Standard 1
1M-E1.Read, write and order integers, whole numbers and rational numbers
PO 1. Compare and order using concrete or illustrated models
A. whole numbers (to millions)
B. common fractions (halves, thirds, fourths, eighths)
C. decimals (thousandths)
PO 2. Represent place value using concrete or illustrated models
A. whole numbers (millions), decimals (thousandths)
PO 3. Read and write whole numbers, integers, common fractions and decimals using real-world situations
A. whole number (millions), decimals (thousandths), fractions (halves, thirds, fourths, eighths)
1M-E2.Relate the basic arithmetic operations to one another (e.g., multiplication and division are inverse operations)
PO 1. Represent the process of multiplication as repeated addition, using concrete or illustrative models
A. whole numbers
PO 2. Represent the process of division as repeated subtraction, partitioning a group and partitioning a whole, using concrete or illustrative models
A. whole numbers
PO 3. Write the family of equations using inverse operations for a given set of numbers
A. whole numbers with addition/ subtraction [(4 + 5 = 9, 5 + 4 = 9, 9 4 = 5, 9 5 = 4) and multiplication/ division]
1M-E3.Demonstrate proficiency with the operations of multiplication and division of whole numbers
PO 1. Calculate multiplication/division
A. three-digit by two-digit to find the
product
B. facts through 12
C. mental math and estimation with multiples of 10
D. one-digit divisor to find quotient with remainder
PO 2. Calculate multiplication and division problems using contextual situations (Grades 4-5, 6-8)
1M-E4.Develop and apply number theory concepts (e.g., primes, factors and multiples) to represent numbers in various ways
PO 1. State the factors for a given whole number
PO 4. Sort numbers by their properties
A. odd, even
1M-E5.Represent and use numbers in equivalent forms (integers, fractions, percent, decimals, exponents, scientific notation and square roots)
PO 2. Demonstrate the relationship and equivalency among
A. decimals, fractions and percents (e.g.,1/2 = .5 = 50% with halves, fourths and tenths)
1M-E6.Recognize that the degree of precision needed in calculating a number depends on how the results will be used and the instruments used to generate the measurements
PO 2. Apply the appropriate strategy (e.g., estimation, approximation, rounding or exact numbers) when calculating to solve problems
PO 3. Demonstrate/describe the magnitude of
A. whole numbers (e.g., "How many apples in the orchard?")
Note: We recommend that this be assessed at the district level.
PO 4. Interpret calculations and calculator results within a contextual situation (Grades 4-5, 6-8)
Standard 2
2M-E1.Construct, read, analyze and interpret tables, charts, graphs and data plots (e.g., box-and-whisker, stem-and-leaf, and scatter plots)
PO 1. Construct A. bar graphs, line graphs, frequency tables and Venn diagrams
PO 2. Interpret and analyze data from graphical representations and draw simple conclusions
A. bar graphs, line graphs, circle graphs, frequency tables and Venn diagrams
2M-E2.Make valid inferences, predictions and arguments based on statistical analysis
PO 1. Formulate predictions from a given set of data and justify predictions
PO 2. Compare a given prediction with the results of an investigation
2M-E3.Display and use measures of range and central tendency (i.e., mean, median and mode)
PO 1. Find the mean, median, mode and range of data using concrete and illustrative models
2M-E4.Use counting strategies to determine all the possible outcomes of a particular event (e.g., the number of ways students can line up to have their pictures taken)
PO 1. Find all possible outcome sets involving
A. two sets of objects (e.g., shirts and pants)
2M-E5.Determine probabilities through experiments and/or simulations and compare the results with the mathematical expectation
PO 1. Make predictions from the results of a student-generated experiment (empirical probability)
A. single events (e.g., spinners)
PO 3. Describe events that are certain or
impossible
PO 5. Identify outcomes that are more likely, less likely or equally
likely to occur
Standard 3
3M-E1.Use algebraic methods (write number sentences, in the form of expressions and equations) to explore, model and describe patterns and functions involving numbers, shapes, data, graphs and data plots
PO 1. Extend simple geometric and number
patterns (e.g., 1, 1, 2, 1, 1, 3, 1, 1, 4 . . .)
PO 2. Create simple geometric and number patterns
PO 3. Describe a rule for a simple pattern (e.g., 5, 10, 15, 20
. . . rule = add five or count by fives)
3M-E4.Analyze functional relationships to explain how a change in one variable results in a change in another
PO 1. Describe a real-life situation in
which a change in one variable results in the change of the other
(e.g., temperature in the classroom goes up and the amount of
clothing goes down)
PO 3. Compute an "output" for a given "input"
in a function
3M-E5.Use patterns and functions to represent and solve problems both formally and informally (e.g., measuring the height a ball bounces by dropping different balls from different starting heights)
3M-E7.Solve simple linear equations and inequalities using a variety of methods (e.g., informal, formal, graphical) and a variety of manipulatives
PO 1. Solve equations using
A. whole numbers with one variable-one step
PO 3. Graph given data points to represent a linear equation
A. on a coordinate grid with whole numbers
Standard 4
4M-E1.Visualize and draw two- and three-dimensional geometric figures with special attention to analyzing and reasoning informally about their properties (e.g., parallelism, perpendicularity and congruence)
PO 1. Classify two-dimensional shapes and three-dimensional figures by their properties
A. by sight
PO 2. Identify the properties of geometric figures using appropriate terminology and vocabulary (e.g., parallelism, perpendicularity and congruency)
A. two-dimensional shapes (three- and four-sided polygons)
PO 3. Draw or build two-dimensional shapes by applying significant properties of each (e.g., draw a rectangle with two sets of parallel sides and four right angles)
4M-E2.Apply geometric properties and relationships such as congruence, similarity, angle measure, parallelism and perpendicularity to real-world situations
PO 1. Design or draw a model (e.g., designing a playhouse, garden) that demonstrates basic geometric relationships, such as
A. parallelism, perpendicularity, similarity
PO 2. Classify triangles by their angles
and sides (e.g., equilateral, acute, isosceles . . .)
PO 5. Identify lines that are parallel and perpendicular
PO 6. Distinguish shapes that are congruent
4M-E3.Perform elementary transformations (e.g., tessellations, flips, slides, rotations)
PO 1. Demonstrate slide, flip or turn using
concrete geometric figures
PO 2. Illustrate, using concrete or pictorial models,
A. slide, flip or turn (e.g., quilts)
PO 3. Draw or build a shape that
A. has symmetry
4M-E4.Represent and solve problems relating to size, shape, area and volume using geometric models
PO 1. Solve problems using given formulas for
A. simple area and perimeter
PO 2. Identify a variety of shapes having the same perimeter and area
Standard 5
5M-E1.Estimate, make and use measurements (U.S. customary and metric) to describe and make comparisons
PO 1. Measure length, volume and weight
in both U.S. customary and metric units (Grades 4-5)
PO 2. Convert measurement units to equivalent units within a given
system (customary and metric) (e.g., 12 inches = 1 foot, 10 decimeters
= 1 meter)
PO 3. Estimate measurements for both U.S. customary and metric
units within either system
5M-E2.Select and use appropriate units and tools to measure to the degree of accuracy required in a particular problem-solving situation
PO 1. State the appropriate tool to measure
in a particular situation (e.g., "What tool would you use
to measure the top of your desk?")
PO 2. State the appropriate unit of measurement in a particular
situation (e.g., "What unit of measurement would you use
to measure the top of your desk?"
PO 3. Measure to the appropriate degree of accuracy to solve problems
(e.g., measuring to the nearest sixteenth of an inch or using
ounces, measuring to the nearest millimeter or using liters)
5M-E3.Estimate, use and describe measures of distance, perimeter, area, volume, capacity, weight, mass and angles
PO 1. Differentiate between perimeter and
area of quadrilaterals using concrete and illustrative models
PO 2. Record estimates and measurements for
A. distance
C. perimeter
E. area
G. weight
5M-E4.Develop and use formulas and procedures to solve problems involving measurement
PO 1. Develop a procedure or formula to calculate
A. area and perimeter of simple polygons
PO 2. Use given formulas to find
A. area and perimeter of simple polygons
5M-E5.Describe how a change in the linear dimension of an object affects its perimeter, area and volume
PO 1. Describe the change in perimeter and area when one dimension of an object is altered
5M-E6.Use calculators and computers to perform basic recursive and iterative processes
PO 1. Solve a problem using the iterative process
A. doubling (e.g., "If you get paid 1 cent the first day, 2 cents the second day, each day doubling the previous day's pay, how much would you get paid on the 20th day?")
PO 2. Generate the interative sequence for the next six terms when given the first four terms (e.g., 4, 7, 10, 13, . . .)
Standard 6
6M-E1.Use models to explain how ratios, proportions and percents can be used to solve problems and apply reasoning processes, such as spatial reasoning and reasoning with proportions and graphs
6M-E2.Construct, use and explain algorithmic procedures for computing and estimating with whole numbers, fractions, decimals and integers
PO 1. Design a method with a series of defined steps for solving a problem; justify the method
6M-E3.Use if . . . then statements to construct simple valid arguments
PO 1. Construct simple valid arguments using if . . . then statements based on
A. graphic organizers (e.g., Venn diagrams
and pictures . . .)
B. geometric shapes