K 1 2 3 4 5 6 7 8 Represent & solve problems involving Understand the Understand ratio multiplication and Use the four place value concepts and use Represent and division operations with system ratio reasoning to solve problems whole numbers to solve problems involving addition Understand solve problems Perform and subtraction properties of operations with Apply and extend Analyze multiplication and Generalize place multi-digit whole previous proportional Understand and Work with radical the relationship value numbers and understandings of relationship and apply properties and integer between understanding for decimals to multiplication and use them to solve of operations and Represent and exponents multiplication and multi-digit whole hundredths division to divide real-world and the relationship solve problems division numbers fractions by mathematical between addition involving addition Understand the Know number Use equivalent fractions problems and subtraction and subtraction connections names and the Multiply & divide Use place value fractions as a between count sequence within 100 understanding strategy to add Apply and extend Apply and extend Add and subtract Add and subtract proportional and properties of and subtract previous previous within 20 within 20 Solve problems relationships, Count to tell the operations to fractions understandings of understanding of involving the four lines, and linear number of objects perform multi- numbers to the operations with Work with Understand place operations, and equations digit arithmetic Apply and extend system of rational fractions to add, addition and value identify & explain Compare numbers previous numbers subtract, multiply, subtraction patterns in Analyze and solve Extend understandings of and divide rational equations Use place value arithmetic linear equations Understand understanding of multiplication and Apply and extend numbers understanding and pairs of addition as fraction division to previous Extend the and properties of Develop simultaneous putting together equivalence and multiply and understandings of Use properties of counting operations to add understanding of linear equations and adding to, ordering divide fractions arithmetic to operations to sequence and subtract fractions as and understand algebraic generate Measure and numbers Define, evaluate, subtraction as Build fractions Geometric expressions equivalent Understand place estimate lengths and compare taking apart and Solve problems from unit measurement: expressions value in standard units functions taking from involving fractions by understand Reason about and measurement and applying and concepts of solve one-variable Solve real-life and Use place value Relate addition Use functions to Work with estimation of extending volume and relate equations and mathematical understanding and subtraction to model numbers 11-19 to intervals of time, previous volume to inequalities problems using and properties of length relationships gain foundations liquid volumes, & understandings of multiplication and numerical and operations to add between for place value masses of objects operations to addition Represent and algebraic and subtract quantities analyze expressions and Geometric Understand Graph points in quantitative equations Measure lengths measurement: decimal notation the coordinate relationships indirectly and by understand for fractions, and plane to solve between iterating length concepts of compare decimal real-world and dependent and units area and relate fractions mathematical independent area to problems variables multiplication and to addition Source: P. Daro, W. McCallum, and J. Zimba (unpublished), Student Achievement Partners, © California Department of Education The Progress to Algebra Continuum in K-8 Updated Attachment 3, Item 12.C. May 3–4. 2012, Mathematics Subject Matter Committee