Operational Sense

Number Sense

Proportional Reasoning

Algebraic Reasoning

Operational sense is when children can make sense of addition, subtraction, multiplication, and division and use them in problem-solving situations. When a child is able to develop a strong understanding of the operations, they can recognize the relationships among them, and develop systems for computing numbers. 

Operational sense starts for students in primary grades where they use counting strategies, combining and partitioning numbers to learn addition and subtraction. In junior grades, students learn the development of operational sense, focusing on multiplication and division. At this level, using meaningful contexts helps students gain an understanding of the operations.

Student Learning

Using the operations and performing calculations depends on an understanding of part-whole relationships. When students can fluently and flexibly work with a variety of computational strategies, they demonstrate operational sense. 

Other characteristics of student learning include:

  • Using algorithms and strategies that make sense to them
  • Understanding the relationships between the operations
  • Developing a range of strategies and algorithms, including those of their own making
  • Determining an appropriate method of computation for the context and numbers involved in the problem

When learning operational sense, solving problems and using models are key instructional components that help students understand the subject.

Student Learning

Using the operations and performing calculations depends on an understanding of part-whole relationships. When students can fluently and flexibly work with a variety of computational strategies, they demonstrate operational sense. 

Other characteristics of student learning include:

  • Using algorithms and strategies that make sense to them
  • Understanding the relationships between the operations
  • Developing a range of strategies and algorithms, including those of their own making
  • Determining an appropriate method of computation for the context and numbers involved in the problem

When learning operational sense, solving problems and using models are key instructional components that help students understand the subject.

Encouraging students to make connections between numbers and relationships allows them to discover new mathematics in efficient, flexible, and innovative ways. In the junior grades, children apply their understanding of base ten relationships as they start to work with larger whole numbers. Building on these relationships allows students to understand the operations of addition, subtraction, division, and multiplication. 

At Dropkick Math, we teach students how to approach math concepts and understand their relationships so they can overcome problems more efficiently on their own. With development strategies for ordering and comparing numbers, students will begin to understand the relative size of numbers, providing them with skills for solving real-life problems. 

No matter where a child is in their number sense development, we are able to provide a fun and educational environment where they can explore their understanding of quantity to numbers. It is important that students have the opportunities to compare and order numbers using various learning methods. Through Dropkick Math’s interactive tools, we can help build your child’s confidence and understanding of mathematics so they can reach their full potential. 

Relationships in Performing Computations

FAQ

Operational sense is the ability to use basic math operations in order to solve problems. This includes being able to do addition, subtraction, multiplication, and division, as well as understanding what each operation means and how it can be used to solve a problem.

One way to help improve operational sense is to provide children with opportunities to practice problem-solving tasks. However, you can also help them better understand the operations by explaining things in context. For example, multiplication means groups of – division can be thought of as splitting a number equally into groups or determining how many times a number fits into a different number. Subtraction can be thought of as removal or difference. Improving operational sense is more about allowing children to do flexible thinking with operations and representing the operations using manipulatives or visual models.

Encouraging students to make connections between numbers and relationships allows them to discover new mathematics in efficient, flexible, and innovative ways. In the junior grades, children apply their understanding of base ten relationships as they start to work with larger whole numbers. Building on these relationships allows students to understand the operations of addition, subtraction, division, and multiplication. 

At Dropkick Math, we teach students how to approach math concepts and understand their relationships so they can overcome problems more efficiently on their own. With development strategies for ordering and comparing numbers, students will begin to understand the relative size of numbers, providing them with skills for solving real-life problems. 

No matter where a child is in their number sense development, we are able to provide a fun and educational environment where they can explore their understanding of quantity to numbers. It is important that students have the opportunities to compare and order numbers using various learning methods. Through Dropkick Math’s interactive tools, we can help build your child’s confidence and understanding of mathematics so they can reach their full potential. 

Relationships in Performing Computations

Relationships in Performing Computations

Encouraging students to make connections between numbers and relationships allows them to discover new mathematics in efficient, flexible, and innovative ways. In the junior grades, children apply their understanding of base ten relationships as they start to work with larger whole numbers. Building on these relationships allows students to understand the operations of addition, subtraction, division, and multiplication. 

 

At Dropkick Math, we teach students how to approach math concepts and understand their relationships so they can overcome problems more efficiently on their own. With development strategies for ordering and comparing numbers, students will begin to understand the relative size of numbers, providing them with skills for solving real-life problems. 

 

No matter where a child is in their number sense development, we are able to provide a fun and educational environment where they can explore their understanding of quantity to numbers. It is important that students have the opportunities to compare and order numbers using various learning methods. Through Dropkick Math’s interactive tools, we can help build your child’s confidence and understanding of mathematics so they can reach their full potential. 

This is a great document that has way more information than is required for our purposes. Here are some areas to focus on:
  • Page 20 Overview & Green box on the bottom of the page - focus more on junior grades than primary grades
  • Page 21 Understanding the Operations - I wouldn’t worry about the third paragraph
  • Page 28 Characteristics of Student Learning
  • Page 32 Relationships Among the Operations and in Performing Computations
  • Page 34 and 35 Characteristics of Student Learning

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