1. Lucky Shopper Subtraction
For this activity you’ll need play money of one $1000 bill, ten $100 bills, ten $10 bills, and ten $1 bills.
And you’ll need three items (things you have on hand (that they would like and you can part with) not already included in the course materials with price tags of $799, $628, and $557, one of which will be purchased by the winner (the “lucky shopper).
This activity is intended to show participants the ridiculousness of requiring trades when subtracting.
Put a play $1000 bill where one person can find it (or draw one name and give that person the $1000 bill reward).
Then, compel that person to make a purchase from your store.
Now, you become somewhat unreasonable as you mandate the traditional algorithm of subtracting ones first.
Once the person has made the selection and hands you the $1000 bill, say you have to subtract the ones first, but there aren’t enough ones.
Suggest you could trade the thousand for hundreds and then trade a hundred for tens and trade a ten for ones. Then make them pay the ones amount first, then the tens, then the hundreds.
To reinforce the confusion, ask the participant to tell you how much they have in bills after each trade (a subtle nod to confusion about the bills/positional place value rather than the amount of money involved).
Explain that counting up to make change is a more typical real-life method than making trades when no calculator is available.

2. Mental Strategies
Last time, we learned that the topic of “place value” extends beyond positional place value. True understanding of place value is in the application of using what you know about the value/ quantity of all parts of a number within a mathematical context.
Just a brief transition slide to remind teachers of the importance of mental math and developing strategies based on quantity.

3. Why Mental Math?
In your red book, briefly review the section “Mental Computation as Relational Thinking” (page 102)
The purpose of these next few slides is for teachers to focus on WHY mental math is important. This is a time to step back and really consider the question of what mathematical experiences will provide strong foundations for students’ future success in math. You may have some teachers who see their job as “prepare kids for ___ test” (perhaps state tests or ACT) and therefore may think they are better off teaching kids whatever pencil/paper procedures they might need. Hopefully this discussion will provide an opportunity to motivate why we believe doing mental math creates strong foundations.
It begins by having teachers review a short section from their Red book reading. You can structure the actual discussion in a variety of ways. You might facilitate a full group discussion. You might have teachers find a partner and use a think/pair format. You might have them switch partners a few times during the discussion – perhaps discussing the same question with more than one partner. The next few slides have various questions to prompt discussion.

4. Why Mental Math?
How does mental computation connect to relational thinking?
Why are mental computation and relational thinking important?
How do mental computation and relational thinking relate to the Common Core Standards?
Here are some questions that will (hopefully) prompt some discussion about the purpose of mental computation.

5. Why Mental Math?
How does mental math prepare students for the mathematics they will do later in life?
How do the instructional activities and manipulatives discussed so far support the development of mental strategies. How does this approach differ from “traditional” methods.
Hopefully there will be some discussion here regarding the use of manipulatives that bring out “structure” support kids in forming the number relationships that are the basis for doing mental math. The big idea of “distancing the setting” might also be discussed here.

6. Standards for Mathematical Practice
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Link to standards
This hidden slide is provided to support connections between mental math and the CCSSI. The link provided is to the PDF of the entire CCSSI and is another way to support a discussion of how mental math connects to the CCSSI

7. Why Mental Math?
Video from Australian Math eduation Research Council
video

8. Mental Strategies 124+73 100-83 329+19 143-39 270-171
This is offered as alternatives to the 4 in a row strategy game.
There are several options here. You can facilitate a traditional number talk with these expressions. Alternatively, you could do a “strategy carousel”, where teachers rotate in groups of 2-3 teachers among the strategy posters. At a poster, the group will pick one of these expressions (or one of their own creation) and record solving the task with the strategy indicated.

9. Cups O’ Gold Visit each game station as we gather.
Participants will rotate through playing the Cups O’ Gold activity stations.
KNP task group T5513
Resume with a reflective discussion on the various tasks and teacher thoughts on how and when to use each.

10. Cup O’ Gold KNP Number Materials T 5513.0
Arrow cards (ones and tens), portion cups and counters T
Arrow cards (ones and tens), portion cups (20) and counters, writing space T
Arrow cards* (ones and tens), portion cups (20 ) and counters, writing space T
Arrow cards* (ones and tens), writing space T
Have participants play Cups o’ Gold. Either have games ready OR have participants make own and then play. Each leader was provided with gold base 10 unit cubes for use with this activity.
KNP task group T5513
Resume with a reflective discussion on the various tasks and teacher thoughts on how and when to use each.
Use Arrow Cards provided yesterday. If you prefer to have a set in each folder, use master provided on Marti website.
* When students are ready, place value dice may be used in place of arrow cards. Note that place value dice provide less support than arrow cards.

11. Representational (Figurative)
CRA
Concrete
Representational (Figurative)
Abstract (Symbolic)
This slide has animations. It begins with the theory of CRA (or CPA) that is likely to be familiar to most teachers.
The animations bring in the extra idea offered by Mary Hynes-Berry during her keynote talk at KCM (2013) – i.e. that students must also be able to take a symbolic/abstract idea and be able to illustrate it with the concrete. For example, a child that fully understands the concept of multiplication, should be able to take the symbolic expression (6x3) and show 6 groups of 3 with objects (or be able to tell a story problem or be able to draw a picture or…)

12. Settings and Situations
Introduce this chart from the appendix of the standards.

13. Problem Situations
Write a problem situation of your assigned type in the range 101 to 1000.
Be prepared to model how your problem might be solved at your assigned CRA level. Feel free to use any materials from our morning activities.
As each person share’s his/her word problem and models a method of solving, everyone will determine
The problems location on the chart
The solutions CRA level
Distribute the CCSSM Situations for Addition and Subtraction.
Give each teacher one assignment strip. Each strip assigns one problem situation, gives the example from the chart and assigns a CRA level for solving. Note - the first 4 pages of strips give the 15 basic types from the chart. The next two pages are included are repeats (but with different CRA levels) in case you have more than 15 teachers in your group. If you have less than 15, either omit or give strips to early finishers and ask them to prepare 2. Teachers will write a story problem in the range AND prepare to model a solution for the assigned CRA level. The strips are numbered in a way that will work for a sharing order.

14. Settings and Situations
This slide can be left up as teachers share their examples and the group discusses the appropriate placement. However, you might prefer to go to a document camera for easier sharing.

15. Table 2: Recommendations1.
Screen all students to identify those at risk for potential mathematics difficulties and provide interventions to students identified as at risk. (Tier 1)
Recommendation 2-8 are for tiers 2-3 2.
Instructional materials for students receiving interventions should focus intensely on in-depth treatment of whole numbers in kindergarten through grade 5 and on rational numbers in grades 4 through 8. These materials should be selected by committee. 3.
Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review. 4.
Interventions should include instruction on solving word problems that is based on common underlying structures. 5.
Intervention materials should include opportunities for students to work with visual representations of mathematical ideas and interventionists should be proficient in the use of visual representations of mathematical ideas. 6.
Interventions at all grade levels should devote about 10 minutes in each session to building fluent retrieval of basic arithmetic facts. 7.
Monitor the progress of students receiving supplemental instruction and other students who are at risk. 8.
Include motivational strategies in tier 2 and tier 3 interventions.
Reminder to link back to IES recommendations. Highlight #4 - word problems. Also ask how CRA thinking relates to other Recommendations. For example, #5.
Source: Authors’ compilation based on analysis described in text.

16. Van De Walle Differentiated Instructions
Differentiated Tasks - Parallel Tasks (46-48)
Differentiated Tasks - Open Questions (48-49)
Learning Centers (49-50)
Tiered Lessons (50-53)
Flexible Grouping (53-54)
There are a variety of ways to let teachers discuss the Van de Walle reading. For example, you might have use the “seed discussion” format from session 1. You might debrief full group and ask some open questions. Feel free to handle this however you like.
One option is to divide teachers into groups, assigning each group one of the above ways to differentiate. Give them a few minutes to review the reading and discussion – then ask each person to share full group the basic idea, an example if appropriate and something they found interesting or surprising or they have a question about.

17. Explore the sections in this book.
What connections do you see to other ideas and activities previously discussed?
Some connections –
Section A “Around the Circle” is similar to Count Around.
Section B introduces Open Number Line. However, it uses a snap cube train initially to provide structure. Section C removes the snap cube train (distancing the setting)

18. Problem String Example
Demonstrate a number talk utilizing a problem string from “Extending Addition and Subtraction” text

19. Now it’s your turn!
You will be given a set of problem strings to read through.
You will choose one of the problem strings, and lead all of us in a number talk using the string.

20. Reflect
What are some important “teacher” actions to remember when leading students in a number talk?
Have teachers share some strategies they know of managing and encouraging math talk

21. Talk Moves
This teachers shares some of her favorite strategies including “revoicing” – having a student repeat what is said, Showing agreement through hand signals, adding on (i.e one student can add to what another says). She also talks about the process of kids changing their minds as they get new information. This video compements a video about using number strings to explore division – we will use that video in days 6-10.
Could link here to the specific recommendations from Math Solutions.