CC Data Analysis and Probability

Unit: Data Analysis and Probability

Grade Level/Course 6 th Math

Teacher: Acosta/Gordon

This unit is combined because the first unit in Everyday Mathematics (EM) covers all of the learning goals. It hits several objectives, both complex and simple in one week and often in one lesson. The unit should take 4 to 5 weeks which is longer that the EM unit. Provide extra practice using skills tutor, AM, Math-drills and other sources. Some are listed in the unit. The unit folder has resources you can use.

Variability refers to the extent to which the scores in a distribution differ from each other. An equivalent definition (that is easier to work with mathematically) says that variability refers to the extent to which the scores in a distribution differ from their mean. If a distribution is lacking in variability, we may say that it is homogenous (note the opposite would be

heterogenous).




Complex

Learning Goals (Question 1)

The student will understand or be able to:

SP1 – Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (Not covered in EM. In 2012- 1·2 , 1·3 ,

1·7)

SP2 – Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. (EM 1·2,

1·3, 1·4, 1·6, 1·7, 1·8)

SP3 – Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. (EM 1·2, 1·3, 1·4, 1·5a, 1·6, 1·12)

SP3 – Recognize that a measure of variation describes how its values vary with a single number. (EM 1·2, 1·3, 1·4, 1·5a, 1·6, 1·12)

SP4 – Display numerical data in plots on a number line.(EM 1·2, 1·5a, 1·7, 1·13, 2·1, 2·3,

2·7, 3·4)

SP5 – Understand what an observation is (e.g. sample size, n size) and how it relates to numerical data sets.

SP5 – Understand how the data was gathered, the importance of the units used in the data sets and justify the appropriateness of the process.( 1·2, 1·11, 1·12)

SP5 – Give quantitative measures of center (median, mean) and variability (range, interquartile range and/or mean absolute deviation)( 1·4, 1·5, 1·5a, 1·6, 1·10, 1·12, 2·1)

SP5 – Describe how the shape of the data distribution may determine the choice of measure of center and variability and that measures of center emphasize different attributes for the data set. (e.g., mean income v. median income).( 1·2, 1·4, 1·5a, 2·1,

3·4, 4·10 Project 10

Note: unit numbers not underlined come from a draft of the EM for 2012 and Lesson numbers in bold indicate lessons that will be adjusted to meet the CCSS and Lesson numbers with an “a” indicate lessons that will be added. (see edm_commoncore_allignment.pdf in unit folder)




Simple

The student will know or be able to:

What variability means (1

·

4, 1

·

5, 1·5a , 1

·

6, 1

·

10, 1

·

12, 2·1)?

What a statistical question is (EM 1

·

2) , (EM 1

·

11) (EM 1

·

12)shown by example throughout unit 1

What is data. (shown by example throughout unit 1)

Calculate mean (done but not explicitly taught because taught in lower grades.)

Identify median and mode (EM 1 · 3)

Calculate range (EM 1

·

3).

Plot data (EM 1

·

6),thru (EM 1

·

7)

That data can be represented in more than one way. (EM 1 · 3) (EM 1 · 11) measures of central tendency (mean and median) (EM 1

·

3) understand outliers. (EM 1

·

2)

Make line plots (EM 1 · 2), line graphs, (EM 1 · 6), Stem-and-Leaf Plot (EM 1 · 3) (EM 1 · 5), histograms, box plots ( http://www.deltastate.edu/docs/math/Mitchell3.pdf

), and bar graphs. (EM 1 · 7)

Report the number of observations (EM 1·2 , 1·3 , 1·7) (just used to determine mean)

Identify and describe the attribute being measured. (done by example and questioning throughout unit)

Find median, mean, range, (EM 1

·

4), (EM 1

·

5), and interquartile range(not covered in

EM)

Choose the most appropriate measure of center (mean or median) ). (EM 1

·

4) and variability (range, interquartile range

Note: unit numbers not underlined come from a draft of the EM for 2012 and

Lesson numbers in bold indicate lessons that will be adjusted to meet the CCSS and

Lesson numbers with an “a” indicate lessons that will be added. (see edm_commoncore_allignment.pdf in unit folder)




Planning for Question 2

Preview

Show brain pop http://www.brai

npop.com/ on statistics to start discussion.

Brief overview of what students will be learning: information can be learned from different types of graphs.

Math messages in

Pretest on identifying types of graphs.

Critical Input Chunk Actively Process

Note: see simple and complex for

Students work more together to information on create different the matchup of types of graphs

EM lessons. based on data they have collected. variability in data and collection of

Work in groups to data. Statistical questions SP1, analyze data displays

SP2 – Teacher lecture/discussio comparing means, medians, n, (EM 1·2, EM

1·11, EM 1·12)

Identify types of etc.

Explain ways in graphs: Make line plots (EM

1·2), line graphs,

(EM 1·6), Stemwhich some graphs show information better than others. and-Leaf Plot

(EM 1·3) (EM

1·5), histograms, box plots

Read Tikki Tikki

Tembo by Arlene

Mosel. One site ( http://www.del

tastate.edu/docs

/math/Mitchell3.

pdf ), and bar graphs. (EM 1·7) had it listed to use for this type of unit, no description on how to use it.

This site will make a line plot using raisons

Skills tutor has lessons in beginning, A, B,

C. http://www.lear

ner.org/courses/ learningmath/da ta/session2/part

_b/making.html

Planning for

Question 3

Analyze ways that data displays can be used to misrepresent information

IXL practice. (20 problems/stude nt/day

Accelerated Math objectives 171-

177 (graphs and line plots),182-

185 (mean, median, mode, range)

Planning for

Question 4




Show brain pop http://www.brai

npop.com/ on statistics, graphs.

Model how to find

Data Landmarks using a Line Plot

Model how to determine

Mean, Median, and Mode of a data set.

View PowerPoints and interactive websites showing different types of graphs.

This sites have: instructions on making a line plot http://ellerbruch.n

mu.edu/cs255/jnor d/lineplot.html

lesson on stem and leaf plot and activity. http://www.wisconline.com/objects

/ViewObject.aspx?I

D=TMH1101 box plot (box and

Whisker plot

( http://www.delt

astate.edu/docs/ math/Mitchell3.p

df )

This site and has an interactive activity http://www.learne

r.org/courses/learn ingmath/data/sessi on2/part_b/index.

html

Video lesson on interquartile range http://www.guara

nteach.com/math/I nterquartile_Range

_in_Box_Plots/5 and info and problems http://www.statca

n.gc.ca/edu/power pouvoir/ch12/5214

890-eng.htm




Arizona Aims

Coach lessons

11, 12, 13, 14,16,

17, 18.

Resources: EveryDay Math Journal Unit 1, games, End of Chapter Assessments, http://www.brainpop.com/ if available, http://www.ixl.com/1c?gclid=CNDunIPluKkCFUgaQgodVUiK8Q ,skills tutor.

Vocabulary words for unit 1 bar graph tally table venn diagram A diagram that shows relationships among sets of things line graph A graph that uses a line to show how data change over time (called broken line graph in everyday math) data table line plot inference set of information a set of data arranged in rows and columns

A graph that shows frequency of data along a number line mean the process of drawing a conclusion by applying observations and your own prior knowledge.

The number found by dividing the sum of a set of numbers by the number of addends; also called the average median

A graph that uses horizontal or vertical bars to display countable data

A table with categories for recording each piece of data with tally marks as it is collected mode range steam and leaf plot frequency table circle graph

The middle number or the average of the two middle numbers in an ordered (listed in order from least to greatest) of data

The numbers or values that occur most often in a set of data

The difference between the greatest and least numbers in a set of data

A data display that shows groups of data arranged by place value.

Digits with higher place values are “stems” and smaller place values are

“leaves”

A table that shows the total for each category or group

A graph that shows how parts of the data are related to the whole set



Teacher: Acosta/Gordon pie chart of data and to each other that uses a circle divided by radii.

A graph that shows how parts of the data are related to the whole set of data and to each other that uses a circle divided by radii. outlier bias central tendency sample benchmarks gap

A data value that stands out from others in a set; outliers can significantly affect measures of central tendency. influence in an unfair way or in a way that moves towards a particular point of view.

A measure used to describe data; the mean, median, and mode are measures of central tendency.

A part of a population

A well-known count or measure that can be used to chedk whether other counts, measures, or estimates make sense.

A break or hole in the data set.

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