Students should be able to demonstrate these concepts by the end of 3rd grade.
http://education.state.mn.us/MDE/EdExc/StanCurri/K-12AcademicStandards/Math/index.html
Math
-Read, write and represent whole numbers up to 100,000. Representations may include numerals, expressions with operations, words, pictures, number lines, and manipulatives such as bundles of sticks and base 10 blocks.
-Use place value to describe whole numbers between 1,000 and 100,000 in terms of ten thousands, thousands, hundreds, tens, and ones.
-Find 10,000 more or 10,000 less than a given 5-digit number. Find 1,000 more or 1,000 less than a given 4-digit or 5-digit number. Find 100 more or 100 less than a given 4 or 5 digit number
-Round numbers to the nearest 10,000 , 1,000 , 100 , or 10. Round up and round down to estimate sums and differences.
-Compare and order whole numbers up to 100,000.
-Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms.
-Use addition and subtraction to solve real world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results.
-Represent multiplication facts by using a variety of approaches, such as repeated addition, equal sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division.
-Solve real world and mathematical problems involving multiplication and division, including both "how many in each group" and "how many groups" division problems.
-Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a 2 or 3 digit number a d 1 digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties.
-Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line.
-Understand that the size of a fractional part is relative to the size of the whole.
-Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator.
-Create, describe, and apply single-operation input-output rules involving addition, subtraction and multiplication to solve problems in various contexts.
-Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real world situations to represent number sentences.
-Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true.
-Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms, and trapezoids.
-Sketch polygons with a given numbers of sides or vertices such as pentagons, hexagons, and octagons.
-Use half units when measuring distances.
-Find the perimeter of a polygon by adding the lengths of the sides.
-Measure distances around objects.
-Tell time to the minute, using digital and analog clocks. Determine elapsed time to the minute.
-Know relationships among units of time.
-Make change up to one dollar in several different ways, including with as few coins as possible,
-Use an analog thermometer to determine temperature to the nearest degree in Fahrenheit and Celsius.
-Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units.