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

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 Practices OVERARCHING HABITS OF MIND 1.Make sense of problems and persevere in solving them 6.Attend to precision REASONING AND EXPLAINING 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others MODELING AND USING TOOLS 4.Model with mathematics 5.Use appropriate tools strategically SEEING STRUCTURE AND GENERALIZING 7.Look for and make use of structure 8.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 Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.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 Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

Instruction that places the highest value on student understanding

CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

Instruction that emphasizes the discussion of alternative strategies

CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

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

CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 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

CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

The use of multiple representations

CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.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 – 5 th 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 – 3 rd 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 – 5 th 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