Math Competencies

Each of the Gateways below represents a phase (early elementary, intermediate, middle, high schools) of learners' path through our PK-12 system. By thinking of them as "gateways" rather than building levels, we can begin to re-imagine learning as the constant and time as the variable.

The competencies on this page represent a sampling of the exemplars that have been drafted to date. Some include corresponding scoring guides. If you are interested in learning more and/or in engaging in professional learning associated with these and other competencies, please contact us to see how we might personalized this learning experience with you.

HIGH SCHOOL (Gateway 4)

Basic Algebraic Competencies - ALG1

(linear, quadratic, intro to exponential, intro to rational, intro to absolute value)

Analyze basic relationships that are modeled mathematically through multiple representations by creating, manipulating, and interpreting equivalent expressions to reveal information in a useful format.
Analyze different types of basic mathematical relations by interpreting the graph and/or the characteristics of other models to understand and predict behavioral trends. (SCORING GUIDE)
Create basic algebraic representations by translating information into a justifiable mathematical model to contribute to understanding internal or external situations.
Solve basic algebraic equations and inequalities by applying and justifying various mathematical rules to explain authentic or hypothetical situations using math as the authority.

Advanced Algebraic Competencies - ALG2

(exponential, polynomial, rational, absolute value, and logarithmic functions, imaginary numbers, transformations [parent functions], sequences and series [arithmetic & geometric], binomial theorem)

Analyze advanced relationships that are modeled mathematically through multiple representations by creating, manipulating, and interpreting equivalent expressions to reveal information in a useful format.
Analyze different types of advanced mathematical relations by interpreting the graph and/or the characteristics of other representations to show that models reveal information but do not, by themselves, make people critical consumers of data. (SCORING GUIDE)
Create advanced algebraic representations by translating information into a justifiable mathematical model to contribute to understanding internal or external situations.
Solve advanced algebraic equations and inequalities by applying and justifying various mathematical rules to explain authentic or hypothetical situations using math as the authority.

Draft Geometric Competencies

Communicate comparisons through universally agreed upon one-to-one representations to make results reproducible and to minimize misinterpretations. (Measurement/Communication)
Construct representations of properties and geometric figures using manipulations and spatial sense to portray abstract concepts and produce concrete artifacts. (Properties/Evidence)
Support conclusions through structured inductive reasoning to defend a conjecture. (Inductive Logic/Evidence)
Prove conclusions through structured deductive arguments to seal an irrefutable truth. (Deductive Logic/Proof)

Draft Probability and Statistics Competencies

Verify statistical integrity by determining the appropriateness of the collection and display of data to explicate biases and to accurately reflect the intent of an investigation.
Determine the likelihood of events by utilizing appropriate rules of advanced probability to make informed, justifiable decisions.
Examine long-term trends by synthesizing data derived from appropriate sampling techniques to predict future events.

Draft Numbers and Operations Competencies

Determine the reasonableness of a solution by using units, comparative sizes, logic, intuition, past experiences, critical thinking, and/or collaboration to ensure a sensible outcome. (Reasonableness/Estimation)
Manipulate quantities by using rules of computation, operations and equivalent representations to solve authentic problems accurately. (Manipulate)
Express quantities in an appropriate format by utilizing an established representation to communicate effectively. (Quantify)

Middle Level (Gateway 3)

8th Grade

Analyze relationships that are modeled mathematically through multiple representations by creating and manipulating functions to contribute to understanding internal or external situations.
Analyze different types of mathematical relations by interpreting the graph and/or the characteristics of the function to understand and predict behavioral trends.
Solve algebraic equations by applying and justifying various mathematical rules to explain authentic or hypothetical situations using math as the authority.

7th Grade

Analyze relationships that are modeled arithmetically and algebraically through multiple representations by creating, manipulating, and interpreting equivalent expressions and equations to contribute to understanding internal or external situations.
Solve arithmetic and algebraic representations by using various mathematical rules and graphs with justification to explain authentic situations using math as the authority.

INTERMEDIATE (Gateway 2)

5th Grade

Make sense of situations using multiple operations with unlike units by attending to precision when designing mathematical representations to explain authentic situations using math as the authority.

4th Grade

Make sense of situations using multiple operations by modeling efficient mathematical representations to apply relationships using math as the authority.

3rd Grade

Make sense of multiplication and division situations by creating, manipulating, and interpreting equivalent expressions and equations to generalize a pattern using math as the authority.

EARLY ELEMENTARY (Gateway 1)

2nd Grade

Solve addition and subtraction problem situations by modeling with efficient methods to apply effective strategies in order to generalize with supporting evidence using math as the authority.

1st Grade

Justify the relationships of addition and subtraction situations by modeling with mathematical representations to make sense of problems using math as the authority.

Kindergarten

Make sense of addition and subtraction situations through reflection and discussion using concrete manipulatives or mathematical representations to apply effective strategies in order to generalize with supporting evidence.

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