Mathematics Cumulative Progress Indicators (CPIs) for the end of the designated grade span

Place a "+" for an expectation that represents a strength & a "-" for a weakness

+ or -

STANDARD 4.4     (DATA ANALYSIS, PROBABILITY, AND DISCRETE MATHEMATICS)     ALL STUDENTS WILL DEVELOP AN UNDERSTANDING OF THE CONCEPTS AND TECHNIQUES OF DATA ANALYSIS, PROBABILITY, AND DISCRETE MATHEMATICS, AND WILL USE THEM TO MODEL SITUATIONS, SOLVE PROBLEMS, AND ANALYZE AND DRAW APPROPRIATE INFERENCES FROM DATA.

A.     Data Analysis

By the end of Grade 2, students will:

 1.         Collect, generate, record, and organize data in response to questions, claims, or curiosity.

·        Data collected from students’ everyday experiences

·        Data generated from chance devices, such as spinners and dice

 2.         Read, interpret, construct, and analyze displays of data.

·        Pictures, tally chart, pictograph, bar graph, Venn diagram

·        Smallest to largest, most frequent (mode)

Building upon knowledge and skills gained in preceding grades, by the end of Grade 3, students will:

 1.         Collect, generate, organize, and display data in response to questions, claims, or curiosity.

·        Data collected from the classroom environment

 2.         Read, interpret, construct, analyze, generate questions about, and draw inferences from displays of data.

·        Pictograph, bar graph, table

Building upon knowledge and skills gained in preceding grades, by the end of Grade 4, students will:

 1.         Collect, generate, organize, and display data in response to questions, claims, or curiosity.

·        Data collected from the school environment

 2.         Read, interpret, construct, analyze, generate questions about, and draw inferences from displays of data.

·        Pictograph, bar graph, line plot, line graph, table

·        Average (mean), most frequent (mode), middle term (median)

Building upon knowledge and skills gained in preceding grades, by the end of Grade 5, students will:

 1.         Collect, generate, organize, and display data.

·        Data generated from surveys

 2.         Read, interpret, select, construct, analyze, generate questions about, and draw inferences from displays of data.

·        Bar graph, line graph, circle graph, table

·        Range, median, and mean

 3.         Respond to questions about data and generate their own questions and hypotheses.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 6, students will:

 1.         Collect, generate, organize, and display data.

·        Data generated from surveys

 2.         Read, interpret, select, construct, analyze, generate questions about, and draw inferences from displays of data.

·        Bar graph, line graph, circle graph, table, histogram

·        Range, median, and mean

·        Calculators and computers used to record and process information

 3.         Respond to questions about data, generate their own questions and hypotheses, and formulate strategies for answering their questions and testing their hypotheses.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 7, students will:

 1.         Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode).

·        Type of display most appropriate for given data

·        Box-and-whisker plot, upper quartile, lower quartile

·        Scatter plot

·        Calculators and computer used to record and process information

 2.         Make inferences and formulate and evaluate arguments based on displays and analysis of data.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 8, students will:

 1.         Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode).

·        Type of display most appropriate for given data

·        Box-and-whisker plot, upper quartile, lower quartile

·        Scatter plot

·        Calculators and computer used to record and process information

·        Finding the median and mean (weighted average) using frequency data.

·        Effect of additional data on measures of central tendency

 2.         Make inferences and formulate and evaluate arguments based on displays and analysis of data.

 3.         Estimate lines of best fit and use them to interpolate within the range of the data.

 4.         Use surveys and sampling techniques to generate data and draw conclusions about large groups.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 12, students will:

 1.         Use surveys and sampling techniques to generate data and draw conclusions about large groups.

·        Advantages/disadvantages of sample selection methods (e.g., convenience sampling, responses to survey, random sampling)

 2.         Evaluate the use of data in real-world contexts.

·        Accuracy and reasonableness of conclusions drawn

·        Bias in conclusions drawn (e.g., influence of how data is displayed)

·        Statistical claims based on sampling

 3.         Design a statistical experiment, conduct the experiment, and interpret and communicate the outcome.

 4.         Estimate or determine lines of best fit (or curves of best fit if appropriate) with technology, and use them to interpolate within the range of the data.

 5.         Analyze data using technology, and use statistical terminology to describe conclusions.

·        Measures of dispersion:  variance, standard deviation, outliers

·        Correlation coefficient

·        Normal distribution (e.g., approximately 95% of the sample lies between two standard deviations on either side of the mean)