Middle Level Mathematics - Grades 4-9

1.0 Standards for Mathematical Practices

Demonstrate ability to embed CCSS-M Mathematical Practices in the instructional process to deepen conceptual understanding.

1.A Make sense of problems and persevere in solving them.

1.B Reason abstractly and quantitatively.

1.C Construct viable arguments and critique the reasoning of others.

1.D Model with mathematics.

1.E Use appropriate tools strategically.

1.F Attend to precision.

1.G Look for and make use of structure.

1.H Look for and express regularity in repeated reasoning.

2.0 Number and Quantity

Candidates demonstrate a conceptual understanding of and procedural facility with operations and number systems.

2.A Understand the structure, properties, characteristics of, and relationships between number systems including whole numbers, integers, rational, real, and complex numbers.

2.B Understand arithmetic operations of different number systems and their properties (integers, rational, and irrational numbers).

2.C Understand the progression of learning that begins with the base-ten number system and operations thereof, builds into understanding of and operations with fractions and rational numbers, and extends to understanding of and operations with real numbers.

3.0 Algebra and Functions

Candidates demonstrate a conceptual understanding of and procedural facility with algebra concepts emphasizing functions.

3.A Solve and graphically represent real life and mathematical problems using numerical and algebraic expressions, equations, inequalities, and systems of equations and inequalities.

3.B Understand the connections between proportional relationships, lines, and linear equations and use them to solve real world and mathematical problems.

3.C Use functional notation and interpret expressions for functions as they arise in terms of the situation they model (e.g., linear, quadratic, simple rational, and exponential).

3.D Understand operations on algebraic expressions and functions (e.g., polynomials, rationals, and roots).

3.E Apply arithmetic properties to algebraic expressions and equations.

3.F Write equations and inequalities in equivalent forms.

3.G Analyze and model functions.

3.H Explain the interrelationship between the various representations of a function (e.g., graphs, tables, algebraic expressions, concrete models, and contexts).

4.0 Geometry and Measurement

Candidates demonstrate a conceptual understanding of geometric properties and relationships as they apply to congruence, similarity, geometric figures, and the Cartesian Coordinate System.

4.A Understand congruence in terms of rigid motion.

4.B Prove theorems involving triangle congruency and similarity.

4.C Apply transformations and use similarity and congruence in mathematical situations.

4.D Understand and perform geometric constructions physically and/or with technology.

4.E Understand the Pythagorean Theorem and apply it to problem solving situations.

4.F Solve real life and mathematical problems involving lines, angle measure, area, surface area, and volume.

4.G Classify, visualize, and describe two-dimensional figures and three-dimensional objects as well as the relationship among them.

4.H Apply geometric concepts to model real world situations.

5.0 Statistics and Probability

Candidates demonstrate conceptual understanding and procedural facility of statistics and probability.

5.A Use appropriate measures of central tendency and distributions to summarize, represent, and interpret categorical and quantitative data.

5.B Understand and evaluate random processes underlying statistical experiments and use random sampling to make inferences about whole populations.

5.C Understand and use the rules of probability to make predictions, evaluate decisions, and solve problems.

5.D Apply probability concepts to model real world situations.

6.0 Ratios and Proportional Relationships

Candidates demonstrate conceptual understanding and procedural fluency in analyzing proportional relationships and solving real world mathematical problems.

6.A Describe and determine additive versus multiplicative perspectives.

6.B Reason and compute with ratios and the constant of proportionality (unit rate) to solve real world and mathematical problems.

6.C Recognize, describe, and represent equivalent ratios, rates, and proportional relationships.

6.D Represent and analyze proportional relationships using tables, graphs, equations, diagrams, concrete and mathematical models, and verbal descriptions of proportional relationships.

6.E Compute the constant of proportionality (unit rate) associated with rational numbers.

6.F Recognize and connect proportional relationships to geometry, measurement, statistics, probability, and function.

6.G Use ratio reasoning to convert measurement units.

6.H Apply ratio and proportion concepts to model real world situations.

7.0 Modeling and Technology

Candidates will be able to connect mathematics with real life problems through the use of mathematical modeling and technology.

7.A Construct mathematical models in the content strands (e.g., look at a real life situation and transpose it into a mathematical problem, solve the problem, and interpret the solution in real life.)

7.B Use the appropriate technology available.

7.B.1 Explore conjectures, visualize, and analyze the mathematics.

7.B.2 Develop concepts and apply them to a context.

8.0 Mathematics Instructional Methodology

Candidates possess a deep understanding of how students learn mathematics and of the pedagogical knowledge specific to mathematics teaching and learning.

8.A Select, use, and determine suitability of the available mathematics curricula, teaching materials, and other resources including manipulatives for the learning of mathematics for all students.

8.B Demonstrate ability to present mathematical concepts using multiple representations (e.g., numerical, graphical, analytical, and contextual).

8.C Demonstrate the ability to guide student discourse in mathematical problem solving, argumentation (creation and critiquing), literacy, and in-depth conceptual understanding.

8.D Demonstrate knowledge of learning progressions, including conceptual and procedural milestones and common misconceptions, within each content domain and connections to instruction.

8.D.1 Demonstrate knowledge of major, supporting, and additional clusters for each grade level.

8.D.2 Demonstrate an understanding of the concept of mathematical rigor including conceptual understanding, procedural skill and fluency, and application.

8.D.3 Demonstrate an understanding of coherent connections within clusters at a grade level and the progression from grade level to grade level that builds on previous learning.

8.E Engage in developmentally and culturally responsive teaching of mathematics that minimizes power and status issues, nurtures a positive mathematics disposition, and utilizes students’ cultural funds of knowledge and experiences as resources for lessons.