Elementary Mathematics

2nd Grade Unit 8: Patterns, Teams, and Paper Clips

BEGIN WITH THE END IN MIND!  common core expectations...




Unit at a Glance

Suggested Dates:
April 21- May 23

Estimated Duration: 25 Days

*Investigation 1: 4 lessons *Investigation 2: 2 lessons *Investigation 3: 5 lessons
*Investigation 4: 5 lessons

*After finishing, use Common Core Investigation 5A sessions, and DPI lessons 2.2 and 2.3.





Smart Board, Promethean, and Power Point Files:



Smart Board:
Place Value Riddles
 




Tools for Teachers

Addition and Subtraction Unit from Common Core Georgia Performance Standards provides additional resources for reteach and extension lessons.

DPI Unit

End of Unit Assessment Rubrics

Investigation Assessment Checklists

Unit 8 Strategies

Unit 8 Extension

Unit 8 Check Up

This site provides an extensive collection of free resources, math games, and hands-on math activities aligned with the Common Core State Standards for Mathematics.
Investigations

Extension 
Project ideas from the Minneapolis Public School District.

2nd Grade At A Glance and 2nd Grade Common Core Comparison

Progression for choosing numbers for tasks
Investigations

K-2 
Literature List

Investigations Vocabulary






*Remember to upload files to share with others, or locate files to use, on the wiki. Be sure to join discussion posts with other colleagues to ask questions, answer questions, and discuss math.
STANDARDS FOR MATHEMATICAL PRACTICE

During this unit, review MP1 and MP5 with students.


After giving a small group time to solve a word problem, bring them back together to share their strategies.  Allow a student to show their work on the board and ask the group, “How did___ know to use subtraction instead of addition to solve this problem?”  This will encourage students to better make sense of the problems they solve (MP1).

As students work to solve Pinching Paperclip problems, you may notice some of them using hundreds boards, open number lines, or drawing strips and singles.  At the end of the lesson, bring them back together to ask them to tell why they chose their particular tool to solve the problems.  This will open dialogue about using appropriate tools strategically (MP5), while also leading to further discussion of which strategies help solve certain problems more efficiently.  Watch the first video clip for MP5 for an example of this practice.



TEAM TIME!
 DISCUSS THE FOLLOWING WITH YOUR GRADE LEVEL TEAM:

Read the teacher note on pages 163-167 entitled “Notating Subtraction Strategies.” Think about which strategy is easier for you to use.  Discuss with your PLC.   Which strategy do you think your students will use the most; why?  Does one strategy show a deeper understanding of subtraction?  If so, how can you get your students to use/show that strategy?

As a team, solve 482-149 without using the traditional algorithm method of borrowing/regrouping.  Can you solve this equation by decomposing the tens and hundreds (2.NBT.7) using two different strategies?  What challenges occurred when solving this equation using “nontraditional” methods?  Discuss with your team the implications of teaching these strategies to your students and having them feel comfortable with composing and decomposing numbers.

Read Chapter 11 in Judy Storeygard’s My Kids Can: Making Math Accessible to All Learners, K-5. This is a great resource on students’ knowledge of subtraction.


OPPORTUNITIES FOR DIFFERENTIATION...

Suggestions for students who are struggling...


Make 100 game to practice combinations of 100.

Discovery Education: “Money and Time Adventures of Lollipop Dragon: Value in Cents; Coin Collections; Dollar and Cents” (38:09) (segments can be used when appropriate) Supports 2.MD.8

Virtual Arrow Cards 

Great website with games to reinforce 2.NBT.7 (3-Digit Addition/Subtraction Split)

Students needing additional practice with missing parts can play Cover Up (introduced in Unit 3) using a smaller amount of counters at first, then work their way up to using more counters as they become more proficient with this skill.

Have students who are struggling with showing more than one strategy to solve a problem pair up with another student who uses a different strategy.  The 2 students will take turns sharing their own strategies and attempt to use what they learned to solve a new problem.

Suggestions for students who fully understand...

Friendly Numbers Subtraction game for students who have a good understanding of decomposing numbers.

Have students who have a clear understanding of solving 3-digit word problems solve multi-step problems using Lessons 3.4 & 3.5 of DPI lessons.

Students who have a clear understanding of subtracting from 100 with Pinching Paperclips can play using 200 or 300 paperclips.  They should be able to pull from the strategies they used pinching 100 paperclips to solve problems using larger numbers.




COMMON CORE STATE STANDARDS IN THIS UNIT

Link to CCSS Unpacking Document

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

2.OA.3- Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

2.NBT.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. Understand the following as special cases: a.100 can be thought of as a bundle of ten tens — called a “hundred.”  b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

2.NBT.2-Count within 1000; skip-count by 5s, 10s, and 100s.

2.NBT.3-Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

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

2.NBT.6-Add up to four two-digit numbers using strategies based on place value and properties of operations.

2.NBT.7-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.  Video for clarification

2.NBT.8-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.



Words you should hear students use in Mathematical Conversations...

Even, odd, sum, addition, subtractions, strategy, hundreds, tens, ones, expanded form   

Write a subtraction story problem on the board and allow students time to solve it showing their work independently.  Show two different strategies for solving the problems on the board (adding up, subtracting back, etc.). Ask students to “turn and talk” and explain to a partner why each strategy works. 

Ask students to think, pair, share; “How are even and odd numbers different?” Listen for students to use the words “left-overs, pairs, equal groups.”

TAKE NOTE FOR EACH INVESTIGATION

INVESTIGATION 1

Understanding what happens when you add odd and even numbers is the main focus of this Investigation.  Sessions 1.1-1.4 support 2.OA.3.  This is an extension of Unit 3, Investigation 3 with odd and even numbers.  



INVESTIGATION 4

Adding numbers using a variety of strategies is the main focus for this Investigation (2.NBT.5).  2.NBT.1 is also used here however, you will need to expand numbers to include hundreds, tens, and ones (also visited in Investigation 5).
INVESTIGATION 2

Students complete the remaining combinations during this Investigation, which supports 2.OA.2 (fluently add and subtract within 20 using mental strategies).  Include 4 two-digit number strings for addition in order to support 2.NBT.6    


INVESTIGATION 5

This is a Common Core Investigation Addition that aligns with 2.NBT.7.  Students will need a lot of hands on work and practice with adding and subtracting 3-digit numbers during this investigation.  They should be able to solve these problems using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

With additional days, visit supplemental lessons 2.2 and 2.3 from DPI lessons.  Both lessons support 2.OA.1, 2.NBT.5 and 2.NBT.7 with addition and subtraction with word problems.


INVESTIGATION 3

Subtracting numbers using a variety of strategies is the main focus for this Investigation (2.NBT.5).  2.NBT.1 is also used here however, you will need to expand numbers to include hundreds, tens, and ones (also visited in Investigation 5). 


CLASSROOM ROUTINES
Today's Number

2.OA.2, 2.NBT.5, 2.NBT.9

Missing addends; addition & subtraction expressions. 

Today’s number routine includes 2-digit numbers; however, 3-digit numbers are appropriate at this time
 
What Time is it?

2.NBT.2, 2.MD.7

Quarter hours, recording digital time, elapsed time-whole, half, and quarter hours (cross over hours).

Since elapsed time is covered, it would be a great opportunity to prepare students for this 3rd grade skill.  Be sure to give them hands-on practice with this.
How Many Pockets?

2.NBT.4

Collecting data; repeated addition; comparing numbers
Quick Images

2.NBT.1, 2.NBT.5, 2.NBT.8

Subtracting tens/ones; related problems. 

Ask students to share strategies of mental math to strengthen 2.NBT.8.