Mathematics

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 Bridges in Mathematics (from the Math Learning Center) as the primary resource to support the teaching and learning of the Virginia Department of Education Standards of Learning for Elementary Mathematics.  Books include:  Number Corner Student Book, Bridges Student Book, and Home Connections.

The Number Corner Student Book accompanies the Number Corner component of Bridges in Mathematics. Number Corner provides 15–20 minutes of daily skill-building instruction focused on developing number sense, computational fluency, mathematical reasoning, and problem-solving strategies. Students use the Number Corner Student Book to complete daily practice activities connected to calendar routines, number patterns, place value, operations, measurement, data, and other essential mathematical concepts.

The Bridges Student Book is the core student workbook used during daily mathematics instruction. It supports participation in whole-class investigations, problem-solving activities, mathematical discussions, and games. Students use the book to record their thinking, solve problems, complete practice activities, and engage with grade-level mathematical concepts throughout each instructional unit. The Bridges Student Book is closely aligned with classroom lessons and helps students develop conceptual understanding, procedural fluency, and problem-solving skills.

Home Connections provides family-friendly mathematics activities and practice opportunities that extend learning beyond the classroom. Activities may include games, discussion prompts, independent practice pages, and real-world mathematical applications that students can complete at home. Home Connections is designed to strengthen the partnership between school and home while reinforcing key mathematical concepts and skills taught during classroom instruction.

While there are Bridges in Mathematics teacher-facing materials available to our APS elementary educators through their APS MyAccess credentials, below are some public-facing links for families to explore and use:

• Math at Home, from the Math Learning Center, where you’ll find activities, online games, practice pages, as well as games.
• Free Apps, from the Math Learning Center, based on the visual models featured through Bridges in Mathematics.  Apps are available in multiple versions: a web app for all modern browsers, and downloadable versions for specific operating systems and devices (such as Apple iOS for iPad).
• Free Lessons and Publications from the Math Learning Center.

Purpose:
Summer Math Packets at the Elementary Level are designed to help students preview important skills and concepts that will prepare students for success in an upcoming math course.

• Students are not required to complete the summer practice in one session.
• Students may break up the packet and complete pieces throughout the summer.
• Answer Keys are available on the last page of each packet.

Rising 1st Grade Summer Math Packet

Rising 2nd Grade Summer Math Packet

Rising 3rd Grade Summer Math Packet

Rising 4th Grade Summer Math Packet

Rising 5th Grade Summer Math Packet

Rising 6th Grade Summer Math Packet

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

Purpose:
Summer Math Review Packets at the Secondary Level are designed to help students review important skills and concepts that will prepare students for success in an upcoming math course.

• Students are not required to complete the summer practice in one session.
• Students may break up the packet and complete pieces throughout the summer.

Work Expectations:
Students that decide to engage in this work are expected to show all work for each problem unless otherwise stated.  Work should be neat and organized so thinking is clearly demonstrated.

Note: An answer key is provided for you to check your work.

Rising Sixth Grade Summer Skills Review Practice and Answer Key

Math 6 Summer Skills Review Practice and Answer Key

Math 6 Advanced and Math 7 Summer Skills Review Practice and Answer Key

Pre-Algebra Summer Skills Review Practice and Answer Key

Algebra 1 Summer Skills Review Practice and Answer Key

Additionally, students have access to IXL Math over the summer, and students can work on different skills in grades at, below, or above their grade-band to reinforce and/or explore new skills.