In Unit 1, Adding and Subtracting Within 20, students build on their 1st grade work and add and subtract within 20. The work they do in this unit sets the foundation for their addition and subtraction work within 100, and more specifically as they work towards fluency in addition and subtraction within 20 by the end of the year. To support their work with addition and subtraction, they also build on their count sequence as they extend from 120 to 200. Throughout this unit, students use advanced strategies to add and subtract flexibly within 20. They use strategies such as making a ten to add, relating addition and subtraction to subtract by using known facts, rewriting unknown addend problems as subtraction problems, subtracting by going down over ten, and converting to better known problems by using fluency facts, doubles facts, and facts within 10. They also contextualize their addition and subtraction work with word problems, building off of their 1st grade work by using tape diagrams to model the situations.
In Unit 2, Adding and Subtracting Within 100, students build on their addition and subtraction work to develop and use strategies to add and subtract within 100. By the end of 2nd grade, students are expected to fluently add and subtract within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction. Students will apply some of the strategies and understandings from their work within 20 from Unit 1 to add and subtract within 100 in this unit. Students also use their understanding of addition and subtraction as they explore categorical data by interpreting and creating bar graphs and picture graphs and ask and answer questions about the data presented. Since students add with up to four addends in this unit, they can practice in context with data. The word problems students see in this unit introduce working within 100 since students have begun to compute within 100. Going forward, students will solve word problems within 100, and here they look at situations with compare word problems.
In Unit 3, Metric Measurement, students build on their understanding of length and measurement by learning about standard units of measurement and tools used to measure objects. In this first unit on measurement, students are introduced to the metric units centimeters and meters. Students use rulers to measure objects on paper and in real life. They then connect this idea of measurement to a number line, exploring similarities and differences between rulers and number lines. Students represent whole numbers as lengths on a number line and will use a number line to represent sums and differences within 100. Given their growing understanding of measurement and number lines, students then display measurement data on line plots and answer questions about these line plots. In their word problem work, students are introduced to two-step word problems and solve in context of metric measurement length.
In Unit 4, Place Value with Numbers to 1,000 & Money, students build on their understanding of place value with the introduction of a new unit, a hundred. By extending their understanding that 10 ones form 1 ten, they learn that 10 tens form 1 hundred. With their knowledge of a hundred, students further their understanding of three-digit numbers by expanding their count sequence to 1,000. Students use their knowledge of number lines as they place, order, compare, and reason with three-digit numbers. In future units, students will use this understanding of the number line structure to use a number line as a tool to add and subtract. Their work with place value is reinforced by their work with money as they identify coins and determine the value of coin collections up to 100 cents or $1, as well as put this to work in context with one-step and two-step word problems.
In Unit 5, Adding and Subtracting Within 1,000, students build on their addition and subtraction work within 100 from Unit 2 and their place value understanding from Unit 4 to add and subtract within 1,000. By the end of 2nd grade, students are expected to have a plethora of strategies and generalizable methods in order to add and subtract 3-digit numbers within 1,000. In this unit, students are introduced to the standard algorithm; however, students are not expected to be fluent or show proficiency with it until Grade 4. Throughout the unit, students expand their strategies and methods by adding and subtracting multiples of tens or hundreds, using concrete manipulatives to model addition and subtraction work, including creating larger units and breaking apart larger units in order to solve. They also move to more abstract strategies and methods. While students have been working with one-step word problems of all types until this point, in this unit, students expand their work with word problems to include two-step word problems. From this point on, students will continue to be exposed to word problems of all types, including two-step situations.
In Unit 6, Customary Measurement, Shapes, and Telling Time, students revisit measurement concepts and skills as they apply them to customary units. Students measure the lengths of objects in inches and draw lines that can be measured to the nearest inch. They use inch rulers and yardsticks as measuring tools to measure and estimate lengths in inches and in feet. Having encountered both customary and metric units, students come to understand that when measuring an object with two different units of measure, the measurement value is relative to the size of the unit. Building on their previous word problem work, students apply their problem-solving skills to solving one-step and two-step word problems involving customary measurement. In this unit, students also build on their geometry skills by reasoning about shapes and their attributes. As students build on their work of shapes, they also extend their work on partitioning shapes into equal shares and describing them, building their foundation for fraction work in third grade. Using their knowledge of partitioning circles, they also relate that to telling time to the nearest half and quarter hours and then tell time to the nearest five minutes. Students' word problem work includes one-step and two-step word problems that include the harder subtypes.
Finally, in Unit 7, Working with Even, Odd, and Equal Groups, students determine if numbers are even or odd. Students build their understanding of equal groups further by working with arrays and later partitioning rectangles to form rows and columns of smaller equal-sized squares.