Content Area –Example - Mathematics
Cluster/Domains – Clusters/Domains are grouping of like concepts taught within the subject and are guided by state, national, or international curriculum and best practices.
Example - Operations and Algebraic Thinking
Essential Standards – These are a subset of the entire curriculum that are the priority knowledge and skills that have endurance and leverage for students’ success in school this year, next year, and beyond. Whereas all standards are important, the prioritizing of standards helps educators to choose between coverage and mastery from a large numbers of standards (DuFour & Marzano, 2011; Reeves, 2010). Essential standards also help make learning expectations more transparent to students and families and helps the school use its resources to achieve high levels of learning for all students. Essential Standards should reflect what knowledge and skills are needed to be successful at the next level, and should be based on the critical work of the grade level. For example, at Grade 3 under the domain or cluster of Operations and Algebraic Thinking, the essential standards identified are:
Actual Standards - These are the actual standards that make up the Essential Standards. These provide more detail on the different elements of the Essential Standards.
Concepts of Multiplication.
3.OA.1. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
3.OA.4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ÷ 3, 6 × 6 = ?.
3.OA.5. Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
Concepts of Division
3.OA.2. Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
3.OA.6. Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
Word Problems
3.OA.3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
3.OA.8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
3.OA.9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
Fact Fluency
3.OA.7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
Learning Targets – Sometimes called “I can” statements, these are daily or weekly goals written into student friendly language. They serve the purpose of helping students know if they are making day to day progress and providing transparency in learning. Each standard can be further subdivided into learning targets as points along the way.
I can use multiplication to solve problems. (3.OA.3)
I can represent the context of a multiplication problem using drawings and equations.(3.OA.3)
Grade 3 Sample Report Card: