Friday, Jun 24, 2016 AM Strong Start Math Project

Agenda Team Work Time Intro to Part-Part-Whole Part-Part-Whole Activities PRR: Van de Walle Article Summary and Reflection Lunch Mathematical Curiosity: Roll Over 16 Subitizing Trajectory Intro Individual Project

Learning Targets We are learning to … Understand how early number concepts develop in Grades K-3. Scaffold experiences for K-3 children that develop a solid understanding of number that will lead to basic fact fluency. Connect early number concept development to CCSSM expectations.

K.OA.3 & K.OA.4

K.OA.3 & K.OA.4 K.OA.3. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). K.OA.4. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

What do you notice about the examples in K.OA.3? What is the difference between these two standards? What is a student thinking when they are working on each one? What might they model? What might they sound like? Write a word problem that would go with each standard

Salute! 3 players sit in a triangle. Two players are 'saluters' and the third is the 'caller.' The two Saluters each grab a card without looking and flip it up to their foreheads. The Caller calls out the sum of the cards. The first Saluter that can figure out their own card gets to take the cards.

Debrief Salute! Start a Games Protocol – we will keep working on this all morning. What math skills do you see at work in Salute? What questions are you wondering about concerning Equitable Engagement and Access?

Part part whole

The Importance of Part-Whole Understanding It is not unusual to find children in second grade who have not developed firm part-whole understanding for numbers 7 through 12 even though by that time they should be adding up to 100. ---Van de Walle, Lovin, Karp, & Bay-Williams, p. 113, 2014

Four Types of Number Relationships Work with 3-5 year olds can focus on helping children construct these 4 relationships once early counting is starting to take root. Review hand-out and summarize what each means.

Part-Whole Relationships Quantities represented by numbers can be decomposed into part-whole relationships. The ability to think about a number in terms of parts is a major milestone in the development of number sense. Of the four number relationships, part-whole ideas are easily the most important! As you are working on part-whole, choose a particular number and focus on it. Spend some time getting to know that number. Use the counters on the table to find all of the different ways the number 9 can be broken into two parts.

Covered Parts Turn over a number card. Together, count out that many counters. Partner 1 hides some of the counters under the tagboard and places the remaining counters in view. Partner 2 counts the counters in view and uses tools to find out how many are under the tagboard. Partner 2 states “I see 2 counters. There are 4 counters hiding. There are 6 counters altogether. Switch roles and repeat!

Try playing the game using each of the tools. Debrief Covered Parts Add the name and description to your Games Protocol. What Foundational Math Concepts have we worked on so far? If a student is struggling, what visual models will you bring in to help them? Try playing the game using each of the tools.

360° How does this build on the other Number Relationships? How is this a step further than Anchoring to 5 or 10? How does this prepare students for addition and subtraction?

Four Types of Number Relationships Work with 3-5 year olds can focus on helping children construct these 4 relationships once early counting is starting to take root. Review hand-out and summarize what each means.

Number Sense “…the ability to work flexibly with numbers, decomposing and regrouping them with confidence, is so critical to young children that it is known to separate high achievers from low achievers in mathematics.” --Jo Boaler (2012). Timed testing and the development of math anxiety. Interacting with numbers flexibly Mathematically confident because the understand numbers

PRR: Van de Walle Read the Intro and Conclusion. Imagine that you are talking with a colleague about your experiences this summer with the Four Number Relationships. Begin to craft some key ideas that you want to share with them to help them see that we need to spend time on the Relationships before moving to operations.

Four Number Relationships for Quantities 1 through 10 K.OA.3 & K.OA.4 Addition and Subtraction Early Counting Subitzing Rote counting One-to-One Correspondence Cardinality Counting and Cardinality Standards Fluency Expectations K.OA.5 – up to 5 1.OA.6 – up to 10 2.OA.2 – up to 20

Morning Reflection/Summary Summarize some key points and classroom ideas related to the topics or focus standards in this session. Focus Topics or Standards Summary of Key Points Classroom Ideas to Try

CURIOSITY about operations with dice

Roll over 16 / Switch 16 Each player has a card deck numbered 1-16. The dice symbols on your top card indicate how many dice you roll. Goal: Be the first player to discard the 16th card from your deck by rolling the numbers needed on the dice. On your turn: Take the indicated number of dice and roll them. Then look to see if you can remove cards from your deck based on the dice rolled. You must roll a die or any combination of dice, equivalent to the card on the top of your deck in order to discard it. You may discard as many cards as you can, according to the roll of the dice, but they must be discarded in order. If your first roll of your turn cannot produce the needed number to match the card number on top of their deck, then your turn is over. Take a risk: When you cannot discard any more cards you may decide to roll the dice a second time, but if you fail to roll the number showing on your top card, your turn is over and the penalty is as follows: If the top card is between 2 and 8 you must return all cards to the deck and start again from number 1. If the top card is between 9 and 16 you must return cards to the deck only back to the MILESTONE card number 8.

Roll over 16 / Switch 16 EXAMPLE 1: Your top card is 1, and you roll as above. You can remove: 1, 2, 3=1+2, but not 4, since you cannot make 4 from the numbers you rolled. Your remove 1,2,3 and can decide whether to take a risk, otherwise your turn is over. EXAMPLE 2: Your top card is 6, and you roll as above. You can remove: 6, 7=6+1 or 5+2, 8=6+2 or 5+2+1, 9=6+2+1, but not 10, since you cannot make 10 from the numbers you rolled. Complete rules and variations: http://www.boardgamecapital.com/switch-16-rules.htm

Curiosity Think about the relationship of your dice to the number you were attempting to roll. What numbers do you want to roll? How does the number of dice relate to the number you are trying to roll? What are you curious about?

Trajectories

Counting Trajectory: Another Look Pass 1: Locate the levels that address the milestones to counting: rote counting, one-to-one correspondence, cardinality. Jot notes in the last column. Pass 2: Make connections to the Counting and Cardinality Standards. (K.CC.1, K.CC.2, K.CC.4, K. CC.5) Jot notes in the last column.

Subitizing Trajectory Sort the cards according how student’s understanding of subitizing will grow. Identify where you see Perceptual and Conceptual Subitizing.

Afternoon Reflection/Summary Summarize some key points and classroom ideas related to the topics or focus standards in this session. Focus Topics or Standards Summary of Key Points Classroom Ideas to Try

Individual project

Individual Project Focus on a standard. Ground that standard by describing it fully, giving examples, and connecting it to the learning trajectories. Create a CORE Assessment (with 3 items) and anticipate responses. Connect it to skills, knowledge and instructional tasks. Create a FOLLOW-UP Assessment for successful students and a FOLLOW-UP Assessment for struggling students. Make the same connections.

Strong Start Math Project University of Wisconsin-Milwaukee, 2015-2018 Disclaimer Strong Start Math Project University of Wisconsin-Milwaukee, 2015-2018   This material was developed for the Strong Start Math project through the University of Wisconsin-Milwaukee, Center for Mathematics and Science Education Research (CMSER). This material may be used by schools to support learning of teachers and staff provided appropriate attribution and acknowledgement of its source. Other use of this work without prior written permission is prohibited—including reproduction, modification, distribution, or re-publication and use by non-profit organizations and commercial vendors. This project was supported through a grant from the Wisconsin ESEA Title II, Part B, Mathematics and Science Partnerships.