1. Region 11 Math and Science Teacher Partnership
Day 2: Number Sense
Addition
Region 11 Math and Science
Teacher Partnership
To Do:
Representation and Connections is brought up continually. Might want to display NCTM Process Standards to reference throughout the day. MDE uses these to define mathematical proficiency as well.
Put the 4 problem types on a chart (join, separate, PPW, and compare) for the Problem Type activity (Terry wrote them on the whiteboard)
Perhaps put the standards on chart paper to reference throughout the session
Put Rekenreks on table (1/pair)
Make agenda chart
Put up “Housekeeping Chart” (addressing when to check techonology, etc.)
Put up Quick Image patterns on magnetic board using magnets to draw around etc.
Post session goals so they can be referred to during the different activities to make them explicit.
Copy Evaluations
Need:
Rekenreks (they have these but show homemade ones so that folks don’t think they are too expensive so can’t do the activities. They are about $6/rack.)
Chart paper, markers

2. Agenda Reflections/Introductions Goals/Standards
Visualizing Numbers using Quick Images
Problem Types and Strategies Review
Defining Number Sense
What is the Rekenrek?
Number Talks using Rekenreks
Tens Frames
Decomposing/Composing Numbers
Number Talks Supporting Derived Facts
Making 10
Closure
PLC Information
8:30-8:40
Introduction: Terry shared what he is excited about today. “Christina, what are you excited for today?”
Christina – told a little background on herself being a PhD student, PD facilitator, MRIS work, teaches night and methods classes, 4th and 5th grade teacher, bldg and district wide alignment in teaching children’s mathematics

3. Reflect and Share
Be prepared to share out 1 insight and 1 question from each group.
What has happened with your students since our last session?
New insights?
What unanswered questions are there?
8:40-8:50
Note: This was not done on the training day but you might want to consider doing some kind of a reflection to gage how they are feeling about Day 1 learning. Could have them meet in 3 corners of the room. K and those who work with K students, Grade 1 and those who work with Grade 1 students, and Grade 2 and those who work with Grade 2 students.
Have groups share out any questions that were not able to be answered within the group. Record on chart paper. Acknowledge that we have a full agenda but if we can sneak these in or incorporate them into the agenda, we will.

4. Housekeeping Details Timeframe Lunch Restrooms Wi-fi access
“Misery is optional”
8:50-9:00 (slides 4-9)

5. Goals
Goals
Pg. 1
I can use ten-frames and Rekenreks to carry out number talks with my students
I can help my students compose and decompose numbers
I can describe several strategies that children use to derive addition facts
I can describe the pre-requisite strategies that children need to use a “make ten” strategy when adding whole numbers.
Rekenreks/bead racks: Today our goal is for you to be able to use things like this to have conversations with your kids.
You will have another tool to help those kids who struggle with other ways of understanding number.
We don’t do a great job of helping primary kids understand number in this country. These models help give students “pictures” in their minds-eye to be able to understand quantity and to be able to pull apart and put numbers back together.
2. I really want you to think about what composing and decomposing numbers means
Student example: what’s 10+4 (given to a 5th grade student). The reason he was struggling with struggling with multiplication was because he was struggling with basic numbers like Now he has good mental strategies. What stuck with him was how to compose and decompose numbers. If you want 5th grade teachers happy with you, teach them how to compose and decompose numbers..
Strategies
We have videos to help illustrate these today

6. Kindergarten Standards
Pg. 1
K.1.2
Use object and pictures to represent situations involving combining and separating.
K Use objects and draw pictures to find the sums and differences of numbers between 0 and 10.
K Compose and decompose numbers up to 10 with objects and pictures.

7. Grade 1 Standards
Pg. 1
1.1.2
Use a variety of models and strategies to solve addition and subtraction problems in real-world and mathematical contexts.
Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations.
Compose and decompose numbers up to 12 with an emphasis on making ten.
1.2.2
Use number sentences involving addition and subtraction basic facts to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.
Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences.
Determine if equations involving addition and subtraction are true.

8. Grade 2 Standards
Pg. 1
2.1.2
Demonstrate mastery of addition and subtraction basic facts; add and subtract one- and two-digit numbers in real-world and mathematical problems
Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtraction to generate basic facts.
Demonstrate fluency with basic addition facts and related subtraction facts.
2.2.2
Use number sentences involving addition, subtraction and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.
Understand how to interpret number sentences involving addition, subtraction and unknowns represented by letters. Use objects and number lines and create real-world situations to represent number sentences.
Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true.

9. Reflection on MN Standards
Pg. 1
What do you see developing across grade levels?
What new ideas seem to appear at a particular grade level?
Quick table talk – some schools’ PLCs have goals that are standards-based

10. Quick Image #1
9:00-9:10
This next activity works on our goal “I can help my students compose and decompose numbers.” In an effort to move them counting all, which I know my kids can do. I want to give them practice with “chunking” or subitizing patterns of dots. Can they recognize a pattern of 3, for example, without having to count out by ones the 3 dots?
We are going to practice some quick image activities which several textbooks have now incorporated into their latest editions (EDM being one of them).
You will have 2 seconds to look at each following dot pattern.
How many red circles are there? Goal is to give you enough time to see it but not enough time to count them all. Ready? Flash for 2 seconds. Then ask, how many did you see?
How did you see it?
What number sentences can we write?
(Share and model how to write participants’ thinking in number sentence from on page 2 of handout.)
Example: 6 How did you see 6? (I saw 2 groups of 3). Terry wrote a number sentence 3+3
Did anyone see something different? (I saw (2+2)+2
Did anyone see something else? I saw 3+2+1

11. Quick Image #2
9:10-9:15
Ready for the next one? (It is harder so they need to be ready.)
Talk to your partner. What did you see?
How many did you see?
How did you see it?
What number sentences can we write?
(Share and model how to write participants’ thinking in number sentence from on page 2 of handout.)
Then Terry showed the handout and drew a line around how the people who shared “chunked” the dots.
Record one example wrong. Do 4+3+4=4+4=8+3=11 (We should not model writing run on sentences like this because mathematically it is not correct. Show the correct way to write it.
Terry made a note about “not paralyzing” people by telling them “Oh, don’t write it that way.” That happened to a person who was teaching and it paralyzed them. We are all learning so please keep that in mind.
We need to make sure that kids are listening to kids. If they keep their hand up while others are talking, they aren’t truly listening. We want ourselves, and kids, to connect to what each other is saying. If we aren’t asking them to connect, I am not sure I am doing my job. My best teaching is when I am connecting student strategies.
What did you see? (I saw 4+4+3) When I write up student thinking, I can showing them how you put together thinking into representation.
Showed how to group them by circling how they counted.
Share out 3 or so examples of how people thought about it.

12. Prep for Quick Image #3 9:15-9:20
Here is a picture to get them ready for Quick Image #3. Some may not have seen these before so might want to do a little pre-work by getting them familiar with what they are looking at. This one was trickier for participants on our training day. It might have been because people weren’t familiar with what they were looking at. Ask…
How many in each row?
How many are red?
How many are white?
Tell them in the next picture they will be using what they know about this Rekenrek to solve a Quick Images activity. They will need to find out how many beads are being displayed in all.

13. Quick Image #3 9:20-9:25 How many did you see? How did you see it?
What number sentences can we write?
(Share and model how to write participants’ thinking in number sentence from on page 2 of handout.)
Had some folks share out who saw it. (
One person shared out that she just orally had the kids share from learning from the first session but did not write down what the kids said. The participant commented that she needs to do this going forward. Terry: When you write things down, you are keeping track of what they said. It’s like leaving bread crumbs so you know where you have been.
I saw 27=10+9+8
I saw (5+5+5) and (5+3+4) and they add up to 27
I saw so 30-3

14. Quick Image #4
9:25-9:38
“Turn to page 2 in handout” if not there already. We will be doing some additional ways to do quick images.
Write down the number sentence that matches how you thought about how many dots in all?
He flashed problem IV and had them write a number sentence on their handout. What’s nice about writing the number sentence is that I get a chance to know what you were thinking.
He walked around and showed examples of what folks wrote. (Use a doc cam for this or app Explain Everything on iPad)
One person wrote out the design they saw and circled.
Terry tried to make a connection between the first two participants who shared. He didn’t see one so he asked the group. “Does anyone see a connection between Michelle and Heidi’s?” Someone said they both saw groups of 2. They both “pulled down” and used chunking even though they chunked it or saw it in different ways.
As Terry showed this, he took a picture and then copied it and pasted it next to the other strategies.
The reason we connect is because there is more of a chance they will use another’s strategy if they are able to connect it to what they are doing. If they see them as separate, they won’t advance in their thinking or the chances are much less.

15. Quick Image #5
9:38-9:48
He flashed problem V and had them write a number sentence on their handout.
Started sharing at 9:30. Made the comment that Number Talks need to be limited to 5 minutes. You have limited time. They are doing it with fractions right now and the fifth graders he works with have amazing number sense due to this.
He gave problem 9/16-1/13. Is this number bigger or less than a 1/2? Just estimate. Their number sense has just really improved. They had to write their response down. Every kid but one got it right (out of 34).
Christina made the point that she went back in to apply her learning and did Number Talks with fourth graders. There was one kid who always would just sit and not participate. She thought she missed making that difference with “that one.” He had a rough background and math not nurtured at home. Now he is in fifth grade. Christina was helping out his class. They were doing some mental math like He thought 400, 500, 33. She turned around and asked him how he did it so quick. He was excited and told her that last year it didn’t really make sense but he thought about it over the summer and he said “You kno,w Mrs. Miller, this is a really good way to add numbers.” Point: Sometimes by listening we learn too and sometimes we need to talk to learn. So sometimes because we don’t see it happening in the moment, it doesn’t mean nothing is happening.

16. Classification of Problem Types
JOIN
(result unknown)
(change unknown)
(start unknown)
SEPARATE
PART PART WHOLE
PART-PART WHOLE
(whole unknown)
(part unknown)
(both parts unknown)
COMPARE
(difference unknown)
(quantity unknown)
(referent unknown)
9:48-9:49
We are now going to move to goal “I can describe several strategies that children use to derive addition facts” by reviewing some of the problem types and strategies children use to solve them from Day 1. (Perhaps make a poster to keep it displayed during this. Terry wrote the 4 types on the whiteboard: Join, Separate, PPW, Compare.)
The problems types were all written out from last time so if you have those, you can refer to those.
If needed, discuss action in join and separate problems vs. static nature of part-part- whole .
Consider drawing diagrams for each type.
Share the Karen Fuson handout, if helpful at this point (note problem names are slightly different as they align with Common Core Standards.)

17. Problem Types and Strategies
Pg. 3
What is the Problem Type?
How many children are in the class? There are 7 boys and 8 girls in Ms. Weil’s class.
Write an example of how this could be solved using each strategy below.
Direct Modeling
Counting On
Derived Facts (Number Sense)/Recall
9:49-10:02
Turn to page 3 in your handout.
Do page 3. What kind of problem is this?
Solve it using the 3 types of strategies learned last time.
9:44 Terry said Direct Modelers say, when you ask them what the dots mean, will say those are boys and those are girls. They count from one.
Counters count to keep track of the counting sequence. It’s not that they just use manipulatives. And just because they use fingers doesn’t make them counters. It’s how they use them that determines and sometimes it is hard to tell.
I am interested in derived facts. What do we have for that.
7+7+1 (wrote as a tree on the board versus on iPad)
8+2+5 (wrote as a tree and did pull down like first one)
then added 5s to get 10+5
Terry made connections to the other strategies as they were shared. What is similar/different?
Is it a join (is there a change over time or an action? No. It is a PPW (static)
Memorization can be dangerous because they won’t develop number sense and algebraic number sense (commutative, associative, distributive properties). The rap songs, etc. that teach them can be dangerous.

18. Problem Types and Strategies
Pg. 4
What is the Problem Type?
Monica has 7 carrots. Abdi gives her some more carrots, now Monica has 13 carrots.
How many carrots did Abdi give Monica?
Write an example of how this could be solved using each strategy below.
Direct Modeling
Counting On
Derived Facts (Number Sense)/Recall
10:02-10:32
Note: This slide has an animation effect on the question in red. When you click, the question will fly in.
This one the question is left off? What do you think it should be? Write it in. (Click and the question will fly in.)
Do page 4 in your handout. What kind of problem is this?
Have folks give examples of derived facts. Record on the white board.
Ask for connections between the strategies being shared.
Note if various ways of thinking show the “action” of the problem. Connect this to the standard too ( )
Then solve it using the 3 types of strategies learned last time.
What about counting and direct modeling? What would that look like?
Counting: 7 then Christina drew hands on the board and labeled each finger as 8, 9, 10, 11, 12, 13
Direct Modeling: Count out 7 carrots. Drew a line to show how many we have. Then she kept counting to 13. Then counted the 6 after the line. This example is actually what? Christina took some time to talk about this problem as there are elements of both in this child’s thinking.
Participants brought up how they are using the tool and determined direct modeling.
Christina changed the numbers to 9 carrots and 13. She had particpant reread the problem with the new numbers. Christina modeled this as she was talking. Then Christina asked, “What did I do?” She followed the exact action of the problem. I couldn’t have started with 10, 11, 12, 13 if I hand’t counted from 1 to 9. Students are starting to transition but the key question is “Did you really need to make those 9?” If they did, they are more of a direct modeler. If they didn’t, they are transitioning to counting.
Regarding planning ahead, Christina brought out cubes. Counted out 13. Then counted the 7. Counted the 6 left. Note: This didn’t make sense to me.
Christina shared a trial and error example too via the doc cam and cubes.
A participant made the comment about the perseverance that kids have when the do trial and error and you need that to be a problem solver. It should be commended even though we do want them to move toward efficiency.
How do we get kids away from just adding all the numbers all the time?
Lots of practice with different kinds of problems so they don’t always make sense of the problem.
Act it out
Some people brought up circling the word “sum” and telling kids that is the unknown. (Might want to think of a way to address this without “shutting down” the person who may bring it up.)
Share out ideas to do next.
Key Question: When we come back from break, what are the differences in these experiences? (box around sum, bring out number sentence, act out sitting at table, act out with kids up front, change to smaller numbers)

19. Problem Types & Strategies
Pg. 5
Write a separate (result unknown) for the number sentence 14-8=?
Write an example of how this could be solved using each strategy below.
Direct Modeling
Counting On
Derived Facts (Number Sense)/Recall
Do if time. We did not have time for this one in the training session.

20. 10 Minute Break
10:32-10:42

21. Jo Boaler Math Professor, Stanford University
Jo Boaler video (How to Learn Math, session 5.1, YouTube)
Jo Boaler on Number Sense
So, what is Number Sense anyway?
10:45-10:58 Jo Boaler (end at about 9:29) – Stanford University professor. Anyone heard of her? Introduce who she is. A couple summers ago did a workshop online. We are going to listen to her version of what is number sense. See how her definition pairs up with yours?
One of main reasons children fail at algebra is due to lack of number sense.
From Wikipedia Jo Boaler is a British education author, and is Professor of Mathematics Education at the Stanford Graduate School of Education.[1] Boaler is involved in promoting mathematics education reform[2] and equitable mathematics classrooms.[2][3][4] She is the CEO and co-founder of Youcubed,[5] a non-profit organization that provides mathematics education resources to parent and educators of K–12 students. She is the author of seven books including, What’s Math Got To Do With It? (2009)[6] and The Elephant in the Classroom (2010),[7] both written for teachers and parents with the goal of improving mathematics education in both the US and UK.[8] Her 1997/2002 book, Experiencing School Mathematics won the "Outstanding Book of the Year" award for education in Britain.[9][10][11][12] Currently she is the Research Commentary Editor for the Journal for Research in Mathematics Education.

22. 5 Minute Reflection on Video
At your table, define number sense.
What did the video make you think more deeply about?
What kinds of activities and experiences build number sense?
10:58-11:03
We want to give opportunity to learn and opportunity to make mistakes (Terry wrote this on the board)
10:56 Share out: What is the definition of number sense?
Ideas shared:
More than just recalling facts (recall is a step below number sense) Careful with this. This is dependent on the kid. It’s not necessarily below. It just doesn’t tell you if a child has number sense.
Understands the relationships between numbers
Compose and decompose numbers flexibly
Magnitude of numbers
Let’s say you are trying to move a counter. How do you move them?
Question from a participant. Is number sense teachable? Christina says that this is messy and Jo wrestles with this. Terry said that he says YES. He’s seen it. They need experiences to develop it and if we don’t give them the experiences, they will not just magically get it.
Participant made the point that it is hard to teach standards and do number sense. Got the feeling she was saying you can’t have both. The idea that “I don’t have time to teach number sense. I need to get them to the right answer on the MCA. They need to know time, and geometry and I can’t spend this much time on number sense.”
Participants were stuck on how to “teach” number sense. Not necessarily making the connection between all of these experiences (problem types, number talks, modeling, strategy sharing, etc.) build number sense.

23. A few Key Ideas with Rekenreks
Show with “just one push” as students gain experience with the Rekenrek.
“Clear the space.”
Store on right. Show on left.
11:03-11:04

24. Rekenreks Mathrack.com School Purchasing
Pg. 6
Mathrack.com School Purchasing
Math Learning Center Online Rekenrek
11:04-11:25 Showed the site online of where to order them (mathrack.com school purchasing)
Goals:
I can help my students compose and decompose numbers
I can use rekenreks to carry out number talks with my students
Background on Rekenrek (therekenrek.com):
“There is perhaps no more important task for primary teachers than to help young children develop powerful understandings of numbers -- their meanings, their relationships to one another, and how we operate with them.   The Rekenrek has recently emerged on the U.S. mathematics education scene as perhaps the most powerful of all manipulative models for young learners.  Developed by mathematics education researchers in the Netherlands (although similar models were used in ancient cultures) the Rekenrek combines various strengths of other manipulatives (e.g., number lines, base-10 blocks, counters, etc.) in one accessible tool. The Rekenrek is comprised of two strings of ten beads each, strategically broken into two groups: five red beads, and five white beads.  Readily apparent in this model is an implicit invitation for children to think in groups of five and ten. The strings of red and white beads (in groups of 5) provide a visual model that encourages young learners to subitize, i.e., to build numbers based on groups of five and ten.”
Notes from Training Day:
Page 6 Moving them from counting to derived fact
When introducing Rekenreks, review how the Rekenrek is put together. Click on second link and talk about “What do you notice?” Turn and talk at table.
With students, talking about the Rekenrek might be the whole math talk for the day. Review how the Rekenrek is put together several times when it is first introduced. Might introduce it during centers, etc.
Part I: Model the problem. Start with 5. How many more to get to 8? Show how you did it.
6, 7, 8 (one way)
Move 1 from top and put to bottom (4+4)
One push
Use what you know about finger patterns (5+3)
5 on top and 3 on bottom
This number talk is meant to emphasize 5. You want them to visualize and see 5 on the rack as 5 reds or 5 whites. But, you can certainly use 4 on top and 4 on bottom. Kids might see 4 on top and 4 more on top too (made up of 1 red and 3 white).
Really emphasize WHY this tool is important and helpful to use.
Also, make point that this is not a first lesson for K that you might do. Work with making 5 etc would more than likely occur first.
Start over:
Make 5
Make 8.
How do you know you have 8? (have a couple people share out)
Class, we are going to clear our space.
In one push, make 5.
Make 9.
How do you know? (have a few people share and model what they say)
How could we make 9 in just one push? (Cause 5 and 4 is 9) This is still an oral activity. Maybe Day 3 or 4 of Math Talk.
Then you can move to recording what they are saying.
Have participants reflect (turn and talk) on HOW this tool bridges counters into using derived facts (5 minutes)

25. I saw 7. How did you see them? How many beads did you see?
5 Minute Number Talk
I saw 7. How did you see them?
How many beads did you see?
11:25-11:30 Christina modeled a 5 minute number talk before lunch (She got done in about 3.5 minutes and then participants reflected on the goals of this lesson)
Part II, Pg. 6
Make
A. 5 on top with 1 push. How many altogether? (Terry modeled with online rekenrek)
B. 5 on top. 2 on bottom. How many? How do you know?
4 on top. 3 on bottom. How many? How do you know?
2 on top, 5 on bottom (show how this is the same total as B. So, they are both the same? It doesn’t matter if 2 is on top or bottom.) Commutative piece will more than likely be brought up by students but if not, bring it out. You could also do a reverse of what they just saw in C. They will likely see that the numbers were just switched.
Goal: What is the goal of this lesson? Ask Participants. (to make 7, Use a previous number set to help them? To use a previous set to help, as a teacher you need to be deliberate about the numbers chosen.)

26. 45 Minute Lunch
11:30-12:15

27. Video using a Rekenrek in a Number Talk
Number Talks K.2 Rekenreks
Pg. 7
Composing & Decomposing Number multiple ways
Guess My Way game
12:15-12:25 Everyone hold up your Rekenrek.
Video on Number Talk using a Rekenrek. She has a Rekenrek “to die for.”
Turn to page 7 in Handout. Read the reflection questions. As you watch the video, be thinking about these questions. Also, after the video, you will be practicing a 5 minute Number Talk with a Rekenrek so be thinking about key components of a Number Talk to include.
She does an activity of “Guess my Way”
Stop video after “2 on top and 2 on bottom.” Ask: What is her goal? Composing and decomposing. So what is she doing? Is she composing or decomposing and why do you think that? (have participants share – she starts with 4. Now make 4 a different way (decomposing). If they started with 4 and were asked to make 8, that would be composing.
Part II: Guess My Way (Kids try to decompose 6 to find out how she decomposed it.)
Note what she said to kids that didn’t have 6? That didn’t have her way?
Feel good? Feel like you can do this?

28. Video reflection
Pg. 7
How does the Rekenrek warm-up with 4 and 6 provide the teacher with information to guide her instructional decisions?
When does the teacher tell or show information to students and when does she provide opportunities for them to make sense of the mathematics?
How is this similar to or different than your math instruction?
Are there number combinations that seem more accessible to the students? How does the teacher build on this foundation?
12:25-12:35
In groups, reflect on these questions.

29. Your Turn
12:35

30. Practicing with Rekenreks
1. Letter and number off.
2. Go off with “like letters” and plan your 5
Minute Rekenrek number talk.
12:35-12:40 Numbering and Lettering Off
“Letter off” A, B, C, D
After each D, number the group – give one handout to divide among that group
Go off with LIKE LETTERS and plan your Rekenrek number talk
12:40-1:00 Planning Time with Like Letters. Tell them they have minutes to plan.

31. 5 Minute Number Talk Rotations
Return to your Number Group space.
Timer
1:00-1:25
RETURN to your NUMBER GROUP space.
Go through each Rekenrek experience, allowing 5 minutes per “letter”
Do not start until I tell you to. “On mark, get set, go” Display timer. 5 minutes/person
Remind participants to tell their group if they will need their Rekenreks or not
Timer beeps at end of each 5 minutes. Do not start the next one until the timer goes off.
Hand out the whole set A-D of problems at end.

32. Key Components of a Number Talk
Talk in your Groups. Write down a few key components you don’t want to forget.
Pg. 8
1:25-1:37
One goal is to honor children’s thinking. With that said, the idea of the beadrack is to move beyond counting by ones. Move with one push.
Many people asked about the most efficient strategy. Christina mentioned that you wouldn’t do this on the first day but eventually you want kids to start thinking about efficiency.
Pg. 8 Key Components of a Number Talk (Terry wrote the following on his iPad. You could write on chart paper.)
Making connections
Not just looking for answers
Atmosphere for all answers
Mixed levels (having all counters in a group won’t be as productive)
Wait time
Letting them use their own words
More than one way to solve/multiple strategies
Clear goals
Terry emphasized reading pages in the Kathy Richardson book. If you haven’t already read it, read it and if you have, read it again.
Be ready to share out.

33. Four Procedures and Expectations Essential to Number Talks (from Number Talks by Sherry Parrish)
Pg. 8
Select a designated location that allows you to maintain close proximity to your students for informal observations and interactions.
Provide appropriate wait time for the majority of students to access the problem.
Accept, respect, and consider all answers.
Encourage student communication throughout the number talk.
1:37-1:40
Note: These are fly-ins on PPT. Click to bring in next bullet.

34. Some Large-Sized Rekenreks
Before we leave Rekenreks, here are a couple ideas for large class ones.

35. 10 Rows of 10

36. Tens Frames Math Learning Center Online Tens Frames Pg. 9 1:40-1:45
Goal: I can use ten-frames and Rekenreks to carry out number talks with my students.
Please put 5 on your ten frame (just with a pen or cubes)
Terry showed some examples via iPad. Could use the Tens Frame app online to show participants’ work too.
Please change yours to show 7. Showed examples. Terry looks to see if they wipe out all cubes and start over or do they just add two to it.
Change it to have just 2 on it. Change to have 9 on it. How many people counted 7 more? How many people just put on until there was 1 missing?

37. Kindergarten Number Talk: A
1:45-1:50 (slides 37-39)
Model a 5 minute Number Talk for Kindergarten. Maybe not have them look at page 10 or they won’t have the quick image experience.
Ask: How many dots do you see? How do you see them?”
Record equations.
Ask for a couple volunteers. Record thoughts next to the picture or on chart paper or whiteboard if not possible to do it iPad style. For K, you can decide whether or not to add the symbols in.
Any connections on how student A thought about it from Student B?

38. Kindergarten Number Talk: B
Go onto next one.
Terry highlighted the math center app and showed it a little bit and that you can change color.

39. Kindergarten Number Talk: C
What did you see? How did you see it? How many altogether? Any other way to see it? Record equations.
Someone might say there were 2 missing in all 3. The goal of this math talk is ways to make 8.
There are some double tens frames for first grade. Go to next page. If no time to do Grade 1, reference them to page 10 of handout.

40. Grade 1 Number Talk: A
1:50-1:55 (If time. Or, you might do Grade 1 instead of K.)
How many do you see?
How do you see them?
Record equations.
You can use this slide and the next two to model Quick Flash. You need to click to appear, click to disappear, and click to reappear.

41. Grade 1 Number Talk: B How many do you see? How do you see them?
Record equations.
Any connections on how student A thought about it from Student B?

42. Grade 1 Number Talk: C How many do you see? How do you see them?
Record equations.
Any connections on how student A thought about it from Student B?
Reference page 10 of handout if haven’t already.

43. Rekenreks or Ten-Frames?
Compare and Contrast these tools in how they support students learning to compose and decompose numbers.
1:55-2:05
5 minutes to talk at tables
5 minutes to share out

44. 10 Minute Break
2:05-2:15

45. Grade 2 Number Talk: Making 10s Using Number Sentences
8+2
8+5
8+4
8+7
Teacher Goal: Making Tens
Anticipate what students will share.
Show sentences one at a time.
Plan how you will record their thinking.
2:15-2:20
Model Number Talk for these problems. They will fly in one at a time upon clicking when using the PPT. Perhaps record on chart paper or white board.
Goals:
I can help my students compose and decompose numbers.
I can describe several strategies that children use to derive addition facts.
I can describe the pre-requisite strategies that children need to use a “make ten” strategy when adding whole numbers.
Three minutes for this math talk. Terry modeled the math talk on page 11 for the 40+4 problem set.
Why is it 44 and not 80, for example?
39+4 = ? How did you do this? Terry recorded. 39+1=>40+3=>43, since 40+4 is 44, I know that 39 is 1 less than 40 so the answer is 43. Or, 30+(9+4)=>30+13=>43
39+15=? Didn’t have time for this one.
39+39=?

46. Grade 2 Number Talk: Looking for Landmark or Friendly Numbers Using Number Sentences
40+4
39+4
39+15
39+39
Teacher Goal: Looking for Landmark or Friendly Numbers
Anticipate what students will share.
Show sentences one at a time.
Plan how you will record their thinking.
2:20-2:25
Reference Page 11 of handout if not already. Might want to do this after the flashing activities.

47. Composing and Decomposing Using a Tens Frame
Pg. 12
In training session we did not have time to do this activity with the tens frame but point out that one could do the same activity that we did on the Rekenrek earlier but with a Ten Frame. In addition to the Quick Images activities, like we practiced earlier, one could also do composing and decomposing activities like those listed on page 12 of the handout.

48. Video: Number Talk Number Talks 2.1 Adding Numbers
Pg. 14
Number Talks 2.1 Adding Numbers
What do you notice about the teacher’s recordings of student thinking?
What else do you want to remember?
2:25-2:30 Video (4 min. 40 sec video)
2:30-2:35 Table reflections on the 2 questions
2:35-2:40 Share out whole group.
What did you notice?
She accepted all answers.
It was hard when they were explaining their thinking but the dots weren’t moved around so it was hard to picture. They should have been able to come up and move them around. (But, is there a reason why she maybe didn’t have them do this?)
She brings out doubles and make 10s (This is a culminating activity that brings together what they have been working on.)

49. Planning a 5 Minute Number Talk
Use the Critical Learning Phases on pp for ideas.
What Math Talk would you craft for your students, using a single or double ten-frame, Rekenrek, or number sentences?
Pg. 15
Bring each time

50. Planning a 5 Minute Number Talk
Pg. 13
Use the same groups as earlier.
Using pg. 13…
Draw a picture of what you would show to your students.
Brainstorm a series of questions you want to ask.
Predict number sentences you think will come up.
2:40-2:50 Plan a Number Talk
Go to same groups and see what happens (a couple people had to leave). Bring rekenreks, ten frames, cubes)

51. 5 Minute Number Talk Rotations
Return to your Number Group space.
Timer
2:50-3:10
Give 5 Minute Number Talks
For time efficiency, plan with same letters A, B. C, D as before and share with same number group.
Do not start the next one until the timer goes off.

52. “Make-a-10” for Addition Strategy
Pg. 16
3 Pre-requisites to use a make-a-ten
strategy effectively
They must…
Know what 2-digit number combinations equal 10 (e.g. 9+1, 8+2, etc.)
Be able to break numbers apart into any of its two addends (e.g. 8=5+3 so that when they do 8+7 they can then do 5+3+7=5+10=15)
Know 10+single digits and beyond (e.g. 10+7=17)
(from Fuson Ch. 6 in Research Companion pg. 74)
3:10-3:15
Goal:
I can describe the pre-requisite strategies that children need to use a “make ten” strategy when adding whole numbers.
If time, might want to have them brainstorm what they think they are before talking about them. If doing this, wait on showing this slide as it has the page number to refer to on it.
According to Fuson, there are 3 things kids need to know in order to find making 10 helpful
Break up ten (they need to know all the ways to make 10. it takes a long time to learn this. They won’t learn it in 2 days.)
They have to be able to break apart numbers into at least 2-digits
They need to know how to add 10 to a number. They need to see 10 as one thing and as ten things. Base 10 isn’t always helpful because they can’ break them apart. They have to exchange and that is difficult for kids to understand when they can’t physcially break apart the ten they have.
Questions?

53. Math Learning Center =>Bridges=>Resources=>Free Apps
Rekenreks
Ten Frames
Number Lines
Math Learning Center =>Bridges=>Resources=>Free Apps
3:15-3:30 Start closing
Be sure they put in .org or add Bridges or Portland OR to their search term as there are hundreds of math learning centers nowadays.

54. 2 Resources to Pick Up CEU sheet
Classroom Conversation A Handout for PLC Meeting 1

55. PLC Calendar Day 1: Number Sense → 3 PLC Meetings
Day 2: Addition → 3 PLC Meetings
Day 3: Subtraction → 3 PLC Meetings
Day 4: Multiplication/Division → 3 PLC Meetings
Day 5: Place Value

56. 3 PLCs #1. Classroom Conversation A #2. Interview
Handout
Use dot cards or own word problems
#2. Interview
Will be posted online in Region 11 folder. Work with 2 students, individually or as a pair
You might want to interview the same 2 students from last time if wanting to follow them all year.
#3. Classroom Conversation B
Will be posted online in Region 11 folder.
#1: Classroom conversation
#2: Interview posted online
#3: Posted online using the book Snowmen at Night

57. Bring Artifacts to PLCs
Teacher notes, photos, or videos from a verbal discussion, students acting out problems, or using manipulatives
Chart paper, photo or video showing a record of student thinking & strategies
Written student work

58. Goals
Goals
Pg. 1
I can use ten-frames and Rekenreks to carry out number talks with my students
I can help my students compose and decompose numbers
I can describe several strategies that children use to derive addition facts
I can describe the pre-requisite strategies that children need to use a “make ten” strategy when adding whole numbers.
Handout or go back to page 1 of your handout.
Rate 1-5 how they feel about each of the following statements. Read through them and rate yourself. Leave on tables.

59. See you in January.
Have wonderful teaching days in November & December and a GREAT winter break!