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 relationship between numbers, quantities, and place value in whole numbers up to 1,000:
1.1 Count, read, and write whole numbers to 1,000 and identify the place value for each digit.
1.2 Use words, models, and expanded forms (e.g., 45 = 4 tens + 5) to represent numbers (to 1,000).
1.3 Order and compare whole numbers to 1,000 by using the symbols <, =, >.
2.0 Students estimate, calculate, and solve problems involving addition and subtraction of two-and three-digit numbers:
2.1 Understand and use the inverse relationship between addition and subtraction (e.g., an opposite number sentence for 8 + 6 = 14 is 14 - 6 = 8) to solve problems and check solutions.
2.2 Find the sum or difference of two whole numbers up to three digits long.
2.3 Use mental arithmetic to find the sum or difference of two two-digit numbers.
3.0 Students model and solve simple problems involving multiplication and division:
3.1 Use repeated addition, arrays, and counting by multiples to do multiplication.
3.2 Use repeated subtraction, equal sharing, and forming equal groups with remainders to do division.
3.3 Know the multiplication tables of 2s, 5s, and 10s (to "times 10") and commit them to memory.
4.0 Students understand that fractions and decimals may refer to parts of a set and parts of a whole:
4.1 Recognize, name, and compare unit fractions from 1/12 to 1/2.
4.2 Recognize fractions of a whole and parts of a group (e.g., one-fourth of a pie, two-thirds of 15 balls).
4.3 Know that when all fractional parts are included, such as four-fourths, the result is equal to the whole and to one.
5.0 Students model and solve problems by representing, adding, and subtracting amounts of money:
5.1 Solve problems using combinations of coins and bills.
5.2 Know and use the decimal notation and the dollar and cent symbols for money.
6.0 Students use estimation strategies in computation and problem solving that involve numbers that use the ones, tens, hundreds, and thousands places:
6.1 Recognize when an estimate is reasonable in measurements (e.g., closest inch).
Algebra and Functions
1.0 Students model, represent, and interpret number relationships to create and solve problems involving addition and subtraction:
1.1 Use the commutative and associative rules to simplify mental calculations and to check results.
1.2 Relate problem situations to number sentences involving addition and subtraction.
1.3 Solve addition and subtraction problems by using data from simple charts, picture graphs, and number sentences.
Measurement and Geometry
1.0 Students understand that measurement is accomplished by identifying a unit of measure, iterating (repeating) that unit, and comparing it to the item to be measured:
1.1 Measure the length of objects by iterating (repeating) a nonstandard or standard unit.
1.2 Use different units to measure the same object and predict whether the measure will be greater or smaller when a different unit is used.
1.3 Measure the length of an object to the nearest inch and/ or centimeter.
1.4 Tell time to the nearest quarter hour and know relationships of time (e.g., minutes in an hour, days in a month, weeks in a year).
1.5 Determine the duration of intervals of time in hours (e.g., 11:00 a.m. to 4:00 p.m.).
2.0 Students identify and describe the attributes of common figures in the plane and of common objects in space:
2.1 Describe and classify plane and solid geometric shapes (e.g., circle, triangle, square, rectangle, sphere, pyramid, cube, rectangular prism) according to the number and shape of faces, edges, and vertices.
2.2 Put shapes together and take them apart to form other shapes (e.g., two congruent right triangles can be arranged to form a rectangle).
Statistics, Data Analysis, and Probability
1.0 Students collect numerical data and record, organize, display, and interpret the data on bar graphs and other representations:
1.1 Record numerical data in systematic ways, keeping track of what has been counted.
1.2 Represent the same data set in more than one way (e.g., bar graphs and charts with tallies).
1.3 Identify features of data sets (range and mode).
1.4 Ask and answer simple questions related to data representations.
2.0 Students demonstrate an understanding of patterns and how patterns grow and describe them in general ways:
2.1 Recognize, describe, and extend patterns and determine a next term in linear patterns (e.g., 4, 8, 12 ...; the number of ears on one horse, two horses, three horses, four horses).
2.2 Solve problems involving simple number patterns.
Mathematical Reasoning
1.0 Students make decisions about how to set up a problem:
1.1 Determine the approach, materials, and strategies to be used.
1.2 Use tools, such as manipulatives or sketches, to model problems.
2.0 Students solve problems and justify their reasoning:
2.1 Defend the reasoning used and justify the procedures selected.
2.2 Make precise calculations and check the validity of the results in the context of the problem.
3.0 Students note connections between one problem and another.
Florida's 2007 mathematics standards:
Click here to link to additional Florida's standards informationMA.2.A.1.1 Identify relationships between the digits and their place values through the thousands, including counting by tens and hundreds.
MA.2.A.1.2 Identify and name numbers through thousands in terms of place value and apply this knowledge to expanded notation.
MA.2.A.1.3 Compare and order multi-digit numbers through the thousands.
MA.2.A.2.1 Recall basic addition and related subtraction facts.
MA.2.A.2.2 Add and subtract multi-digit whole numbers through three digits with fluency by using a variety of strategies, including invented and standard algorithms and explanations of those procedures.
MA.2.A.2.3 Estimate solutions to multi-digit addition and subtraction problems, through three digits.
MA.2.A.2.4 Solve addition and subtraction problems that involve measurement and geometry.
MA.2.G.3.1 Estimate and use standard units, including inches and centimeters, to partition and measure lengths of objects.
MA.2.G.3.2 Describe the inverse relationship between the size of a unit and number of units needed to measure a given object.
MA.2.G.3.3 Apply the Transitive Property when comparing lengths of objects.
MA.2.G.3.4 Estimate, select an appropriate tool, measure, and/or compute lengths to solve problems.
MA.2.A.4.1 Extend number patterns to build a foundation for understanding multiples and factors – for example, skip counting by 2's, 5's, 10's.
MA.2.A.4.2 Classify numbers as odd or even and explain why.
MA.2.A.4.3 Generalize numeric and non-numeric patterns using words and tables.
MA.2.A.4.4 Describe and apply equality to solve problems, such as in balancing situations.
MA.2.A.4.5 Recognize and state rules for functions that use addition and subtraction.
MA.2.G.5.1 Use geometric models to demonstrate the relationships between wholes and their parts as a foundation to fractions.
MA.2.G.5.2 Identify time to the nearest hour and half hour.
MA.2.G.5.3 Identify, combine, and compare values of money in cents up to $1 and in dollars up to $100, working with a single unit of currency.
MA.2.G.5.4 Measure weight/mass and capacity/volume of objects. Include the use of the appropriate unit of measure and their abbreviations including
cups, pints, quarts, gallons, ounces (oz), pounds (lbs), grams (g), kilograms (kg), millitiers (mL) and liters (L).
MA.2.A.6.1 Solve problems that involve repeated addition.
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.
2.1 Number and Operations: Develop an understanding of the base-ten numeration system and place-value concepts.
2.1.1 Write, compare, and order whole numbers to 1000.
2.1.2 Understand and apply base-ten numeration, and count in multiples of one, two, five, ten, and one hundred.
2.1.3 Compose and decompose whole numbers less than one thousand by place value (e.g., 426 as 4 hundreds + 2 tens + 6 ones and 400 + 20 + 6).
2.1.4 Use place value and properties of operations to find and use equivalent representations of numbers (such as 35 represented by 35 ones, 3 tens and 5 ones, or 2 tens and 15 ones).
2.2 Number and Operations and Algebra: Develop fluency with addition facts and related subtraction facts, and with multi-digit addition and subtraction.
2.2.1 Apply, with fluency, sums to 20 and related subtraction facts.
2.2.2 Solve multi-digit whole number problems by applying various meanings (e.g., taking away, and comparing) and models (e.g., combining or separating sets, using number lines, and hundreds charts) of addition and subtraction.
2.2.3 Develop fluency with efficient procedures for adding and subtracting multi-digit whole numbers and understand why the procedures work on the basis of place value and number properties.
2.2.4 Select and apply efficient methods to estimate sums and differences or calculate them mentally depending on the numbers and context involved.
2.2.5 Determine the value of mixed collections of coins to $1.00.
2.3 Measurement: Develop an understanding of linear measurement and facility in measuring.
2.3.1 Determine length by finding the total number of equal-length units that are placed end-to-end without gaps or overlaps.
2.3.2 Apply concepts of partitioning (the mental activity of slicing the length of an object into equal-sized units) and transitivity (e.g., if object A is longer than object B and object B is longer than object C, then object A is longer than object C).
2.3.3 Demonstrate an understanding that using different measurement units will result in different numerical measurements for the same object.
2.3.4 Explain the need for equal length units and the use of standard units of measure.
2.3.5 Use rulers and other measurement tools to estimate and measure length in common units (e.g., centimeter and inch).
2.3.6 Use the measurement process: choose an appropriate measurement unit, compare that unit to the object, and report the number of units.
2.3.7 Demonstrate an understanding of time and use of time relationships (e.g., how many minutes in an hour, days in a week, and months in a year).
2.3.8 Tell time in increments of five minutes using analog and digital clocks.
Members of Asia-Pacific Economic Cooperation:
Click here to 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.)