Table of Contents
- California's 2007 mathematics standards.
- Florida's 2007 mathematics standards.
- Oregon's 2007 mathematics standards.
- Members of Asia-Pacific Economic Cooperation.
- Florida's 2007 mathematics standards.
California's 2007 mathematics standards:
Click here to link to additional California's standards informationNumber Sense
1.0 Students understand the place value of whole numbers:
1.1 Count, read, and write whole numbers to 10,000.
1.2 Compare and order whole numbers to 10,000.
1.3 Identify the place value for each digit in numbers to 10,000.
1.4 Round off numbers to 10,000 to the nearest ten, hundred, and thousand.
1.5 Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6).
2.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division:
2.1 Find the sum or difference of two whole numbers between 0 and 10,000.
2.2 Memorize to automaticity the multiplication table for numbers between 1 and 10.
2.3 Use the inverse relationship of multiplication and division to compute and check results.
2.4 Solve simple problems involving multiplication of multidigit numbers by one-digit numbers (3,671 x 3 = __).
2.5 Solve division problems in which a multidigit number is evenly divided by a one-digit number (135 ÷ 5 = __).
2.6 Understand the special properties of 0 and 1 in multiplication and division.
2.7 Determine the unit cost when given the total cost and number of units.
2.8 Solve problems that require two or more of the skills mentioned above.
3.0 Students understand the relationship between whole numbers, simple fractions, and decimals:
3.1 Compare fractions represented by drawings or concrete materials to show equivalency and to add and subtract simple fractions in context (e.g., 1/2 of a pizza is the same amount as 2/4 of another pizza that is the same size; show that 3/8 is larger tha 3.2 Add and subtract simple fractions (e.g., determine that 1/8 + 3/8 is the same as 1/2).
3.3 Solve problems involving addition, subtraction, multiplication, and division of money amounts in decimal notation and multiply and divide money amounts in decimal notation by using whole-number multipliers and divisors.
3.4 Know and understand that fractions and decimals are two different representations of the same concept (e.g., 50 cents is 1/2 of a dollar, 75 cents is 3/4 of a dollar).
Algebra and Functions
1.0 Students select appropriate symbols, operations, and properties to represent, describe, simplify, and solve simple number relationships:
1.1 Represent relationships of quantities in the form of mathematical expressions, equations, or inequalities.
1.2 Solve problems involving numeric equations or inequalities.
1.3 Select appropriate operational and relational symbols to make an expression true (e.g., if 4 _ 3 = 12, what operational symbol goes in the blank?)
1.4 Express simple unit conversions in symbolic form (e.g., __ inches = __ feet x 12).
1.5 Recognize and use the commutative and associative properties of multiplication(e.g., if 5 x 7 = 35, then what is 7 x 5? and if 5 x 7 x 3 = 105, then what is 7 x 3 x 5?).
2.0 Students represent simple functional relationships:
2.1 Solve simple problems involving a functional relationship between two quantities (e.g., find the total cost of multiple items given the cost per unit).
2.2 Extend and recognize a linear pattern by its rules (e.g., the number of legs on a given number of horses may be calculated by counting by 4s or by multiplying the number of horses by 4).
Measurement and Geometry
1.0 Students choose and use appropriate units and measurement tools to quantify the properties of objects:
1.1 Choose the appropriate tools and units (metric and U.S.) and estimate and measure the length, liquid volume, and weight/mass of given objects.
1.2 Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them.
1.3 Find the perimeter of a polygon with integer sides.
1.4 Carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes).
2.0 Students describe and compare the attributes of plane and solid geometric figures and use their understanding to show relationships and solve problems:
2.1 Identify, describe, and classify polygons (including pentagons, hexagons, and octagons).
2.2 Identify attributes of triangles (e.g., two equal sides for the isosceles triangle, three equal sides for the equilateral triangle, right angle for the right triangle).
2.3 Identify attributes of quadrilaterals (e.g., parallel sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square).
2.4 Identify right angles in geometric figures or in appropriate objects and determine whether other angles are greater or less than a right angle.
2.5 Identify, describe, and classify common three-dimensional geometric objects (e.g., cube, rectangular solid, sphere, prism, pyramid, cone, cylinder).
2.6 Identify common solid objects that are the components needed to make a more complex solid object.
Statistics, Data Analysis, and Probability
1.0 Students conduct simple probability experiments by determining the number of possible outcomes and make simple predictions:
1.1 Identify whether common events are certain, likely, unlikely, or improbable.
1.2 Record the possible outcomes for a simple event (e.g., tossing a coin) and systematically keep track of the outcomes when the event is repeated many times.
1.3 Summarize and display the results of probability experiments in a clear and organized way (e.g., use a bar graph or a line plot).
1.4 Use the results of probability experiments to predict future events (e.g., use a line plot to predict the temperature forecast for the next day).
Mathematical Reasoning
1.0 Students make decisions about how to approach problems:
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
1.2 Determine when and how to break a problem into simpler parts.
2.0 Students use strategies, skills, and concepts in finding solutions:
2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.
2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
2.4 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
2.6 Make precise calculations and check the validity of the results from the context of the problem.
3.0 Students move beyond a particular problem by generalizing to other situations:
3.1 Evaluate the reasonableness of the solution in the context of the original situation.
3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
3.3 Develop generalizations of the results obtained and apply them in other circumstances.
Florida's 2007 mathematics standards:
Click here to link to additional Florida's standards informationMA.3.A.1.1 Model multiplication and division including problems presented in context: repeated addition,multiplicative comparison, array, how many combinations, measurement, and partitioning.
MA.3.A.1.2 Solve multiplication and division fact problems by using strategies that result from applying number properties.
MA.3.A.1.3 Identify, describe, and apply division and multiplication as inverse operations.
MA.3.A.2.1 Represent fractions, including fractions greater than one, using area, set and linear models.
MA.3.A.2.2 Describe how the size of the fractional part is related to the number of equal sized pieces in the whole.
MA.3.A.2.3 Compare and order fractions, including fractions greater than one, using models and strategies.
MA.3.A.2.4 Use models to represent equivalent fractions, including fractions greater than one, and identify representations of equivalence.
MA.3.G.3.1 Describe, analyze, compare and classify two-dimensional shapes using sides and angles – including acute, obtuse, and right angles – and connect these ideas to the definition of shapes.
MA.3.G.3.2 Compose, decompose, and transform polygons to make other polygons, including concave and convex polygons with three, four, five, six, eight, or ten sides.
MA.3.G.3.3 Build, draw and analyze two-dimensional shapes from several orientations in order to examine andapply congruence and symmetry.
MA.3.A.4.1 Create, analyze, and represent patterns and relationships using words, variables, tables and graphs.
MA.3.G.5.1 Select appropriate units, strategies and tools to solve problems involving perimeter.
MA.3.G.5.2 Measure objects using fractional parts of linear units such as 1/2, 1/4 and 1/10
MA.3.G.5.3 Tell time to the nearest minute and to the nearest quarter hour, and determine the amount of time elapsed.
MA.3.A.6.1 Represent, compute, estimate and solve problems using numbers through hundred thousands.
MA.3.A.6.2 Solve non-routine problems by making a table, chart, or list and searching for patterns.
MA.3.S.7.1 Construct and analyze frequency tables, bar graphs, pictographs, and line plots from data, including data collected through observations, surveys, and experiments.
Oregon's 2007 mathematics standards:
Click here to link to additional Oregon's standards informationIt is essential that these standards be addressed in contexts that promote problem solving, reasoning, communication, making connections, and designing and analyzing representations.
3.1 Number and Operations: Develop an understanding of fractions and fraction equivalence.
3.1.1 Represent common fractions (e.g., halves, thirds, fourths, tenths) as equal parts of a whole, parts of a set, or points or distances on a number line.
3.1.2 Recognize and demonstrate that sizes of fractional parts are relative to the size of the whole.
3.1.3 Use fractions to represent numbers that are equal to, less than, or greater than one.
3.1.4 Solve problems that involve comparing and ordering fractions by using models, benchmarks (0, ½, 1), or common numerators or denominators.
3.1.5 Identify equivalent fractions using models, including the number line.
3.1.6 Add common fractions with like denominators.
3.2 Number and Operations, Algebra, and Data Analysis: Develop understandings of multiplication and division, and strategies for basic multiplication facts and related division facts.
3.2.1 Represent and apply the concept of multiplication as repeated addition.
3.2.2 Represent and apply the concept of division as repeated subtraction and forming equal groups.
3.2.3 Apply models of multiplication (e.g., equal-sized groups, arrays, area models, equal “jumps” on number lines and hundreds charts) and division (e.g., repeated subtraction, partitioning, and sharing) to solve problems.
3.2.4 Apply increasingly sophisticated strategies based on the number properties (e.g., place value, commutative, associative, distributive, identity, and zero) to solve multiplication and division problems involving basic facts.
3.2.5 Apply the inverse relationship between multiplication and division (e.g., 5 x 6 = 30, 30 ÷ 6 = 5) and the relationship between multiples and factors.
3.2.6 Represent, analyze and extend number patterns using rules that involve multiplication and/or addition (e.g., {3, 6, 9, 12, …}, .{1, 2, 4, 8, …} ).
3.2.7 Analyze frequency tables, bar graphs, picture graphs, and line plots; and use them to solve problems involving addition, subtraction, multiplication, and division.
3.3 Geometry and Measurement: Describe and analyze properties of two-dimensional shapes, including perimeters.
3.3.1 Identify right angles in two-dimensional shapes and determine if angles are greater than or less than a right angle (obtuse and acute).
3.3.2 Identify, describe, compare, analyze, and informally classify triangles by their sides and angles.
3.3.3 Identify, describe, compare, analyze, and classify quadrilaterals (square, rectangle, parallelogram, rhombus, and trapezoid) by their sides and angles.
3.3.4 Identify, describe, and compare pentagons, hexagons, and octagons by the number of sides or angles.
3.3.5 Investigate and describe the results of decomposing, combining, and transforming polygons to make other polygons.
3.3.6 Build, draw, and analyze two-dimensional shapes to understand attributes and properties of two-dimensional space.
3.3.7 Determine an appropriate unit, tool, or strategy to find the perimeter of polygons.
3.3.8 Use attributes and properties of two-dimensional shapes to solve problems including applications involving parallel and perpendicular lines, congruence, symmetry, and perimeter
Members of Asia-Pacific Economic Cooperation:
link to Asia-Pacific Economic Cooperation membersStandards are available for Australia , China , Japan, Malaysia, New Zealand, Singapore, and several US versions through this wiki group link .
( Note that some have large PDF files.)