2019-2020 HISD @ H.O.M.E. Project-Based Learning ... › cms › lib2 › TX01001591...If everyone had 2 pets, the values occur with the same frequency; therefore, there is no mode

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 6

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 1 of 12

Student Weekly Learning Targets

Students will be able to describe the center, spread, and shape of a data distribution (MATH.6.12B, MATH.6.12C, MATH.6.12D). The student should be able to demonstrate and verify the following:

• I can calculate the mean.

• I can calculate the median.

• I can calculate the range.

• I can calculate the mode.

Monday – The Mode and the Mean

Dogs, Cats, and More!

Mohammed surveyed seven of his friends to find out how many pets they own. The results of his survey are displayed in the table below.

Number of Pets

Mark Justin Mary Tim Sara Nancy Jim

2 1 2 2 3 1 3

What patterns do you notice within the data set? I noticed … If we wanted to represent Mohammed’s data with counters or pennies, how would we do this? HINTS: ● How many pets does Mark have? So, how many counters should you place in Mark’s column? ● How can we line up the counters, so it is easy to compare the numbers of pets each person has?

http://www.houstonisd.org/cms/lib2/TX01001591/Centricity/Domain/21808/HISD-Graduate-Vision.pdf





GLOBAL GRADUATE






Page 2 of 12


ANSWER:

© Houston ISD Mathematics Curriculum

1. What value(s) occur(s) most frequently?

2. How many times does this value appear?

3. What does this mean in terms of the data?

The mode of a data set is the data value or values that occur (appear) most frequently in a data set. Make an inference … When all values occur with the same frequency, that is, they appear the same number of times, what is the mode? When all values have the same frequency… ANSWERS: In the prior data set, the mode is 2 because it occurs most often (question 1). In fact, “two pets” occurs three times (question 2). This means that the majority or most of Mohammed’s friends (3 out of 7) have 2 pets (question 3). If everyone had 2 pets, the values occur with the same frequency; therefore, there is no mode for the data set.






GLOBAL GRADUATE






Page 3 of 12


List Mohammed’s friends’ names in ascending (increasing) order according to the number of pets that they own.

1. Who has the fewest number of pets? How many pets does he/she have?

2. Who has the most pets? How many pets does he/she have?

3. Find the difference between greatest number of pets and the least number of pets. Justify.

4. What do you call this difference?

ANSWERS: Justin and Nancy have the fewest number of pets. They each have 1 pet. Sara and Jim have the most pets. They each have 3 pets. The difference is 2 because 3 ‒ 2 = 1. This difference between the greatest number and the least number is called the range of the data. The Mean (Average)

Linda’s First Semester Grades

Math ELA Science Social

Studies Elective

90 86 88 85 83

How many grades are in the table? Now, find the sum or total of all Linda’s first semester grades. Write your answer in the sixth column and title it “TOTAL.” Next, divide the sum or total by the number of grades. What is the quotient? Write your answer in the seventh column. What do we call your answer in the seventh column? Label the seventh column with your answer. The resulting table must look like this:






GLOBAL GRADUATE






Page 4 of 12


Linda’s First Semester Grades

Math ELA Science Social

Studies Elective Total Average

90 86 88 85 83 432 86.4

In elementary school, we learned how to calculate the average of our grades. SUMMARIZE: What are the two steps in calculating the average of a set of values?

The first thing we do is … Then, we …

In middle school, we shall refer to average as mean. In everyday terms, a mean “levels out” or “evens out” the data. The steps for calculating the mean (or average) are:

(1) Find the sum or total of the values by adding them up all. (2) Divide the sum or total by how many values there are.

Practice Calculating the Mean: What is the mean for the number of pets owned by Mohammed’s friends?






GLOBAL GRADUATE






Page 5 of 12

Tuesday – The Median

The Median The median of a data set is the middle value (for an odd number of data) or the mean (average) of the two middle values (for an even number of data) in an ordered list of data. Let’s try it! Try to find the middle number in the data set below.

72, 72, 72, 73, 73, 74, 81, 81, 82, 88, 90, 91, 92, 95, 95 Did you find that the median was 81? There are several ways to find the median. Explain your process for determining that 81 is the median value. One way to determine the median is given below.


Pair up the values beginning at each endpoint. The value in the very middle of the pairs is the median value. Another method is to count how many values are in the list. For the list above, there are 15 items. Divide 15 in half and the result is 7.5. That means the median should have seven values on one side of it and seven values on the other side of it … that would be value #8. The value in the eighth place is …







GLOBAL GRADUATE






Page 6 of 12


The key to finding the median for a data set is to place the values in order. The median cannot be found until the data is ordered. Now, consider the following data set.

0.5, 1.5, 2.5, 4.0

What do you notice about the data set? How that will impact finding the median? Complete the notice and wonder statements below. I notice … I wonder … In the data set above, there are four items. The median falls between the two middle values. That means, for this data set, the median is between 1.5 and 2.5. What number is exactly in the middle of 1.5 and 2.5? Did you guess 2 (or 2.0)? That is correct! The way that we find the median for data sets that have an even number of items is to average the two middle values together (another words, we find the mean between the two middle values).

(1.5 + 2.5) ÷ 2 = 4.0 ÷ 2 = 2.0 = 2 Find the median for the following data set.

8, 10, 6, 4, 12, 6, 8, 14






GLOBAL GRADUATE






Page 7 of 12


HINTS:

• Did you place the data set in order?

• Did you find that the middle two values were in the 4th and 5th positions? Since both the 4th and 5th position is represented by the numbers 8, the average is 8. So, the median is 8. Now, try to find the median when the data is given in a graph. What is the median of the data represented in the dot plot below?

Image from HMH Go Math 6 with permission

HINT: The data in the dot plot is represented by the list below:

21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 24



https://clever.com/in/redirector?url=https%3A%2F%2Fmy.hrw.com%2Fsp%2Faccess%3Fsp%3Dhrw%26connection%3DTX-Houstonisd-01023770&link_type=external&link_source=admin_created&hash=f417d98e5694d26a8d4f93cc2cfdbe29794884c44c018b43998bcc28461e9a72

https://drive.google.com/a/houstonisd.org/file/d/1wAbK4Z3E8pn6b5qCjw6_4DeD16T6U-yJ/view?usp=sharing




GLOBAL GRADUATE






Page 8 of 12

Wednesday – Rolling Down the Center

For the following activity, you will need to have 7 dice. If you do not have access to dice, write the numbers 1, 2, 3, 4, 5, and 6 on separate pieces of paper. Fold them up and place them into a cup. Each time you must roll a dice, place all six papers into the cup and draw out one number. Repeat this process four times if you are asked to roll 4 dice. Repeat the process 5 times if you are asked to roll 5 dice, etc. ROLLING DOWN THE CENTER Activity 1 – Roll 4 dice and write the resulting numbers in the boxes below. Calculate the mean:

Add up the four dice = ________ → Divide by the number of dice (4) = _____ (If there is a decimal, round to the nearest tenth) Calculate the mode: Which number occurs most frequently? _________ (If there isn’t one, write “no mode”) Calculate the range: Subtract the smallest value from the largest value = _________ Calculate the median: Put the numbers in order from least to greatest = ______ ______ ______ ______ The two middle numbers are = ______ ______ Find the average of the two middle numbers (add them up and divide by 2) = ______






GLOBAL GRADUATE






Page 9 of 12


Activity 2 – Roll 5 dice and write the resulting numbers in the boxes below. Calculate the mean:

Add up the five dice = ________ → Divide by the number of dice (5) = _____ (If there is a decimal, round to the nearest tenth) Calculate the mode: Which number occurs most frequently? _________ (If there isn’t one, write “no mode”) Calculate the range: Subtract the smallest value from the largest value = _________ Calculate the median: Put the numbers in order from least to greatest = _____ _____ _____ _____ _____ Find the middle number = ______ Activity 3 – Roll 6 dice and write the resulting numbers in the boxes below. Calculate the mean:

Add up the six dice = ________ → Divide by the number of dice (6) = _____ (If there is a decimal, round to the nearest tenth) Calculate the mode: Which number occurs most frequently? _________ (If there isn’t one, write “no mode”) Calculate the range: Subtract the smallest value from the largest value = _________ Calculate the median: Put the numbers in order from least to greatest = ______________________________ The two middle numbers are = ______ ______ Find the average of the two middle numbers (add them up and divide by 2) = ______






GLOBAL GRADUATE






Page 10 of 12


Activity 4 – Roll 7 dice and write the resulting numbers in the boxes below.

Calculate the mean:

Add up the seven dice = ________ → Divide by the number of dice (7) = _____ (If there is a decimal, round to the nearest tenth) Calculate the mode: Which number occurs most frequently? _________ (If there isn’t one, write “no mode”) Calculate the range: Subtract the smallest value from the largest value = _________ Calculate the median: Put the numbers in order from least to greatest = ______________________________ Find the middle number = ______






GLOBAL GRADUATE






Page 11 of 12

Thursday – Summarizing Measures of Center

Summarize the process of identifying and calculating the mean, median, mode, and range by completing a graphic organizer. Fill the blanks with the correct words and values.






GLOBAL GRADUATE






Page 12 of 12

Thursday – Summarizing Measures of Center

Check your understanding: (1) What do we call the value that occurs most frequently?

(2) If we put the values in ascending (increasing) order, what do we call the value that extends from the smallest

data value to the largest data value?

(3) If we averaged all our data values, what number would we get? (4) If we put the values in ascending order, what do we call the “middle” value?

Friday – Checking Understanding

Practice calculating mean, median, mode and range A horse trainer kept track of the distance that each of his horses ran last week. The results are displayed in the table below.

Keeping Track at the Race

Distance Ran (miles)

Blue Thunder 4

Zander 1

Jericho 8

Tyson 10

Wind Chaser 6

Dario 5

Flash 11

Red 3

Moscow 4

Shangri-La 9

Lady 5

Calculate the mean, median, mode, and range of the data set.

Student-Produced Weekly Product

Student correctly completes the Checking Understanding task that assesses understanding of calculating the measures of center and spread.



Documents

2019-2020 HISD @ H.O.M.E. Project-Based Learning ... › cms › lib2 › TX01001591...If everyone had 2 pets, the values occur with the same frequency; therefore, there is no mode