Long Descriptions for Chapter One

Figure 1.1: Mathematics Performance (PISA)

Boys / Girls, Mean score, 2018 or latest available.

Source: Organization for Economic Co-operation and Development (2021)

Figure 1.2: Big Ideas for Sixth Grade

The graphic illustrates the connections and relationships of some sixth-grade mathematics concepts. Direct connections include:

• Variability in Data directly connects to: The Shape of Distributions, Relationships Between Variables
• The Shape of Distributions directly connects to: Relationships Between Variables, Variability in Data
• Fraction Relationships directly connects to: Patterns Inside Numbers, Generalizing with Multiple Representations, Model the World, Relationships Between Variables
• Patterns Inside Numbers directly connects to: Fraction Relationships, Generalizing with Multiple Representations, Model the World, Relationships Between Variables
• Generalizing with Multiple Representations directly connects to: Patterns Inside Numbers, Fraction Relationships, Model the World, Relationships Between Variables, Nets & Surface Area, Graphing Shapes
• Model the World directly connects to: Fraction Relationships, Relationships Between Variables, Patterns Inside Numbers, Generalizing with Multiple Representations, Graphing Shapes
• Graphing Shapes directly connects to: Model the World, Generalizing with Multiple Representations, Relationships Between Variables, Distance & Direction, Nets & Surface
• Nets & Surface directly connects to: Graphing Shapes, Generalizing with Multiple Representations, Distance & Direction
• Distance & Direction directly connects to: Graphing Shapes, Nets & Surface Area
• Relationships Between Variables directly connects to: Variability in Data, The Shape of Distributions, Fraction Relationships, Patterns Inside Numbers, Generalizing with Multiple Representations, Model the World, Graphing Shapes

Note: The sizes of the circles vary to indicate the relative importance of the topics. The connecting lines between circles show links among topics and suggest ways to design instruction so that multiple topics are addressed simultaneously.

The size of the circles, from largest to smallest, is as follows:

• Relationships Between Variables (largest)
• Generalizing with Multiple Representations
• Graphing Shapes
• Model the World
• Fraction Relationships
• Patterns Inside Numbers
• Nets & Surface Area
• Distance & Direction (this, along with the two that follow, are the same size and smallest in the list)
• Variability in Data
• The Shape of Distributions

Figure 1.3: The Why, How and What of Learning Mathematics

Figure 1.4: Content Connections, Mathematical Practices, and Drivers of Investigation

A spiral graphic shows how the Drivers of Investigation (DIs), Standards for Mathematical Practice (SMPs) and Content Connections (CCs) interact. The DIs are the “Why,” described as, “In order to ...”: DI1, Make Sense of the World (Understand and Explain); DI2, Predict What Could Happen (Predict); DI3, Impact the Future (Affect). The SMPs are the “How,” listed under “Students will ...”: SMP1, Make sense of problems and persevere in solving them; SMP2, Reason abstractly and quantitatively; SMP3, Construct viable arguments and critique the reasoning of others; SMP4, Model with mathematics; SMP5, Use appropriate tools strategically; SMP6, Attend to precision; SMP7, Look for and make use of structure; SMP8, Look for and express regularity in repeated reasoning. Finally, the CCs are the “What,” listed under, “While ...”: CC1, Reasoning with Data; CC2, Exploring Changing Quantities; CC3, Taking Wholes Apart, Putting Parts Together; CC4, Discovering Shape and Space.