circles and rectangles to begin building an understanding of fractions. Through measurement and data, students develop an understanding of linear measurements, time, and money.
Table 1.1 (page 12) shows some of the key mathematics concepts teachers expect students to learn in grades preK–2. Timing for teaching these key concepts is driven by grade and by the vertical trajectory NCTM’s (2006) Curriculum Focal Points for Prekindergarten Through Grade 8 Mathematics first defines. These key mathematical concepts give an overview of the more specific local standards your team will teach each unit.
Source: Adapted from NCTM, 2006.
Figure 1.2: Mathematics Unit Planner.
Visit go.SolutionTree.com/MathematicsatWork for a free reproducible version of this figure.
Table 1.1: Mathematics Concepts and Skills for Grades PreK—2
Source: Adapted from NCTM, 2006.
In grades preK–2, students are developing an understanding of number and number relationships to develop number sense and mathematical reasoning. In preK and kindergarten, students learn how to count and use numbers to determine how many objects are in a set and to subitize (tell how many objects they see without counting; for example, roll a die and see five without counting all five dots). Students learn that each number means one more in terms of quantity, and they compare numbers using groups of objects, and later, numerals. Students write numbers to 20 by the end of kindergarten, 120 in first grade, and 1,000 in second grade.
Operations and algebraic thinking in preK–2 focuses on students making connections between counting and the operations of addition and subtraction. Students use strategies to make sense of and solve addition and subtraction word problems within a given set of numbers. Students are expected to find the missing value in different parts of the equation. Students use models, drawings, and equations to represent their thinking. Within this strand, students also develop fluency with addition and subtraction within 5 by kindergarten, 10 in first grade, and 20 in second grade. Your team should keep in mind that NCTM (2014b) defines fluency as students having efficient, accurate, and flexible procedures, not as the ability to complete a given number of problems in a specified number of seconds or minutes.
Students develop number sense by thinking flexibly with numbers and understanding the relationships between numbers and operations. They develop an understanding of magnitude of number and how the number system works beginning in preK. Students start with ones in preK and end with hundreds, tens, and ones in second grade with an additional understanding of 1,000. Place value provides a way to compare numbers, make sense of addition and subtraction strategies using tools and drawings, and apply properties of operations related to addition and subtraction with larger numbers. Using base-ten place value, students can add 13 + 24 by adding 1 ten + 2 tens to get 3 tens and 3 ones + 4 ones to get 7 ones, for a total of 3 tens 7 ones which is 37.
For measurement and data, students learn to recognize measurable attributes and apply that learning to compare objects. Students in first grade begin to measure length indirectly and strengthen their sense of numbers while counting and comparing units of length. This learning extends to second grade where students use standard units and measuring tools. Students in first and second grade also begin to display data in bar and picture graphs and answer questions about those graphs. In first grade, students tell and write time to the nearest half hour and to the nearest five minutes in second grade. Students in second grade also solve word problems related to money. Teachers in preK–1 can introduce students to money as they discuss base-ten numbers, using dimes for tens, pennies for ones, and dollars for hundreds.
In the area of geometry, students identify and name two- and three-dimensional shapes. Students also compose shapes, making a connection to how they also compose numbers. In preK and kindergarten, students identify shapes in the world and begin to sort shapes. In first and second grade, students begin to partition circles and rectangles as an introduction to fractions in third grade. In second grade, students build an array as an introduction to multiplication understanding in third grade.
Your team may want to explore mathematics learning progressions as defined in your state standards or reference online mathematics learning progression documents, such as those developed by the Common Core Standards Writing Team (n.d.) or Achieve the Core’s (n.d.) coherence map. Your team may also want to engage in a book study, perhaps referencing NCTM resources related to understanding the essential content and skills needed for mathematics in preK–2, such as Catalyzing Change in Early Childhood and Elementary Mathematics: Initiating Critical Conversations (NCTM, 2020). You might also consider Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity (Cross, Woods, & Schweingruber, 2009). This resource provides great insight into mathematics teaching and learning at the early childhood level, including preK.
With so much mathematics content to learn, your team’s planning of units helps your team to ensure a guaranteed and viable mathematics curriculum within your grade level and across grades preK–2. Planning the units together to more deeply learn your own grade-level content and its importance in the primary grade trajectory builds teacher team self-efficacy.
Connections Between Mathematics Content and Unit Planning
For each mathematics unit in your grade level, you support your team’s progress toward better understanding of the standards that support the guaranteed and viable mathematics curriculum. Together, you and your team use the Mathematics Unit Planner in figure 1.2 (page 11) to record answers to the following questions.
• What exactly do students need to know and be able to do in this unit?
• Which mathematics standards should we commonly assess? When?
• How does the mathematics learning in this unit connect to the standards students must learn in previous or future units?
• Which academic mathematics vocabulary and notations must students learn to read, write, and speak in the unit to be proficient with the standards?
• What are examples of higher- and lower-level-cognitive-demand mathematical tasks students should be able to demonstrate proficiency with if they have learned the standards?
• Which mathematical tools or technology should students learn or utilize to demonstrate an understanding of the standards in the unit?
Answering these questions as a team creates more equitable student learning experiences from one teacher to the next. Additionally, developing your teacher efficacy strengthens your instructional practices. Consequently, student learning improves because your entire team is working to ensure each student learns the organized mathematics content from one unit to the next.
Chapter 2 provides tools and protocols that help your preK, kindergarten, first-, or second-grade mathematics team unpack standards in the unit and
