Vacaville USD December 8, 2014 KINDERGARTEN Session 2 Vacaville USD December 8, 2014

AGENDA Problem Solving and Patterns Math Practice Standards and High Leverage Instructional Practices Number Talks Dot Patterns, Ten Frames, and Rekenreks Word Problems Comparing Numbers Addition

Expectations We are each responsible for our own learning and for the learning of the group. We respect each others learning styles and work together to make this time successful for everyone. We value the opinions and knowledge of all participants.

Cubes in a Line How many face units (squares) can you see when cubes are put together?

Cubes in a Row How many squares do you see on 1 cube?

Cubes in a Row How many squares do you see on 2 cubes?

Cubes in a Row You are going to be given 2 strips of paper like this: _____________ _____________ number of cubes number of face units 7

Cubes in a Row What patterns do you see? How could those patterns help you figure out how many squares you would see?

Hundred’s Charts What if we recorded the data on a hundred’s chart? What patterns might Kindergarten students notice?

Cubes in a Row How many squares do you see on 1 cube? Let’s mark that on a hundred’s chart.

Cubes in a Row How many squares do you see on 2 cubes? Let’s mark that on a hundred’s chart. How can you keep track of what sides you have counted?

Math Practice Standards Remember the 8 Standards for Mathematical Practice

CCSS Mathematical Practices REASONING AND EXPLAINING Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Make sense of problems and persevere in solving them OVERARCHING HABITS OF MIND Attend to precision MODELING AND USING TOOLS Model with mathematics Use appropriate tools strategically SEEING STRUCTURE AND GENERALIZING Look for and make use of structure Look for and express regularity in repeated reasoning

High Leverage Instructional Practices

High-Leverage Mathematics Instructional Practices An instructional emphasis that approaches mathematics learning as problem solving. Make sense of problems and persevere in solving them.

An instructional emphasis on cognitively demanding conceptual tasks that encourages all students to remain engaged in the task without watering down the expectation level (maintaining cognitive demand) Make sense of problems and persevere in solving them.

Instruction that places the highest value on student understanding Make sense of problems and persevere in solving them. Reason abstractly and quantitatively

Instruction that emphasizes the discussion of alternative strategies Construct viable arguments and critique the reasoning of others

Instruction that includes extensive mathematics discussion (math talk) generated through effective teacher questioning Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning

Teacher and student explanations to support strategies and conjectures Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others

The use of multiple representations Make sense of problems and persevere in solving them. Model with mathematics Use appropriate tools strategically

Number Talks

What is a Number Talk? Also called Math Talks A strategy for helping students develop a deeper understanding of mathematics Learn to reason quantitatively Develop number sense Check for reasonableness Number Talks by Sherry Parrish

What is Number Talk? A pivotal vehicle for developing efficient, flexible, and accurate computation strategies that build upon key foundational ideas of mathematics such as Composition and decomposition of numbers Our system of tens The application of properties

Key Components Classroom environment/community Classroom discussions Teacher’s role Mental math Purposeful computation problems

Classroom Discussions What are the benefits of sharing and discussing computation strategies?

K.1 – Kindergarten Number Talk using ten frames and dot cards Think about the following questions as you watch.

How does the teacher build students’ fluency with small numbers? What questions does the teacher pose to build understanding? What strategies are the students using to build meaning of the numbers? How does the teacher support student communication during the number talk?

K.2 – Kindergarten Number Talk Using Rekenreks Think about the following questions as you watch.

What instructional strategies does the teacher use to engage the students? How does the teacher use rekenreks as a tool to build fluency with small numbers? What role does the game “Can You Guess My Way?” play on the number talk? What mathematical understandings and misconceptions are being addressed?

Do you see evidence of students demonstrating: Developing number sense Developing fluency with small numbers Subitizing Making tens

Tools for Solving Problems Counters Ten-frames Rekenreks Number Line / Hundred’s Chart

Solving Word Problems

3 Benefits of Real Life Contents Engages students in mathematics that is relevant to them Attaches meaning to numbers Helps students access the mathematics.

Word Problems Concrete Representational Abstract ACT IT OUT!!! Draw a model 1 to 1 representation Bar or scaled representation Abstract Write a number sentence Use a strategy

Practice Problems How could students act out these problems using manipulatives? How could students begin to record (draw) the process of solving these problems?

Numbers, Bears, and Beds Do you remember the song about 10 little monkeys jumping on the bed?

Numbers, Bears, and Beds Well, my story is about bears jumping on the bed.

Comparing, Bears, and Beds I see 4 bears on the bed and 1 bear on the floor. Are there more bears on the bed or on the floor?

Comparing, Bears, and Beds On the bed. How do you know?

Comparing, Bears, and Beds

Addition, Bears, and Beds I see 4 bears on the bed and 1 bear on the floor. How many bears are there?

Addition, Bears, and Beds How many bears are there? 5

Addition, Bears, and Beds What addition sentence could I write? 4 + 1 = 5

2 + 1 = 3

Addition

Addition, Bears, and Beds Now I am going to give you an addition problem. I want you to build it using the beds and bears, draw a model of what you built (using a dot for each bear), and write the answer.

3 + 1 = ____ 4

3 + 1 = ____ 4    

Addition Strategies So what strategies did we just use? What other strategies could we use? What strategies do we want to encourage?