In this unit, students learn to solve new types of addition and subtraction story problems. As students make sense of the problems and share the ways they solve them, they deepen their understanding of addition, subtraction, and the relationship between these operations. These new problem types also elicit computation strategies, such as counting on, that students will use throughout the year as they add and subtract within 20 and develop fluency within 10.

In kindergarten, students solved a limited number of story problem types within 10. They made sense of story problems by acting them out with objects and drawings. As they compared different ways to represent and solve these problems, including the use of expressions, students developed an understanding of addition as adding to or putting together and subtraction as taking from or taking apart.

Here, students are introduced to three of the new problem types for grade 1:

• Add To, Change Unknown
• Put Together/Take Apart, Addend Unknown
• Compare, Difference Unknown

Each of these problem types involves an unknown addend. Still, they all provide unique opportunities for students to learn about the relationship between addition and subtraction as they make sense of the actions or relationships in the problems.

Throughout the unit, it is important to maintain a focus on sense-making as students share and compare the different ways they represent and solve problems. It is recommended to read the story problems aloud to all students during this unit to ensure access to the mathematics. Students will continue to use objects and drawings during the unit and throughout the year to make sense of problems and show their thinking.

In the next unit, students will solve addition and subtraction problems within 20 and work with equations with a symbol for the unknown in all positions. They will also further develop their fluency within 10.

In this unit, students develop an understanding of 10 ones as a unit called “a ten” and use the structure of \(10 + n\) to add and subtract within 20.

In kindergarten, students composed and decomposed the numbers 11–19 into 10 ones and some more ones. In a previous unit, students solved story problems of all types with unknown values in all positions and numbers within 10. They used the relationship between addition and subtraction, drawings and equations, and various tools (10-frames, connecting cubes, two-color counters) to represent the quantities in the problems. They learned that the values represented by the numbers or expressions on each side of an equation are equal.

Here, students decompose and recompose addends to find the sum of two or three numbers. For example, to find the value of \(9 + 6\), they may decompose 6 into 1 and 5, compose the 1 and 9 into 10, and find \(10 + 5\).

Subtraction work occurs throughout the unit and becomes the focus in the last section. Students consider taking away and counting on as methods for subtracting. They understand subtraction as an unknown-addend problem and use their knowledge of addition to find the difference of two numbers.

For instance, students may reason about the value of \(10-6\) by:

Taking away 6 from 10.

Counting on to 10, starting from 6.

Using an addition fact, \(6 + 4 = 10\).

Students solve story problems throughout the unit and learn two new problem types—Add To, Start Unknown and Take From, Change Unknown. Students compare the structure of different types of story problems as they practice adding and subtracting within 20.

This unit develops students’ understanding of the structure of numbers in base ten, allowing them to see that the two digits of a two-digit number represent how many tens and ones there are.

In a previous unit, students counted forward by one and ten within 100 in the Choral Count routine. They learned that 10 ones make a unit called a “ten” and that a “teen number” is a ten and some ones.

As students count and group quantities, they generalize the structure of two-digit numbers in terms of the number of tens and ones. This understanding enables students to transition from counting by one to counting by ten and then counting on. For example, to count to 73, students may count 7 tens and then count on—71, 72, 73.

Students interpret and use multiple representations of two-digit numbers: connecting cubes, base-ten diagrams, words, and expressions. Connecting cubes in towers of 10 and singles are used instead of base-ten blocks, so units of ten can be physically composed and decomposed with the cubes. Base-ten blocks will be introduced in grade 2. Here are some representations for 73:

7 tens and 3 ones
3 ones and 7 tens

\(70 + 3\)
\(63 + 10\)
\(60 + 13\)

Students also represent two-digit numbers with drawings. They may start by drawing towers of ten and showing each unit of one within each ten. Later, students simplify their drawings to show rectangles for tens and small squares for ones. Encourage students to use the drawings that make sense to them. Students that use abstract drawings should express how many ones each ten represents.

Students should have access to connecting cubes—towers of 10 and singles —in all lessons to help students make sense of base-ten representations. Some students may also benefit from access to double 10-frames and two-color counters. Students should be encouraged to work toward using connecting cubes in towers of 10 and singles.

Later in the unit, students use the value of the digits to compare two-digit numbers. Students learn to use comparison symbols (\(<\), \(>\)) to record their comparisons. The unit concludes with opportunities for students to explore different ways of using tens and ones to represent two-digit numbers.

In this unit, students add within 100, using place value and properties of operations in their reasoning.

In a previous unit, students composed, decomposed, and compared numbers within 100. They reasoned about units of tens and ones and represented numbers with connecting cubes, base-ten drawings, expressions, and equations in different ways (for example, \(65 = 60+5\) and \(65 = 50 + 15\)). In this unit, students build on these understandings of place value to find sums.

Students begin by adding a two-digit number with another two-digit number or with a one-digit number where it is not necessary to compose a new ten. Then they observe cases in which adding some ones together requires composing a new ten.

Two broad methods for finding sums are explored: adding on by place (adding on tens, then ones), and adding units by place (combining tens with tens and ones with ones).

They also compare methods from earlier work, such as counting on and making use of known sums, including sums of 10.

\(23+45\)
Add on tens, then add on ones:

Students make sense of methods for adding (especially as it relates to composing a ten when adding ones and ones). They work with a variety of representations—connecting cubes in towers of 10 and singles, base-ten drawings, expressions, and equations. They also use different representations to share their thinking with others.

Expressions and equations are presented horizontally to encourage students to make sense of the numbers and ways of adding rather than apply an algorithm. Eventually, students write equations to represent their thinking. For example, to find the sum of \(52+46\) , they might write:

Students are not expected to write or use equations in any specific way. Even in activities that focus on interpreting and writing equations, students should have continued access to drawings and other tools. Provide access to connecting cubes in towers of 10 and singles throughout the unit.

In this unit, students extend their knowledge of linear measurement while continuing to develop their understanding of operations, algebraic thinking, and place value.

In kindergarten, students identified attributes of objects that can be compared, such as length, weight, and capacity. In this unit, students compare the lengths of objects by lining them up at their endpoints, and explore ways to compare lengths of two objects that cannot be lined up.

From there, students transition to the idea of iterating length units, or using the same length unit, to measure the lengths of objects and to communicate measurements clearly.

Students begin by using the length of a connecting cube as a unit of measurement. Because connecting cubes snap together, students can focus on counting the length of the cubes without worrying about any gaps or overlaps in the units.

Later, students measure with length units that don’t connect together, such as paper clips and centimeter cubes (small cubes). Throughout the unit, students do not use formal units of length, and therefore centimeter cubes are referred to as small cubes. Students develop precision as they make sure that there are no gaps or overlap in the units used to measure.

Students measure some lengths by iterating small units, yielding measurements of over 100 length units. Students consider how to count and represent these larger groups of units—up to 120—with a written number. They use familiar representations (connecting cubes and base-ten drawings) to recognize 100 as 10 tens, but do not consider the unit of a hundred until grade 2.

Later in the unit, students solve problems in various contexts, including measurement. They revisit Compare, Difference Unknown story problems and learn to solve Compare, Bigger Unknown and Smaller Unknown problems about lengths. Next, students are introduced to a new problem type: Take From, Start Unknown. They practice solving all story problems types with unknowns in all positions.

In this unit, students focus on geometry and time. They expand their knowledge of two- and three-dimensional shapes, partition shapes into halves and fourths, and tell time to the hour and half hour. Center activities and warm-ups continue to enable students to solidify their work with adding and subtracting within 20 and adding within 100.

In kindergarten, students learned about flat and solid shapes. They named, described, built, and compared shapes. They learned the names of some flat shapes (triangle, circle, square, and rectangle) and some solid shapes (cube, sphere, cylinder, and cone).

Here, students extend those experiences as they work with shape cards, pattern blocks, geoblocks, and solid shapes. They develop increasingly precise vocabulary as they use defining attributes (“squares have four equal-length sides”) rather than nondefining attributes (“the square is blue”) to describe why a specific shape belongs to a given category. Students should focus on manipulating, comparing, and composing shapes and using their own language, rather than learning the formal definitions of shapes.

Draw 3 shapes that are not rectangles.

How do you know these are not rectangles?​​​​​​

Next, students transition to thinking about how to partition shapes into halves and fourths or quarters. These experiences allow students to learn the language of fractions. They come to understand that each piece gets smaller as the number of equal pieces increases.

In the last section, students tell time to the hour and the half hour. They learn about the hour and minute hands and what an analog clock looks like when the hour hand moves from one hour to the next. The experience of partitioning circles helps students make sense of time on the clock. Students see that a clock shows half hours when the minute hand has moved halfway around the clock from the hour, and the time can be written as “half past” or “___:30.”

In this unit, students revisit major work and fluency goals of the grade, applying their learning from the year. 

In Section A, students add and subtract within 20, concurrently working toward the goal of adding and subtracting fluently within 10. In Section B, they practice solving story problems of familiar types (those introduced in earlier units). In Section C, students count and represent numbers within 120.

Each of these topics is critical for students’ readiness for the work in grade 2, in which students will expand their understanding of place value and add and subtract within 100.

What number is shown?
Record an estimate that is too low, too high, and about right.

The sections in this unit are standalone sections, not required to be completed in order. The goal is to offer ample opportunities for students to integrate the knowledge they have gained and to practice skills related to the expected fluencies of the grade.