Mathematics Unit Planner
Once your team determines the mathematics units for your grade level (detailing the standards and time line for each unit) for the year, your collaborative team can plan for student learning on a unit-by-unit basis (see figure 1.2; Kanold & Schuhl, 2020).
The Mathematics Unit Planner in figure 1.2 provides a template your team can use as you develop a shared understanding of what students are expected to learn in each unit of study. The numbered sections in the Mathematics Unit Planner correspond with the seven elements of unit planning. Throughout this book, you will see numbered headings that correspond with these seven areas. (Find completed examples of unit planners for preK in figure 3.12 [page 58], kindergarten in figure 4.11 [page 79], first grade in figure 5.11 [page 105], and second grade in figure 6.11 [page 129].)
Once the elements of the Mathematics Unit Planner (see figure 1.2) are complete, your team can use the information to plan for common assessments and daily lesson design (see Mathematics Assessment and Intervention in a PLC at Work [Kanold, Schuhl, et al., 2018] and Mathematics Instruction and Tasks in a PLC at Work [Kanold, Kanold-McIntyre, et al., 2018]). Additionally, you and your collaborative team can reference the unit planner for each successive unit in the year and from one year to the next as your team continues to deepen its own understanding of the required student learning.
In Principles to Actions, the National Council of Teachers of Mathematics (NCTM, 2014a) shares, “Effective mathematics teaching begins with a shared understanding among teachers of the mathematics that students are learning and how this mathematics develops along learning progressions” (p. 12). Therefore, before diving into each individual unit plan for the year, as a team, first consider the mathematical content students are learning in your grade. Additionally, make sense of the mathematical content trajectories, or progressions, that students are learning across your preK–2 band.
Mathematics Concepts and Skills for Grades PreK–2
Students in grades preK–2 develop their understanding of number, place value, and addition and subtraction. They grow their knowledge related to geometry and measurement. Throughout these foundational primary years, students first learn to count sequentially and read, write, and name numbers. They determine how to quantify a group of objects using a number. They compare numbers and learn to conceptualize the differences in value represented by two or more numbers. They also develop flexibility with numbers and use patterns to grow place-value understanding. In geometry, students identify, describe, compose, decompose, and analyze two- and three-dimensional shapes and, by second grade, create arrays for early multiplication understanding. They partition 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