The big ideas in kindergarten include: representing and comparing whole numbers, initially with sets of objects; understanding and applying addition and subtraction; and describing shapes and space. More time in kindergarten is devoted to numbers than to other topics.
The mathematical work for kindergarten is partitioned into 8 units:
Math in Our World
Numbers 1–10
Flat Shapes All Around Us
Understanding Addition and Subtraction
Composing and Decomposing Numbers to 10
Numbers 0–20
Solid Shapes All Around Us
Putting it All Together
The big ideas in grade 1 include: developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; developing understanding of whole-number relationships and place value, including grouping in tens and ones; developing understanding of linear measurement and measuring lengths as iterating length units; and reasoning about attributes of, and composing and decomposing geometric shapes.
The mathematical work for grade 1 is partitioned into 8 units:
Adding, Subtracting, and Working with Data
Addition and Subtraction Story Problems
Adding and Subtracting within 20
Numbers to 99
Adding within 100
Length Measurements within 120 units
Geometry and Time
Putting it All Together
The big ideas in grade 2 include: extending understanding of the base-ten number system, building fluency with addition and subtraction, using standard units of measure, and describing and analyzing shapes.
The mathematical work for grade 2 is partitioned into 9 units:
Adding, Subtracting, and Working with Data
Adding and Subtracting within 100
Measuring Length
Addition and Subtraction on the Number Line
Numbers to 1,000
Geometry, Time, and Money
Adding and Subtracting within 1,000
Equal Groups
Putting it All Together
The big ideas in grade 3 include: developing understanding of multiplication and division and strategies for multiplication and division within 100; developing understanding of fractions, especially unit fractions (fractions with numerator 1); developing understanding of the structure of rectangular arrays and of area; and describing and analyzing two-dimensional shapes.
The mathematical work for grade 3 is partitioned into 8 units:
Introducing Multiplication
Area and Multiplication
Wrapping Up Addition and Subtraction within 1,000
Relating Multiplication to Division
Fractions as Numbers
Measuring Length, Time, Liquid Volume, and Weight
Two-dimensional Shapes and Perimeter
Putting it All Together
The big ideas in grade 4 include: developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.
The mathematical work for grade 4 is partitioned into 9 units:
Factors and Multiples
Fraction Equivalence and Comparison
Extending Operations to Fractions
From Hundredths to Hundred-thousands
Multiplicative Comparison and Measurement
Multiplying and Dividing Multi-digit Numbers
Angles and Angle Measurement
Properties of Two-dimensional Shapes
Putting it All Together
The big ideas in grade 5 include: developing fluency with addition and subtraction of fractions, developing understanding of multiplication and division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions), extending division to two-digit divisors, developing understanding of operations with decimals to hundredths, developing fluency with whole number and decimal operations, and developing understanding of volume.
The mathematical work for grade 5 is broken into 8 units:
Finding Volume
Fractions as Quotients and Fraction Multiplication
Multiplying and Dividing Fractions
Wrapping Up Multiplication and Division with Multi-digit Numbers
Place Value Patterns and Decimal Operations
More Decimal and Fraction Operations
Shapes on the Coordinate Plane
Putting it All Together
Grade 3:
Unit 1 - Playground Forces
In this unit, students think about the forces that can act on a swing set. Students begin by considering mechanical forces and how balanced and unbalanced forces change the motion of objects. They then explore electrical charges and how like and unlike charges exert forces on each other. Finally, students focus on magnetic forces and magnetic fields. While considering electric and magnetic forces, students examine forces that do not require objects to be in contact and that vary in magnitude as a function of the distance between objects. To summarize their learning, students design a better swing set that takes advantage of the different forces that they have studied.
Unit 2 - Life Cycles for Survival
In this unit, students explore the many ways in which organisms grow and change throughout their life cycles and how organisms depend on each other for survival. Students begin by examining how plants and animals change and grow throughout their life cycle. They observe patterns in the life cycles of seemingly different organisms such as trees, lion cubs, and mayflies. Next, students look for patterns in how traits are passed on from parents to their offspring and think about how those traits help organisms survive. Students use observations and data to make predictions about parents and their offspring and construct arguments for why some traits are important for an organism’s survival. Finally, students examine how organisms can cooperate and help each other survive. They use evidence to construct an argument for why some animals, such as humpback whales, live together in groups. Students apply the core ideas of the unit by analyzing the life cycle of leafcutter ants and identifying the traits that help the ants work together to survive in the rain forest.
Unit 3 - Surviving in Changing Environments
In this unit, students examine how organisms are able to survive in changing environments. To start the unit, students observe tracks created by a modern organism, a snake, and compare the tracks to those of a dinosaur. Students dive deeper into the unit topics, by examining an image of a fossil fi sh and look for evidence that can help explain what the environment was like long ago. Students are then introduced to a kangaroo rat and asked to identify the traits of the rat that help it to survive in its habitat. They analyze data and investigate how organisms are adapted to particular habitats and make observations and predictions about how the traits of an animal help it to survive. Next, students examine the salt harvest mouse and use evidence to construct an argument for how environmental changes affect its ability to survive in its marshland habitat. Students summarize their learning for this unit by researching their local geological history and communicating evidence of the type of organisms that survived in the area during three different time periods.
Grade 4:
Unit 1 - Car Crashes
In this unit, students learn about forces, energy, and collisions by studying the physics of car crashes. They
begin by examining a jet taking off and landing and make observations and predictions about how forces cause objects, like jets and cars, to start or stop moving. Next, students investigate roller coasters to learn about energy and how it can change forms. By making observations and analyzing data, they learn about different types of energy and examine the cause-and-effect relationships between forces that are applied to objects and changes in energy. Then, students relate changes in motion to the motion of cheetahs. They determine which traits enable the cheetah
to run so much faster than a human. They learn about how speed is measured and make connections between an object’s speed and the forces it experiences. Finally, students examine what happens when two objects moving with a lot of speed, such as a bat and a ball, or two cars, collide with each other. They make predictions about the energy transformations that occur during a collision and connect energy transformations to the forces that are exerted on the colliding objects. Students apply the core ideas of this concept by identifying the properties of a race car that help it achieve a high speed and predicting how its energy will change if it collides with a wall.
Unit 2 - Energy Resources
In this unit, students are presented with the movement of water flowing down a waterfall and are asked to consider
the energy involved in this movement. To begin their study of this phenomenon, students consider how energy is used to power remote-controlled cars and other devices. They observe that energy can be transferred from place to place in the form of sound, light, heat, and electricity. Building on this, students obtain information to describe that energy, used to move cars, can be derived from fuels extracted from natural resources. In some cases, fuels are burned to extract their energy, while in other cases, renewable energy resources can be harnessed, as in the case of wind turbines. Students use what they have learned about nonrenewable and renewable energy resources to evaluate the impact that energy use has on the environment, including pollution from burning fossil fuels. Finally, to summarize their learning, students return to harnessing the power of water and consider the damming of the Colorado River with the Hoover Dam. They research the benefits and drawbacks of the dam and propose solutions to address the environmental harm human use of energy causes.
Unit 3 - Earth's Changing Surface
In this unit, students examine the mechanisms that cause changes in the Earth’s surface over time. Students are first presented with an image of a sandcastle being washed away. They use this as a model for how rocks can be broken down by weathering. Then, students examine the cause and effect relationships between processes such as erosion and deposition and the formation of landforms such as canyons, valleys, and deltas. Students examine how maps and images can be used to model the relationships between landforms and even show structures under the ocean. Finally, students take a deep dive into exploring the distribution of volcanoes on Earth, the nature of volcanic eruptions, and the impacts of eruptions on humans. Students summarize their learning for this unit by examining maps of Iceland and making predictions about the forces that have shaped its geography over time.
Grade 5:
Unit 1 - What is Matter Made Of?
In this unit, students investigate the nature of matter. They are introduced to the mystery of water in an uncovered fish bowl decreasing over time. They work to explain this anchor phenomenon by thinking about another real-world example of holding a hot cup of chocolate and begin to describe the properties of matter using words and measurements. Then, students continue investigating changes to matter when adding or removing thermal energy to water by describing physical changes in matter as a result of heating, cooling, and mixing. Based on their observations, they analyze types of models and develop their own model of matter based on the core idea that matter consists of particles too small to be seen. Finally, using their models, students conduct an investigation to study the loss of water volume from a fish bowl over time.
Unit 2 - From Matter to Organisms
In this unit, students use what they know about the needs of living things to build a model of an ecosystem. To develop this model, students begin by investigating the plant producers at the bottom of the food chain. They accumulate evidence to support an argument that plants get materials they need for growth from air and water. Then, they explore food chains and food webs to build model that describes the movement of these materials among plants, animals, decomposers, and the environment. Students realize that, to use these materials, animals extract energy from food, and this energy is the same energy that plants obtain from the sun. Finally, students design and construct a model ecosystem that represents this flow of matter and energy.
Unit 3 - Interacting Earth Systems
In this unit, students are presented with the problem of Earth’s shrinking freshwater supply. In particular, students address the issue of recycling wastewater by distinguishing the recycling of greywater versus blackwater. To design a solution to this problem, students begin their research by developing models of how the geosphere, biosphere, hydrosphere, and atmosphere interact. Next, they focus on the hydrosphere to describe the distribution of water on Earth in various reservoirs. Because the amount of water stored in surface freshwater reservoirs is so limited, students next obtain and combine information about how communities can use science to protect freshwater resources. Finally, students apply their strategies to a watershed in Michigan. Using data collected from the ecosystem, students design solutions for reducing pollution in this freshwater ecosystem.