STRONG START Thursday, June 23, 2016 Morning

Agenda Game Protocol: Dice Tasks Early Number Relationships: Subitizing Break Early Number Relationships: 1 More/1 Less Lunch Early Number Relationships: Anchors to 5 and 10 Rekenreks Intro to Team Projects

Dice Tasks From Day 3 Debriefing

Game Protocol Mathematical Curiosities Foundational Math Concepts Math Skill Purposeful Questions for Skills Equitable Engagement and Access Best Use 15 min Debrief Racing Bears with game protocol

Learning Targets

Learning Targets We are learning to … Understand how early number concepts develop in Grades K-2. Scaffold experiences for K-2 children that develop a solid understanding of number that will lead to basic fact fluency. Connect early number concept development to CCSSM expectations.

Dot Patterns

Dot Pattern

Find the Same Amount Lay the cards out face up. Pick one card in the collection. Find another card with the same amount. Tell how you know they are the same. Take turns and continue finding pairs.

Debrief of Find the Same Amounts Imagine you are watching your students play each game. What would success tell you about their mathematical understanding with Find the Same Amounts? What would struggles tell you about their mathematical understanding with Find the Same Amounts?

Through the Lens of the Math Content As you reflect on the use of the dot patterns, what do they help young child understand about numbers in relationship to the CCSSM standards? 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).

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.

360° Connection Looking Backward How does this idea relate to counting and cardinality? Looking Forward How does this idea relate to addition and subtraction?

Dot Pattern

Planning for Dot Pattern Describe in words and number the different ways someone may "see" each of your three dot patterns. Show how you will record each way.

YOUR TURN to practice (Groups of 2) Subitizing Practice YOUR TURN to practice (Groups of 2) Teacher flashes a Dot Pattern Card to your group for 3-5 seconds Teacher flashes the dot pattern another time for 3 seconds so student can make adjustments to their thinking Teacher asks students to explain how they saw the dot pattern Student explains how many dots they saw and how they saw them. Record the matching expression Teacher records student thinking on their white board. Make connections between their different ways of seeing the number

Professional Reading and Reflection

Beyond Counting by Ones Read “Beyond Counting By Ones: ‘Thinking in Groups’ as a Foundation for Number and Operation Sense” (Huinker, 2011). Write down how this reading clarified your understanding of subitizing and its importance for connecting counting with cardinality.

Focus Topics or Standards 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

Thursday, June 23, 2016 Afternoon STRONG START Thursday, June 23, 2016 Afternoon

Learning Targets We are learning to … Understand how early number concepts develop in Grades K-2. Scaffold experiences for K-2 children that develop a solid understanding of number that will lead to basic fact fluency. Connect early number concept development to CCSSM expectations.

1 or 2 MORE/Less

Connections Now, what if I space this a little differently Please memorize this eleven digit number​ 25811141720 Now, what if I space this a little differently 2 5 8 11 14 17 20 What pattern do you see? Now, please memorize this eleven digit number. When we learn facts, seeing relationships is critical!

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.

More than counting.. Requires students to reflect on they way that numbers are related to each other. Let’s take 4 and 6 for example. 6 is two more than 4 4 is two less than 6 Counting on is a useful tool to construct these ideas. We want students to understand where a number falls on the number line and its relationship to other numbers.

Make a 2 more set Grab a set of Dot Cards. Your task is to construct a set of counters that is two more than the set shown on the card. What connections can you make to solving addition and subtraction problems?

Hierarchical Inclusion If I have 7 of something, I also have 6, 5, 4… What would it look like if a student understood this idea? How would it cause issues if a student did not understand this idea?

Ladybug book Show this on the Number Path. What happens each time you turn a page? Which ladybug is the "Number 1" bug? When is that one there? https://www.youtube.com/watch?v=t8Yp0hTEK8E

Assessing this Relationship 10 frames – call out numbers and have students show you that many counters Intentionally start to call numbers that are 1 or 2 more and 1 or 2 less Watch who clears their board and who is able to add on or take away just the needed amount

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.

360° Connection Looking Backward How does this idea relate to counting and cardinality? Looking Forward How does this idea relate to addition and subtraction?

Benchmarks or Anchors to Five and Ten

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.

Anchoring to the Numbers 5 & 10 “Anchoring to 5” is the ability to understand the relationship of numbers specifically to the number 5. “Anchoring to 10” is the ability to understand the relationship of numbers specifically to the number 10.

Five Frame Place ____ on your frame. What can you tell me about the number? How many more do you need to get to 5? CCLM

Five Frame Place ____ on your frame. What can you tell me about the number? How many more do you need to get to 5? CCLM

How many do you see? How many more do you need to get to 5? What can you tell me about three? How many more do you need to get to 5?

How many do you see? How do you see them? How many more do you need to get to 5?

How many do you see? How do you see them? How many more do you need to get to 5?

Your turn! Anchoring Quantities to 5 Materials number cards: 6, 7, 8, 9 and a 5 frame Fill your 5 frame. Turn over a card. Add counters next to the five frame to show how many are on the number card. Discuss how each number is anchored to 5. Sentence frame: 8 is 3 more than 5; 5 is 3 less than 8 ____ is _____ more than 5; 5 is ___ less than ____. 8

Making Connections to Operations Teachers can write expressions like “2 + 3”and “4 + 1” to show the operation. “It is helpful for students to have experience just with the expression so they can conceptually chunk this part of the equation.” (OA Progressions, p. 8)

How many do you see? How do you see them? You were just anchoring quantities to 5!

Your turn! Anchoring Quantities to 5 Materials number cards: 6, 7, 8, 9 and a 5 frame Fill your 5 frame. Turn over a card. Add counters next to the five frame to show how many are on the number card. Discuss how each number is anchored to 5. Sentence frame: 8 is 3 more than 5; 5 is 3 less than 8 ____ is _____ more than 5; 5 is ___ less than ____. 8

Ten Frame

Extending Up to 10 How many dots do you see? How do you see them? How many more to 10? How do you know?

Extending Up to 10 How many dots do you see? How do you see them? How many more to 10? How do you know? https://www.youtube.com/watch?v=jOOJLSpeXVY

How many dots do see? How do you see them? How many more to 10? How do you know? State the pair numbers that make ten. How might we anchor these images back to 5?

Frames for Structuring Number Knowledge Five Frame K-3; K-4; K-5 Ten Frame K-4; K-5; Grade 1 Two Critical Ideas: Structure number knowledge with anchors to five and ten through the use of five and ten frames. Provide experiences that encourage students to look for and regularly use relationships among numbers to solve problems. Double Ten Frame Showing 8 + 6 Grade 1; Grade 2 Huinker (2012) Structuring Number Knowledge with Anchors to Five and Ten p. 5

The use of ten frames provides a visual tool that supports students in the mathematical practice to “look for and make use of structure” (MP7). The structure is knowledge of ten. This includes developing part-whole understanding of ten through its decompositions and its relationships to other numbers. Huinker, 2012, p. 7

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

PRR Huinker (20102): Structuring Number Knowledge with Anchors to Five and Ten Pull out 2-3 quotes that show the mathematical benefits of using five and ten frames in PK-2 classrooms and comment on them. Reflect on the power of visual representations in instruction that leads to fact fluency.

Rekenrek

What? Developed at the Freudenthal Institute in the Netherlands. Widely used in other countries to help students reason about numbers, subitize, build fluency, and compute using number relationships. Take a look at your rekenrek… What do you notice about its structure? Turn and share

Getting Acquainted Context is key -- story problem Vocabulary – be consistent Start position Beads “in play” or “working” Beads “out of play” or “at rest” All beads are “in play”

Getting Started With Rekenreks Show me!! Rekenrek Flash! Make and Match With numeral cards With five frames With ten frames With dot patterns

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.

Focus Topics or Standards 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

Team Projects

Team Project Administrator Information & Individual Strong Start Implementation Goals The purpose of this project is to begin a conversation on ways to strengthen your school’s mathematics program based on Strong Start Math learning.