Math Student Profiles and Situations
Below you will find the conceptual understanding and skills, problem solving and reasoning, application fluency goals that students will have in each grade level.
Kindergarten
Conceptual Understanding and Skills

Representing, relating, and operating on whole numbers, initially with sets of objects.

Describing shapes and space.
Problem Solving and Reasoning
Problem solving in Kindergarten is very much based on reallife situations and tangible manipulatives. Children are encouraged to explain their thinking and reasoning in a concrete manner, often using objects or drawings.
Application and Fluency
Emphasizes exploratory learning and the application of math through play, storytelling, and everyday tasks. The goal is to make children comfortable with numbers and shapes in their environment.
Grade 1
Conceptual Understanding and Skills

Developing understanding of addition, subtraction, and strategies for addition and subtraction within 20.

Developing understanding of whole number relationships and place value, including grouping in tens and ones.

Developing understanding of linear measurement and measuring lengths as iterating length units.

Reasoning about attributes of, and composing and decomposing geometric shapes.

Students are expected to solve simple word problems, understand time (hours and halfhours).
Problem Solving and Reasoning
Problemsolving in G1 often revolves around straightforward scenarios where students apply basic addition or subtraction. Students start to develop reasoning skills by explaining their thought processes and may begin to tackle simple word problems.
Application and Fluency
Emphasizes building fluency with addition and subtraction within 20, introducing students to the concept of math as a part of everyday life, and applying math in simple, realworld contexts.
Grade 2
Conceptual Understanding and Skills

Extending understanding of baseten notation, like counting in fives, tens, and multiples of hundreds, tens and ones, and recognizing that the digits in each place represent amounts of thousands, hundreds, tens or ones.

Building fluency with addition and subtraction within 100, and solve problems within 1000;

Using standard units of measure, like length.

Describing and analyzing shapes.
Problem Solving and Reasoning
Problemsolving becomes more complex and integrated. Students encounter a wider variety of word problems, including those that require two or more steps and the application of logic to solve. There is a stronger focus on developing strategies for problemsolving and on understanding and explaining the reasoning behind these strategies.
Application and Fluency
Students are expected to achieve fluency in addition and subtraction within 100 or more, and they start to apply these skills in more varied and complex contexts. Students learn to use their math knowledge in practical situations more independently.
Grade 3
Conceptual Understanding and Skills

Developing understanding of multiplication and division and strategies for multiplication and division within 100

Developing understanding of fractions, especially unit fractions

Developing understanding of the structure of rectangular arrays and of area

Describing and analyzing twodimensional shapes.
Problem Solving and Reasoning
Encourages students to use 4 different operations in more complex problemsolving that often requires analytical thinking, multiple steps, or the selection from various problemsolving strategies. They are expected to explain their reasoning and use logical steps to solve problems, fostering critical thinking skills.
Application and Fluency
Requires students to apply mathematical concepts in more abstract contexts, including those that go beyond tangible manipulatives. This level aims for fluency not just in addition and subtraction but also in multiplication and division, preparing students for more complex applications of math in realworld scenarios.
Grade 4
Conceptual Understanding and Skills

Developing understanding and fluency with multidigit multiplication, and developing understanding of dividing to find quotients involving multidigit dividends.

Developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers.

Understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.
Problem Solving and Reasoning
There is a shift towards more abstract thinking and problemsolving. Students are expected to solve more complex problems, often requiring multiple steps and the application of reasoning over rote memorization.
Application and Fluency
Students are expected not just to understand mathematical operations but to apply them in various contexts, including those that may not be straightforward. This includes the application of arithmetic operations in measurement, geometry, and understanding quantities and operations in base ten.
Grade 5
Conceptual Understanding and Skills

Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions).

Extending division to 2digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations.

Developing understanding of volume.
Problem Solving and Reasoning
Requires students to apply math knowledge in more complex and sometimes nonroutine problemsolving situations. The problems often cover multiple steps and demand a higher level of reasoning and the application of multiple mathematical concepts simultaneously.
Application and Fluency
Builds on this fluency and requires students to apply their skills in broader contexts, such as interpreting data sets in more complex ways, understanding the principles of geometry and volume, and beginning to apply arithmetic operations to algebraic expressions.
Grade 6
Conceptual Understanding and Skills

Connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems.

Completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers.

Writing, interpreting, and using expressions and equations.

Developing understanding of statistical thinking.
Problem Solving and Reasoning
Grade 6 students are encouraged to solve realworld problems involving ratios, rates, and percent, making use of their conceptual understanding and mathematical reasoning. They must interpret and compute quotients of fractions, and solve problems by applying their understanding of ratios, rates, and unit rates, as well as closely examining and writing expressions and equations including variables.
Application and Fluency
In addition to solving problems, students also practice and apply mathematics to everyday situations. They should be able to fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation and solve problems involving the four operations with rational numbers (including integers). Building on their work with geometry in previous grades, they further delve into mathematical reasoning with shapes and their attributes.
Grade 7
Conceptual Understanding and Skills

Connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems.

Completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers.

Writing, interpreting, and using expressions and equations.

Developing understanding of statistical thinking.
Problem Solving and Reasoning
Problemsolving and reasoning are integral to Grade 7 math. Students are expected to engage in solving realworld and mathematical problems involving angle measure, area, surface area, and volume. They use their understanding of ratios, proportional relationships, and linear equations to solve single and multistep problems. Students also explore the concept of probability, developing the ability to analyze chance processes and assess the likelihood of possible events.
Application and Fluency
In Grade 7, students build on the procedural fluency gained in earlier grades by applying their skills to complex problems that require understanding of the operations with rational numbers, use of expressions and linear equations, and creation and interpretation of data displays. They should be able to apply proportional reasoning to diverse situations and solve problems that involve percent increase or decrease. Students work on engaging in mathematical practices that allow them to express mathematical ideas precisely and to use the language of algebra to represent and solve problems.
Grade 8
Conceptual Understanding and Skills

Formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations.

Grasping the concept of a function and using functions
to describe quantitative relationships. 
Analyzing two and threedimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.
Problem Solving and Reasoning
Problemsolving and reasoning are integral to Grade 7 math. Students are expected to engage in solving realworld and mathematical problems involving angle measure, area, surface area, and volume. They use their understanding of ratios, proportional relationships, and linear equations to solve single and multistep problems. Students also explore the concept of probability, developing the ability to analyze chance processes and assess the likelihood of possible events.
Application and Fluency
In Grade 7, students build on the procedural fluency gained in earlier grades by applying their skills to complex problems that require understanding of the operations with rational numbers, use of expressions and linear equations, and creation and interpretation of data displays. They should be able to apply proportional reasoning to diverse situations and solve problems that involve percent increase or decrease. Students work on engaging in mathematical practices that allow them to express mathematical ideas precisely and to use the language of algebra to represent and solve problems.