
These are the concepts taught in this unit
Subject(s)
High School Mathematics
Grade/Course
Integrated Math I
Unit of Study
Unit 1: Patterns in Data
Unit Type(s)
❑Topical ❑X Skillsbased ❑ Thematic
Pacing
20 days
Unit Abstract
Students will develop tools and strategies that will help them make sense of data and communicate their conclusions. The focus will be on displaying data (to observe shape, location, outliers, clusters, and gaps) and then computing and interpreting summary statistics, such as measures of center (mean, median, and mode) and measures of variability (range, interquartile range, and standard deviation).
Common Core Essential State Standards
Conceptual Category: Statistics and Probability; Number and Quantity
Domain: 1) Interpreting Categorical & Quantitative Data (SID)
2) Quantities (NQ)
Clusters:
1) Summarize, represent, and interpret data on a single count or measurement
variable. (SID)
Summarize, represent, and interpret data on two categorical and quantitative
variables. (SID)
2) Reason quantitatively and use units to solve problems. (NQ)
Standards:
NQ.1 USE units as a way to understand problems and to guide the solution of multistep problems; CHOOSE and INTERPRET units consistently in formulas; CHOOSE and INTERPRET the scale and the origin in graphs and data displays.
NQ.2 DEFINE appropriate quantities for the purpose of descriptive modeling.
NQ.3 CHOOSE a level of accuracy appropriate to limitations on measurement when reporting quantities.
SID.1 REPRESENT data with plots on the real number line (dot plots,
histograms, and box plots).
SID.2 USE statistics appropriate to the shape of the to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
SID.3 INTERPRET differences in shape, center, and spread in the context of
the data sets, accounting for possible effects of extreme data points (outliers).
SID.5 SUMMARIZE categorical data for two categories in twoway frequency
tables. INTERPRET relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). RECOGNIZE possible associations and trends in the data.
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
“Unpacked” Concepts
(students need to know)
“Unwrapped” Skills
(students need to be able to do)
COGNITION
DOK
Numbers can be interpreted as quantities with appropriate units, scales, and levels of accuracy to effectively model and make sense of real world problems.
NQ.1
I can label units through multiple steps of a problem.
I can choose appropriate units for real world problems involving formulas.
I can use and interpret units when solving formulas.
I can choose an appropriate scale and origin for graphs and data displays.
I can interpret the scale and origin for graphs and data displays.
NQ.2
I can identify the variables or quantities of significance from the data provided.
I can identify or choose the appropriate unit of measure for each variable or quantity.
NQ.3
I can report measured quantities in a way that is reasonable for the tool used to make the measurement.
I can report calculated quantities using the same level of accuracy as used in the problem statement.
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Various graphical displays of data reveal important patterns that can be interpreted within the context of the data.
Relate the shape of a distribution to the location of its mean and median.
Compare data sets using measures of center, measures of variability, and data displays that group data.
Recognize the importance of having the same scales on graphs that are used to compare data distributions.
Understand how measures of center respond to changes in the number and magnitude of data values (including outliers).
Summarize categorical data for two categories in twoway frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
SID.1
I can choose the best representation (dot plot, histogram, box plot) for a set of data.
I can decide if a representation preserves all the data values or presents only the general characteristics of a data set.
Dot plot:
I can choose the appropriate scale to represent data on a number line.
I can construct a dot plot for a set of data.
Histogram:
I can construct a histogram for a set of data.
Box plot:
I can calculate the fivenumber summary for a set of data.
I can construct a box plot based on the fivenumber summary.
SID.2
I can describe the center of the data distribution (mean or median).
I can choose the histogram with the largest mean when shown several histograms.
I can describe the spread of the data distribution (interquartile range or standard deviation).
I can choose the histogram with the greatest standard deviation when shown several histograms.
I can choose the boxandwhisker plot with the greatest interquartile range when shown several boxandwhiskers plots.
I can compare the distributions of two or more data sets by examining their shapes, centers, and spreads when drawn on the same scale.
SID.3
I can interpret the differences in the shape, center, and spread of a data set in the context of a problem.
I can identify outliers for the data set.
I can predict the effect an outlier will have on the shape, center, and spread of a data set.
I can decide whether to include the outliers as part of the data set or to remove them.
SID.5
I can read and interpret the data displayed in a twoway frequency table.
I can write clear summaries of data displayed in a twoway frequency table.
I can calculate percentages using the ratios in a twoway frequency table to yield relative frequencies.
I can calculate join, marginal, and conditional relative frequencies.
I can interpret and explain the meaning of relative frequencies in the context of a problem.
I can make appropriate displays of joint, marginal, and conditional distributions.
I can describe patterns observed in the data.
I can recognize the association between two variables by comparing conditional and marginal percentages.
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Essential Questions
Corresponding Big Ideas
In what ways can the choice of units, quantities, and levels of accuracy impact a solution?
Interpret numbers as quantities with appropriate units, scales, and levels of accuracy to effectively model and make sense of real world problems.
What types of patterns do different graphical displays reveal about data sets? How do we interpret those patterns within the context of the data?
Use various graphical displays of data to reveal important patterns of data in a set and interpret those patterns in the context of the data.
How do you decide which measure of center to use when summarizing a set of data?
Compute measures of center and variability for sets of data and interpret the meaning of those statistics.
What effect do transformations have on the shape, center, and spread of distributions?
Transform distributions by adding a constant or my multiplying by a positive constant and recognize how those transformations affect shape, center, and spread of distributions.
Vocabulary
Dot plot, histogram, box plot, 5number summary, median, lower quartile, upper quartile, minimum value, maximum value, frequency, interval, scale, distribution, shape, center, spread, mean, interquartile range, standard deviation, data distribution, outlier, scatter plot, linear, twoway frequency table, relative frequency, joint relative frequency, marginal relative frequency, conditional relative frequency
Language Objectives
Key Vocabulary
NQ.1
NQ.2
NQ.3
SID.1
SID.2
SID.3
SID.5
SWBAT define and give examples of vocabulary specific to the standards:
dot plot data distribution
histogram outlier
box plot twoway frequency table
5number summary relative frequencies
median scatter plot
lower quartile frequency
upper quartile scale
minimum value maximum value
distribution shape
center spread
mean interquartile range
standard deviation
Language Function
SID.1
SWBAT use visuals to explain the processes of constructing dot plots, histograms, and box plots.
SID.2
SWBAT give a stepbystep process of how to compare measures of center and spread for two or more data sets using a series of related sentences.
SID.3
SWBAT use visuals to explain the differences in shape, center, and spread for data sets while accounting for possible effects of outliers.
SID.5
SWBAT use visuals to explain possible associations and trends in the data.
Language Skill
SID.2
SWBAT use drawings on the number line, solve word problems involving dot plots, histograms, and box plots.
SID.1, 2, 3
SWBAT create original contexts to match data sets.
Lesson Tasks
SID.1
SWBAT explain how they used manipulatives to represent a number of objects to a partner.
SID.2
SWBAT persuade a partner that his/her measure of spread is the most accurate given the context of the data.
SID.3
SWBAT use number lines and technology, etc. to demonstrate and explain differences in shape, center, and spread (including outliers when appropriate).