GEOMETRY AND MEASUREMENT
❚ Identify positions of objects in space, and use appropriate language (e.g., beside, inside, next to, close to, above, below, apart) to describe and compare their relative positions.
❚ Recognize and compare the attributes of length, volume/capacity, weight, area, and time using appropriate language.
DATA ANALYSIS, STATISTICS, AND PROBABILITY
❚ Collect, sort, organize, and draw conclusions about data using concrete objects, pictures, numbers, and graphs.
Grades 1 and 2
NUMBER SENSE AND OPERATIONS; PATTERNS, RELATIONS, AND ALGEBRA
❚ Name and write (in numerals) whole numbers up to 1,000, identify the place value of the digits, and order the numbers.
❚ Identify and distinguish among multiple uses of numbers, including cardinal, ordinal, and numbers as labels and as measurements.
❚ Identify and represent common fractions (1⁄2, 1⁄3, 1⁄4) as parts of wholes and parts of groups, and numbers on a number line.
❚ Identify the value of all U. S. coins and $1, $5, $10, and $20 bills. Find the value of a collection of coins and dollar bills and different ways to represent an amount of money up to $5. Use appropriate notation (e.g., 69¢, $1.35).
❚ Demonstrate an understanding of the various meanings of addition and subtraction. ❚ Estimate, calculate, and solve problems involving addition and subtraction of two-digit
numbers.
❚ Describe functions related to trading, including coin trades (e.g., five pennies make one nickel).
MEASUREMENT
❚ Identify parts of the day (e.g., morning, afternoon, evening), week, month, and calendar.
Grades 1 and 2 (continued)
❚ Tell time at quarter-hour intervals on analog and digital clocks using a.m. and p.m. DATA ANALYSIS, STATISTICS, AND PROBABILITY
❚ Use interviews, surveys, and observations to gather data about themselves and their surroundings.
❚ Organize, classify, represent, and interpret data using tallies, charts, tables, bar graphs, pictographs, and Venn diagrams, and interpret the representations. ❚ Formulate inferences (draw conclusions) and make educated guesses (conjectures)
about a situation based on information gained from data.
Grades 3 and 4
NUMBER SENSE AND OPERATIONS; PATTERNS, RELATIONS, AND ALGEBRA
❚ Exhibit an understanding of the base 10 number system by reading, modeling, writing, and interpreting whole numbers to at least 100,000.
❚ Demonstrate an understanding of fractions as part of unit wholes, as parts of a collection, and as locations on a number line.
❚ Select, use, and explain models to relate common fractions and mixed numbers (1⁄2, 1⁄3, 1⁄4, 1⁄5, 1⁄6, 1⁄8, 1⁄12, and 1 1⁄2), find equivalent fractions, mixed numbers, and decimals, and order fractions.
❚ Select and use appropriate operations (addition, subtraction, multiplication, division) to solve problems, including those using money.
❚ Use pictures, models, tables, charts, graphs, words, number sentences, and mathematical notations to interpret mathematical relationships.
❚ Solve problems involving proportional relationships, including unit pricing and map interpretation.
❚ Determine how a change in one variable relates to a change in a second variable. MEASUREMENT
❚ Carry out simple unit conversions within a system of measurement system, e.g., hours to minutes, cents to dollars, yards to feet or inches.
Grades 3 and 4 (continued)
DATA ANALYSIS, STATISTICS, AND PROBABILITY
❚ Collect and organize data using observations, measurements, surveys, or experiments and identify appropriate ways to display the data.
❚ Match representations of a data set such as lists, tables, or graphs with the actual set of data.
❚ Construct, draw conclusions, and make predictions from various representations of data sets, including tables, bar graphs, pictographs, line graphs, line plots, and tallies.
Grades 5 and 6
NUMBER SENSE AND OPERATIONS; PATTERNS, RELATIONS, AND ALGEBRA
❚ Exhibit an understanding of place value to billions and thousandths.
❚ Demonstrate an understanding of fractions as a ratio of whole numbers, as part of unit wholes, as parts of a collection, and as locations on a number line.
❚ Identify and determine common equivalent fractions, mixed numbers, decimals, and percents.
❚ Find and position integers, fractions, mixed numbers, and decimals (both positive and negative) on a number line.
❚ Produce and interpret graphs that represent the relationship between two variables in everyday situations.
❚ Identify and describe relationships between two variables with a constant rate of change. Contrast these with relationships where the rate of change is not constant.
MEASUREMENT
❚ Solve problems involving proportional relationships and units of measurement, e.g., same system unit conversions, scale models, maps, and speed.
Grades 5 and 6 (continued)
DATA ANALYSIS, STATISTICS, AND PROBABILITY
❚ Describe and compare data sets using the concepts of median, mean, mode, maximum, minimum, and range.
❚ Construct and interpret stem and leaf plots, line plots, and circle graphs.
❚ Predict the probability of outcomes of simple experiments and test the predictions. Use appropriate ratios between 0 and 1 to represent the probability of the outcome and associate the probability with the likelihood of the event.
Grade 7 and 8
NUMBER SENSE AND OPERATIONS; PATTERNS, RELATIONS, AND ALGEBRA
❚ Compare, order, estimate, and translate among integers, fractions and mixed numbers, decimals, and percents.
❚ Use ratios and proportions in the solution of problems, in particular problems involving unit rates, scale factors, and rate of change.
❚ Determine when an estimate rather than an exact answer is appropriate and apply in problem situations.
❚ Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic expressions. Include arithmetic and geometric progressions, e.g., compounding.
❚ Use tables and graphs to represent and compare linear growth patterns. In particular, compare rates of change and x- and y-intercepts of different linear patterns.
MEASUREMENT
❚ Select, convert (within the same system of measurement), and use appropriate units of measurement or scale.
Grades 7 and 8 (continued)
DATA ANALYSIS, STATISTICS, AND PROBABILITY
❚ Describe the characteristics and limitations of a data sample. Identify different ways of selecting a sample, e.g., convenience sampling, responses to a survey, random sampling.
❚ Select, create, interpret, and utilize various tabular and graphical representations of data, e.g., circle graphs, Venn diagrams, scatterplots, stem-and-leaf plots, box-and- whisker plots, histograms, tables, and charts.
❚ Find, describe, and interpret appropriate measures of central tendency (mean, median, and mode) and spread (range) that represent a set of data. Use these notions to compare sets of data.