Math: Curriculum Project Team

Recognizing that effective teaching is the most important factor in student learning, our teachers need to know and understand the mathematics they teach, as well as participate in on-­‐going professional development to enhance knowledge of content and best practices. To incorporate the following best practices effectively, teachers need to routinely reflect and collaborate on instructional practices, student progress, and understand the mathematics they teach at a deep enough level to be able to explain and apply their understanding in a variety of situations.

Below is an outline of “guidelines for powerful and meaningful” math teaching and learning:

1. All students understand that mathematics is a dynamic, coherent, and interconnected set of ideas.
2. All students are supported in developing a deep understanding and the ability to use mathematical concepts powerfully.
3. All students understand and use counting strategies, number concepts, operations, and computational procedures to solve problems in context.
4. All students engage in reasoning algebraically as early as kindergarten and throughout their K‐12 school years.
5. All students build an understanding of mathematical concepts in algebra, geometry, measurement, data, statistics and probability, through the use of real-­‐world, realistic, authentic, and meaningful contexts within and outside of mathematics courses.
6. All students participate in an ongoing assessment process that provides an understanding of what students know and guides meaningful decisions about the instruction and support required to move the learning forward.
7. The focus of instruction should enable all students to successfully engage in critical cognitive processes by:

• Helping students to make connections to their prior mathematical knowledge, and between mathematical concepts and procedures.
• Providing students with authentic, challenging, intriguing, mathematically rich, and even counterintuitive problem solving tasks that require them to think and build mathematical knowledge and perseverance.
• Guiding students in how to use representational strategies that include:
• Discussing the problem in small groups (language representations).
• Using manipulatives (concrete, physical representations and tactile sense).
• Acting it out (representations of sequential actions and bodily kinesthetic sense).
• Drawing a model, diagram, or graph (visual, pictorial representations).
• Making a list or table (symbolic representations).
• Encouraging and helping students to communicate their ideas by using a full range of language representations – speaking, writing, reading and listening.

When observing math instruction in the BSD, one should see aspects of each of the following practices:

Purpose

• The activity is based on a grade level Learning Target, or a transferable skill building to the Learning Target*.
• The lesson is clearly linked to previous and future lessons leading students to understand the connections.
• The learning needs – academic background, life experience, culture and language – of students are the basis of teaching points for all students or some groups of students in order to ensure their success and help them make meaning of key mathematical concepts.
• The Learning Target is communicated through verbal and visual strategies and is used as the basis for students as they check for their understanding.

Student Engagement

• Questions are posed to probe and deepen students’ mathematical understanding and to uncover misconceptions. Errors are expected and celebrated because brain research shows that is when the most learning takes place.
• Students are engaged in inquiry in order to uncover concepts, clarify and deepen understanding, and assess their thinking.
• Students are productively collaborating, participating in quality discourse and taking ownership of their learning in ways that support their mathematical learning.
• Students are engaged – speaking, reading, writing and/or listening – in meaningful struggle related to an authentic, challenging, intriguing, mathematically rich, and even counterintuitive, problem-­solving task.

Curriculum & Pedagogy

• The tasks, materials and/or assessments are aligned to the purpose of the Learning Target and differentiated to be appropriately challenging and supportive for all students.
• All the tasks/activities are aligned to a clearly articulated Learning Target or purpose to which the students can connect their work and mathematical thinking and have opportunities to explore math topics more deeply.
• When appropriate, teachers use language supports and scaffolds (sentence frames, accountable talk, vocabulary, etc.) as well as hands-­‐on materials and visual aids.
• Students are using one or more representational strategies – discussion, manipulatives, acting it out, drawing a model, diagram or graph, making a list or table – to explore and solve an authentic, challenging, intriguing, mathematically rich problem.
• Students are engaged in tasks and activities that promote learning and independence and are encouraged to explore multiple solution processes.

Assessment for Student Learning

• Students are given multiple assessment opportunities with the instruction and support required to move them forward.
• Assessments are aligned to Learning Targets allowing students to demonstrate their level of proficiency.
• Students are using assessment data to assess their progress, set learning goals, and/or monitor their progress over time.
• Teachers use formative assessment data to drive and adjust instruction.

Classroom Environment and Culture

• The arrangement of materials, supports, and physical environment scaffold student learning and the purpose of the activity.
• Resources, materials and technology are used to promote student learning and aligned to the Learning Targets or purpose. All students have access to what they need to support their individual learning.
• The transitions promote learning and maximize instructional time.
• Students understand and adhere to the classroom norms appropriately and their actions demonstrate divergent thinking, risk taking, respect, and a desire to collaborate.

ALT 1 - I can count to 100 by ones. 

ALT 2 - I can count to 100 by tens. 

ALT 3 - I can write the numbers that represent a given number of objects from zero to twenty.

ALT 4 - I can use counting strategies to determine the number of objects and I can understand the relationship between numbers and quantities.

ALT 5 - I can compare sets of groups of objects to tell more, less, or equal to.

ALT 6 -I can show addition as putting together and adding to -and- subtraction as taking apart and taking from

ALT 7 - I can use mental strategies to fluently and accurately add and subtract within 5. 

ALT 8 - I can use place value to find the tens and ones of the numbers 11-19.

ALT 9 - I can describe measurable attributes of an object and directly compare 2 objects with measurable attributes.

ALT 10 - I can classify objects into categories and sort and count objects into a specified category.

ALT 11 - I can identify and describe shapes (two- and three-dimensional.) Shapes include: squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres.

ALT 12 - I can analyze, compare, and compose two- and three-dimensional shapes.

 

MP 1 - Make sense of problems and persevere in solving them.

MP 2 - Reason abstractly and quantitatively.

MP 3 - Construct viable arguments & critique the reasoning of others.

MP 4 - Model with mathematics.

MP 5 - Use appropriate tools strategically.

MP 6 - Attend to precision.

MP 7- Look for and make use of structure.

MP 8 - Look for and express regularity in repeated reasoning.

ALT 1 - I can learn, represent and solve problems involving addition and subtraction and I understand the relationship between them.

ALT 2 - I can add and subtract fluently up to 10. 

ALT 3 - I can count, read, and write to 120 starting at any number less than 120.

ALT 4 - I understand place value up to two digit numbers and can compare within 100.

ALT 5 - I use place value understanding and properties of operations to add and subtract with 100.

ALT 6 - I can measure the lengths of objects and name the length unit.

ALT 7 - I can tell and write time.

ALT 8 - I can organize, represent, and interpret data.

ALT 9 - I can reason with shapes and their attributes.

 

MP 1 - Make sense of problems and persevere in solving them.

MP 2 - Reason abstractly and quantitatively.

MP 3 - Construct viable arguments & critique the reasoning of others.

MP 4 - Model with mathematics.

MP 5 - Use appropriate tools strategically.

MP 6 - Attend to precision.

MP 7- Look for and make use of structure.

MP 8 - Look for and express regularity in repeated reasoning.

ALT 1 - I can add and subtract using place value strategies.

ALT 2 - I can use mental math strategies to fluently add and subtract within 20.

ALT 3 - I can work with equal groups of objects to gain foundations for multiplication.

ALT 4 - I understand place value and can compare two three-digit numbers.

ALT 5 - I can measure and estimate lengths using standard and metric systems.

ALT 6 - I can tell and write time to the nearest 5 minutes.

ALT 7 - I can solve word problems involving dollars and cents.

ALT 8 - I can represent and interpret data.

ALT 9 - I can reason with shapes and their attributes.

 

MP 1 - Make sense of problems and persevere in solving them.

MP 2 - Reason abstractly and quantitatively.

MP 3 - Construct viable arguments & critique the reasoning of others.

MP 4 - Model with mathematics.

MP 5 - Use appropriate tools strategically.

MP 6 - Attend to precision.

MP 7- Look for and make use of structure.

MP 8 - Look for and express regularity in repeated reasoning.

ALT 1 - I can represent and solve problems involving multiplication and division.

ALT 2 - I can understand properties of operations and the relationship between multiplication and division.

ALT 3 - I can fluently multiply and divide within 100.

ALT 4 - I can fluently add and subtract within 1,000.

ALT 5 - I can describe and represent fractions as equal parts of a whole or set, compare fractions, and identify equivalent fractions.

ALT 6 - I can solve problems involving measurement and estimation of intervals of time.

ALT 7 - I can solve problems involving measurement and estimation of liquid volumes and masses of objects.

ALT 8 - I can represent and interpret data.

ALT 9 - I can measure the area of a rectilinear shape.

ALT 10 - I can find the perimeter of different polygons.

ALT 11 - I can reason with shapes and their attributes.

 

MP 1 - Make sense of problems and persevere in solving them.

MP 2 - Reason abstractly and quantitatively.

MP 3 - Construct viable arguments & critique the reasoning of others.

MP 4 - Model with mathematics.

MP 5 - Use appropriate tools strategically.

MP 6 - Attend to precision.

MP 7- Look for and make use of structure.

ALT 1 - I can use multi-digit addition and subtraction to solve problems.

ALT 2 - I can use multi-digit multiplication and division to solve problems.

ALT 3 - I can apply my understanding of factors and multiples.

ALT 4 - I can create and analyze patterns with unknown rules.

ALT 5 - I can read, write, and compare numbers with place value to a million.

ALT 6 - I can add, subtract, order and compare fractions and decimals and multiply fractions by whole numbers.

ALT 7 - I can solve problems involving measurement and measurement conversions, including distance, time, volume, mass and money.

ALT 8 - I can understand the concepts of angles, and I can accurately measure angles.

ALT 9 - I can draw and identify lines and angles, and classify shapes by properties of their lines and angles.

 

MP 1 - Make sense of problems and persevere in solving them.

MP 2 - Reason abstractly and quantitatively.

MP 3 - Construct viable arguments & critique the reasoning of others.

MP 4 - Model with mathematics.

MP 5 - Use appropriate tools strategically.

MP 6 - Attend to precision.

MP 7 - Look for and make use of structure.

ALT 1 - I can write and interpret numerical expressions.

ALT 2 - I can analyze patterns and relationships and graph points on a coordinate plane to solve problems.

ALT 3 - I can understand the place value system.

ALT 4 - I can perform operations to fluently solve problems with multi-digit whole numbers.

ALT 5 - I can perform operations to fluently solve problems involving decimals to the hundredths place.

ALT 6 - I can fluently add and subtract fractions.

ALT 7 - I can multiply and divide fractions (unit fraction divided by whole numbers and whole numbers divided by unit fractions).

ALT 8 - I can understand and apply concepts of volume.

ALT 9 - I can classify two-dimensional figures into categories based on their properties.

 

MP 1 - Make sense of problems and persevere in solving them.

MP 2 - Reason abstractly and quantitatively.

MP 3 - Construct viable arguments & critique the reasoning of others.

MP 4 - Model with mathematics.

MP 5 - Use appropriate tools strategically.

MP 6 - Attend to precision.

MP 7- Look for and make use of structure.

ALT 1 - Communicates clearly and explains my reasoning so others can follow how a problem is solved.

ALT 2 - Reasons mathematically to solve problems in real-life context.

ALT 3 - Recognizes patterns and describes them as relationships or general rules.

ALT 4 - Uses ratio concepts and ratio reasoning to solve problems.

ALT 5 - Computes, applies and extends previous understandings of rational numbers fluently.

ALT 6 - Applies and reasons algebraically using expressions, one-variable equations and inequalities.

ALT 7 - Solves mathematical problems involving area, surface area, and volume.

ALT 8 - Develops an understanding of statistical variability and summarizes and describes distributions.Math 6/7

ALT 1 - Communicates clearly and explains reasoning so others can follow how a problem is solved.

ALT 2 - Reasons mathematically to solve problems in real-life context.

ALT 3 - Recognizes patterns and describes them as relationships or general rules.

ALT 4 - Uses ratio concepts and ratio reasoning to solve problems.

ALT 5 - Computes, applies and extends previous understandings of rational numbers fluently.

ALT 6 - Applies and reasons algebraically using expressions, one-variable equations and inequalities.

ALT 7 - Solves mathematical problems involving area, surface area and volume.

ALT 8 - Develops an understanding of statistical variability, summarizes and describes distributions, and investigates probability.

ALT 9 - Analyzes proportional relationships and uses them to solve real-world and mathematical problems.

ALT 10 - Applies and extends previous understandings of operations with fractions.

ALT 1 - Communicates clearly and explains reasoning so others can follow how a problem is solved.

ALT 2 - Reasons mathematically to solve problems in real-life context.

ALT 3 - Recognizes patterns and describes them as relationships or general rules.

ALT 4 - Analyzes proportional relationships and uses them to solve real-world and mathematical problems.

ALT 5 - Applies and extends previous understandings of operations with fractions.

ALT 6 - Uses properties of operations to generate equivalent expressions, and solves real-world mathematical problems using numeric and algebraic expressions and equations.

ALT 7 - Draws, constructs, and describes geometric figures and relationships between them, and solves problems involving angle measure, area, surface area, and volume.

ALT 8 - Develops understanding of statistical variability and investigates chance processes to develop, use, and evaluate probability models.

ALT 1 - Communicates clearly and explains reasoning so others can follow how a problem is solved.

ALT 2 - Reasons mathematically to solve problems in real-life contact.

ALT 3 - Recognizes patterns and describes them as relationships or general rules.

ALT 4 - Uses properties of operations, proportional relationships, and fractions to generate expressions and solve equations.

ALT 5 - Draws, constructs, and describes geometric figures and relationships between them, and solves problems involving angle measure, area, surface area, and volume.

ALT 6 - Works with expressions and equations using integer exponents.

ALT 7 - Analyzes and solves linear equations and systems of linear equations.

ALT 8 - Defines, evaluates, compares, and uses linear functions to model relationships between quantities and bivariate data.

ALT 9 - Understands congruence and similarity using transformational geometry, triangle-angle relationships, and parallel lines cut by transversals.

ALT 10 - Understands and applies the Pythagorean Theorem using rational and irrational numbers.

 

 

ALT 1 - Communicates clearly and explains reasoning so others can follow how a problem is solved.

ALT 2 - Reasons mathematically to solve problems in real-life context.

ALT 3 - Recognizes patterns and describes them as relationships or general rules.

ALT 4 - Works with expressions and equations using integer exponents.

ALT 5 - Analyzes and solves linear equations and systems of linear equations.

ALT 6 - Defines, evaluates, compares and uses linear functions to model relationships between quantities.

ALT 7 - Investigates patterns of association in bivariate data.

ALT 8 - Understands congruence and similarity using transformational geometry, triangle-angle relationships, and parallel lines cut by transversals, as well as, the volume of cylinders, cones and spheres.

ALT 9 - Understands and applies the Pythagorean Theorem using rational and irrational numbers.

ALT 1 - I can perform basic math computations fluently.

ALT 2 - I can solve problems using whole number operations including word problems.

ALT 3 - I can solve problems using fraction and decimal operations including word problems.

ALT 4 - Communicates clearly and explains reasoning so others can follow how a problem is solved.

ALT 5 - Reasons mathematically to solve problems using patterns and models in both a pure and applied context.

ALT 1 - Understands and applies the characteristics of a function. (CCSS.A.REI.10, CCSS.F.IF.1&4)

ALT 2 - Identifies, uses and solves for variables. (CCSS.A.REI.1&3), (CCSS.A.REI.5-7), (CCSS.A.REI.3&12), (CCSS.G.GPE.4-7, CCSS.G.CO.2-5)

ALT 3 - Uses and applies geometric properties to mathematics. (CCSS.G.CO.10-11, CCSS.G.MG.1-3), (CCSS.G.GPE.4-7, CCSS.G.CO.2-5)

ALT 4 - Applies the rules of statistics and probability to mathematics. (CCSS.S.ID.1-3, CCSS.S.IC.6), (CCSS.S.ID)

ALT 5 - Communicates clearly and explains reasoning so others can follow how a problem is solved.

ALT 6 - Recognizes patterns and describe them as relationships or general rules.

ALT 7 - Reasons mathematically to solve problems in real-life context.

ALT 1 - Understands and applies the characteristics of a function. (CCSS.A.REI.10, CCSS.F.IF.1&4)

ALT 2 - Identifies, uses and solves for variables. (CCSS.A.REI.1&3), (CCSS.A.REI.5-7), (CCSS.A.REI.3&12), (CCSS.G.GPE.4-7, CCSS.G.CO.2-5)

ALT 3 - Uses and applies geometric properties to mathematics. (CCSS.G.CO.10-11, CCSS.G.MG.1-3), (CCSS.G.GPE.4-7, CCSS.G.CO.2-5)

ALT 4 - Applies the rules of statistics and probability to mathematics. (CCSS.S.ID.1-3, CCSS.S.IC.6), (CCSS.S.ID)

ALT 5 - Communicates clearly and explains reasoning so others can follow how a problem is solved.

ALT 6 - Recognizes patterns and describe them as relationships or general rules.

ALT 7 - Reasons mathematically to solve problems in real-life context.

ALT 1 - Understands and applies the characteristics of a function. (CCSS.A.REI.10, CCSS.F.IF.1&4)

ALT 2 - Identifies, uses and solves for variables. (CCSS.A.REI.1&3), (CCSS.A.REI.5-7), (CCSS.A.REI.3&12), (CCSS.G.GPE.4-7, CCSS.G.CO.2-5)

ALT 3 - Uses and applies geometric properties to mathematics. (CCSS.G.CO.10-11, CCSS.G.MG.1-3), (CCSS.G.GPE.4-7, CCSS.G.CO.2-5)

ALT 4 - Applies the rules of statistics and probability to mathematics. (CCSS.S.ID.1-3, CCSS.S.IC.6), (CCSS.S.ID)

ALT 5 - Simplifies real and complex expressions.

ALT 6 - Communicates clearly and explains reasoning so others can follow how a problem is solved.

ALT 7 - Reasons mathematically to solve problems using patterns and models in both a pure and applied context.

ALT 1 - Understands and applies the characteristics of a function. (CCSS.A.REI.10, CCSS.F.IF.1&4)

ALT 2 - Identifies, uses and solves for variables. (CCSS.A.REI.1&3), (CCSS.A.REI.5-7), (CCSS.A.REI.3&12), (CCSS.G.GPE.4-7, CCSS.G.CO.2-5)

ALT 3 - Uses and applies geometric properties to mathematics. (CCSS.G.CO.10-11, CCSS.G.MG.1-3), (CCSS.G.GPE.4-7, CCSS.G.CO.2-5)

ALT 4 - Applies the rules of statistics and probability to mathematics. (CCSS.S.ID.1-3, CCSS.S.IC.6), (CCSS.S.ID)

ALT 5 - Simplifies real and complex expressions.

ALT 6 - Communicates clearly and explains reasoning so others can follow how a problem is solved.

ALT 7 - Reasons mathematically to solve problems using patterns and models in both a pure and applied context.

ALT 1 - Determines theoretical probability using models (mostly counting trees).

ALT 2 - Determines theoretical probability using fractions, including two-way tables.

ALT 3 - Calculates experimental probability and understanding its relation to theoretical probability.

ALT 4 - Calculates geometric probability.

ALT 5 - Calculates and interprets expected value.

ALT 6 - Identifies sample and population in a study, and determines whether a sampling method and procedure includes bias.

ALT 7 - Displays and describes the distribution of data using various graphs.

ALT 8 - Applies the Normal Distribution to solve problems.

ALT 9 - Develops a regression line and equation to make predictions in the context of the problem.

ALT 1 - Communicates clearly and explains reasoning so others can follow how a problem is solved

ALT 2 - Reasons mathematically to solve problems in real-life context

ALT 3 - Recognizes patterns and describes them as relationships or general rules

ALT 4 - Analyzes the transformation of trigonometric functions graphically, symbolically, numerically, verbally and within contextualized data exploration

ALT 5 - Simplifies trigonometric expressions and solves trigonometric equations

ALT 6 - Finds features of functions in multiple forms

ALT 7 - Constructs new functions represented in any form

ALT 8 - Constructs and explains the process of the transformation of a function of any form

ALT 9 - Analyzes and solves exponential and logarithmic functions

ALT 10 - Analyzes polynomial functions represented in a variety of forms

ALT 11 - Analyze rational functions represented in a variety of forms

ALT 1 - Communicates clearly and explains reasoning so others can follow how a problem is solved

ALT 2 - Reasons mathematically to solve problems in real-life context

ALT 3 - Recognizes patterns and describes them as relationships or general rules

ALT 4 - Uses two-way frequency tables and regression models to summarize, represent, and interpret data on two variables

ALT 5 - Analyzes the transformation of trigonometric functions graphically, symbolically, numerically, verbally and within contextualized data exploration

ALT 6 - Simplifies trigonometric expressions and solves trigonometric equations

ALT 7 - Solves problems that involve arithmetic and geometric sequences and series, and infinite geometric series

ALT 8 - Applies the Normal Distribution to solve problems

ALT 9 - Uses confidence intervals to estimate the value of a parameter from information obtained from a sample

ALT 10 - Finds features of functions in multiple forms

ALT 11 - Constructs new functions represented in any form

ALT 12 - Constructs and explains the process of the transformation of a function of any form

ALT 13 - Analyzes and solves exponential and logarithmic functions

ALT 14 - Analyzes polynomial functions represented in a variety of forms

ALT 15 - Analyze rational functions represented in a variety of forms

ALT 1 - Communicates clearly and explains reasoning so others can follow how a problem is solved

ALT 2 - Reasons mathematically to solve problems in real-life context

ALT 3 - Recognizes patterns and describes them as relationships or general rules

ALT 4 - Applies algebra to solve relevant problems and make informed decisions through the use of formulas, graphs, and patterns

ALT 5 - Applies geometry to solve relevant problems and make informed decisions through the use of formulas, relationships, and the fundamental awareness of shapes in both 2-dimensional and 3-dimensional space

ALT 6 - Applies statistics to solve relevant problems and make informed decisions through the uses of tables, graphs, charts, probabilities, and hypothesis testing

ALT 7 - Demonstrates an ability to use logic and reasoning to model a problem, create and debate arguments, and conclude with a solution

ALT 8 - Uses a variety of questioning strategies to elicit deeper thinking from self and others

ALT 1 - I can find features of functions in multiple forms.

ALT 2 - I can construct new functions represented in any form.

ALT 3 - I can construct and explain the process of the transformation of a function of any form.

ALT 4 - I can analyze exponential and logarithmic functions and solve exponential and logarithmic equations.

ALT 5 - I can analyze polynomial functions represented in a variety of forms.

ALT 6 - I can analyze rational functions represented in a variety of forms.

ALT 7 - I can define and evaluate periodic functions.

ALT 8 - I can analyze the transformation of trigonometric functions graphically, symbolically, numerically, verbally and within contextualized data exploration.

ALT 9 - I can prove trigonometric identities and apply identities to find exact values.

ALT 10 - I can solve trigonometric equations.

ALT 11 - I can solve problems involving the angle measure and side length of right and oblique triangles.

ALT 12 - I can solve problems using vectors.

ALT 13 - I can apply parametric equations to solve problems involving circular, elliptical motion and/or parabolic trajectories.

ALT 14 - I can solve problems with complex numbers in both rectangular and trigonometric form.

ALT 15 - Communicates clearly and explains reasoning so others can follow how a problem is solved.

ALT 16 - Reasons mathematically to solve problems using patterns and models in both a pure and applied context.

ALT 1 - Communicates clearly and explains reasoning so others can follow how a problem is solved

ALT 2 - Reasons mathematically to solve problems in real-life context

ALT 3 - Recognizes patterns and describes them as relationships or general rules

ALT 4 - Uses Calculus to both predict and explain the observed local and global behavior of a function

ALT 5 - Uses a derivative to interpret the behavior of a function and explains the logic of a solution to a problem modeled by a function

ALT 6 - Computes the derivative of functions

ALT 7 - Applies derivatives to various situations and to solve problems

ALT 8 - Uses the properties and numerical approximations to find and interpret definite integrals

ALT 9 - Uses a variety of techniques to find the anti-derivative of functions

ALT 10 - Applies anti-differentiation to various situations and to solve problems

ALT 1 - Communicates clearly and explains reasoning so others can follow how a problem is solved

ALT 2 - Reasons mathematically to solve problems in real-life context

ALT 3 - Recognizes patterns and describes them as relationships or general rules

ALT 4 - Demonstrates an understanding of the concept of a series

ALT 5 - Demonstrates an understanding of series of constants

ALT 6 - Uses a variety of tests and techniques to determine convergence or divergence of series of constants

ALT 7 - Demonstrates an understanding of Taylor Series

ALT 8 - Uses formal manipulation of Taylor series and shortcuts to computing Taylor series

ALT 9 - Uses calculus to both predict and explain the observed local and global behavior of a function

ALT 10 - Uses a derivative to interpret the behavior of a function and explains the logic of a solution to a problem modeled by a function

ALT 11 - Computes the derivative of functions

ALT 12 - Applies derivatives to various situations and to solve problems

ALT 13 - Uses the properties and numerical approximations to find and interpret definite integrals

ALT 14 - Uses a variety of techniques to find the anti-derivative of functions

ALT 15 - Applies anti-differentiation to various situations and to solve problems

ALT 1 - Finds the limit of a function at a given domain values or extreme values.

ALT 2 - Determines if a function is continuous on an interval, or describe the type of discontinuity.

ALT 3 - Finds a derivative using the definition.

ALT 4 - Determines which differentiation technique can be used and applied to find a derivative and higher derivatives.

ALT 5 - Solves contextualized problems using differentiation techniques.

ALT 1 - Communicates clearly and explains reasoning so others can follow how a problem is solved

ALT 2 - Reasons mathematically to solve problems in real-life context

ALT 3 - Recognizes patterns and describes them as relationships or general rules

ALT 4 - Identifies, understands, and performs operations on infinite series and sequences

ALT 5 - Understands and applies parametric equations, polar coordinates, and conic sections

ALT 6 - Understands and applies vector geometry

ALT 7 - Understands Calculus of Vector-Values Functions

ALT 8 - Communicates understanding of Calculus III

ALT 9 - Applies understanding of Calculus III

ALT 1 - Communicates clearly and explains reasoning so others can follow how a problem is solved

ALT 2 - Reasons mathematically to solve problems in real-life context

ALT 3 - Recognizes patterns and describes them as relationships or general rules

ALT 4 - Applies matrix theory to solve and transform

ALT 5 - Uses matrix operations and identifies determinants

ALT 6 - Understands and identifies Eigenvectors & Eigenvalues

ALT 7 - Understands and applies Orthogonality

ALT 8 - Communicates understanding of linear algebra

ALT 9 - Applies understanding of linear algebra

ALT 1 - Communicates clearly and explains reasoning so others can follow how a problem is solved

ALT 2 - Reasons mathematically to solve problems in real-life context

ALT 3 - Recognizes patterns and describes them as relationships or general rules

ALT 4 - Writes formulas and solves problems involving sequences and series

ALT 5 - Calculates interest, rates, present values and future values of money

ALT 6 - Works with numbers in various forms including scientific notation, unit conversion and significant figures

ALT 7 - Works with other functions

ALT 8 - Applies geometric principles to solve problems involving distance, area, angles and volume

ALT 9 - Analyzes and interprets descriptive statistics

ALT 10 - Computes and reasons about probabilities

ALT 11 - Applies hypothesis testing to understand statistical independence

ALT 12 - Uses Linear Regression to model data

ALT 13 - Uses differential calculus concepts

ALT 14 - Uses integral calculus concepts

ALT 15- Meets requirements for exploration in the IB program

ALT 16 - Demonstrates prior knowledge of selected MAI content

ALT 1 - Communicates clearly and explains reasoning so others can follow how a problem is solved

ALT 2 - Reasons mathematically to solve problems in real-life context

ALT 3 - Recognizes patterns and describes them as relationships or general rules

ALT 4 - Writes formulas and solves problems involving sequences and series

ALT 5 - Calculates interest, rates, present values and future values of money

ALT 6 - Works with numbers in various forms including scientific notation, unit conversion and significant figures

ALT 7 - Expands binomial expressions using the binomial theorem

ALT 8 - Uses the fundamental vocabulary and symbolic language of functions and reasons about their key characteristics

ALT 9 - Performs transformations of graphs and their respective algebraic representations

ALT 10 - Uses linear, quadratic and higher degree polynomial equations (and inequalities), graphs, and various algebraic forms

ALT 11 - Uses rational functions, graphs and various algebraic forms

ALT 12 - Uses exponential and logarithmic functions, graphs and various algebraic forms

ALT 13 - Builds new functions from existing functions, including inverses and composition

ALT 14 - Applies techniques to solve right and non-right triangles

ALT 15 - Manipulates circular functions and uses them to model periodic phenomena

ALT 16 - Proves trigonometric identities and applies identities to find exact values

ALT 17 - Solves trigonometric equations

ALT 18 - Applies geometric principles to solve problems involving distance, angles, area and volume

ALT 19 - Applies vectors, lines and planes in pure and applied contexts

ALT 20 - Analyzes and interprets descriptive statistics

ALT 21 - Computes and reasons about probabilities

ALT 22 - Interprets characteristics of various probability distributions

ALT 23 - Uses Linear Regression to model data

ALT 24 - Uses differential calculus concepts

ALT 25 - Uses differential calculus techniques

ALT 26 - Uses integral calculus concepts

ALT 27 - Uses integral calculus techniques

ALT 28 - Applies calculus in pure and applied contexts

ALT 29 - Meets requirements for exploration in the IB program

ALT 1 - Communicates clearly and explains reasoning so others can follow how a problem is solved

ALT 2 - Reasons mathematically to solve problems in real-life context

ALT 3 - Recognizes patterns and describes them as relationships or general rules

ALT 4 - Writes formulas and solves problems involving sequences and series

ALT 5 - Expands binomial expressions using the binomial theorem

ALT 6 - Uses and applies complex numbers

ALT 7 - Uses proof by mathematical induction and contradiction

ALT 8 - Solves problems involving polynomial functions and graphs

ALT 9 - Works with vectors in both algebraic and geometric contexts

ALT 10 - Applies vectors, lines and planes in pure and applied contexts

ALT 11 - Analyzes and interprets descriptive statistics

ALT 12 - Computes and reasons about probabilities

ALT 13 - Interprets characteristics of various probability distributions

ALT 14 - Uses Linear Regression to model data

ALT 15 - Uses differential calculus concepts

ALT 16 - Uses differential calculus techniques

ALT 17 - Uses integral calculus concepts

ALT 18 - Uses integral calculus techniques

ALT 19 - Applies calculus in pure and applied contexts

ALT 20 - Analyzes differential equations

ALT 21 - Uses and applies power series to represent and approximate functions

ALT 22 - Reasons about continuity, differentiability, and limits

ALT 23 - Meets requirements for exploration in the IB program

ALT 24 - Demonstrates prior knowledge of selected MAA content

ALT 1 - Communicates clearly and explains reasoning so others can follow how a problem is solved

ALT 2 - Reasons mathematically to solve problems in real-life context

ALT 3 - Recognizes patterns and describes them as relationships or general rules

ALT 4 - Applies algebraic concepts and techniques

ALT 5 - Performs transformations of graphs and their respective algebraic representations

ALT 6 - Solves and manipulates trigonometric identities and equations using a variety of methods

ALT 7 - Works with vectors in both algebraic and geometric contexts

ALT 8 - Uses vectors in pure and applied contexts

ALT 9 - Computes and reasons about probabilities

ALT 10 - Interprets characteristics of various probability distributions

ALT 11 - Uses differential calculus concepts

ALT 12 - Uses differential calculus techniques

ALT 13 - Uses integral calculus concepts

ALT 14 - Uses integral calculus techniques

ALT 15 - Applies calculus in pure and applied contexts

ALT 16 - Recognizes and solves optimization problems

ALT 17 - Meets requirements for exploration in the IB

ALT 1 - Communicates clearly and explains reasoning so others can follow how a problem is solved

ALT 2 - Reasons mathematically to solve problems in real-life context

ALT 3 - Recognizes patterns and describes them as relationships or general rules

ALT 4 - Uses and applies complex numbers

ALT 5 - Uses induction and reasons about sequences and series

ALT 6 - Analyzes features of functions and their graphs and uses function notation

ALT 7 - Derives and applies trigonometric identities and circular functions

ALT 8 - Works with vectors in both algebraic and geometric contexts

ALT 9 - Applies vectors in pure and applied contexts

ALT 10 - Solves problems involving planes

ALT 11 - Computes and reasons about probabilities

ALT 12 - Analyzes and interprets descriptive statistics

ALT 13 - Interprets characteristics of various probability distributions

ALT 14 - Uses differential calculus concepts

ALT 15 - Uses differential calculus techniques

ALT 16 - Uses integral calculus concepts

ALT 17 - Uses integral calculus techniques

ALT 18 - Applies calculus in pure and applied contexts

ALT 19 - Meets requirements for exploration in the IB program

ALT 20 - Reasons about continuity and differentiability

ALT 21 - Analyzes differential equations

ALT 22 - Uses and applies power series to represent and approximate functions

ALT 23 - Reasons about convergence or divergence

ALT 24 - Solves problems involving graph theory in pure contexts

ALT 25 - Solves problems in applied contexts using graph algorithms

ALT 26 - Applies rules of number theory

ALT 27 - Solves problems involving congruences and modular arithmetic

ALT 28 - Applies algebraic concepts and techniques

ALT 1- Communicates clearly and explains reasoning so others can follow how a problem is solved

ALT 2- Reasons mathematically to solve problems in real-life context

ALT 3- Recognizes patterns and describes them as relationships or general rulesALT - Works with numbers in various forms including scientific notation, unit conversion, and significant figures

ALT 4 - Solves sequences and series of numerical patterns to solve problems

ALT 5 - Calculates interest, rates, present values and future values of money

ALT 6 - Uses measures of center, measures of spread and various data displays to describe numerical data

ALT 7 - Applies the rules of sets

ALT 8 - Applies the rules of logic

ALT 9 - Applies the rules of probability

ALT 10- Applies understanding of normal distributions to solve problems relating to percentile

ALT 11 - Uses Linear Regression to model data

ALT 12 - Applies hypothesis testing to understand statistical independence

ALT 13 - Understands techniques to solve right and non-right triangles

ALT 14 - Applies principles of trigonometry to problems involving three dimensional shapes

ALT 15 - Applies concepts of coordinate geometry

ALT 16 - Applies linear mathematical models

ALT 17 - Applies quadratic functions

ALT 18 - Applies other types of functions

ALT 19 - Meets requirements, such as the internal assessment, for exploration in the IB

ALT 1 - Solves problems using probability and counting rules.

ALT 2 - Solves problems using probability distributions.

ALT 3 - Chooses and applies the proper measurement of central tendency, variation, and position.

ALT 4 - Organizes and chooses a proper graphical display for a data set.

ALT 6 - Uses confidence intervals to estimate the value of a parameter from information obtained from a sample.

ALT 7 - Defines and uses correct statistical vocabulary in context, written work and oral explanations.

ALT 1 - Determines if a sample mean or the difference of sample means found from a data set is statistically significant in comparison to the population mean or the difference of population means by using a statistical comparison test.

ALT 2 - Determines if sample proportions or the difference of sample proportions found from a data set is statistically significant in comparison to the population proportion or the difference of population proportions by using a statistical comparison test.

ALT 3 - Determines if sample variance (standard deviation) or the difference of sample variances (standard deviations) found from a data set is statistically significant in comparison to the population variance (standard deviation) or the difference of populations variations (standard deviations) by using a statistical comparison test.

ALT 4 - Finds the correlation and the linear regression model from a data set and determines the predication interval about a value y’.

ALT 5 - Uses the chi-square goodness of fit or chi-square test to determine statistical significance.

ALT 6 - Determines if one or more means differ significantly statistically.

ALT 7 - Uses nonparametric statistics when the population from which the samples are selected is not normally distributed to test hypotheses.

 

ALT 1 - Communicates clearly and explains reasoning so others can follow how a problem is solved

ALT 2 - Reasons mathematically to solve problems in real-life context

ALT 3 - Recognizes patterns and describes them as relationships or general rules

ALT 4 - Displays, describes, and analyzes univariate categorical and quantitative data

ALT 5 - Displays, describes, and analyzes bivariate quantitative data

ALT 6 - Uses and analyzes appropriate methods of collecting data

ALT 7 - Applies probability rules and models

ALT 8 - Analyzes distributions

ALT 9 - Uses and analyzes statistical inference for proportions

ALT 10 - Uses and analyzes statistical inference for means

ALT 11 - Uses and analyzes statistical inference for multivariate data