Mathematics

Our math program at the Upper Primary is focused on building procedural fluency through conceptual understanding and number sense.  Students learn and use multiple models and strategies to show conceptual understanding and develop flexibility and fluency in all computational skills. The 8 mathematical practices are an integral part of our curriculum and instruction. Instruction follows the Common Core State Standards for Mathematics and uses Bridges in Mathematics as our primary resource for instructional content.  Students have opportunities and support to engage in rich and challenging tasks that allow for productive struggle as they make sense of mathematical ideas and relationships. These tasks promote reasoning and problem-solving, meaningful mathematical discourse, and a positive mathematical mindset. Through the use of ongoing assessment, teachers implement various instructional strategies that meet students at their present level of learning and allow for depth, complexity, and extended learning. This practice affords students voice and choice in their learning, with self-evaluation and reflection naturally embedded.

HKIS Math Philosophy

We believe mathematics is a universal language that allows us to make sense of fundamental principles, ideas, patterns, problems and phenomena that surround us. Through exploring abstract and contextual mathematics, students will investigate applications and uses of mathematics in the world around them. Such investigations provide opportunities for students to engage in critical thinking and reasoning. Students will learn how to communicate and justify their thinking in multiple ways. Students will come to understand that mathematicians focus on big ideas in mathematics and the connections between ideas.

Students will be able to independently and collaboratively use their learning in mathematics to:

1. Persevere and solve problems logically, creatively and confidently.
2. Reason abstractly and quantitatively.
3. Communicate thinking in a variety of situations and disciplines.
4. Demonstrate the ability to process and plan by choosing efficient strategies and effective tools and resources.
5. Apply learning in multiple ways and in familiar, unfamiliar and real-world contexts.

We agree that mathematics education happens best when we provide opportunities for students to:

1. Take risks and make mistakes in an emotionally safe environment that values growth.
2. Build a conceptually based foundation that moves between concrete, symbolic and abstract, in order to develop deep understanding.
3. Reason and justify their thinking individually and with others.
4. Think creatively and critically.
5. Develop fact fluency through working with and exploring numbers in meaningful number activities.
6. Ask questions, construct knowledge and reflect on the learning process. 

Five Strands of Mathematical Proficiency

At HKIS, we develop students’ deep understanding of mathematics through meaningful exposure to and practice with the Five Strands of Mathematical Proficiency. These components work together and are interwoven and interdependent, forming the overarching framework for our daily mathematics instruction. The five strands describe what it truly means for a child to be successful in mathematics - ensuring that students not only learn mathematical skills, but also understand the ideas behind them, know how to approach and solve problems, explain their reasoning, and develop confidence and persistence as learners. 

Conceptual Understanding: High achievers in mathematics understand the meaning of the operations and underlying math concepts of all areas of mathematics.

Productive Disposition: High achievers in mathematics are persistent.

Adaptive Reasoning: High achievers in mathematics can defend their thinking and critique the reasoning of others.

Strategic Competence: High achievers in mathematics are good problem posers and problem solvers.

Procedural Fluency: High achievers in mathematics can effectively, efficiently, and flexibly choose and use a variety of strategies to compute. 

Standards for Mathematical Practice

The Standards for Mathematical Practice from the Common Core State Standards guide our teaching and learning in mathematics. While the Five Strands of Mathematical Proficiency describe what it means to be mathematically successful, the Mathematical Practices describe how students think and work to develop that proficiency. These practices reflect the habits and approaches of productive mathematical thinkers and are intentionally embedded in daily instruction. Through exploration and investigation, we support children in communicating their ideas, representing their thinking, and reflecting on their mathematical experiences.

Grade Overviews

Based on Common Core State Standards for Mathematics (CCSS-M) critical areas of focus and domains

Grade 3

Critical Areas of Focus: 

1. Developing understanding and strategies for multiplication and division within 100.
2. Developing understanding of fractions, especially unit fractions.
3. Developing understanding of the structure of rectangular arrays and of area.
4. Describing and analyzing two-dimensional shapes.

Content Standards: 

Grade 4

Critical Areas of Focus: 

1. Developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends.
2. Developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers.
3. Understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

Content Standards: 

Grade 5

Critical Areas of Focus: 

1. Developing fluency with addition and subtraction of fractions, and developing an understanding of the multiplication of fractions and of division of fractions.
2. Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations.
3. Developing understanding of volume.

Content Standards: