | 161 kb |

File Type: |

## Percent of a Number

percent_of_a_number_set_a.pdf | |

File Size: | 192 kb |

File Type: |

percent_of_a_number_set_b.pdf | |

File Size: | 136 kb |

File Type: |

## Quiz 2

## One More Try

l6_one_more_try_task_sheet.pdf | |

File Size: | 347 kb |

File Type: |

## 1st Period Master Chart

## 2nd Period Master Chart

## 3rd Period Master Chart

## 4th Period Master Chart

## 5th Period Master Chart

## 6th Period Master Chart

## Follow-up on One More Try

l7_follow_up_one_more_try_task_sheet.pdf | |

File Size: | 305 kb |

File Type: |

## Analyzing Events

l8_analyzing_events_task_sheet.pdf | |

File Size: | 432 kb |

File Type: |

## Follow-up on Analyzing Events

l9_follow_up_analyzing_events_task_sheet.pdf | |

File Size: | 378 kb |

File Type: |

## Predicting to Win

l10_predicting_to_win_task_sheet.pdf | |

File Size: | 481 kb |

File Type: |

## Exploring Probabilities

a5_-_exploring_probabilities.pdf | |

File Size: | 896 kb |

File Type: |