|1. ||Identify and generate equivalent forms of whole numbers; e.g., 36, 30 + 6, 9 x 4, 46 - 10, number of inches in a yard. (ORC Resources)|
|2. ||Use place value concepts to represent whole numbers and decimals using numerals, words, expanded notation and physical models. For example:
a. Recognize 100 means "10 tens" as well as a single entity (1 hundred) through physical models and trading games.
b. Describe the multiplicative nature of the number system; e.g., the structure of 3205 as 3 x 1000 plus 2 x 100 plus 5 x 1.
c. Model the size of 1000 in multiple ways; e.g., packaging 1000 objects into 10 boxes of 100, modeling a meter with centimeter and decimeter strips, or gathering 1000 pop-can tabs.
d. Explain the concept of tenths and hundredths using physical models, such as metric pieces, base ten blocks, decimal squares or money. (ORC Resources)|
|3. ||Use mathematical language and symbols to compare and order; e.g., less than, greater than, at most, at least, <, >, =, , . (ORC Resources)|
|4. ||Count money and make change using coins and paper bills to ten dollars. (ORC Resources)|
|5. ||Represent fractions and mixed numbers using words, numerals and physical models. (ORC Resources)|
|6. ||Compare and order commonly used fractions and mixed numbers using number lines, models (such as fraction circles or bars), points of reference (such as more or less than 1/2), and equivalent forms found using physical or visual models. (ORC Resources)|
|7. ||Recognize and use decimal and fraction concepts and notations as related ways of representing parts of a whole or a set; e.g., 3 of 10 marbles are red can also be described as 3/10 and 3 tenths are red. (ORC Resources)|
|8. ||Model, represent and explain multiplication; e.g., repeated addition, skip counting, rectangular arrays and area model. For example:
a. Use conventional mathematical symbols to write equations for word problems involving multiplication.
b. Understand that, unlike addition and subtraction, the factors in multiplication and division may have different units; e.g., 3 boxes of 5 cookies each. (ORC Resources)|
|9. ||Model, represent and explain division; e.g., sharing equally, repeated subtraction, rectangular arrays and area model. For example:
a. Translate contextual situations involving division into conventional mathematical symbols.
b. Explain how a remainder may impact an answer in a real-world situation; e.g., 14 cookies being shared by 4 children. (ORC Resources)|
|10. ||Explain and use relationships between operations, such as:
a. relate addition and subtraction as inverse operations;
b. relate multiplication and division as inverse operations;
c. relate addition to multiplication (repeated addition);
d. relate subtraction to division (repeated subtraction). (ORC Resources)|
|11. ||Model and use the commutative and associative properties for addition and multiplication. (ORC Resources)|
|12. ||Add and subtract whole numbers with and without regrouping. (ORC Resources)|
|13. ||Demonstrate fluency in multiplication facts through 10 and corresponding division facts.
|14. ||Multiply and divide 2- and 3-digit numbers by a single-digit number, without remainders for division.
|15. ||Evaluate the reasonableness of computations based upon operations and the numbers involved; e.g., considering relative size, place value and estimates (ORC Resources)|