Mathematics

Mathematics instruction in APS is aligned to the five Process Standards for Mathematics developed by the National Council of Teachers of Mathematics and promoted by the Virginia Department of Education.

Mathematical Problem Solving

Students will apply mathematical concepts and skills and the relationships among them to solve problem situations of varying complexities. Students also will recognize and create problems from real-world data and situations within and outside mathematics and then apply appropriate strategies to determine acceptable solutions. To accomplish this goal, students will need to develop a repertoire of skills and strategies for solving a variety of problem types. A major goal of the mathematics program is to help students apply mathematics concepts and skills to become mathematical problem solvers.

Mathematical Communication

Students will communicate thinking and reasoning using the language of mathematics, including specialized vocabulary and symbolic notation, to express mathematical ideas with precision. Representing, discussing, justifying, conjecturing, reading, writing, presenting, and listening to mathematics will help students to clarify their thinking and deepen their understanding of the mathematics being studied. Mathematical communication becomes visible where learning involves participation in mathematical discussions.

Mathematical Reasoning

Students will recognize reasoning and proof as fundamental aspects of mathematics. Students will learn and apply inductive and deductive reasoning skills to make, test, and evaluate mathematical statements and to justify steps in mathematical procedures. Students will use logical reasoning to analyze an argument and to determine whether conclusions are valid. In addition, students will use number sense to apply proportional and spatial reasoning and to reason from a variety of representations.

Mathematical Connections

Students will build upon prior knowledge to relate concepts and procedures from different topics within mathematics and see mathematics as an integrated field of study. Through the practical application of content and process skills, students will make connections among different areas of mathematics and between mathematics and other disciplines, and to real-world contexts. Science and mathematics teachers and curriculum writers are encouraged to develop mathematics and science curricula that support, apply, and reinforce each other.

Mathematical Representations

Students will represent and describe mathematical ideas, generalizations, and relationships using a variety of methods. Students will understand that representations of mathematical ideas are an essential part of learning, doing, and communicating mathematics. Students should make connections among different representations – physical, visual, symbolic, verbal, and contextual – and recognize that representation is both a process and a product.

The textbooks and online text resources are just one aspect of the media and methodology used to create rich instructional units.

Arlington Public Schools uses the following purchased resources to support the teaching and learning of the Virginia Department of Education Standards of Learning for Mathematics.

• Savvas Realize/enVision
  Do the Math (Intervention)
  Bridges (Intervention)
  Kathy Richardson (Intervention)
  Project M2 and M3: Mentoring Young Mathematicians

Elementary Math Resources

More to come for Summer 2026

Five Process Standards of Mathematics (Developed by the National Council of Teachers of Mathematics and Promoted by the Virginia Department of Education)

Mathematical Problem Solving Students will apply mathematical concepts and skills and the relationships among them to solve problem situations of varying complexities. Students also will recognize and create problems from real-world data and situations within and outside mathematics and then apply appropriate strategies to determine acceptable solutions. To accomplish this goal, students will need to develop a repertoire of skills and strategies for solving a variety of problem types. A major goal of the mathematics program is to help students apply mathematics concepts and skills to become mathematical problem solvers.

Mathematical Communication Students will communicate thinking and reasoning using the language of mathematics, including specialized vocabulary and symbolic notation, to express mathematical ideas with precision. Representing, discussing, justifying, conjecturing, reading, writing, presenting, and listening to mathematics will help students to clarify their thinking and deepen their understanding of the mathematics being studied. Mathematical communication becomes visible where learning involves participation in mathematical discussions.

Mathematical Reasoning Students will recognize reasoning and proof as fundamental aspects of mathematics. Students will learn and apply inductive and deductive reasoning skills to make, test, and evaluate mathematical statements and to justify steps in mathematical procedures. Students will use logical reasoning to analyze an argument and to determine whether conclusions are valid. In addition, students will use number sense to apply proportional and spatial reasoning and to reason from a variety of representations.

Mathematical Connections Students will build upon prior knowledge to relate concepts and procedures from different topics within mathematics and see mathematics as an integrated field of study. Through the practical application of content and process skills, students will make connections among different areas of mathematics and between mathematics and other disciplines, and to real-world contexts. Science and mathematics teachers and curriculum writers are encouraged to develop mathematics and science curricula that support, apply, and reinforce each other.

Mathematical Representations Students will represent and describe mathematical ideas, generalizations, and relationships, using a variety of methods.  Students will understand that representations of mathematical ideas are an essential part of learning, doing, and communicating mathematics.  Students should make connections among different representations – physical, visual, symbolic, verbal, and contextual – and recognize that representation is both a process and a product.

Arlington Public Schools uses the following purchased resources to support the teaching and learning of the Virginia Department of Education Standards of Learning for Mathematics. Textbooks and online text resources are just one aspect of the media and methodology used to create rich instructional experiences for our students.

• Savvas Realize
  IXL
  DeltaMath
  Bridges (Intervention)
  Do the Math (Intervention)

For School Year 2026 – 2027

APS Middle School Math Course Progressions

APS High School Math Course Progressions

Data Points that are Considered in the Mathematics Course Recommendation Process for Rising 6th Graders Include:

• Statewide Upper Quartile of Grade 5 Standards of Learning (SOL) scores (for auto-enrollment in an advanced mathematics course in sixth grade)
• Virginia Standards of Learning (SOL) Grade 4 Mathematics Assessment Score
• Virginia Standards of Learning (SOL) Grade 5 Mathematics Assessment Score
• Cognitive Abilities Test (CogAT) Quantitative Score
• Cognitive Abilities Test (CogAT) Nonverbal Score
• Grade 5 End-of-Year MAP Growth Math Assessment Score

Note:  APS administers the CogAT at the elementary school level. The test is divided into three sub-tests: Verbal, Non-Verbal, and Quantitative. For math course recommendations, the two subtest used are quantitative and nonverbal. The Advanced Academics Coach (AAC) at each child’s elementary site can provide additional information about CogAT.

For families selecting a math course for Fall 2026 as part of the Course Request Form (CRF) process in Spring 2026, the Math Office recommends that you talk with your child about their math performance, and as a family, consider whether Math 6 or Math 6 Advanced is the best fit for the student.

The Math Office will share course recommendations with families in July 2026 after reviewing data available at the end of the school year.  If you have questions after receiving a course recommendation in July, please contact the math coach at the middle school your child will be attending.

Data Points that are Considered in the Mathematics Course Recommendation Process for Rising 7th and 8th Graders Include:

• Statewide Upper Quartile of Standards of Learning (SOL) scores (for auto-enrollment in an advanced mathematics course)
• Virginia Standard of Learning (SOL) Score from Currently Enrolled Math Course
• Grade Level End End-of-Year MAP Growth Math Assessment Score
• Grades from Quarter 1, Quarter 2, and Quarter 3 of the Currently Enrolled Math Course

Secondary Math Resources

• Math 6 Summer Review Packet
• Math 7 Summer Review Packet
• Pre-Algebra for 8th Graders Summer Review Packet
  • Note: Pre-Algebra for 6th Graders students might review the Math 6, Math 7, and Pre-Algebra for 8th Graders packets.  Pre-Algebra for 7th Graders students might review both the Math 7 and Pre-Algebra for 8th Graders packets.
• Algebra I (and Intensified Algebra I) Summer Review
  • Please note the header says Intensified Geometry – this packet reviews Algebra topics most essential for Geometry – (created by W-L Teachers)
• Geometry Intensified Summer Review – (created by W-L Teachers)

Due to the nature of High School summer review packets (teachers may collect these, evaluate these, and may assign a grade) keys are not posted for High School Credit courses’ summer review packets.