Elementary Curriculum
Kindergarten
Kindergarten Mathematics Pacing and Units of Study
How can we use mathematics to organize and make sense of our world? Students in Kindergarten begin to develop number sense through counting, recognizing, representing, and comparing quantities. Students are given time to develop number sense with smaller numbers, gradually working with larger quantities until they ultimately rote count to 100, compare quantities to 30, and compose and decompose numbers to 10.
Quarter 1
Unit 1: Building a Mathematical Community Through the Data Cycle
During this unit, teachers will facilitate the formation of a mathematics community and have students develop a positive mathematics identity. The focus is not to teach standards explicitly but to spend time building routines and exploring manipulatives. Each lesson will progress through three activities to build mathematical communities and have the opportunity to teach routines and procedures.
Standards Covered: K.PS.1
Unit 2: Exploring Numeracy
The focus of this unit is to provide students with the opportunity to build early numeracy through at least ten with counting and comparing. Students will focus on decomposing to five. The standards in this unit (counting, comparing, and decomposing) are connected to use counting to develop understandings of number relationships.
Standards Covered: K.NS.1, K.NS.2
Unit 3: Objects and their Attributes
The main focus of this unit is sorting, classifying, and describing objects based on their attributes (e.g., size, shape, color, thickness). Teachers should continue to teach the data cycle while highlighting the attributes of the objects being used within each topic. This is the only unit in which sorting, classifying, and describing items by their attributes is explicitly addressed, so time should be spent building students’ vocabulary of different colors, sizes, thickness, textures, etc.
Standards Covered: K.PS.1
Quarter 2
Unit 4: Exploring Numeracy (Numbers to 20)
The focus of this unit is to apply earlier learning to numbers up to 20. Students will work with decomposing numbers to 5 as they explore contextual problems to 5. Teen numbers are discussed in terms of tens and ones.
Standards Covered: K.NS.1, K.NS.2, K.CE.1
Begin Unit 5: Plane Figures and Patterns
Students have been working with plane figures throughout the year. This unit provides an opportunity for students to gain more formal knowledge of plane figures as they compare and construct circles, triangles, squares, and rectangles. Students have informally studied patterns during classroom routines and throughout their lessons. This unit allows for the use of more formal vocabulary, including the core of a repeating pattern. The unit provides the opportunity to combine the use of shape and pattern vocabulary.
Standards Covered: K.MG.2, K.PFA.1
Quarter 3
Complete Unit 5: Plane Figures and Patterns
Students have been working with plane figures throughout the year. This unit provides an opportunity for students to gain more formal knowledge of plane figures as they compare and construct circles, triangles, squares, and rectangles. Students have informally studied patterns during classroom routines and throughout their lessons. This unit allows for the use of more formal vocabulary, including the core of a repeating pattern. The unit provides the opportunity to combine the use of shape and pattern vocabulary.
Standards Covered: K.MG.2, K.PFA.1
Unit 6: Expanding Numeracy (Numbers to 50)
The focus of this unit is for students to count from 0 to 50. They will group collections of 50 or fewer objects into groups of tens and ones. This lays the foundation for understanding place value. Students will expand on their experience with composing and decomposing numbers and will become more fluent with these skills.
Standards Covered: K.NS.1, K.NS.2, K.CE.1
Begin Unit 7: Measurement
The focus of this unit is for students to begin exploring measurement by comparing two objects. They will reason about which is longer, taller, heavier, or holds more. This sets the foundation for later study of formal measurement skills. Students will also apply calendar concepts when discussing which of two events takes longer.
Standards Covered: K.MG.1
Quarter 4
Unit 7: Measurement
The focus of this unit is for students to begin exploring measurement by comparing two objects. They will reason about which is longer, taller, heavier, or holds more. This sets the foundation for later study of formal measurement skills. Students will also apply calendar concepts when discussing which of two events takes longer.
Standards Covered: K.MG.1
Unit 8: Fluency with Numbers (Numbers to 100)
The focus of this unit is to provide meaningful counting experiences, from 0 to 100. Students will state the number before and after, without counting, between 1 and 20 and group collections of up to 100 objects into groups of tens and leftovers. Students will compose and decompose numbers to 10 and model and identify the number that makes 10 when added to a given number. Students will also solve single-step contextual problems. Students will continue to develop their understanding of the base 10 number system and build a strong foundation for future learning.
Standards Covered: K.NS.1, K.CE.1
Unit 9: The Data Cycle
Throughout the year, the data cycle has been an integral part of our classroom routines. Students have engaged in asking questions, exploring and generating data, representing their findings, and interpreting results. In this unit, students will further enhance their understanding by using object graphs and picture graphs within the data cycle, including a focus on naming coins. Additionally, students will develop their calendar skills with a focus on describing the units of time represented -- the days of the week and the months of the year.
Standards Covered: K.PS.1, K.MG.3
First Grade
First Grade Mathematics Pacing and Units of Study
How can we use mathematics to organize and make sense of our world? Students in first grade develop their number sense in relation to the counting sequence and base ten number system (moving from counting to grouping) and internalizing number combinations to develop basic fact fluency and reasoning skills. Using contextual situations that come from their world, students become fluent with
numbers to 20 and develop number sense for numbers up to 120.
Quarter 1
Unit 1: Building a Mathematical Community
During this unit, teachers will facilitate the formation of a mathematics community and have students develop a positive mathematics identity. The focus is not to teach standards explicitly but to spend time building routines and exploring manipulatives. Each lesson will progress through three activities to build mathematical communities and have the opportunity to teach routines and procedures.
Standards Covered: 1.PS.1
Unit 2: Counting and Numbers Part 1
This unit focuses on providing meaningful counting experiences by 1s and 10s to a minimum of 100. Students will read and write numerals and represent, compare, and order quantities 0-40 and multiples of 10 to 100. Focusing on 0-40 and multiples of 10 as benchmark numbers, students will continue to develop
their understanding of our base 10 number system, building a solid foundation for future learning.
Standards Covered: 1.NS.1, 1.NS.2, 1.CE.1
Unit 3: Addition and Subtraction Part 1
In Unit 3, students in First Grade extend their Kindergarten knowledge of the part-part-whole relationships up to five to the part-part-whole relationships up to ten by investigating various fluency strategies. Students will apply strategies to represent, solve, and justify contextual addition and subtraction problems within ten. Students will engage in meaningful experiences which will allow them to think flexibly and develop skills for automaticity. Throughout the school year, with continued strategy investigations and applications, students will develop automaticity of addition and subtraction facts within ten.
Standards Covered: 1.CE.1
Quarter 2
Unit 4: Sorting and Classifying Objects
In this unit, students will embark on an engaging exploration of data through the use of object graphs and tables. The focus will be on understanding the data cycle—posing questions, collecting data, organizing and representing data, and analyzing and communicating results. Students will develop foundational skills in sorting and classifying objects, as well as in creating and interpreting data representations.
Standards Covered: 1.PS.1
Unit 5: Counting and Number Part 2
The focus of this unit is to build on the counting and place value strategies and understandings that were introduced in Unit 2. Students will use the patterns of counting and the place value system to compare and order numbers to 100. Students will continue to engage with number patterns to determine the equivalency between coins and to find the value of a collection of coins by skip counting. This unit provides an opportunity for students to engage with counting in context to compare nonstandard measurement units for volume.
Standards Covered: 1.NS.1, 1.NS.2, 1.CE.1
Quarter 3
Unit 6: Addition and Subtraction Part 2
The focus of this unit is for students to apply fluency strategies within ten from Unit 3 to represent, solve, and justify contextual addition and subtraction problems within twenty. Students will extend part-part-whole relationships up to twenty by investigating various fluency strategies and will engage in meaningful experiences to apply the strategies flexibly. Throughout the school year, with continued strategy investigations and applications, students will develop automaticity of addition and subtraction facts within ten.
Standards Covered: 1.CE.1
Unit 7: Shapes and Fractions
The focus of this unit is to provide meaningful experiences that will focus on shapes and fractions. Students will identify, draw, sort and describe plane shapes by their attributes and compose larger plane shapes by combining simple plane figures. Students will also use mathematical reasoning to solve problems that involve partitioning models into halves and fourths. They will work with contextual problems and justify equal shares.
Standards Covered: 1.MG.2, 1.NS.3
Unit 8: Counting and Number Part 3
The focus of this unit is to extend the counting and place value understandings developed in Units 2 and 5. In this final counting and number unit, students explore how the number patterns extend beyond 100. Experiences crossing the century mark help students make important connections that will be further explored with 3-digit place value in 2nd grade. Students will also explore measurement using non-standard measurement units for length and weight.
Standards Covered: 1.NS.1, 1.NS.2, 1.MG.1
Quarter 4
Unit 8: Counting and Number Part 3
The focus of this unit is to extend the counting and place value understandings developed in Units 2 and 5. In this final counting and number unit, students explore how the number patterns extend beyond 100. Experiences crossing the century mark help students make important connections that will be further explored with 3-digit place value in 2nd grade. Students will also explore measurement using non-standard measurement units for length and weight.
Standards Covered: 1.NS.1, 1.NS.2, 1.MG.1
Unit 9: Time and Pattern
Students have been informally discussing time as part of their classroom routines throughout the year. This unit provides formal instruction on telling time on digital and analog clocks and describing the passage of time on the calendar. Students investigate repeating and increasing patterns with geometric figures, objects, pictures, movements, or colors.
Standards Covered: 1.MG.3, 1.PFA.1
Unit 10: Addition and Subtraction Part 3
The focus of this unit is for students to apply fluency strategies to represent, solve, and justify contextual addition and subtraction problems within twenty. Students will also review part-part-whole relationships up to twenty. This unit will also focus on the exploration of data through the use of picture graphs and tables. The focus will be on understanding the data cycle—posing questions, collecting data, organizing and representing data, and analyzing and communicating results. Students will develop foundational skills in sorting and classifying objects, as well as in creating and interpreting data representations.
Standards Covered: 1.CE.1, 1.PS.1
Second Grade
Second Grade Mathematics Pacing and Units of Study
The Grade 2 Standards enhance the understanding of numbers and spatial concepts, covering three-digit numbers. Students will internalize all number combinations up to 20. This fluency will help students tackle both simple and complex problems involving addition or subtraction, with addends and minuends not exceeding 100. Work with solid figures and measurement of length, weight, and volume will be done using U.S. Customary units to the nearest whole unit. Additionally, students will delve into the data cycle which involves creating questions, gathering data, organizing, analyzing, and presenting findings.
Quarter 1
Unit 1: Building a Mathematical Community
During this unit, teachers will facilitate the formation of a mathematics community and have students develop a positive mathematics identity. The focus is not to teach standards explicitly but to spend time building routines and exploring manipulatives. Each lesson will progress through three activities to build mathematical communities and have the opportunity to teach routines and procedures.
Standards Covered: 2.PS.1
Unit 2: Addition and Subtraction Part 1
This unit focuses on the composition and decomposition of numbers to 20 and should be incorporated through spiraled practice throughout the year. Through the understanding of number relationships such as equality, part-part-whole, and inverse relationships, students can develop strategies to solve basic fact problems and problems in context. During this unit, students should engage in meaningful experiences to develop a variety of strategies to think flexibly and develop skills for automaticity. Throughout the school year, with continued strategy investigations and application, students will build automaticity of addition and subtraction facts within twenty.
Standards Covered: 2.CE.1
Unit 3: Number Sense Part 1
The focus of this unit is to understand and apply patterns to build flexibility with 2 digit numbers. Development of the base ten system occurs in this unit as well as how it applies to money concepts. Throughout the unit, continue to build connections to the passage of time and the data cycle by utilizing knowledge of pattern, counting and comparing numbers.
Standards Covered: 2.NS.1, 2.NS.2, 2.NS.4, 2.PFA.1
Quarter 2
Unit 4: Addition and Subtraction Part 2
The focus of this unit is on composition/decomposition of numbers to 20 and should be incorporated through spiraled practice throughout the year. Through the understanding of number relationships such as equality, part-part-whole and inverse relationships, students can develop strategies to attack basic fact problems and story contexts. During this unit students should engage in meaningful experiences to develop a variety of strategies to think flexibly and develop skills for automaticity. Throughout the school year, with continued strategy investigations and applications, students will develop automaticity of addition and subtraction facts within ten.
Standards Covered: 2.CE.1, 2.NS.1, 2.NS.4
Unit 5: Geometry
The focus of this unit is to develop the students understanding of two- and three-dimensional shapes by identifying, describing, and comparing geometric figures. They will explore the relationships among these shapes, including concepts of symmetry and congruence, which connect to ideas about fractional parts of a whole. Additionally, students will create and extend repeating and increasing patterns using objects and pictures, strengthening their pattern recognition and spatial reasoning skills.
Standards Covered: 2.MG.3, 2.MG.4, 2.PFA.1
Unit 6: Number Sense Part 2
The focus of this unit is for students to deepen their understanding of the base ten system to be able to represent, compare and order three-digit numbers to 999. This is the final unit where students will be exposed to formal lessons involving money concepts (2.NS.4) and therefore should be formally assessed at the end of this unit. The data cycle concepts continue with the incorporation of larger numbers.
Standards Covered: 2.NS.1, 2.NS.2, 2.NS.4
Quarter 3
Complete Unit 4: Addition and Subtraction Part 2
The focus of this unit is on composition/decomposition of numbers to 20 and should be incorporated through spiraled practice throughout the year. Through the understanding of number relationships such as equality, part-part-whole and inverse relationships, students can develop strategies to attack basic fact problems and story contexts. During this unit students should engage in meaningful experiences to develop a variety of strategies to think flexibly and develop skills for automaticity. Throughout the school year, with continued strategy investigations and applications, students will develop automaticity of addition and subtraction facts within ten.
Standards Covered: 2.CE.1, 2.NS.1, 2.NS.4
Unit 7: Addition, Subtraction, Patterns, and Data
The focus of this unit is to build students' fluency in recalling addition and subtraction facts within 20 while solving single-step and multistep problems involving whole numbers up to 100 without the need for regrouping. Students will estimate, represent, and justify their solutions using a variety of strategies. They will also engage in the data cycle by posing questions, collecting, organizing, and representing data using pictographs and bar graphs. Additionally, students will describe, extend, and create repeating and increasing numerical patterns up to 200, focusing on addition.
Standards Covered: 2.CE.1, 2.PS.1, 2.PFA.1,
Begin Unit 8: Fractions
The focus of this unit is to go beyond simply naming and identifying fractions, encouraging students to deepen their understanding of fraction concepts introduced in first grade. The focus is on using models and fair shares in problem-solving contexts. Ample time should be dedicated to exploring the relationship between the number of parts needed to form a whole and the size of those parts
Standards Covered: 2.NS.3
Quarter 4
Unit 8: Fractions
The focus of this unit is to go beyond simply naming and identifying fractions, encouraging students to deepen their understanding of fraction concepts introduced in first grade. The focus is on using models and fair shares in problem-solving contexts. Ample time should be dedicated to exploring the relationship between the number of parts needed to form a whole and the size of those parts.
Standards Covered: 2.NS.3
Unit 9: Addition and Subtraction Part 4
The focus of this unit is to build students' fluency in recalling addition and subtraction facts within 20 while solving single-step and multistep problems involving whole numbers up to 100. Students will estimate, represent, and justify their solutions using a variety of strategies. Additionally, students will represent and justify expressions as being equal or not equal.
Standards Covered: 2.CE.1
Unit 10: Measurement
This unit focuses on introducing standard units of measurement for length, weight, and volume. Students will explore the purpose of using standard units, how to choose the appropriate unit of measure, and which tools are best suited for measuring specific attributes. Additionally, the unit will make connections to tools and units used for measuring time.
Standards Covered: 2.MG.1, 2.MG.2
Third Grade
Third Grade Mathematics Pacing and Units of Study
How can students use mathematics to organize and make sense of their world? Students deepen their understanding of number and quantity as they transition from additive to multiplicative thinking. Meaningful exploration and representations are provided to help students see the relationship between addition and multiplication and work with the inverse relationship between multiplication and division
Quarter 1
Unit 1: Building a Mathematical Community
During this unit, teachers will facilitate the formation of a mathematics community and have students develop a positive mathematics identity. The focus is not to teach standards explicitly but to spend time building routines and exploring manipulatives. Each lesson will progress through three activities to build mathematical communities and have the opportunity to teach routines and procedures.
Standards Covered: SOL 3.PS.1
Unit 2: Place Value/Addition and Subtraction Part 1
The focus of this unit begins with students thinking flexibly about composing and decomposing numbers using the base-ten system and demonstrating an understanding of this system to compare and order whole numbers. Students will apply their understanding of number sense to determine appropriate strategies
to solve addition and subtraction problems and justify their estimate and solution to those problems. Students will apply their understanding of addition and subtraction when engaging with perimeter and increasing and decreasing patterns.
Standards Covered: 3.NS.1, 3.NS.2, 3.CE.1, 3.PFA.1, 3.MG.2
Assessment Window: October 7 - October 11, 2024
Unit 3: Multiplication and Division Part 1
The concepts of multiplication and division will be developed through the use of contextual problems, models, and inverse relationships. Time and money will provide contexts for students to apply making equal groups, repeated addition, and skip counting patterns.
Standards Covered: 3.NS.4, 3.CE.2, 3.MG.3
Assessment Window: October 28 - November 1, 2024
Quarter 2
Unit 4: Geometry
The focus of this unit is to deepen and expand knowledge of polygons, which are made of 3-8 line segments, by exploring, classifying, and reasoning about their characteristics. Students will use this knowledge to explore the changes that result from combining and subdividing polygons. Using pictures and objects,
students will continue their exploration of increasing and decreasing patterns.
Standards Covered: 3.MG.4, 3.PFA.1,
Assessment Window: November 18 - November 22, 2024
Unit 5: Adding and Subtracting Part 2
Students revisit addition and subtraction as they work to solve problems about their world that involve larger numbers. Students apply the data cycle to collect data and solve problems that involve bar graphs.
Standards Covered: 3.CE.1, 3.PS.1
Assessment Window: December 16 - December 20, 2024
Begin Unit 6: Fractions Part 1
Through reasoning and various models, students will develop a deep understanding of fractions with denominators of 2, 3, 4, 5, 6, 8, and 10, with which they can identify, compose, and decompose within context. Using unit fractions, students will count fractional parts to identify and represent improper fractions and mixed numbers. The focus of this unit is to develop fraction sense by reasoning about fractions and mixed numbers using a variety of representations and contexts. Students will use region/area, length, and set models to represent, identify, compose, decompose fractions into different components. In Unit 9: Fractions Part 2, students will use these understandings to compare fractions with and without models.
Standards Covered: 3.NS.3
Assessment Window: January 27 - January 31, 2025
Quarter 3
Complete Unit 6: Fractions Part 1
Through reasoning and various models, students will develop a deep understanding of fractions with denominators of 2, 3, 4, 5, 6, 8, and 10, with which they can identify, compose, and decompose within context. Using unit fractions, students will count fractional parts to identify and represent improper fractions and mixed numbers. The focus of this unit is to develop fraction sense by reasoning about fractions and mixed numbers using a variety of representations and contexts. Students will use region/area, length, and set models to represent, identify, compose, decompose fractions into different components. In Unit 9: Fractions Part 2, students will use these understandings to compare fractions with and without models.
Standards Covered: 3.NS.3
Unit 7: Multiplication and Division Part 2
Students will deepen their understanding of multiplication and division strategies by focusing on multiples of 0, 1, 2, 4, 5, 8, and 10. They will apply reasoning strategies such as doubling, properties, and inverse relationships to solve contextual problems.
Standards Covered: 3.CE.2
Unit 8: Measurement Part 1
Students engage with real-world measurement experiences by estimating and calculating the length, weight/mass, or liquid volume of various objects. These activities naturally lead to solving problems involving perimeter and area, reinforcing understanding of polygons.
Standards Covered: 3.MG.1, 3.MG.2
Unit 9: Fractions Part 2
In this unit, students will represent and compare proper and improper fractions and mixed numbers with the denominators of 2, 3, 4, 5, 6, 8, and 10. Students will build on their work in Unit 6, Fractions Part I, in which they used models to identify, compose and decompose fractions, and worked with unit fractions. In Unit 9, Fractions Part 2, students will utilize reasoning, their understanding of unit fractions, and their understanding of fraction decomposition to compare fractions with and without models.
Standards Covered: 3.NS.3
Quarter 4
Unit 10: Measurement Part 2
In Unit 3, students gained a foundational understanding of working with money and time. This unit offers opportunities to solidify these skills and introduce the concepts of groups of money between $2.00 and $5.00, as well as elapsed time.
Standards Covered: 3.NS.4, 3.MG.3
Assessment Window: Week of April 7-11, 2025
Unit 11: Multiplication and Division Part 3
Standards Covered: 3.CE.2
Assessment Window: Week of May 5-9, 2025
Fourth Grade
Grade 4 Mathematics Pacing and Units of Study
How can we use mathematics to organize and make sense of our world? Students in fourth grade begin to leverage their understanding of number relationships by organizing and reasoning mathematically through a variety of contextual problems using multiple representations to justify their thinking. Students are given the time to explore and develop connections between fractions and decimals.
Quarter 1
Unit 1: Building a Mathematical Community
During this unit, teachers will facilitate the formation of a mathematics community and have students develop a positive mathematics identity. The focus is not to teach standards explicitly but to spend time building routines and exploring manipulatives. Each lesson will progress through three activities to build mathematical communities and have the opportunity to teach routines and procedures.
Standards Covered: 4.PS.1
Unit 2: Addition and Subtraction
The focus of this unit begins with students thinking flexibly about composing and decomposing numbers using the base 10 system, demonstrating an understanding of this system to compare and order whole numbers. Students apply the understanding of number sense to determine appropriate strategies to solve addition and subtraction single and multi-step problems in context. Students will apply their understanding of addition and subtraction when engaging with increasing and decreasing patterns. Students will also develop an understanding of equality and be able to explain that quantities on both sides of an equation must be equal.
Standards Covered: 4.NS.1, 4.NS.2, 4.CE.1 4.PFA.1
Assessment Window: September 16 to September 20, 2024
Unit 3: Fraction Number Sense and Probability
The focus of this unit begins through fraction reasoning by various models; students will develop an understanding of fractions with denominators 12 or less. Students will use their understanding of fractions to compose and decompose fractions with which they will represent, compare, and order fractions (proper, improper, and mixed numbers) with and without models. Working with equivalent fractions provides students the opportunity to review the multiplication facts they learned in third grade and preview the multiplication facts they will be working with this year. Probability provides an interesting and practical application of this fraction number sense.
Standards Covered: 4.NS.3, 4.PS.2
Assessment Window: October 21 to October 25, 2024
Begin Unit 4: Multiplication and Division 1
Students move from additive to multiplicative reasoning. This unit provides students the opportunity to develop and apply multiplicative reasoning through problem solving, patterns, and measurement. Problem-solving incorporates addition, subtraction, and division. Division is limited to quotients that do not have a remainder during this unit. It is through this application and strategic repetition of multiplication and division facts that students develop fluency with multiplication and division through 12 x 12.
Standards Covered: 4.CE.2, 4.PFA.1, 4.MG.3
Assessment Window: December 2 to December 6, 2024
Quarter 2
Complete Unit 4: Multiplication and Division 1
Students move from additive to multiplicative reasoning. This unit provides students the opportunity to develop and apply multiplicative reasoning through problem solving, patterns, and measurement. Problem-solving incorporates addition, subtraction, and division. Division is limited to quotients that do not have a remainder during this unit. It is through this application and strategic repetition of multiplication and division facts that students develop fluency with multiplication and division through 12 x 12.
Standards Covered: 4.CE.2, 4.PFA.1, 4.MG.3
Assessment Window: December 2 to December 6, 2024
Unit 5: Statistics and Measurement
The data cycle has been a focus of classroom routines throughout the year as students have asked questions, explored, and generated data, represented their findings, and interpreted results. This unit provides for a culminating activity where students engage in all steps of the data cycle. As line graphs are the focus for fourth grade, elapsed time comes in as a natural connection.
Standards Covered: 4.MG.2, 4.PS.1
Assessment window December 16 to December 20
Begin Unit 6: Decimal Number Sense and Computation
Students use reasoning and their understanding of the base ten system to represent, compare, and order decimals through thousandths with and without models. Students are expected to use concrete and visual models to support their understanding of the processes, to justify, and to determine fraction and decimal equivalents. The development of decimal number sense is applied to computation when estimating and computing sums and differences of decimals through thousandths to solve single and multi-step problems in context.
Standards Covered: 4.NS.4, 4.NS.5, 4.CE.4
Assessment Window: January 27 to January 31, 2025
Quarter 3
Complete Unit 6: Decimal Number Sense and Computation
Students use reasoning and their understanding of the base ten system to represent, compare, and order decimals through thousandths with and without models. Students are expected to use concrete and visual models to support their understanding of the processes, to justify, and to determine fraction and decimal equivalents. The development of decimal number sense is applied to computation when estimating and computing sums and differences of decimals through thousandths to solve single and multi-step problems in context.
Standards Covered: 4.NS.4, 4.NS.5, 4.CE.4
Assessment Window: January 27-31, 2025
Unit 7: Fraction Computation
The focus of this unit is how students will use their fractional number sense and their understanding of composing and decomposing fractions to add and subtract fractions with like denominators of 2, 3, 4, 5, 6, 8, 10, and 12 with and without models. Students will use their understanding of counting by unit fractions and repeated addition to solve single-step contextual problems involving multiplication of a whole number (12 or less) and a unit fraction.
Standards Covered: 4.CE.3
Assessment Window: February 10-14, 2025
Unit 8: Geometry and Measurement
In this unit, students will dive deeper into learning about quadrilaterals and other 2D and 3D shapes by exploring, classifying, and comparing their properties. As they discover the unique characteristics of different quadrilaterals, they will also learn how to develop and use formulas for finding the area and perimeter of squares and rectangles—building on the work they started during earlier computation lessons. Additionally, students will get hands-on experience with real-world measurement activities. They will practice estimating and measuring things like length, weight, mass, and liquid volume, which will also give them more practice with their math skills, especially computation and estimation. These real-world connections make the learning more meaningful and help students see how math applies outside the classroom.
Standards Covered: 4.MG.1, 4.MG.3, 4.MG.4, 4.MG.5, 4.MG.6
Assessment Window: March 24-28, 2025
Quarter 4
Unit 9: Multiplication and Division 2
In this unit, students will expand their understanding of multiplication and division by exploring various strategies to solve 2-digit by 2-digit multiplication problems. They will also learn to determine the quotient and remainder when dividing a three-digit number by a one-digit divisor. Through the context of division problems, students will gain a deeper understanding of how to interpret both the quotient and the remainder
Standards Covered: 4.CE.2
Assessment Window: Week of May 5-9, 2025
Fifth Grade
Grade 5 Mathematics Pacing and Unit Guides
Quarter 1
Unit 1: Building a Mathematical Community
During this unit, teachers will facilitate the formation of a mathematics community and have students develop a positive mathematics identity. The focus is not to teach standards explicitly but to spend time building routines and exploring manipulatives. Each lesson will progress through three activities to build mathematical communities and have the opportunity to teach routines and procedures.
Standards Covered: 5.PS.1
Unit 2: The Structure of Numbers and Problem Solving with Whole Numbers
In this unit, students will start to consider the structure of numbers. This unit provides the opportunity to solve problems using the order of operations. This focus on structure is expanded to considering whether a number is prime or composite and identifying the prime factorization of a number. Additional context for
exploring the structure of numbers comes from exploring patterns with whole numbers. Additionally, students will start to explore variables and will solve contextual problems using whole numbers.
Standards Covered: 5.NS.2, 5.CE.1, 5.MG.2, 5.PFA.2, 5.PFA.1, 5.CE.4
Assessment Window: October 7 to October 11, 2024
Begin Unit 3: Decimal and Fraction Number Sense
Students reason through the use of fraction and decimal models by encountering multiple meanings for fractions and decimals. Students demonstrate the flexibility of thinking by exploring efficient ways to represent equivalency between fractions and decimals and to compare and order fractions and decimals
through opportunities to justify their solutions orally, in writing, or with a model. Probability provides a natural context for applying the relationship between fractions and decimals.
Standards Covered: 5.NS.1
Assessment Window: November 18 to November 22, 2024
Quarter 2
Complete Unit 3: Decimal and Fraction Number Sense
Students reason through the use of fraction and decimal models by encountering multiple meanings for fractions and decimals. Students demonstrate the flexibility of thinking by exploring efficient ways to represent equivalency between fractions and decimals and to compare and order fractions and decimals
through opportunities to justify their solutions orally, in writing, or with a model. Probability provides a natural context for applying the relationship between fractions and decimals.
Standards Covered: 5.NS.1
Assessment Window: November 18 to November 22, 2024
Unit 4: Decimal Computation
The focus of this unit is to apply the understanding of decimal number sense to determine appropriate strategies to solve addition, subtraction, multiplication, and division problems while justifying their estimates and solutions to problems. Students will discover decimal computation is used every day and will be provided opportunities to determine when it is appropriate to use mental math, paper, pencil, or a calculator and use methods that make sense to ourselves and others.
Standards Covered: 5.CE.3, 5.PFA.1
Assessment Window: December 16 to December 20, 2024
Unit 5: Measurement
In this unit, students will explore everyday occurrences of estimating and measuring length, mass, and liquid volume using metric units. Important connections are made with the metric system and decimal place value. Experiences of measuring familiar objects will help students establish benchmarks and facilitate the use of the appropriate units of measure to make estimates when solving practical problems.
Standards Covered: 5.MG.1
Assessment Window: January 13 to January 17, 2024
Quarter 3
Unit 6: Fraction Computation
The focus of this unit moves from decimal computation in previous units to fraction computation. Students will use what they learned in unit 3 related to fraction number sense to estimate and determine the sum or difference of fractions. While students are adding and subtracting two fractions with like and unlike denominators, they can revisit their work with prime factorization from unit 2 as one strategy that could be used for simplifying. Students will use their fractional number sense and computation skills to work with fraction patterns in various representations and solve fraction contextual problems.
Standards Covered: 5.CE.2, 5.PFA.1
Assessment Window: February 24-28, 2025
Unit 7: Geometry and Measurement
The focus of this unit is to classify and measure angles and triangles within context. While developing procedures for finding area and volume through hands-on exploration, students will use multiple representations to solve problems, including those in context, involving perimeter, area, and volume. Much of what we do requires knowing where we are and in which direction we are facing. Spatial reasoning and geometric thinking allow us to operate within our world.
Standards Covered: 5.MG.2, 5.MG.3, 5.PFA.1
Assessment Window: March 24-28, 2025
Quarter 4
Unit 8: Probability and Algebra
The focus of this unit is to deepen student understanding of probability concepts learned in 4th grade through representing the sample space in different ways and using the constructed sample space to determine the probability of an event. Students will apply the Fundamental Counting Principle to find the possible number of outcomes of a probability event. In addition, this unit extends the work on variables that students have explored in other units in problems solving contexts. Students will use their knowledge of variables to write expressions and create word problems to match an equation with a variable.
Standards Covered: 5.PS.3, 5.PFA.2
Assessment Window: Week of April 7-11, 2025
Unit 9: Data
Students continue whole number calculations in this unit, expanding their work to include solving contextual problems with larger numbers. Contexts for problem solving include data collected from an application of the data cycle. Students follow up their work with calculating measures of center in Unit 1 by thinking more about the structure of numbers in this unit. They didn’t realize it, but the order of operations played a crucial role when calculating the mean of a data set. This unit provides the opportunity to solve problems using the order of operations.
Standards Covered: 5.PS.1, 5.PS.2
Assessment Window: Week of May 5-9, 2025