Data Analysis, Probability, Ratio and Proportion
Primary grades 4-8
Data Analysis
Facts, Concepts, and Generalizations
- Data can be arranged in different ways.
- Data can be represented differently in different forms.
- Some representations are better than others.
- Organization of data can help interpretation (graphs, charts, tables, Venn diagrams...)
- Different data measures may be appropriate to describe different sets of data.
- Bar graphs are... and are used with categorical data.
- Samples can be used to make predictions.
- Range of data is the spread or difference between the least and most set of quantities (smallest and largest quantities) Range is affect most by an extreem quantity.
- Mean is the the quotient of the sum of data points divided by the number of data points; (arithmetic mean or average) is the sum of the value of each item divided by the number of items.
- Median is the middle point or the average of the middle points of a sequence of data points arranged by value; the value at the midpoint of a frequency distribution such that there is an equal probability of falling above or below it. Median is the middle set of data.
- Mean is equal to the number of cases plus one divided by 2. It would be the middle value in an odd numbers set of cases or the mid point between the two middle sets of cases in an even number of cases.
- Mode is the data point that occurs most frequently in a set of data.
- Measure of central tendency includes average, mean, mode, median...
- Scatter plot
- Stem and leaf plot... A stem and leaf plot can be used to find mean, median, or mode.
- Line graph
- Pie chart
- Categorical data is
- Continuous data is
- Different scales on a graph creates different impressions of the same data.
- Normal curve of distribution is also know as the Gaussian curve.
Indicators or Outcomes
- Collect, construct, and interpret data displays and compute mean, median, and mode.
- Make predictions from data and explain reasoning and informal measures of central tendency.
- Analyze statistical claims and design experiments, and they may use simulations to model real-world situations.
- Some understanding of sampling and make predictions based on experiments or data.
- Comfortable using various graphs to represent different types of data in different situations.
Instructional Idea and activities
Probability
Indicators or Outcomes
Conduct experiments or simulations to demonstrate< theoreticalprobability and relative frequency.
Facts, Concepts, and Generalizations
- An event has a set of outcomes. The smallest set of outcomes is the empty set or impossibility.
- Events are impossible, possible, or certain.
- Probability is how likely an outcome is to occur.
- Probability can be used to make predictions.
- Probability can be determined theoretically (Use reasoning to find the total possible outcomes, the total of each specific outcome, and the proportion of the specific to the total).
- Probability can be determined experimentally (Experimentally collect data for each specific outcome and use it to calculate the proportion of the specific to the total).
- Probabilities can be written in the form of a fraction, decimal, and percent.
- Probability is between 0 and 1.
- A fair game is one where all participants have equal chance of success.
- A tree diagram can be used to identify all outcomes of events.
Instructional Idea and activities
Ratio and Proportion
Facts, Concepts, and Generalizations
- Ratio is the relationship of one thing to another. Can be used to compare quantities.
- Ratio can be show with words (written and oral), fractional form, and quantities separated with a colon).
- Rates are ratios.
- Rates and ratios can be used to make predictions.
- Ratio tables can be used to make predictions.
- Ratios are used with measurement
- Cross products can be used to determine if two ratios are equivalent.
- Proportion is the relationship of a part to a whole
- Percent is part of one hundred
- Proportion uses the relationship of equality between two ratios.
Instructional Idea and activities