New Colorado P-12 Academic Standards

Current Display Filter: Mathematics - All - by Specific Prepared Graduate Competency - (Remove PGC Filter)

Content Area: Mathematics
Grade Level Expectations: High School
Standard: 3. Data Analysis, Statistics, and Probability

Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations) - (Remove PGC Filter)

Concepts and skills students master:

1. Visual displays and summary statistics condense the information in data sets into usable knowledge

Evidence Outcomes 21st Century Skill and Readiness Competencies

Students Can:

  1. Summarize, represent, and interpret data on a single count or measurement variable. (CCSS: S-ID)
    • Represent data with plots on the real number line (dot plots, histograms, and box plots). (CCSS: S-ID.1)
    • Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. (CCSS: S-ID.2)
    • Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). (CCSS: S-ID.3)
    • Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages and identify data sets for which such a procedure is not appropriate. (CCSS: S-ID.4)
    • Use calculators, spreadsheets, and tables to estimate areas under the normal curve. (CCSS: S-ID.4)
  2. Summarize, represent, and interpret data on two categorical and quantitative variables. (CCSS: S-ID)
    • Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data1 (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. (CCSS: S-ID.5)
    • Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. (CCSS: S-ID.6)
      • Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. (CCSS: S-ID.6a)
      • Informally assess the fit of a function by plotting and analyzing residuals. (CCSS: S-ID.6b)
      • Fit a linear function for a scatter plot that suggests a linear association. (CCSS: S-ID.6c)
  3. Interpret linear models. (CCSS: S-ID)
    • Interpret the slope2 and the intercept3 of a linear model in the context of the data. (CCSS: S-ID.7)
    • Using technology, compute and interpret the correlation coefficient of a linear fit. (CCSS: S-ID.8)
    • Distinguish between correlation and causation. (CCSS: S-ID.9)

Inquiry Questions:

  1. What makes data meaningful or actionable?
  2. Why should attention be paid to an unexpected outcome?
  3. How can summary statistics or data displays be accurate but misleading?

Relevance & Application:

  1. Facility with data organization, summary, and display allows the sharing of data efficiently and collaboratively to answer important questions such as is the climate changing, how do people think about ballot initiatives in the next election, or is there a connection between cancers in a community?

Nature Of:

  1. Mathematicians create visual and numerical representations of data to reveal relationships and meaning hidden in the raw data.
  2. Mathematicians reason abstractly and quantitatively. (MP)
  3. Mathematicians model with mathematics. (MP)
  4. Mathematicians use appropriate tools strategically. (MP)

1 including joint, marginal, and conditional relative frequencies.

2 rate of change. (CCSS: S-ID.7)

3 constant term. (CCSS: S-ID.7)

Content Area: Mathematics
Grade Level Expectations: Eighth Grade
Standard: 3. Data Analysis, Statistics, and Probability

Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations) - (Remove PGC Filter)

Concepts and skills students master:

1. Visual displays and summary statistics of two-variable data condense the information in data sets into usable knowledge

Evidence Outcomes 21st Century Skill and Readiness Competencies

Students Can:

  1. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. (CCSS: 8.SP.1)
  2. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. (CCSS: 8.SP.1)
  3. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.1 (CCSS: 8.SP.2)
  4. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.2 (CCSS: 8.SP.3)
  5. Explain patterns of association seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. (CCSS: 8.SP.4)
    • Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. (CCSS: 8.SP.4)
    • Use relative frequencies calculated for rows or columns to describe possible association between the two variables.3 (CCSS: 8.SP.4)

Inquiry Questions:

  1. How is it known that two variables are related to each other?
  2. How is it known that an apparent trend is just a coincidence?
  3. How can correct data lead to incorrect conclusions?
  4. How do you know when a credible prediction can be made?

Relevance & Application:

  1. The ability to analyze and interpret data helps to distinguish between false relationships such as developing superstitions from seeing two events happen in close succession versus identifying a credible correlation.
  2. Data analysis provides the tools to use data to model relationships, make predictions, and determine the reasonableness and limitations of those predictions. For example, predicting whether staying up late affects grades, or the relationships between education and income, between income and energy consumption, or between the unemployment rate and GDP.

Nature Of:

  1. Mathematicians discover new relationship embedded in information.
  2. Mathematicians construct viable arguments and critique the reasoning of others. (MP)
  3. Mathematicians model with mathematics. (MP)

1 Know that straight lines are widely used to model relationships between two quantitative variables. (CCSS: 8.SP.2)

2 For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. (CCSS: 8.SP.3)

3 For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? (CCSS: 8.SP.4)

Content Area: Mathematics
Grade Level Expectations: Sixth Grade
Standard: 3. Data Analysis, Statistics, and Probability

Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations) - (Remove PGC Filter)

Concepts and skills students master:

1. Visual displays and summary statistics of one-variable data condense the information in data sets into usable knowledge

Evidence Outcomes 21st Century Skill and Readiness Competencies

Students Can:

  1. Identify a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.1 (CCSS: 6.SP.1)
  2. Demonstrate 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. (CCSS: 6.SP.2)
  3. Explain 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. (CCSS: 6.SP.3)
  4. Summarize and describe distributions. (CCSS: 6.SP)
    • Display numerical data in plots on a number line, including dot plots, histograms, and box plots. (CCSS: 6.SP.4)
    • Summarize numerical data sets in relation to their context. (CCSS: 6.SP.5)
      • Report the number of observations. (CCSS: 6.SP.5a)
      • Describe the nature of the attribute under investigation, including how it was measured and its units of measurement. (CCSS: 6.SP.5b)
      • Give 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. (CCSS: 6.SP.5c)
      • Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. (CCSS: 6.SP.5d)

Inquiry Questions:

  1. Why are there so many ways to describe data?
  2. When is one data display better than another?
  3. When is one statistical measure better than another?
  4. What makes a good statistical question?

Relevance & Application:

  1. Comprehension of how to analyze and interpret data allows better understanding of large and complex systems such as analyzing employment data to better understand our economy, or analyzing achievement data to better understand our education system.
  2. Different data analysis tools enable the efficient communication of large amounts of information such as listing all the student scores on a state test versus using a box plot to show the distribution of the scores.

Nature Of:

  1. Mathematicians leverage strategic displays to reveal data.
  2. Mathematicians model with mathematics. (MP)
  3. Mathematicians use appropriate tools strategically. (MP)
  4. Mathematicians attend to precision. (MP)

1 For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages. (CCSS: 6.SP.1)

Content Area: Mathematics
Grade Level Expectations: Fifth Grade
Standard: 3. Data Analysis, Statistics, and Probability

Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations) - (Remove PGC Filter)

Concepts and skills students master:

1. Visual displays are used to interpret data

Evidence Outcomes 21st Century Skill and Readiness Competencies

Students Can:

  1. Represent and interpret data. (CCSS: 5.MD)
    • Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). (CCSS: 5.MD.2)
    • Use operations on fractions for this grade to solve problems involving information presented in line plots.1 (CCSS: 5.MD.2)

Inquiry Questions:

  1. How can you make sense of the data you collect?

Relevance & Application:

  1. The collection and analysis of data provides understanding of how things work. For example, measuring the temperature every day for a year helps to better understand weather.

Nature Of:

  1. Mathematics helps people collect and use information to make good decisions.
  2. Mathematicians model with mathematics. (MP)
  3. Mathematicians use appropriate tools strategically. (MP)
  4. Mathematicians attend to precision. (MP)

1 For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. (CCSS: 5.MD.2)

Content Area: Mathematics
Grade Level Expectations: Fourth Grade
Standard: 3. Data Analysis, Statistics, and Probability

Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations) - (Remove PGC Filter)

Concepts and skills students master:

1. Visual displays are used to represent data

Evidence Outcomes 21st Century Skill and Readiness Competencies

Students Can:

  1. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). (CCSS: 4.MD.4)
  2. Solve problems involving addition and subtraction of fractions by using information presented in line plots.1 (CCSS: 4.MD.4)

Inquiry Questions:

  1. What can you learn by collecting data?
  2. What can the shape of data in a display tell you?

Relevance & Application:

  1. The collection and analysis of data provides understanding of how things work. For example, measuring the weather every day for a year helps to better understand weather.

Nature Of:

  1. Mathematics helps people use data to learn about the world.
  2. Mathematicians model with mathematics. (MP)
  3. Mathematicians use appropriate tools strategically. (MP)
  4. Mathematicians attend to precision. (MP)

1 For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. (CCSS: 4.MD.4)

Content Area: Mathematics
Grade Level Expectations: Third Grade
Standard: 3. Data Analysis, Statistics, and Probability

Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations) - (Remove PGC Filter)

Concepts and skills students master:

1. Visual displays are used to describe data

Evidence Outcomes 21st Century Skill and Readiness Competencies

Students Can:

  1. Represent and interpret data. (CCSS: 3.MD)
    • Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. (CCSS: 3.MD.3)
    • Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs.1 (CCSS: 3.MD.3)
    • Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters. (CCSS: 3.MD.4)

Inquiry Questions:

  1. What can data tell you about your class or school?
  2. How do data displays help us understand information?

Relevance & Application:

  1. The collection and use of data provides better understanding of people and the world such as knowing what games classmates like to play, how many siblings friends have, or personal progress made in sports.

Nature Of:

  1. Mathematical data can be represented in both static and animated displays.
  2. Mathematicians model with mathematics. (MP)
  3. Mathematicians use appropriate tools strategically. (MP)
  4. Mathematicians attend to precision. (MP)

1 For example, draw a bar graph in which each square in the bar graph might represent 5 pets. (CCSS: 3.MD.3)

Content Area: Mathematics
Grade Level Expectations: Second Grade
Standard: 3. Data Analysis, Statistics, and Probability

Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations) - (Remove PGC Filter)

Concepts and skills students master:

1. Visual displays of data can be constructed in a variety of formats to solve problems

Evidence Outcomes 21st Century Skill and Readiness Competencies

Students Can:

  1. Represent and interpret data. (CCSS: 2.MD)
    • Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. (CCSS: 2.MD.9)
    • Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. (CCSS: 2.MD.10)
    • Solve simple put together, take-apart, and compare problems using information presented in picture and bar graphs. (CCSS: 2.MD.10)

Inquiry Questions:

  1. What are the ways data can be displayed?
  2. What can data tell you about the people you survey?
  3. What makes a good survey question?

Relevance & Application:

  1. People use data to describe the world and answer questions such as how many classmates are buying lunch today, how much it rained yesterday, or in which month are the most birthdays.

Nature Of:

  1. Mathematics can be displayed as symbols.
  2. Mathematicians make sense of problems and persevere in solving them. (MP)
  3. Mathematicians model with mathematics. (MP)
  4. Mathematicians attend to precision. (MP)

Content Area: Mathematics
Grade Level Expectations: First Grade
Standard: 3. Data Analysis, Statistics, and Probability

Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations) - (Remove PGC Filter)

Concepts and skills students master:

1. Visual displays of information can used to answer questions

Evidence Outcomes 21st Century Skill and Readiness Competencies

Students Can:

  1. Represent and interpret data. (CCSS: 1.MD)
    • Organize, represent, and interpret data with up to three categories. (CCSS: 1.MD.4)
    • Ask and answer questions about the total number of data points how many in each category, and how many more or less are in one category than in another. (CCSS: 1.MD.4)

Inquiry Questions:

  1. What kinds of questions generate data?
  2. What questions can be answered by a data representation?

Relevance & Application:

  1. People use graphs and charts to communicate information and learn about a class or community such as the kinds of cars people drive, or favorite ice cream flavors of a class.

Nature Of:

  1. Mathematicians organize and explain random information
  2. Mathematicians model with mathematics. (MP)