This opening section gives teachers opportunities to assess students’ fluency with addition and subtraction facts within 10 and monitor how students approach adding and subtracting.

The first several lessons focus on making a ten as a strategy to add and subtract, which helps students gain fluency with facts within 20 and supports the work with larger numbers such as composing and decomposing numbers as a way to add and subtract. In the last lesson of the section, students use strategies learned in grade 1 to add within 50.

Some activities take place in centers, enabling teachers to also introduce routines and structures while helping students develop mental strategies for adding and subtracting.

In this section, students explore situations and problems that involve categorical data and learn new ways to represent such data. 

Students begin by representing data about their class in a way that makes sense to them. Then they are introduced to picture graphs and bar graphs. Students learn the conventions of these graphs as they create them. They discuss the types of questions that can be asked and answered by the graphs, including those that require combining and comparing different categories. 

Students have previously represented and reasoned about quantities in story problems. In grade 1, students compared quantities using diagrams with discrete partitions. In the previous section, they reasoned about quantities in bar graphs. Here students learn to use tape diagrams as another way to make sense of the relationship between two quantities and between addition and subtraction.

Students explore Compare story problems with an unknown difference, an unknown larger number, and an unknown smaller number. Tape diagrams help students to visualize these structures and support them in reasoning about strategies to solve problems, such as counting on or counting back. The table highlights the different types of problems in this section.

difference unknown	bigger unknown	smaller unknown
Lin counts 28 boats. Diego counts 32 boats. How many more boats does Diego count?	Lin finds 28 more shells than Diego. Diego finds 32 shells. How many shells does Lin find?	Lin sees 32 starfish. Diego sees 28 fewer starfish than Lin. How many starfish does Diego see?

Students also write equations to reason about questions that ask “how many more?” and “how many less?” They recognize that different equations and diagrams can be used to represent the same difference between two numbers.