FOURTH GRADESession 2

Vacaville USD

October 30, 2014

AGENDA• Problem Solving, Patterns, Expressions and

Equations• Math Practice Standards and High Leverage

Instructional Practices• Number Talks

– Computation Strategies

• Multiplication and Division

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 faces (face units) are there when: 6 cubes are put together?

10 cubes are put together?

100 cubes are put together?

n cubes are put together?

Questions?

What do I mean by a “face unit”?

Do I count the faces I can’t see?

Cubes in a Line

How many faces (face units) are there when: 6 cubes are put together?

10 cubes are put together?

100 cubes are put together?

n cubes are put together?

Cubes in a Line

Cubes in a Line

Cubes in a Line

Cubes in a Line

Cubes in a Line

Cubes in a Line

We found several different number sentences that represent this problem.

• What has to be true about all of these number sentences?

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

CCSS Mathematical Practices1. Make sense of problems and persevere in

solving them.2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning

CCSS Mathematical Practices1. Make sense of problems and persevere in

solving them.2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning

• 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)

CCSS Mathematical Practices1. Make sense of problems and persevere in

solving them.2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning

CCSS Mathematical Practices1. Make sense of problems and persevere in

solving them.2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning

• Instruction that places the highest value on student understanding

CCSS Mathematical Practices1. Make sense of problems and persevere in

solving them.2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning

CCSS Mathematical Practices1. Make sense of problems and persevere in

solving them.2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning

• Instruction that emphasizes the discussion of alternative strategies

CCSS Mathematical Practices1. Make sense of problems and persevere in

solving them.2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning

CCSS Mathematical Practices1. Make sense of problems and persevere in

solving them.2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning

• Instruction that includes extensive mathematics discussion (math talk) generated through effective teacher questioning

CCSS Mathematical Practices1. Make sense of problems and persevere in

solving them.2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning

CCSS Mathematical Practices1. Make sense of problems and persevere in

solving them.2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning

• Teacher and student explanations to support strategies and conjectures

CCSS Mathematical Practices1. Make sense of problems and persevere in

solving them.2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning

CCSS Mathematical Practices1. Make sense of problems and persevere in

solving them.2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning

• The use of multiple representations

CCSS Mathematical Practices1. Make sense of problems and persevere in

solving them.2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning

CCSS Mathematical Practices1. Make sense of problems and persevere in

solving them.2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning

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 Math 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

5 Goals for Math Classrooms

• Number sense• Place Value• Fluency• Properties• Connecting mathematical ideas

Clip 5.6 – 5th Grade

Subtraction: 1000 – 674 • Before we watch the clip, talk at your

tables–What possible student strategies might

you see?–How might you record them?

• What evidence is there that the students understand place value?

• How do the students’ strategies exhibit number sense?

• How does fluency with smaller numbers connect to the students’ strategies?

• How are accuracy, flexibility, and efficiency interwoven in the students’ strategies?

Clip 3.7 – 3rd Grade

Array Discussion: 8 x 25 • Before we watch the clip, talk at your

tables–What possible student strategies might

you see?–How might you record them?

• How does the array model support the student strategies?

• How does breaking the factors into friendly numbers promote the goals of efficiency and flexibility?

• How do the teacher’s questions foster an understanding of multiplication?

• What math understandings and misunderstandings are addressed with this model?

Clip 5.5 – 5th Grade

Division String: 496 ÷ 8 • Before we watch the clip, talk at your

tables–What possible student strategies might

you see?–How might you record them?

• What evidence is there that students understand place value?

• How do students build upon their understanding of multiplication to divide?

• How does the teacher connect math ideas throughout the number talk?

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.

Hannah has $500. She buys a camera for $435 and 4 other items for $9 each. Now Hannah wants to buy speakers for $50. Does she have enough money to buy the speakers?

The Lane family took a road trip. During the first week, they drove 907 miles. The second week they drove 297 miles more than the first week. How many miles did they drive during the two weeks?

Katrina spent $500 on her new tablet. Her father spent 4 times as much to buy his new computer. How much more did her father spend?

Multiplication

Strategies for Multiplication

• Repeated Addition• Skip Counting• Equal Groups• Arrays and Area Models• Partial Products• Traditional US Algorithm

Multiplication

67 x 3• Solve using at least 3 different strategies

C – R – A

• Concrete• Representational • Abstract

Multiplication

467 x 35• Solve using at least 3 different strategies

Did your choice of strategies change as the numbers got larger?

Division

Strategies for Division

• Repeated Subtraction• Skip Counting• Equal Groups• Arrays and Area Models• Partial Quotients• Traditional US Algorithm

Division

Measurement vs Fair Share?

47 3• Strategy 1: Representational

Measurement• Strategy 2: Representational

Fair Share

Concrete

• Use base 10 chips and recording sheet

437 3