This section focuses on developing students’ fluency with addition and subtraction within 10. Being able to count on by 1, 2, or 3 and make 10 are helpful steps toward fluency because most sums within 10 can be found with those methods. Students have a chance to self-assess the sums they know from memory and those they are still working on. (Fluency is not expected until the end of the school year.)

Note that the term “sum” has so far been used to refer to a number—the total we have when adding two or more numbers. Here, the term is also used to refer to an addition expression like because it represents the sum of two quantities.

The 10-frame can help students visualize sums of 10. For example, this 10-frame may allow students to recall several related facts:

Changing one counter from red to yellow illustrates , and changing a counter from yellow to red illustrates . Seeing ways to make 10 will support students in later work of adding and subtracting within 20 and within 100.

Students are introduced to Add To, Start Unknown story problems. Because the starting number is unknown, students may find this challenging. Encourage them to act out the stories and apply what they have learned about adding within 10 to solve these problems.

In this section, students explore the idea of composing and decomposing numbers to add up to three addends within 20. They make use of the base-ten structure and the commutative and associative properties when adding, and discover the usefulness of grouping numbers to make a sum of 10 (or a unit of ten).

For instance, to find the value of , they can rearrange the addends to group 4 and 6, which makes 10, and add the 7.

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Making a ten is also helpful when finding the sum of two addends. For example, to find the value of , students can take 1 from the 5 and group it with the 9 to make 10, and then add the 4.

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Although this section focuses on making a ten, students may use other facts they know to find sums. For example, given , students who know the value of may think of it as .

In this section, students subtract within 20. They rely on the relationship between addition and subtraction and the idea of making a ten to do so. Students encounter subtraction expressions and unknown-addend equations, and use taking-away and counting-on methods to find differences.

For example, given , students may take away 5 to get to 10 and then take away another 3 to find the difference of 7.

They may also start with 8 and count on by 2 to get 10, and then add another 5 to reach 15.  They see that the difference is 7.

In this section, students begin exploring the structure of the base-ten system and the idea of place value as they work with teen numbers.

Students see that a new unit, a ten, is composed from 10 ones, and that teen numbers are composed of 1 unit of ten plus 1 to 9 ones. Double 10-frames are used here as they encourage students to see this structure (MP7).

Unlike in connecting cube towers, where identifying a unit of ten means counting individual cubes, the unit of ten—and whether it is complete—is evident in double 10-frames.

The structure of teen numbers and double 10-frames help students add and subtract teen numbers.

Here students work only with expressions that do not require composing or decomposing a ten, for example, and . They notice that the unit of ten doesn’t change and relate the sum to the adding or subtracting of ones.

Students encounter a new problem type—Take From, Change Unknown—in which the number that needs to be subtracted to get a difference is unknown. Encourage students to act out the story problems or to use double 10-frames and counters to make sense of the situations. 

While they are not expected to write equations that match the action in a story, students do write equations that they may use to solve problems and explain how their equations relate to the stories. In doing so, they reason quantitatively and abstractly (MP2).