Bridges Competencies & Experiences
Bridges is designed to enable students to achieve competency in specific areas by year-end while at the same time providing experiences that expose them to areas that will be mastered in subsequent years. The Competencies and Experiences outlined below capture this integrated plan across grades K-5. For details select View from the table below or download documents by Grades K-2 or Grades 3-5.
See also Scope and Sequence documents K-5 summary / NCTM strands and K-5 by month.
| Subject Area | Grades K-2 | Grades 3-5 |
| Number Sense and Numeration | View | View |
| Computation | View | View |
| Algebraic Thinking | View | View |
| Data Analysis and Probability | View | View |
| Measurement | View | View |
| Geometry | View | View |
| Grades 3-5 Computation | ||
| Third Grade | Fourth Grade | Fifth Grade |
| COMPETENCIES | ||
| Use strategies (e.g., doubles, neighbors) in the development and demonstration of computational fluency with addition and subtraction facts to 20. | Add and subtract up to 4-digit numbers with and without regrouping using models and a variety of efficient paper/pencil and mental strategies. | Handle addition, column addition, and subtraction with multi-digit numbers (5 or more digits) in an efficient manner, making judicious use of mental strategies, estimation, rounding, and calculators. |
| Use models, pictures, and/or numbers to demonstrate the meaning of addition (joining two or more sets) and subtraction (taking away or finding the difference between two sets). Use the relationship between addition and subtraction (e.g., fact families) to solve problems. | Know and fluently use multiplication facts through 10 x 10. Develop efficient strategies for quickly determining division facts with divisors to 10 and dividends to 100. | Know and fluently use the multiplication and division facts through 10’s, as well as factors and multiples through 100. |
| Add and subtract up to 3-digit numbers with and without regrouping using models and a variety of efficient paper/pencil and mental strategies. | Develop efficient ways to determine factors of whole numbers to 100 using an understanding of number relationships and models such as arrays. | Multiply 2-digit by 2-digit numbers using a variety of efficient mental and paper/pencil strategies. Multiply by powers of ten up to 1,000 to simplify calculations. |
| Use models, pictures, and/or numbers to demonstrate an understanding of multiplication and division as repeated addition/ subtraction, equal groups of objects, arrays, or skip counting. | Mentally add and subtract multiples of 10, 100, or 1000 to or from a number. Mentally multiply or divide multiples of 10 or 100 (e.g., 40 x 70 or 2700 ÷ 30). | Divide 3-digit by 1-digit numbers with and without remainders using a variety of efficient mental and paper/pencil strategies. |
| Demonstrate computational fluency with multiplication facts up to 5 x 10. Develop and use strategies for multiplication facts up to 10 x 10. Use various strategies to multiply a 2-digit number by a 1-digit number. | Use different models of division such as grouping, sharing, and repeated subtraction to solve problems (including situations that involve remainders). | Calculate and explain addition and subtraction of commonly used fractions and decimals to thousandths. |
| Use estimation strategies such as rounding and front-end loading to solve problems and check the accuracy of the solutions. | Multiply and divide 2- and 3-digit numbers by 1-digit numbers, using a variety of concrete, visual, and paper/pencil methods. | Describe, compare, choose and accurately use strategies and operations for a variety of problem situations. |
| Identify and apply the operation needed (addition, subtraction, multiplication or division) for solving a problem. | Add and subtract commonly used fractions and decimals to hundredths using concrete models, money amounts, and visual representations. | Identify the order of operations in a multi-step problem. |
| Count, add, subtract, and estimate money amounts up to $10. Make change from $5. Use decimal notation to show money amounts to $10. | Solve addition, subtraction, multiplication, and division story problems using a variety of efficient paper/pencil and mental strategies. | Estimate the results of operations performed on whole numbers, fractions, and decimals, and use the estimate to determine the reasonableness of the final answer. |
| Select methods and tools (rounding, estimation, paper/pencil, calculator) appropriate to a particular context for operations with whole numbers. | Apply the commutative, associative, distributive, and identity properties to calculations with whole numbers and decimals. | |
| Apply the commutative, associative, distributive, and identity properties to calculations with whole numbers. | ||
| EXPERIENCES | ||
| Explore mental addition and subtraction of multiples of 10, 100, or 1000 to or from a number. | Explore column addition with multi-digit numbers and addition, subtraction and estimation with larger numbers (5 or more digits). | Compute and perform multiplication and division of simple fractions, and apply these procedures to solve problem situations |
| Explore the concept of division with and without remainders through solving story problems and creating multiplication/division fact families to go along with arrays. | Use percent models (such as a 100’s grid) to interpret current events news stories and advertisements that relate to students’ lives. | |
| Explore the commutative, associative, and distributive properties of multiplication, as well as the special properties of 0 and 1 in multiplication and division. | Determine common percentages of a number (e.g., 10%, 20%, 50%, 75%) or estimate percentages by rounding. | |