SIXTH GRADESession 2

Vacaville USD

October 28, 2014

AGENDA• Problem Solving, Patterns, Expressions and

Equations• Math Practice Standards and High Leverage

Instructional Practices• Number Talks

– Computation Strategies

• Understanding Integers

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 “fat 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?

Cubes in a Line

Let’s agree to use the simplest form of the equation:

F = 4n + 2

• What does F stand for?

• What does n stand for?

Cubes in a Line

F = 4n + 2

• Suppose I have 250 cubes. How many faces will that be?

• John says he has 602 face units. How many cubes does he have?

• Kris says he has 528 faces units. How many cubes does he have?

Equivalent Expressions

Which of the following expressions are equivalent? Why?• 2(x + 4)• 8 + 2x• 2x + 4• 3(x + 4) − (4 + x)• x + 4

Math Practice Standards

• Remember the 8 Standards for Mathematical Practice

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

Math Content Standards

• Look at your 6th Grade Content Standards – Expressions and Equations

• Which standards would be addressed by using problems such as these?

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 – Mathematical Practice 1

• 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) – Mathematical Practice 1

• Instruction that places the highest value on student understanding – Mathematical Practices 1 and 2

• Instruction that emphasizes the discussion of alternative strategies – Mathematical Practice 3

• Instruction that includes extensive mathematics discussion (math talk) generated through effective teacher questioning – Mathematical Practices 2, 3, 6, 7, and 8

• Teacher and student explanations to support strategies and conjectures – Mathematical Practices 2 and 3

• The use of multiple representations – Mathematical Practices 4 and 5

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 5.4 – 5th Grade

Division: 150 ÷ 15; 300 ÷ 15• Before we watch the clip, talk at your

tables–What possible student strategies might

you see?–How might you record them?

• What mathematical relationships are being built upon during the class discussion?

• How do the students’ strategies exhibit number sense?

• What understandings and misconceptions does the area model help the students confront?

• What understandings and misconceptions do students have about the area model?

Number Talks

Illustrative Mathematics Task• Reasoning about Multiplication and

Division and Place Value, Part 1• How could you use problems like these as

part of a number talk to see what students understanding about multiplication, division and place value?

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.

Expressions and Equations

6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

Integers

Integers• What are negative numbers?

-5 -4 -3 -2 -1

Integers• How are negative numbers used and why

are they important?

Integers• What are opposites?

• How are they shown on a number line?

-5 -4 -3 -2 -1

Integers• What is the absolute value of a number?

-5 -4 -3 -2 -1

Integers• How do we use positive and negative

numbers to represent quantities in real-world contexts?

Finish labeling all of the points on the number line.• Locate -3 on the number line• What is the opposite of -3?

– Where is it located on the number line?• What is the absolute value of -3?

– Where do you see that on the number line?• How far is it from -3 to 5?

– How can you use the number line to solve this?

-5 -4 -3 -2 -1

Integers and the Real World

• Comparing Temperatures

• Absolute Value and Ordering 1

Coordinate

Grid

Coordinate

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Coordinate Grid

• Naming Points – Secret Message

Coordinate

Grid