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Transcript of Vacaville USD October 28, 2014. AGENDA Problem Solving, Patterns, Expressions and Equations Math...
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SIXTH GRADESession 2
Vacaville USD
October 28, 2014
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AGENDA• Problem Solving, Patterns, Expressions and
Equations• Math Practice Standards and High Leverage
Instructional Practices• Number Talks
– Computation Strategies
• Understanding Integers
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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.
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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?
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Questions?
What do I mean by a “fat unit”?
Do I count the faces I can’t see?
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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?
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Cubes in a Line
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Cubes in a Line
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Cubes in a Line
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Cubes in a Line
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Cubes in a Line
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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?
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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?
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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?
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Equivalent Expressions
Which of the following expressions are equivalent? Why?• 2(x + 4)• 8 + 2x• 2x + 4• 3(x + 4) − (4 + x)• x + 4
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Math Practice Standards
• Remember the 8 Standards for Mathematical Practice
• Which of those standards would be addressed by using a problem such as this?
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Math Content Standards
• Look at your 6th Grade Content Standards – Expressions and Equations
• Which standards would be addressed by using problems such as these?
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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
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High Leverage Instructional Practices
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High-Leverage Mathematics Instructional Practices
• An instructional emphasis that approaches mathematics learning as problem solving – Mathematical Practice 1
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• 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
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• Instruction that places the highest value on student understanding – Mathematical Practices 1 and 2
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• Instruction that emphasizes the discussion of alternative strategies – Mathematical Practice 3
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• Instruction that includes extensive mathematics discussion (math talk) generated through effective teacher questioning – Mathematical Practices 2, 3, 6, 7, and 8
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• Teacher and student explanations to support strategies and conjectures – Mathematical Practices 2 and 3
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• The use of multiple representations – Mathematical Practices 4 and 5
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Number Talks
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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
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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
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Key Components
• Classroom environment/community• Classroom discussions• Teacher’s role• Mental math• Purposeful computation problems
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Classroom Discussions
• What are the benefits of sharing and discussing computation strategies?
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• 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
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5 Goals for Math Classrooms
• Number sense• Place Value• Fluency• Properties• Connecting mathematical ideas
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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?
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• 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?
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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?
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• 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?
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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?
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Solving Word Problems
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3 Benefits of Real Life Contents
• Engages students in mathematics that is relevant to them
• Attaches meaning to numbers
• Helps students access the mathematics.
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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.
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Integers
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Integers• What are negative numbers?
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Integers• How are negative numbers used and why
are they important?
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Integers• What are opposites?
• How are they shown on a number line?
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Integers• What is the absolute value of a number?
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Integers• How do we use positive and negative
numbers to represent quantities in real-world contexts?
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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?
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Integers and the Real World
• Comparing Temperatures
• Absolute Value and Ordering 1
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Coordinate
Grid
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Coordinate
Grid
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Coordinate Grid
• Naming Points – Secret Message
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Coordinate
Grid