2nd Grade Mathematics

Unit 6: Addition and Subtraction within 1,000

Teacher Resource Guide

2012 - 2013

In Grade 2, instructional time should focus on four critical areas:

  1. Extending understanding of base-ten notation;

Students extend their understanding of place value. This includes ideas of counting in fives, tens, and multiples of hundreds, tens, and ones, as well as number relationships involving these units, including comparing. Students understand multi-digit numbers (up to 1000) written in base-ten notation, recognizing that the digits in each place represent amounts of thousands, hundreds, tens, or ones (e.g., 853 is 8 hundreds + 5 tens + 3 ones).

  1. Building fluency with addition and subtraction;

Students use their understanding of addition to develop fluency with addition and subtraction within 100. They solve problems within 1000 by applying their understanding of models for addition and subtraction, and they develop, discuss, and use efficient, methods to compute sums and differences of whole numbers in base-ten notation. They apply methods that are appropriate for the context and the numbers involved to mentally calculate sums and differences for numbers with only tens or only hundreds.

  1. Using standard units of measure;

Students recognize the need for standard units of measure (centimeter and inch) and they use rulers with the understanding that linear measure involves iteration (repetition) of units. They recognize that the smaller the unit, the more iterations they need to cover a given length.

  1. Describing and analyzing shapes

Students describe and analyze shapes by examining their sides and angles. Students investigate, describe, and reason about decomposing and combining shapes to make other shapes. Through building, drawing, and analyzing two- and three-dimensional shapes, students develop a foundation for understanding area, volume, congruence, similarity, and symmetry in later grades.

2nd Grade Mathematics 2012-2013

Unit / Time Frame / Test By
TRIMESTER 1 / 1: Addition and Subtraction
(within 20) / 7 weeks / 8/27-10/12 / October 12
2: Data/Measurement / 5 weeks / 10/15 - 11/27 / November 27
TRIMESTER 2 / 3: Addition and Subtraction
(within 100- Developing Skills) / 6 weeks / 12/3 - 1/18 / January 18
4: Addition and Subtraction
(within 100- Fluency) / 6 weeks / 1/21 - 3/1 / March 1
TRIMESTER 3 / 5: Geometry / 5 weeks / 3/4 - 4/12 / April 12
6: Addition and Subtraction
(within 1,000) / 6 weeks / 4/15 – 5/30 / May 31

Math Wiki:

2nd Grade 2012-2013Page 1

Unit 6: Addition and Subtraction within 1,000 April 15- May 30 (6 weeks)

Big Ideas / Essential Questions
An equation helps us to understand what is known and what is unknown in a problem. / Why do we write equations before solving a problem?
Identifier / Standards / Mathematical Practices
STANDARDS / 2.OA.2
2.NBT.8 / 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.
Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. / 1) Make sense of problems and persevere in solving them.
2) Reason abstractly and quantitatively.
3) Construct viable arguments and critique the reasoning of others.
4) Model with mathematics.
5) Use appropriate tools strategically.
6) Attend to precision.
7) Look for and make use of structure.
8) Look for and express regularity in
repeated reasoning.
2.NBT.5
2.NBT.8 / Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
2.NBT.7
2.NBT.8 / Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
2.NBT.9 / Explain why addition and subtraction strategies work, using place value and the properties of operations.
Identifier / Standards / Bloom’s / Skills / Concepts
STANDARDS / 2.OA.2
2.NBT.8 / 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.
Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. / Analyze (4) / Fluently
(add subtract w/in 20) / addition
subtraction
2.NBT.5
2.NBT.8 / Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. / Apply (3) / Fluently (add
subtract w/in 100) / add
subtract
2.NBT.7
2.NBT.8 / Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. / Apply (3) / Add & subtract
w/in 1000 / hundreds
tens
ones
strategy
2.NBT.9 / Explain why addition and subtraction strategies work, using place value and the properties of operations. / Understand (2) / Explain (why strategies work) / add & subtract
place value
Instructional Strategies for ALL Students
Critical Reading Prior to Instruction:
Math Expressions, Teacher’s Edition Volume I, Houghton Mifflin, 2009, p. 309L-N
Teaching Student-Centered Mathematics Grades K-3, Van de Walle & Lovin, Pearson, 2006, p. 70-77 (building resource, SPED)
Children’s Mathematics, Carpenter, Heinemann, 1999 (CGI year 1 text)
Real-world context – For students to reach the level of rigor intended for the operations of addition and subtraction in the Iowa Core, they must develop understanding of the operations within real-world contexts. The tendency in the United States is to have students solve a lot of problems in a single class period. The focus of these lessons seems to be on how to get answers. In Japan, however, a complete lesson will often revolve around one or two problems and the related discussion. (Reys & Reys, 1995).A lesson built around word problems focuses on how students solve the problem. They may use words, pictures, and numbers to explain how they solved the problem and why they think they are correct. Allow students to use physical materials or drawings. Someone else should be able to understand how they solved the problem when looking at their paper.
Addition and Subtraction problem types – There are four structures for addition and subtraction problems: Join, Separate, Part-Part-Whole, and Compare.
See page 8 of this guide for further explanation of the problem types. Many times the emphasis is on the easier join and separate problems with the result unknown. These problem types are where the “put together” and “take away” definitions of addition and subtraction come from. There are many other problem types for addition and subtraction, therefore students need regular opportunities to solve all of the different types of problems in order to reach the level of rigor described in the Iowa Core.
Routines/Meaningful Distributed Practice
Distributed Practice that is Meaningful and Purposeful
Practice is essential to learn mathematics. However, to be effective in improving student achievement, practice must be meaningful, purposeful, and distributed.
  • Meaningful: Builds on and extends understanding
  • Purposeful: Links to curriculum goals and targets an identified need based on multiple data sources
  • Distributed: Consists of short periods of systematic practice distributed over a long period of time
Routines are an excellent way to achieve the mandate of Meaningful Distributed Practice outlined in the Iowa Core Curriculum. The skills presented during routines do not necessarily reinforce the lesson concept for that day. Routines may be used to address a need for small increments of exposure to a skill or review of skills already taught. Routine activities may be repeated several days in a row, allowing for a build-up of conceptual understanding, or can be visited and re-visited over a period of time. Routines can be inserted as the schedule allows; in short intervals throughout the day or as a lesson opener or closer. Selection of the routine should be made based on informal teacher observation and formative assessments.
Skill / Standard
Mentally add or subtract 10 or 100 to/from a given number / 2.NBT.8
Tell and write time to nearest 5 minutes / 2.MD.7
Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies / 2.MD.8
Place value / 2.NBT.1
Read and write numbers to 1,000 (number names and expanded form) / 2.NBT.3
Use addition to find the total number of objects in an array / 2.OA.4
Count within 1,000; skip-count by 5s, 10s and 100s / 2.NBT.2
Picture and Bar Graphs / 2.MD.10
Other skills students need to develop based on teacher observation and formative assessments.

READ PRIOR TO TEACHING THIS UNIT: This unit continues to work on multi-digit addition and subtraction. Please read the standards that are to be taught in this unit. Students are expected to: Fluently add/subtract numbers within 20 (the facts), Add/subtract within 100 using a place value strategy, and Add/subtraction numbers within 1,000 using models, drawings, decomposing numbers, etc. Present word problems everyday throughout this unit. Be sure to include the various problem types. Allow students time to explore these problems, develop their own understanding, and solve the problem in their own way. Have students share strategies that work. Push students to use a more efficient strategy than the one they used during the previous units. Give students lots and lots of experiences with problems in a context. You may teach the following lessons in order, but you need to include word problems throughout the entire unit. There is one document on the Wiki with a bank of word problems.

Math Expressions Lesson Progression
Lesson / Teacher’s Edition
Pages / Standards
Wiki: Word problems / Present word problems throughout the unit. There is a bank of problems at the end of this resource guide.
Unit 11, Lesson 2, Activities 1-3: Place Value / These lessons can be taught and continued throughout the first part of this unit as distributed practice. / 764 / 2.NBT.7
Unit 11, Lesson 5, Activities 2: Grouping ones, tens and hundreds / These are story problems in which students have to group ones, tens and hundreds. / 786 / 2.NBT.7
Unit 11, Lesson 6, Activity 1: Quarters (money) / This lesson is about money and can be done during MDP/routine time / 792 / 2.MD.8
Unit 11, Lesson 9, Activity 1: Add over the Hundred / 810 / 2.NBT.7
Unit 11, Lesson 10, Activity 2: Solve Word Problems / Students are solving word problems and explaining their thinking. Allow students to choose a strategy. There is not one correct way to solve a word problem. Give the students time to share the strategies they use. / 817 / 2.NBT.5, 2.NBT.7
Unit 11, Lesson 12, Activity 1: 3-digit Addition / 832 / 2.NBT.7
Unit 11, Lesson 13, Activities 1-2: Word Problems with Unknown Addends / Make sure students are exposed to the various problem types. There is a chart on the Wiki that explains the different problem types. Allow students to choose a strategy. / 838 / 2.NBT.7
Unit 11, Lesson 14, Activity 2: Subtraction Word Problems / Students will view these problems differently. It says they are subtraction problems, but some students may think of it as an addition problem. / 845 / 2.NBT.5
Unit 11, Lesson 15, Activity 1: Subtraction from Numbers with Zeros / Students are able to use a strategy of their choice. Some students may count up instead of subtracting. Often times we see students make mistakes when subtracting 297 from 302. They get confused about trading and crossing out the zero. Instead, a student can count up. 297 and 3 more is 300 and 2 more is 302 so the answer is 5. / 854 / 2.NBT5
Unit 11, Lesson 17, Activity 1: Subtract from any
3-digit Number / This subtraction lesson is on ungrouping so students are able to make a trade. Not all students will use this method. / 866 / 2.NBT.5
Unit 11, Lesson 18, Activity 1: Practice Ungrouping / Students decide when to ungroup. Not all students will need this lesson because they may use a different strategy for subtracting. / 874 / 2.NBT.5
Unit 11, Lesson 20, Activity 1: Unknown Start and Comparison Problems / 886 / 2.NBT.5, 2.NBt.7
Unit 11, Lesson 21, Activities 1-2 & Extra Practice: Addition and Subtraction Word Problems / Students should solve problems in a context (word problems) EVERYDAY in this unit. Do not wait until the end of the unit to present word problems. / 892 / 2.NBT.5, 2.NBt.7
Unit 11, Lesson 22, Activity 2: Money Activities / This may be taught during MDP/routine and continued as a center during the math block / 898 / 2.MD.8

2nd Grade 2012-2013Page 1

Unit 6: Addition and Subtraction within 1,000 April 15- May 30 (6 weeks)

Table 1. Common addition and subtraction situations.[1]

Iowa Core Mathematics, p. 92;

Result Unknown / Change Unknown / Start Unknown
Add to / Two bunnies sat on the grass. Three more bunnies hopped there. How many bunnies are on the grass now?
2 + 3 = ? / Two bunnies were sitting on the grass. Some more bunnies hopped there. Then there were five bunnies. How many bunnies hopped over to the first two?
2 + ? = 5 / Some bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on the grass before?
? + 3 = 5
Take from / Five apples were on the table. I ate two apples. How many apples are on the table now?
5 – 2 = ? / Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat?
5 – ? = 3 / Some apples were on the table. I ate two apples. Then there were three apples. How many apples were on the table before?
? – 2 = 3
Total Unknown / Addend Unknown / Both Addends Unknown4
Put Together/
Take Apart2 / Three red apples and two green apples are on the table. How many apples are on the table?
3 + 2 = ? / Five apples are on the table. Three are red and the rest are green. How many apples are green?
3 + ? = 5, 5 – 3 = ? / Grandma has five flowers. How many can she put in her red vase and how many in her blue vase?
5 = 0 + 5, 5 = 5 + 0
5 = 1 + 4, 5 = 4 + 1
5 = 2 + 3, 5 = 3 + 2
Difference Unknown / Bigger Unknown / Smaller Unknown
Compare3 / ("How many more?" version): Lucy has two apples. Julie has five apples. How many more apples does Julie have than Lucy?
("How many fewer?" version): Lucy has two apples. Julie has five apples. How many fewer apples does Lucy have than Julie?
2 + ? = 5, 5 – 2 = ? / (Version with "more"): Julie has three more apples than Lucy. Lucy has two apples. How many apples does Julie have?
(Version with "fewer"): Lucy has 3 fewer apples than Julie. Lucy has two apples. How many apples does Julie have?
2 + 3 = ?, 3 + 2 = ? / (Version with "more"): Julie has three more apples than Lucy. Julie has five apples. How many apples does Lucy have?
(Version with "fewer"): Lucy has 3 fewer apples than Julie. Julie has five apples. How many apples does Lucy have?
5 – 3 = ?, ? + 3 = 5
Adapted from Box 2-4 of Mathematics Learning in Early Childhood, National Research Council (2009, pp. 32, 33).
2These take apart situations can be used to show all the decompositions of a given number. The associated equations, which have the total on the left of the equal sign, help children understand that the = sign does not always mean makes or results in but always does mean is the same number as.
3For the Bigger Unknown or Smaller Unknown situations, one version directs the correct operation (the version using more for the bigger unknown and using less for the smaller unknown). The other versions are more difficult.
4Either addend can be unknown, so there are three variations of these problem situations. Both Addends Unknown is a productive extension of this basic situation, especially for small numbers less than or equal to 10.

2nd Grade 2012-2013Page 1

Unit 6: Addition and Subtraction within 1,000 April 15- May 30 (6 weeks)

Addition/Subtraction Story Bank

Join, Result Unknown / Add to, Result Unknown

Ms. Smith has ___erasers. She wants to buy ___ more. How many erasers would she have then?

Lisa has ____ Hershey Kisses in her desk. She finds ____ more in her book bag. How many does she have in all?

There are ____ students in our class. ____ more students joined our class. How many students are there in our class all together?

Laura has ____ pumpkins. She gathers ____ more. How many pumpkins does Laura have now?

Jodi read ____ pages one night. The next night she read ____ pages. How many pages did she read in all?

Tom has ____ pencils. He wants to buy ____ more. How many pencils would Tom have?

Pinkalicious has ____ pink cupcakes. She gets ____ more pink cupcakes. How many cupcakes does Pinkalicious have now?