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3.1
Number and Operations
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3.1.1
Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.
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3.1.1.PO 1
Express whole numbers through six digits using and connecting multiple representations.
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3.1.1.PO 2
Compare and order whole numbers through six digits by applying the concept of place value.
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3.1.1.PO 3
Count and represent money using coins and bills to $100.00.
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3.1.1.PO 4
Sort whole numbers into sets and justify the sort.
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3.1.1.PO 5
Express benchmark fractions as fair sharing, parts of a whole, or parts of a set.
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3.1.1.PO 6
Compare and order benchmark fractions.
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3.1.2
Understand and apply numerical operations and their relationship to one another.
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3.1.2.PO 1
Add and subtract whole numbers to four digits.
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3.1.2.PO 2
Create and solve word problems based on addition, subtraction, multiplication, and division.
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3.1.2.PO 3
Demonstrate the concept of multiplication and division using multiple models.
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3.1.2.PO 4
Demonstrate fluency of multiplication and division facts through 10.
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3.1.2.PO 5
Apply and interpret the concept of multiplication and division as inverse operations to solve problems.
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3.1.2.PO 6
Describe the effect of operations (multiplication and division) on the size of whole numbers.
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3.1.2.PO 7
Apply commutative, identity, and zero properties to multiplication and apply the identity property to division.
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3.1.3
Use estimation strategies reasonably and fluently while integrating content from each of the other strands.
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3.1.3.PO 1
Make estimates appropriate to a given situation or computation with whole numbers.
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3.2
Data Analysis, Probability, and Discrete Mathematics
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3.2.1
Understand and apply data collection, organization, and representation to analyze and sort data.
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3.2.1.PO 1
Collect, record, organize, and display data using frequency tables, single bar graphs, or single line graphs.
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3.2.1.PO 2
Formulate and answer questions by interpreting and analyzing displays of data, including frequency tables, single bar graphs, or single line graphs.
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3.2.2
Understand and apply the basic concepts of probability.
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3.2.3
Understand and demonstrate the systematic listing and counting of possible outcomes.
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3.2.3.PO 1
Represent all possibilities for a variety of counting problems using arrays, charts, and systematic lists; draw conclusions from these representations.
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3.2.3.PO 2
Solve a variety of problems based on the multiplication principle of counting.
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3.2.4
Understand and apply vertex-edge graphs.
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3.2.4.PO 1
Color complex maps using the least number of colors and justify the coloring.
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3.2.4.PO 2
Investigate properties of vertex-edge graphs
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3.2.4.PO 2.a
circuits in a graph,
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3.2.4.PO 2.b
weights on edges, and
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3.2.4.PO 2.c
shortest path between two vertices.
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3.2.4.PO 3
Solve problems using vertex-edge graphs.
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3.3
Patterns, Algebra, and Functions
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3.3.1
Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.
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3.3.1.PO 1
Recognize, describe, extend, create, and find missing terms in a numerical sequence.
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3.3.1.PO 2
Explain the rule for a given numerical sequence and verify that the rule works.
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3.3.2
Describe and model functions and their relationships.
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3.3.2.PO 1
Recognize and describe a relationship between two quantities, given by a chart, table or graph, in which the quantities change proportionally, using words, pictures, or expressions.
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3.3.2.PO 2
Translate between the different representations of whole number relationships, including symbolic, numerical, verbal, or pictorial.
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3.3.3
Represent and analyze mathematical situations and structures using algebraic representations.
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3.3.3.PO 1
Record equivalent forms of whole numbers to six digits by constructing models and using numbers.
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3.3.3.PO 2
Use a symbol to represent an unknown quantity in a given context.
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3.3.3.PO 3
Create and solve simple one-step equations that can be solved using addition and multiplication facts.
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3.4
Geometry and Measurement
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3.4.1
Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.
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3.4.1.PO 1
Describe sequences of 2-dimensional figures created by increasing the number of sides, changing size, or changing orientation.
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3.4.1.PO 2
Recognize similar figures.
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3.4.1.PO 3
Identify and describe 3-dimensional figures including their relationship to real world objects: sphere, cube, cone, cylinder, pyramids, and rectangular prisms.
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3.4.1.PO 4
Describe and compare attributes of two- and three-dimensional figures.
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3.4.2
Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations.
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3.4.2.PO 1
Identify a translation, reflection, or rotation and model its effect on a 2-dimensional figure.
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3.4.2.PO 2
Identify, with justification, all lines of symmetry in a 2-dimensional figure.
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3.4.4
Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.
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3.4.4.PO 1
Determine elapsed time
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3.4.4.PO 1.a
across months using a calendar
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3.4.4.PO 1.b
by hours and half hours using a clock.
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3.4.4.PO 2
Apply measurement skills to measure length, weight, and capacity using US Customary units.
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3.4.4.PO 3
Convert units of length, weight, and capacity
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3.4.4.PO 3.a
inches or feet to yards,
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3.4.4.PO 3.b
ounces to pounds, and
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3.4.4.PO 3.c
cups to pints, pints to quarts, quarts to gallons.
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3.4.4.PO 4
Determine the area of a rectangular figure using an array model.
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3.4.4.PO 5
Measure and calculate perimeter of 2-dimensional figures
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3.5
Structure and Logic
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3.5.2
Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize their applications.
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3.5.2.PO 1
Analyze a problem situation to determine the question(s) to be answered.
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3.5.2.PO 2
Identify relevant, missing, and extraneous information related to the solution to a problem.
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3.5.2.PO 3
Select and use one or more strategies to efficiently solve the problem and justify the selection.
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3.5.2.PO 4
Determine whether a problem to be solved is similar to previously solved problems, and identify possible strategies for solving the problem.
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3.5.2.PO 5
Represent a problem situation using any combination of words, numbers, pictures, physical objects, or symbols.
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3.5.2.PO 6
Summarize mathematical information, explain reasoning, and draw conclusions.
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3.5.2.PO 7
Analyze and evaluate whether a solution is reasonable, is mathematically correct, and answers the question.
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3.5.2.PO 8
Make and test conjectures based on data (or information) collected from explorations and experiments.
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