The big ideas that define each unit of InsightMath connect to one another within and across grade levels. The Mathematics Framework for California Public Schools defines four Content Connections that provide structure to the connected network of big ideas: Reasoning with Data, Exploring Changing Quantities, Taking Wholes Apart and Putting Parts Together, and Discovering Shape and Space. These Content Connections provide a framework for designing and understanding a progression of big ideas across the curriculum in keeping with the CA CCSSM principles of focus, coherence, and rigor. Table 1 highlights those connections within and among grade levels through the lens of the four Content Connections.
Table 2: Progression of Big Ideas, Grades 3-6
| Content Connection | Big Ideas: Grade Three | Big Ideas: Grade Four | Big Ideas: Grade Five | Big Ideas: Grade Six |
| Reasoning with Data | Measuring the size of an object requires choosing an appropriate attribute, tool, and unit to match the situation. | Multiplication can be used to compare quantities and measurements. | Creating geometric structures and categories helps to analyze and organize space. | Rates and percentages are specific ratios that help to compare numbers or measures by their relative values. |
| Reasoning with Data | Asking questions and using data to critically answer those questions help to make sense of the world. | Time can be represented with a variety of models that can help to solve problems and interpret data. | n/a | How data is represented and analyzed can impact how it is interpreted. |
| Exploring Changing Quantities | The place value system is based on patterns, which makes expressing and working with numbers efficient. | Understanding the patterns and regularity of the base-ten place value system helps to compare and compute with multidigit numbers. | Multiplying and dividing by powers of 10 is the foundation for decimal numbers. Multidigit computation can be reduced to repeated processes based on a series of single-digit computations. | The base-ten system allows all four operations to be performed with algorithms involving a series of single-digit computations. |
| Exploring Changing Quantities | n/a | Multiplication can help to discover, understand, and explain relationships between numbers. | Division of multidigit numbers is a repeated process of estimating partial quotients based on multiples of the divisor. | Division can be performed by multiplying due to the inverse relationship between multiplication and division. |
| Exploring Changing Quantities | Relating known facts and using flexible models and strategies can help to multiply and divide efficiently and fluently. | Using known facts and place value properties flexibly can help to perform multidigit multiplication strategically and efficiently. | Extending place value patterns and fraction understanding can help to multiply and divide decimals. | n/a |
| Exploring Changing Quantities | Understanding properties and using flexible models and strategies can help to multiply and divide efficiently and fluently. | Multiplication and division models and strategies can be extended and applied to division problems involving multidigit numbers and remainders. | n/a | Algebraic equations can be used to model and solve real-world problems. |
| Exploring Changing Quantities | n/a | n/a | n/a | Algebra is a way of expressing generalizations. |
| Taking Wholes Apart, Putting Parts Together | n/a | Thinking flexibly about how fractions, whole numbers, and mixed numbers are composed can help to add and subtract efficiently. | Using flexible fraction and multiplication interpretations helps to multiply and divide with fractions. | n/a |
| Taking Wholes Apart, Putting Parts Together | Multiplication and division are the mathematics of equal groups. | Equal-groups thinking can help when multiplying and comparing quantities involving fractions. | Quantities can be added and subtracted when the units are the same size. | Numbers and measures can be compared by their relative values. |
| Taking Wholes Apart, Putting Parts Together | Any number can be represented in an infinite number of different, but equivalent, ways. | Any number can be represented in an infinite number of different, but equivalent, ways. | n/a | Any number or expression can be represented in an infinite number of ways that have the same value. |
| Discovering Shape and Space | Fractions extend the number system to include numbers that represent equal parts of a whole. | n/a | n/a | The number system can be extended to include negative numbers, which are reflections of their positive counterparts over the origin. |
| Discovering Shape and Space | Area is a way to describe and quantify two-dimensional space. | n/a | Multiplication can help to discover, understand, and explain three-dimensional space and relationships between numbers. | The size of objects can be quantified in one, two, or three dimensions to serve a particular purpose or context. |
| Discovering Shape and Space | Two-dimensional shapes can be described by many different attributes, some of which can be quantified (e.g., perimeter, area) and some of which define what the shape is called (e.g., quadrilateral). | Properties of two-dimensional shapes are determined by the parts that make up the shape and the relationships between those parts. | Creating geometric structures and categories helps to analyze and organize space. | n/a |