Let’s Play! Conduct the CPV Introductory Activity with participants. This activity was developed by Becky Reister and her directions and notes are in Day 4 folder and below. You will need some paper play money (hundreds, tens, ones). Materials: play money (tens and ones, maybe some hundreds) Participants stand in a circle. Hold the play money behind your back (don’t let anyone see it). You set the stage with something like, “Okay, for this activity, we are all going to pretend that we are squirrels. When the weather starts getting colder, what do squirrels do? (gather acorns). Yes! So, in just a moment, I am going to scatter some things that we can pretend are acorns. You are going to be “squirrely” and gather as many as you can. When you are finished gathering, go back to your seat and count what you collected. Ready? (this is when you throw the tens and ones into the air) Participants go back to their seats, and count. Walk around and listen. Next, challenge them to figure out how much they have between partners/ table groups. Walk around. If anyone asks about making trades, then make that happen with extra bills you have. Call the group back together. Make it fun by finding out which table had the best squirrels.  Okay.. Here comes the math connection. Ask, “What was the first thing you did when you counted your collection” (sorted). Okay, then what did you do next? (counted the tens, then the ones). “Mmm.. Intresting. So with the materials, it was a natural process to sort, then start counting with the tens. (turn and write a traditional stacked algorithm on the board/ chart paper (something like 47 + 26). Well.. When student see problems like this in school, where do we tell them they need to start? (this is when many will have an amazed look on their face… “with the ones”) Why? Did you start with the ones with the money? With “stuff”, you sorted and started with the tens. With bare number tasks, it becomes a procedure “just because?” Let’s try to add these two numbers like we would if we were squirrels (add tens to 60, ones to 13, … 73).

What about 48? quantitative verbal symbolic “five” 5 Purpose – Remind teachers of the 3 aspects of number. Have them generate aspects of “48”. Bring out increased challenge for all aspects (i.e. naming “four” and “eight” but together it’s “forty eight”, symbol now has two parts and order matters, Quantity can be chunked as “4 tens and 8 ones”, 3 tens and 18 ones”, “4 tens, 1 five and 3 ones”, can be shown in many different settings. May hint at multilplicative structures now but not the focus (i.e. 2 groups of 24, 4 groups of 12, etc. Will revisit at beginning of MD unit). Numbers as conceptual and cultural entities possess three distinct components: verbal (i.e., four), numeral (i.e., 4), and quantity (i.e.,    ) (Wright 1994; Wright, Martland, and Stafford 2006), and neurological confirmation of these different aspects may be found in Dehaene’s (1992) triple-code model, which describes the location of neural activity as a function of number aspect. From the article on Page 177 verbal symbolic “five” 5

What IS Conceptual Place Value? “Thus, being able to flexibly increment and decrement by ones and tens, and later also by hundreds, is critical knowledge for developing facile mental computation. We refer to this critical knowledge as conceptual place value (CPV)”. Developing Number Knowledge, 2012. Wright, Robert J., Ellemor-Collins, David., and Tabor, Pam. Sage Publications. p 77

Vocabulary Incrementing – increase of some amount Decrementing – decrease of some amount Decuple – multiple of ten Decade – is ten items or counts 14……… 24………34………44……… 54

Strategy Carousel Divide into 3 groups. 27 + 35 65 – 39 49 + 49 Divide into 3 groups. Each group will start with one of the posters. The group will write down ways to solve the expression. Groups will rotate, each time discussing the methods recorded and adding to them. The time to rotate will be called by the facilitator. Prepare chart paper with the problems as headings. Larger cohorts may need to do 4 posters. If so, use next slide.

Number Talks! Problems: 52 + 37 57 + 35 62 - 21 73 - 29 Purpose: participants develop mental math strategies and learn some of the labels as given in the red book. Facilitate number talks modeling the ideas of the red book pages 100-107; use arrow notation to capture participants’ mental strategies. 45 minutes is scheduled for this. Feel free to add in additional addition & subtraction tasks. Your teachers will need to wear their “student” hat (i.e. solve math problems) and “teacher hat” (begin thinking about the names of these strategies and ways to record student thinking). You can also reverse the process by having them start with a strategy and think of problems that can be solved naturally using that process.

Name that Strategy! NZ math Video: 34-8 NZ math Video: 37+9

Second Grade Strategies Full video is available in the KCM video archives. Link to video