Adding and Subtracting Within 1,000

Unit Summary

In Unit 5, 2nd grade students build on their addition and subtraction work from adding and subtracting two 2-digit numbers and patterns within 10 to develop and use strategies 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 (2.NBT.B.7). In this unit, students are introduced to adding and subtracting 3-digit numbers within 1,000 using the standard algorithm, however students are not expected to be fluent or show proficiency with the standard algorithm until Grade 4. By extending their adding and subtracting work within 100 from Unit 2, students will use some of the strategies and understandings in their work within 1,000. This helps students with their work throughout their grade 2 mathematics and beyond. 

In Topic A, students begin the unit by adding multiples of tens or hundreds. This is a continuation of the work done in Unit 2 where they added multiples of tens fluently within 100. Similarly, they also build off their Unit 1 and 2 work by applying strategies of compensation to adding three-digit numbers in order to get to a benchmark hundred. 

Topic B focuses on methods for adding within 1,000. In this topic students use concrete manipulatives to represent their addition work. From there, they use their knowledge of concrete models to draw pictorial representations. Then finally, students move to more abstract representations, including the standard algorithm. Students use their knowledge of hundreds, tens, and ones as they show up to two compositions of a new hundred and a new ten. 

In Topic C, students begin the topic by subtracting multiples of tens or hundreds. As similar work was completed in Topic A of this unit, students will also maintain a constant difference in order to subtract without needing to regroup.

In Topic D, students focus on subtraction within 1,000 and similarly move through concrete representations to pictorial, using place value drawings, and later more abstract representations to solve. Students use their place value knowledge to subtract with up to two decompositions of a hundred into 10 tens and ten into 10 ones in order to subtract in situations where there are not enough tens or ones. Students also explore how they can relate subtraction to addition in order to subtract as well as continue to practice abstract adding using the standard algorithm to check their work. 

Finally, in Topic E students build on their work with word problems by solving more difficult problem types of one-step story problems as well as harder subtypes of two-step story problems. They  build on their Unit 1 word problem work by continuing to use tape diagrams to represent the problem and using symbols to represent the unknown in their equations. They also use their knowledge of solving twice for two-step story problems from Unit 4 (2.OA.A.1). By the end of second grade students should be proficient in two-step word problem combinations of two middle difficulty problem types with addition and subtraction. Also, in this topic students will use their skills of making new hundreds in the context of  adding up to four two-digit numbers and going beyond 100 (2.NBT.B.6) and explain the strategies they used to solve addition and subtraction problems (2.NBT.B.9). 

The work students explore in this unit provides them with a better understanding of numbers and patterns first brought on in the foundation for their work in Unit 2. Students will continue to practice their fluency with 100 throughout their 2nd grade work as they continue to solve word problems within 100.