Unit 1: Place Value and Multi-digit Addition and Subtraction

When students understand the structure of the base ten system, they can quantify the value of larger numbers and manipulate them as a strategy for multi-digit addition and subtraction, mental math, estimations, and comparisons.

In this unit, students focus on place value and the uniformity of the base-ten system. This allows students to generalize their knowledge of place value and use this understanding to perform multi-digit addition and subtraction within 1,000,000. This unit will help students gain a practical understanding of addition and subtraction and the relationship between the two operations in a real world context. Students will also apply their understanding of place value in order to estimate and round numbers as a strategy to support mental math. Mental math will provide students with methods to estimate sums and differences as well as validate their answers.

Unit 2: Multiplication with Whole Numbers

When students understand the patterns in the base ten system, they can use place value, properties of operations, and visual representations to multiply multi-digit numbers.

In this unit, students broaden and deepen their experiences with multiplication to include multiplying numbers through thousands by one-digit numbers and finding the product of two two-digit numbers. To expand on their conceptual understanding of place value and multiplication, students will use models such as arrays and area models for single-digit multiplication and expand this understanding to multi-digit multiplication. Students are expected to apply their understanding of multi-digit multiplication to numeric calculations and real world problem solving situations, including multi-step problems.

Unit 3: Division with Whole Numbers

When students understand the patterns in the base ten system, they can use place value, properties of operations, and visual representations to divide multi-digit numbers.

In this unit, students apply the understanding of multiplication and multi- digit numbers to explore the concept of division of numbers through thousands, with or without remainders. Students relate multiplication models and methods to division as they learn strategies for division based on place value, properties of operations, and the relationship between multiplication and division. Students illustrate and explain calculations using visual and symbolic representations. Students apply division in real world situations and correctly interpret and communicate a remainder.

Unit 4: Equations with Word Problems

Students understand and use the structures from the various word problem types in order to comprehend, model, write equations with variables, and persevere through problem solving.

In this unit, students apply computation strategies and learn problem solving skills. Their work involves using the language of math to represent problems from real-world contexts. Visual models and word problem structures are used to interpret and represent various mathematical situations. Students interpret word problems as Add To/Take From, Put Together/Take Apart, Additive Comparison, Equal Groups, Array/Area, and/or Multiplicative Comparison to model and write equations—with a variable representing the unknown—for one-step, two-step, and multi-step problems. Students also discover patterns in our number system involving factors, multiples, and square numbers. They use this understanding to identify a number as prime or composite.

Unit 5: Measurement

Measurement systems are built on patterns and structures that allow us to convert units of measurement, know and understand relative sizes of units, solve real-world problems, and analyze measurement data.

In this unit, students explore the relationship within customary units and within metric units as they build on their knowledge of measurement systems, time concepts, area, and perimeter. They use the four operations to solve problems involving distance, weight, capacity, and time. Students build on their knowledge of line plots as they represent and solve addition/subtraction problems using fractions on line plots. They work to understand and use the formulas for area and perimeter as ways to measure and describe objects and space in the world around them.

Unit 6: Fractions and Operations

Students understand that fractions are numbers representing quantities less than, equal to, and greater than 1, as they apply the properties of operations to fractions.

In this unit, students build upon their conceptual understanding of fractions as numbers. Students compose and decompose fractions. This leads to a deeper conceptual understanding of addition and subtraction with fractions and mixed numbers having the same denominator. Students then make connections to repeated addition being represented as multiplication. Students are expected to apply their understanding of fractions to numerical calculations and real world problem solving situations.

Unit 7: Fractions and Decimals

When students see the connections between fraction and decimal structures, they can transfer and apply equivalent fraction concepts to understand relative quantities, comparisons, and multiple representations of the same quantity.

In this unit, students build upon the concepts of fractions presented in previous third and fourth grade units. Students use their conceptual knowledge of fractions to develop procedures to compare fractions and to find equivalent fractions using common denominators. Another goal of this unit is to develop a deep understanding of decimal numbers by relating decimals to fractions and whole-number place values. Students use models, such as number lines, as powerful tools to represent the value of both fractions and decimals and to compare and order each. Students use the relationship between decimals and fractions to build decimal concepts, including decimal place value and comparing decimals less than and greater than 1.

Unit 8: Geometry

Students understand how identifying parts of shapes with specific attributes and using measurements help to analyze objects in their everyday lives.

In this unit, students broaden their understanding of plane geometric figures including points, lines, line segments, rays, angles, and polygons. Students will apply their understanding of fractions to angle measurements in relation to a circle. Students learn how to estimate angle measurements using benchmark angles as well as accurately measure angles using a protractor. Students also apply their understanding of geometric properties and measurement, such as parallel and perpendicular lines and length, to identify certain types of quadrilaterals and triangles. Categorizing and classifying shapes and angles based on their attributes will support exploration of relationships among shapes and will deepen students’ understanding of 2D geometry.