Understand numbers, ways of representing numbers, relationships among numbers, and number systems
Understand meanings of operations and how they relate to one another
Compute fluently and make reasonable estimates
Students engage in problem solving, communicating, reasoning, connecting, and representing as they:
Name and write (in numerals) whole numbers to 1000, iden-tify the place values of the digits, and order the numbers.
Identify and distinguish among multiple uses of numbers, including cardinal (to tell how many) and ordinal (to tell which one in an ordered list), and numbers as labels and as measurements.
Identify and represent common fractions (1/2, 1/3, 1/4) as parts of wholes, parts of groups, and numbers on the number line.
Compare whole numbers using terms and symbols, e.g., less than, equal to, greater than (<, =, >).
Identify odd and even numbers and determine whether a set of objects has an odd or even number of elements.
Identify the value of all U.S. coins, and $1, $5, $10, and $20 bills. Find the value of a collection of coins and dollar bills and different ways to represent an amount of money up to $5. Use appropriate notation, e.g., 69¢, $1.35.
Demonstrate an understanding of various meanings of addition and subtraction, e.g., addition as combination (plus, combined with, more); subtraction as comparison (how much less, how much more), equalizing (how many more are needed to make these equal), and separation (how much remaining).
Understand and use the inverse relationship between addition and subtraction (e.g., 8 + 6 = 14 is equivalent to 14 - 6 = 8 and is also equivalent to 14 - 8 = 6) to solve problems and check solutions.
Know addition facts (addends to ten) and related subtraction facts, and use them to solve problems.
Demonstrate the ability to add and subtract three-digit numbers accurately and efficiently.
Demonstrate in the classroom an under-standing of and the ability to use the conventional algorithms for addition (two 3-digit numbers and three 2-digit numbers) and subtraction (two 3-digit numbers).
Estimate, calculate, and solve problems involving addition and subtraction of two-digit numbers. Describe differences between estimates and actual calculations.
Exploratory Concepts and Skills
Use concrete materials to investigate situations that lead to multiplication and division.
Develop and use strategies for addition and subtraction of multi-digit whole numbers. Check by estimation.
Investigate addition of common fractions, e.g., 1/2 + 1/2 = 1, 1/4 + 1/4 = 1/2.
Understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally.