2nd Grade Math focuses on four critical areas: (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes.

Unit 1

15 Lessons

Students extend their knowledge of addition and subtraction within 20 to fluently add and subtract within 20 using various strategies. This work is put into practice as students solve familiar word problem types using tape diagrams and equations to represent what is happening mathematically.

Unit 2

21 Lessons

Students develop strategies based on place value, properties of operations, and the operational relationship between addition and subtraction to add and subtract within 100 fluently. Students will use these strategies to add up to four two-digit numbers and explain why these strategies work. Students also explore categorical data.

Unit 3

13 Lessons

Students develop the foundational skills of measuring length by exploring metric measurement and develop the understanding of number lines and measurement data with line plots.

Unit 4

22 Lessons

Students extend their place value knowledge to 1,000 and use this knowledge to represent and compare three-digit numbers. Students are also introduced to money, identifying coins and their value, and determining the value of coin collections.

Unit 5

25 Lessons

Students add and subtract within 1,000 using strategies based on place value, properties of operations, and the operational relationship between addition and subtraction in order to add and subtract within 1,000. Students will use these strategies to add up to two 3-digit numbers concretely, pictorially and abstractly and explain why these strategies work.

Unit 6

15 Lessons

Students extend their measurement understanding to work with customary units, reason with shapes and their attributes, partition shapes into equal shares and describe them, and extend knowledge of time by reading and representing time to the nearest five minutes.

Unit 7

12 Lessons

Students analyze even and odd numbers and work with equal groups to form arrays and partition rectangles into equal-sized squares.

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.

Students in second grade math focus on 4 critical areas: Extending understanding of base-ten notation, building fluency with addition and subtraction, using standard units of measure, and describing and analyzing shapes.

The major work of the course focuses on the following Common Core State Standards:

*2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.**2.NBT.A.2 Count within 1000; skip-count by 5s, 10s, and 100s.**2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.**2.OA.B.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.**2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.**2.NBT.B.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.**2.NBT.B.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Explanations may be supported by drawings or objects.**2.MD.B.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.**2.MD.D.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.*

*2.OA.B.2*: Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers.

*2.NBT.B.5*: Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Learn how to develop students' procedural skill and fluency within Fishtank Math curriculum with our Procedural Skill and Fluency Teacher Tool.

In second grade, students extend their understanding of addition and subtraction situations by extending their work in problems within 100 and represent and solve situational problems of all types. As students work on one-step situations they are introduced to start unknown add to and take from situational problems as well as comparative problems where the language suggests the wrong operation. Additionally students are asked to extend their work with the various situational types by solving two-step problems. Their work with two-step situational problems does not include extensive work with the newer and more difficult subtypes. Learn how to develop students' word problem solving skills in the Fishtank Math curriculum with our Word Problem Teacher Tool.

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