Common Core State Standards 6 – 8...
Transcript of Common Core State Standards 6 – 8...
![Page 1: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/1.jpg)
Common Core State Standards 6 – 8 Mathematics
Presented by NC Department of Public Instruc8on
![Page 2: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/2.jpg)
Statistics and Probability Progression
6th grade Statistical thinking Measures of central tendency (median and
mean) Measures of variability (Mean Absolute
Deviation (M.A.D.) and Inter-quartile Range) Dot plots, box plots and histograms
10/11/11 • page 2
![Page 3: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/3.jpg)
7th grade Compare two distributions using measures of
center and measures of variability Probability
10/11/11 • page 3
Statistics and Probability Progression
![Page 4: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/4.jpg)
8th grade Scatter plots Linear models – no linear regression Two-way tables for categorical data
10/11/11 • page 4
Statistics and Probability Progression
![Page 5: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/5.jpg)
High School Math One Interpret shape, center, spread and outliers Incorporate technology Standard deviation Scatter plots, linear models, LSRL and
correlation coefficient Two-way tables (joint, marginal, and
conditional relative frequencies)
10/11/11 • page 5
Statistics and Probability Progression
![Page 6: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/6.jpg)
Finding the Median from a Dot Plot
10/11/11 • page 6
![Page 7: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/7.jpg)
If you only know the MEDIAN…
Turn and Talk: What information can you give about the
data set?
What information can’t you give about the data set?
10/11/11 • page 7
![Page 8: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/8.jpg)
Turn and Talk
Remove two values from the original data set so that:
a. The median stays the same b. The median increases c. The median decreases
10/11/11 • page 8
![Page 9: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/9.jpg)
Finding the Median from a Dot Plot
10/11/11 • page 9
![Page 10: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/10.jpg)
Turn and Talk
Add two values to the original data set so that
a. The median stays the same b. The median increases c. The median decreases
10/11/11 • page 10
![Page 11: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/11.jpg)
What does it mean to understand the “mean”?
10/11/11 • page 11
![Page 12: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/12.jpg)
Mean As A Fair Share • Use snap cubes to represent the number
of letters in each of the birth places on the red card.
10/11/11 • page 12
• Manipulate the snap cubes so that each city has the same number of letters.
• What strategies did you use to determine this amount?
![Page 13: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/13.jpg)
What If… 1. Were there any “a-ha” moments?
10/11/11 • page 13
2. Reference Practice 3: Construct viable arguments and critique the reasoning of others. Give examples of how this practice was evidenced with this task.
3. Reference Practice 6: Attend to precision. Give examples of how this practice was evidenced with this task.
![Page 14: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/14.jpg)
More “MEAN” Problems Susan has four 20-point projects for math class.
Susan’s scores on the first 3 project are shown below: Project 1: 18 Project 2: 15 Project 3: 16 Project 4: ???
What does she need to make on Project 4 so that her average for the four projects is 17? Explain how you found your answer.
10/11/11 • page 14
![Page 15: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/15.jpg)
BREAK
10/11/11 • page 15
![Page 16: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/16.jpg)
10/11/11 • page 16
Seven people were asked, “How many keys are on your key ring?”
One result from the poll is that the average number of keys was 4.
![Page 17: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/17.jpg)
What are possibilities for the distribution for the number of keys for seven people with the requirement that the mean number of keys be 4?
Use the number line to create a dot plot with 7 data points and a mean of 4.
10/11/11 • page 17
![Page 18: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/18.jpg)
Summing Up
1. What strategies did you use to create your data set?
10/11/11 • page 18
2. Reference Practice 1: Make sense of problems and persevere in solving them. Give examples of how this practice was evidenced with this task.
![Page 19: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/19.jpg)
If you only know the MEAN and the number of data points…
10/11/11 • page 19
Turn and Talk: What information can you give about the
data set?
What information can’t you give about the data set?
![Page 20: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/20.jpg)
Differing Distributions
Which distribution shows data values that differ the least from the mean of 4?
10/11/11 • page 20
Which distribution shows data values that differ the most from the mean of 4?
How would you order the other distributions from least to most difference from a mean of 4?
![Page 21: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/21.jpg)
Finding the Mean Absolute Deviation (M.A.D.)
10/11/11 • page 21
Mean 4 + 4 + 4 = 12 -3 + (-3) + (-3) + (-3) = -12
|-3| + |-3| + |-3| + |-3| + |4| + |4| + |4| = 24 24/7 = 3.43
![Page 22: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/22.jpg)
In the Classroom…
10/11/11 • page 22
Based on this informa8on, would you revise the order of the distribu8ons?
![Page 23: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/23.jpg)
Check Your Answers • Distribution 1: M.A.D. = 0
10/11/11 • page 23
• Distribution 7: M.A.D. = 1.42 • Distribution 3: M.A.D. = 1.71 • Distribution 5: M.A.D. = 2.00 • Distribution 2 and 6: M.A.D. = 2.57 • Distribution 4: M.A.D. = 2.86 • Distribution 8: M.A.D. = 3.43
![Page 24: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/24.jpg)
Summing Up • What does a small M.A.D. tell us about a
data set? • What does a large M.A.D. tell us about a
data set? • What does a M.A.D. of 2.89 tell us about
the distribution of keys? • How could you change the data set to
increase the M.A.D.?
10/11/11 • page 24
![Page 25: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/25.jpg)
Finding the M.A.D.
10/11/11 • page 25
DATA SET DEVIATION FROM THE MEAN (19.6)
ABSOLUTE DEVIATION
3
7
5
13
20
23
39
23
40
23
![Page 26: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/26.jpg)
Finding the M.A.D.
10/11/11 • page 26
DATA SET DEVIATION FROM THE MEAN (19.6)
ABSOLUTE DEVIATION
3 -‐16.6
7 -‐12.6
5 -‐14.6
13 -‐6.6
20 0.4
23 3.4
39 19.4
23 3.4
40 20.4
23 3.4
![Page 27: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/27.jpg)
Finding the M.A.D.
10/11/11 • page 27
DATA SET DEVIATION FROM THE MEAN (19.6)
ABSOLUTE DEVIATION
3 -‐16.6 16.6
7 -‐12.6 12.6
5 -‐14.6 14.6
13 -‐6.6 6.6
20 0.4 0.4
23 3.4 3.4
39 19.4 19.4
23 3.4 3.4
40 20.4 20.4
23 3.4 3.4
100.8/10 M.A.D. = 10.08
![Page 28: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/28.jpg)
10/11/11 • page 28
Mean as the Balancing Point
4 5 6 7 8 9 10 11 12 13
Mean
3
5
5
1
3
2
3
2
2
![Page 29: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/29.jpg)
Middle School Standards
10/11/11 • page 29
Statistics and Probability 6.SP
6th Grade Statistics: Develop understanding of statistical variability. 3. Recognize that a measure of center for a numerical
data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
![Page 30: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/30.jpg)
10/11/11 • page 30
6th Grade Statistics: Summarize and describe distributions. 4. Display numerical data in plots on a number line, including dot plots,
histograms, and box plots.
6. Summarize numerical data sets in relation to their context, such as by: c. Giving quantitative measures of center (median and/or mean) and
variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
Middle School Standards Statistics and Probability 6.SP
![Page 31: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/31.jpg)
Middle School Standards
10/11/11 • page 31
Statistics and Probability 7.SP
7th Grade Statistics: Draw informal comparative inferences about two populations. 3. Informally assess the degree of visual overlap of two numerical
data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.
4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
![Page 32: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/32.jpg)
Heights of Basketball Players vs.
Heights of Soccer Players
10/11/11 • page 32
Basketball Players: 185, 185, 185, 185, 185, 185, 185, 185, 185 Soccer Players: 175, 175, 175, 175, 175, 175, 175, 175, 175
174 175 176 177 178 179 180 181 182 183 184 185 186
![Page 33: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/33.jpg)
Heights of Basketball Players vs.
Heights of Soccer Players
10/11/11 • page 33
Basketball Players: 175, 180, 182, 184, 185, 186, 187, 190, 195 Soccer Players: 165, 170, 172, 174, 175, 176, 177, 180, 185
165 170 175 180 185 190 195 200
Basketball Players
Soccer Players
![Page 34: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/34.jpg)
In 7th grade, students understand…
10/11/11 • page 34
1. A full understanding of the data requires considera8on of the measures of variability as well as mean or median.
2. Variability is responsible for the overlap of two data sets and that an increase in variability can increase the overlap.
3. Median is paired with the interquar8le range and mean is paired with the mean absolute devia8on .
![Page 35: Common Core State Standards 6 – 8 Mathematicsmaccss.ncdpi.wikispaces.net/file/view/Math+6-8+powerpoint.pdf · Statistics and Probability Progression 6th grade Statistical thinking](https://reader031.fdocuments.in/reader031/viewer/2022022015/5b4fcd077f8b9a166e8d2529/html5/thumbnails/35.jpg)
10/11/11 • page 35