FIRST GRADESession 2

Vacaville USD

December 5, 2014

AGENDA• Problem Solving and Patterns• Math Practice Standards and High Leverage

Instructional Practices• Number Talks

– Computation Strategies

• Word Problems• Addition and Subtraction Strategies

– Facts– Double digit plus single digit

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 can you see when cubes are put together?

Cubes in a Row

• How many face units do you see on 1 cube?

Cubes in a Row

• How many face units do you see on 2 cubes?

• How can you keep track of what sides you have counted?

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 face units there would be?

Math Practice Standards

• Remember the 8 Standards for Mathematical Practice

• Which of those standards would be addressed by using a problem such as this?

CCSS Mathematical PracticesO

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nREASONING AND EXPLAINING2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others

MODELING AND USING TOOLS4. Model with mathematics5. Use appropriate tools strategically

SEEING STRUCTURE AND GENERALIZING7. Look for and make use of structure8. 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.

1. 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)

1. Make sense of problems and persevere

in solving them.

Instruction that places the highest value on student understanding

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively

Instruction that emphasizes the discussion of alternative strategies

3. Construct viable arguments and critique the reasoning of others

Instruction that includes extensive mathematics discussion (math talk) generated through effective teacher questioning 2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of others

6. Attend to precision

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

Teacher and student explanations to support strategies and conjectures

2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of others

The use of multiple representations

1. Make sense of problems and persevere in solving them.

4. Model with mathematics

5. 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?

• Students have the opportunity to:– Clarify their own thinking– Consider and test other strategies to see if

they are mathematically logical– Investigate and apply mathematical

relationships– Build a repertoire of efficient strategies– Make decisions about choosing efficient

strategies for specific problems

4 Goals for K-2 Classrooms

• Developing number sense• Developing fluency with small numbers• Subitizing• Making tens

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?

Clip 2.1 – 2nd Grade

Addition: 8 + 6 (using 10-frames)• Before we watch the clip, talk at your

tables–What possible student strategies might

you see?–How might you record them?

• What role do the 10-frames play in developing fluency with small numbers?

• What questions does the teacher use to build understanding about composing and decomposing numbers?

• How does the use of double 10-frames support the goal of K-2 number talks?

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

– ACT IT OUT!!!• Representational

– Draw a model • 1 to 1 representation• Bar or scaled representation

• Abstract– Write a number sentence– Use a strategy

Word Problems

• Practice problems

Math Facts

Tools• Ten frames• Rekenreks• Number lines• Ten sticks / counters

Math Facts

Strategies• Counting all / Counting On• Doubles / Doubles +/- 1• Making tens• Using known facts

Developing Strategies

• We are going to give you a series of problems (number talks) designed to promote specific strategies

• With a partner– Solve each problems using all of the tools– Decide which tool or tools best support

students in understanding and developing that strategy

1st Grade Number Talks

• Start with visuals and move to symbolic

Counting All / Counting On A

Counting All / Counting On B

Counting All / Counting On C

Counting All / Counting On

• 6 + 3

• 6 + 5

• 6 + 7

Doubles/Near Doubles

Doubles/Near Doubles A

Doubles/Near Doubles B

Doubles/Near Doubles C

Doubles/Near Doubles

• 4 + 4

• 4 + 3

• 3 + 3

• 3 + 4

Making Tens

Making Tens A

Making Tens B

Making Tens C

Making Tens A

• 9 + 1

• 9 + 3 + 1

• 9 + 5 + 1

Making Tens B

• 8 + 2

• 8 + 2 + 4

• 8 + 6

Making Tens C

• 7 + 3

• 7 + 5

• 7 + 8

Making Friendly Numbers A

• 8 + 2

• 8 + 6

• 8 + 5

Making Friendly Numbers B

• 6 + 6

• 9 + 6

• 9 + 8

Additional Tools

• Hundreds Chart

Extending Friendly Numbers A

• 4 + 3

• 14 + 3

• 34 + 3

Extending Friendly Numbers B

• 6 + 8

• 26 + 8

• 56 + 8

Extending Friendly Numbers C

• 4 + 5

• 40 + 50

• 46 + 50

Extending Friendly Numbers D

• 6 + 2

• 60 + 20

• 63 + 20