1. CCGPS Mathematics 2nd Grade Update Webinar Unit 2: Becoming Fluent with Addition and Subtraction September 13, 2013
Update presentations are the result of collaboration between members of 2012 and 2013 Unit Review and Revision Teams
Microphone and speakers can be configured by going to: Tools – Audio – Audio setup wizard
Turtle Toms-
Elementary Mathematics Specialist
These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

2. 2013 2nd Grade Resource Revision Team
Sondra Brewer
Early County Schools
Andrea Cramsey
Jefferson City Schools- thank goodness, she’s here today!
Chad Dow
Atlanta Public Schools
Karen Gerow
Oglethorpe County
Whitney Naman
For Unit 1, we were joined by Katie Breedlove, who was part of the 2012 unit review and revision team.

3. What’s New in Second Grade Unit 2?
Becoming Fluent with Addition and Subtraction

4. The 2nd Grade Unit Writing Team
Sondra Brewer
Early County Schools
Andrea Cramsey
Jefferson City Schools
Chad Dow
Atlanta Public Schools
Karen Gerow
Oglethorpe County
Whitney Naman

5. They look the same…what are the major changes in the units?
Standards for Mathematical Practice (SMP)
Number Talks
Formatting
Task charts
Formative Assessment Lesson (FAL)

6. Standards for Mathematical Practice (SMP)
The unit overview provides a brief list of the SMPs and examples of learning experiences within the unit that support the development of these mathematical practices.

7. Standards For Mathematical Practice (SMP)
At the beginning of every task, there is a list of only the SMPs that are covered in that task.

8. Formative Assessment Lessons (FAL)
The Formative Assessment Lessons (FAL) are intended to support teachers with the formative assessment process.
They are typically implemented two-thirds of the way through the instructional unit. The results should then be used to inform the instruction that will take place for the remainder of the unit.
They assess student understanding of important concepts and problem solving abilities, and they help teachers move each student’s mathematical reasoning forward.

9. Number Talks
Opportunities for students to mentally compute and discuss strategies with peers
Approximately 5-15 minutes long
Student centered
Teacher is facilitator

10. Don’t have the book?
Look and learn here:
matics.org/index.p hp/number-talks
erspectives.com/nu m_talks.html
olutions.com/index .cfm?page=wp10& crid=553
henry.k12.ga.us/P age/37071
2.org/bullard/Num berTalksK-2.pdf
Concepts and skills to maintain should include Number Talks to reinforce properties of operation, mental computation, and flexible ways of solving computational problems. For more information, refer to Number Talks by Sherry Parrish
Number Talks

11. Formatting
The layout is standardized from task to task and unit to unit.
Reproducible sheets are more user friendly, and there are places for students to write answers.
Page breaks fall in logical places.

12. Task charts
The task chart includes the type and purpose of each task.

13. Task Charts The task table now includes the mathematical
standards addressed in each task.

14. What other important changes are there in Unit 2?
Common Misconceptions are addressed in the Overview section at the beginning of the unit
No new tasks have been added
The wording in the original tasks has been revised as needed to be more teacher and student friendly
More teacher commentary is included and is based on classroom experiences and observations
For example, from
PRACTICE TASK: Subtraction Story Problems
Also, students need to check their work to see if their answer makes sense in terms of the problem situation. They need ample opportunities to solve a variety of problems and develop the habit of reviewing their solution after they think they have finished answering the problem. Encouraging students to create a mental picture for what they are reading and to create drawings to represent what is going on in story problems is necessary to help them progress from concrete understandings to more abstract understandings.

15. Questions/Concerns?
Purpose of the Frameworks-intended to guide teachers as they implement CCGPS
Every lesson in the unit does not need to be taught. Time restraints may limit this. Choose tasks that are best suited for your students.
Because tasks build on knowledge acquired from previous tasks, it is recommended not to skip from tasks presented early in the unit to tasks late in the unit.
Make the tasks “your own”, if something is not working, change it to make it better (and be sure to let us know!).
Collaborate, collaborate, collaborate!

16. Resources
Wikispace-all the math goodness you need (except for the frameworks) is kept on the math wikispace provided by the GaDOE.
Please sign up for the Mathematics K-5 list serve-
Van De Walle- fresh off the press there is a new edition that is aligned to CCSS
One of the best websites out there!

17. What’s STRATEGY all about?
Quantity representation- decomposition of number
Some interesting background info- Students with poor number sense often fail to move beyond sequential counting. Sequential counting remains their primary strategy for calculations. This persists. They fail to make the connection to understanding various tools’ (number line, 0-99 chart) usefulness in decomposition of number and making ten, both of which are more efficient strategies.
VandeWall goes on to underscore- the most common and perhaps most important model for this anchoring to five and ten relationship is the ten frame to support children’s development of relating given numbers to the critical benchmarks of the base ten system. We really want to encourage children to deepen their understanding of the BAMT strategy. “Break apart and make ten. This helps students to see quantities as made by smaller chunks, and they become able to separate and combine these chunks more freely.
How?
Develop internal images of numbers with quantity (dot cards, ten frames)
Build internal bridge between objects and numeral
Anchor to 5 and 10
Help students see numbers from multiple viewpoints (number talks)
Number line- help students see that the number line represents distances “hopped” comparison of distance- which is different from using the number line as a prompt for counting or operations.
Hundred chart- number relationships become the focus as opposed to sequential counting. Ten more, ten less, magnitude of number.
Leer and Yoshida, NCTM 2010

18. A quick word about Key Words:
You’ve heard this before.
Very tempting, especially in light of the problem types chart. Yeah, so not a magic bullet- actually causes more problems than it solves. Push Robyn’s blog here.

19. Thanks to Education Week for these slides.
This statement is so powerful. This unit is all about finding the useful relationships inherent in our number system. If students can find and see them, and see how they are useful when doing the relatively heavy-lifting of computation, we are remaining true to the spirit of the standards. The strategies, which we are about to discuss, can be used over and over again, in different situations, with different sized numbers (so useful as we move to NBT.7, adding and subtracting within 1000, and NBT.8- adding and subtracting 10 or 100 from numbers )
Thanks to Education Week for these slides.

20. If we just show students strategies, and require they use just those, then we’ve lost the plot. They need to need them. They need your skilled guidance and questioning to see them, reason about them, and ascertain how these mathematical patterns and relationships can be useful. Tasks help develop this. They provide a situation which facilitates the need for the use of the patterns and relationships.

21. Examples & Explanations
Strategies for Addition:
Counting on
Doubles and near doubles
Making Ten
Multiples of Ten
Front-end addition
Counting on- simple addition with close numbers- becomes inefficient with larger numbers because it is too easy to lose track (unless you are using a number line and large jumps!)
Doubles and near doubles- use what is known about doubles to solve near doubles 7+7, 6+7 and 7+8 or 7+9 (8+8!)
Making ten- decompose an addend to make ten with the other addend, then add on the rest. 7+5= 7+3+2= 10+2
Multiples of ten- outgrowth of making ten, but with larger numbers, using the known relationships = = 32
Front-end addition- left to right, so adding the largest place values first.
37+21=
28+16= = 30+14=44
What do students gain through use of front end addition? Can it be rushed? Students will often do this naturally, because it makes more sense and builds place value. No carrying.

22. Examples & Explanations
Strategies for Subtraction:
Counting back and counting on
Think addition
Doubles and near doubles
Making Ten/using ten
Compensation
Expansion
Counting on- simple subtraction with close numbers- becomes inefficient with larger numbers because it is too easy to lose track of how many you counted. (unless you are using a number line and large jumps!)
Inverse relationship between add and sub- builds on fact families- 3+5=8 helps with 8-3
Doubles and near doubles- use what is known about doubles to solve near doubles 14-7, 16-8 and 14-8 or 16-9 (8+8!)
Making ten- decompose subtrahend to make ten with minuend. 15-8= =10-3=7 (the cool thing is, when you have used some of these strategies, you see multiple ways to solve the problem!)
Compensation- outgrowth of making ten, but with larger numbers, using the known relationships = =20-3=17
Expansion- replaces borrowing- builds better number sense Expand the second number. Expand 45, so 40 and 5. Subtract the 40 from 74, leaving 34. Subtract 5 from 34, using make ten or another strategy. Works really well, and makes sense. More sense than learning the steps for borrowing.
Think addition- hop from the lower number to the higher number, add up the hops to get the answer.

23. Addition Number Talk Strings
Make Wholes
Make a Landmark #
Hey! These are my slides from the 5th grade Unit 2 Update!
So, why does this matter? Let’s look at 5th grade- when students are doing operations with addition.
Here are two addition strategies which are built on second grade strategy understandings that can be used for decimal number talks.
We have been making tens, or making hundreds, with decimals, this becomes making wholes.
Landmark numbers- 1.9 is close to 2, so how much should I take from the other addend to make 1.9 into 2?
Adapted from Number Talks by Sherry Parrish

24. Get those 2nd graders ready, please!!
Number Talk Strings
Addition
Adding Up in Chunks
Subtraction
Adding Up
Students might also a break each number into its place value strategy.
2 – – – – 0.8
Get those 2nd graders ready, please!!
Adding up in chunks- add the wholes, then the tenths
Think Addition- how far from 1.5 to 2? , etc..
See how important your work is? Spend plenty of time on strategy understanding and development. It is the gateway to procedural fluency, and fact fluency.
Adapted from Number Talks by Sherry Parrish

25. Number Talk Tips Use hand signals to ensure 100% participation
Present multiple ways of solving
Don’t be afraid to use a Think-Pair-Share in your number talk
Create a class strategy chart
Use a ticket out the door and weekly assessments to give students pencil and paper opportunities to practice explaining their mental math strategies.
Number Talks
Just a quick booster shot on Number Talks:
Hand signals-
fist on chest- still thinking
1 finger- have an answer and 1 strategy
2 or more fingers- have an answer and corresponding number of strategies
Itchy fingers- “I’m so excited, I’m itching to tell you!”
There are many concepts and skills to maintain for 5th grade students. These are spelled out in the frameworks. I’d like to draw your attention to the last item: Use number talks to reinforce properties of operations and mental computation. Remember to choose problems for number talks strategically. The problems shouldn’t be chosen at random, but rather to address the needs of students, based on formative assessment, standards, and the tasks at hand.

26. How to develop all of these?
Task 1, Incredible Equations, is essentially directions for a number talk.
Do number talks regularly, expand them to include equations that support strategy development.
Not sure about the strategies yourself?
VandeWalle, “Teaching Student-Centered Mathematics
Fosnot, “Young Mathematicians at Work”
Remember, you are building to NBT.7 (within 1000)

27. CCGPS Overview
“educators will need to pursue, with equal intensity, three aspects of rigor in the major work of each grade: conceptual understanding, procedural skill and fluency, and applications.“
What’s the difference between procedural skill and fluency, and conceptual understanding and application?

28. Does this student have:
procedural skill and fluency?
conceptual understanding?
the ability to apply mathematics?
This student is asked to find the distance between two exits on a sign on the interstate. One is 1 and ¼ miles away, and the other is 1 and ½ miles away. The video has been sped up, because it took some time for the student to determine what to do. What do you notice? What do you wonder? How right would you say this student thinks he is?

29. Does this student have:
procedural skill and fluency?
conceptual understanding?
the ability to apply mathematics?
Same student, immediately after solving the first problem. What do you notice? What do you wonder? How correct would you say this student thinks he is?
Why is math important to us, after schooling ends? How is it useful? Do we need conceptual understanding, procedural fluency, and an ability to apply our understanding?
How can we tell when a student understands?
Procedural skill is an essential piece and it is just as important as developing conceptual understanding and ability to apply mathematics. But we often teach students procedural mathematics with the belief that they will be able to apply when a context is presented. Some are able to do so, but most will struggle just as this student did. And if all we require is procedural, we’ll never know they are unable to apply the mathematics in context.

30. Writing in Math
Standards for Mathematical Practice require students to express their thinking and record their strategies in written form.

31. Standards for Mathematical Practice
SMP 1 – Students are required to explain their thinking when making sense of a problem.
SMP 2 – Students are required to construct viable arguments and critique the reasoning of others.

32. Why Write in Math Class?
Marilyn Burns (2004): “Writing in math class supports learning because it required students to organize, clarify, and reflect on their ideas—all useful processes for making sense of mathematics. In addition, when students write, their papers provide a window into their understandings, their misconceptions and their feelings about the content.”

33. Math Journals Purposes: Record strategies and solutions
Reflect upon learning
Explain and justify thinking
Provide a chronological record of student math thinking throughout the year
Means of assessment to guide future instruction
Might this provide a window into understanding?

34. Can you see the connections?
Visual images
Recording thinking
Explaining thinking
Conceptual understanding
Procedural fluency
Application
Visual images, recorded in journals, explained in discussions, lead to conceptual understanding, and the building of solid procedural fluency along with an ability to apply. And that’s why we learn mathematics, so we can apply it.
Use of flashcards- what does the research say? Flashcards work for memorization if used on known facts. They cement memorization. So, don’t drill what they don’t know because you are using precious time which could be used to build understanding.

35. Feedback http://ccgpsmathematicsk-5.wikispaces.com/
Turtle Toms-
Elementary Mathematics Specialist

36. 2nd Grade Math Resource Revision Team
Sondra Brewer- Teacher, Early County Schools
Andrea Cramsey-Teacher, Jefferson City Schools
Chad Dow- Teacher, Atlanta Public Schools
Karen Gerow– Instructional Coach, Oglethorpe County Schools
Whitney Namen-Teacher, Atlanta Public Schools
Thank you, Andrea!

37. Turtle Toms Program Specialist (K-5) tgunn@doe.k12.ga.us
Thank You! Please visit to share your feedback, ask questions, and share your ideas and resources! Please visit to join the K-5 Mathematics listserve. Follow on Twitter!
Turtle Toms Program Specialist (K-5)
These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.