| Students demonstrate number sense, including an understanding of number systems and operations and how they relate to one another. Students compute fluently and make reasonable estimates using paper and pencil, technology-supported and mental methods. |
| Indicators for grade 3 |
| 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.
(ORC Resources) |
| 14. | Multiply and divide 2- and 3-digit numbers by a single-digit number, without remainders for division.
(ORC Resources) |
| 15. | Evaluate the reasonableness of computations based upon operations and the numbers involved; e.g., considering relative size, place value and estimates (ORC Resources) |