Elementary Mathematics Benchmarks, Probability and Statistics Strand
Kindergarten
PS.K.1 Recognize and use words that represent time, temperature, and money.
a. Recognize and use the words day, night, morning, afternoon, evening, yesterday, today, tomorrow.
- Identify daily landmark times such as bedtime or lunch time.
b. Recognize the role of clocks and calendars in measuring and keeping track of time.
c. Know that thermometers measure temperature and that degree is the word used to name a temperature.
d. Identify U.S. coins by name.
Grade 1
PS.1.1 Use picture graphs to pose and solve problems.
a. Interpret picture graphs in words (orally) and with numbers.
- Answer questions about the meaning of picture graphs.
b. Create picture graphs of counts and measurements from collected or provided data.
- Represent data both in horizontal and vertical forms.
- Label axes or explain what they represent.
- Pose and answer comparison questions based on picture graphs.
Grade 2
PS.2.1 Tell, estimate, and calculate with time.
a. Tell, write, and use time measurements from analog (round) clock faces and from digital clocks and translate between the two.
- Round off to the nearest five minutes.
- Understand and use different ways to read time, e.g., "nine fifteen" or "quarter past nine," "nine fifty" or "ten to ten."
- Understand a.m. and p.m.
b. Understand the meaning of time as an interval and be able to estimate the passage of time without clock measurement.
c. Understand and use comparative phrases such as "in fifteen minutes," "half an hour from now," "ten minutes late."
PS.2.2 Count, add, and subtract money.
a. Read, write, add, and subtract money up to 10 dollars.
- Handle money accurately and make change for amounts of $10 or less by counting up.
- Use the symbols $ and ¢ properly.
- Recognize and use conventional ("decimal") monetary notation and translate back and forth into $ and ¢ notation.
- Add and subtract monetary amounts in both $ and ¢ and conventional notation.
- Use a calculator to check monetary calculations and also to add lists of three or more amounts.
- Estimate answers to check for reasonableness of hand or calculator methods.
PS.2.3 Represent measurements by means of bar graphs.
a. Collect data and record them in systematic form.
b. Select appropriate scales for a graph and make them explicit in labels.
- Employ both horizontal and vertical configurations.
- Recognize an axis with a scale as a representation of the number line.
- Compare scales on different graphs.
- Use addition and subtraction as appropriate to translate data (gathered or provided) into measurements required to construct a graph.
c. Create and solve problems that require interpretation of bar or picture graphs.
Grade 3
Note: Probability and Statistics is not a focus in grade 3 of these expectations.
Grade 4
PS.4.1 Record, arrange, present, and interpret data using tables and various types of graphs.
a. Create and interpret line, bar, and circle graphs and their associated tables of data.
- Create and label appropriate scales for graphs.
- Prepare labels or captions to explain what a table or graph represents.
- Solve problems using data presented in graphs and tables.
- Employ fractions and mixed numbers, as needed, in tables and graphs.
Grade 5
PS.5.1 Find, interpret, and use the average (mean) of a set of data.
a. Calculate the average of a set of data that includes whole numbers, fractions, and decimals.
Note: Emphasize that data is plural and datum is singular, the name for a single number in a set of data.
- Infer characteristics of a data set given the mean and other incomplete information.
Grade 6
PS.6.1 Understand the meaning of probability and how it is expressed.
a. The probability of an event is a number between zero and one that expresses the likelihood of an occurrence.
- The probibility of an occurrence is the ratio of the number of actual occurrences to the number of possible occurrences.
- Understand different ways of expressing probabilities—as percentages, decimals, or odds.
Example: If the probability of rain is .6, the weather forecaster could say that there is a 60% chance of rain or that the odds of rain are 6:4 (or 3:2).
- If p is the probability that an event will occur, then 1 – p is the probability that it will not occur.
Example: If the probability of rain is 60%, then the probability that it will not rain is 100% – 60% = 40%. (Equivalently, 1 – .60 = .40.)