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Elementary Common Core Team Training Math Lesson Summer 2013

Elementary Common Core Team Training Math Lesson Summer 2013

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Page 1: Elementary Common Core Team Training Math Lesson Summer 2013

Elementary Common Core Team TrainingMath Lesson

Summer 2013

Page 2: Elementary Common Core Team Training Math Lesson Summer 2013

Learning Goals

Increase knowledge of the Standards for Mathematical Practices

Unpack the Common Core Standards using Unpacking Standards Graphic Organizer

Success Criteria Identify the Eight Mathematical Practices in a

lesson Unpack Common Core Standards using the

Unpacking Document

Page 3: Elementary Common Core Team Training Math Lesson Summer 2013

Parking Lot Questions

Page 4: Elementary Common Core Team Training Math Lesson Summer 2013

“Good Math Students”

Think about a few students who are “really good” in math.

How do they approach problems? How do they solve problems? How do they discuss their strategies?

“Common Core will have kids thinking out loud, discussing solutions with each other, and explaining their answers.”

-Stateimpact.npr.org/florida/2013

Page 5: Elementary Common Core Team Training Math Lesson Summer 2013

Standards for Mathematical Practice

What are they?

What do they look like in a K-5 classroom?

Page 6: Elementary Common Core Team Training Math Lesson Summer 2013

Do You Know The Mathematical Practices?

INDIVIDUALLY:Take a moment and jot down the

Mathematical Practices on the sticky note provided.

Page 7: Elementary Common Core Team Training Math Lesson Summer 2013

Do You Know The Mathematical Practices?

WITH A PARTNER:Pair-Share:

Share with your partner the list you wrote down. Compare your lists.

Page 8: Elementary Common Core Team Training Math Lesson Summer 2013

Do You know The Mathematical Practices?

Rate YourselfWhat is your knowledge of the Mathematical Practices today? Place your sticky on the scale.

Page 9: Elementary Common Core Team Training Math Lesson Summer 2013

Do You Know The Mathematical Practices?

Progression ScaleLevel 4- I can state all 8 Mathematical Practices and I use them daily in

my classroom.Level 3- I can state all 8 Mathematical Practices and I may use them in

my classroom.Level 2- I can state half of the Mathematical Practices.Level 1- I can state 2 of the Mathematical Practices.Level 0- What is a Mathematical Practice?

Page 10: Elementary Common Core Team Training Math Lesson Summer 2013

Standards for Mathematical Practice

Mathematical Practices1. 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.

Page 11: Elementary Common Core Team Training Math Lesson Summer 2013

Standards for Mathematical Practice

The Standards for Mathematical Practices describe the behaviors of mathematically proficient students.

Page 12: Elementary Common Core Team Training Math Lesson Summer 2013

Structure of Standards

Standards for Mathematical PracticeA set of 8 standards that describe the ways in which the mathematical content standards should be approached.

Standards for Mathematical ContentThese standards define what students should understand and be able to do in their study of mathematics.

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“HOW”

“What”

Page 13: Elementary Common Core Team Training Math Lesson Summer 2013

MP 1 - Make Sense of Problems and Persevere in Solving Them

• Make sense of the meaning of the task• Find an entry point or a way to start the

task• Focus on concrete manipulatives before

moving to pictorial representations• Develop a foundation for problem-solving

strategies• Reexamine the task when they are stuck• Ask, “Does my answer make sense?”

2b, 3c

Page 14: Elementary Common Core Team Training Math Lesson Summer 2013

What does MP 1 look like in a classroom?

“Old” problem (little or no rigor) Tina had ten balloons. She gave seven of them away. How many balloons did Tina have then?

“New” problem (with rigor)Burger Barn has one small table that can seat four people. They also have one large table that can seat double that amount. Fifteen (15) people came in at lunch time. How many people did not get a seat?

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Page 15: Elementary Common Core Team Training Math Lesson Summer 2013

MP 2 - Reason Abstractly and Quantitatively

• Make sense of quantities and their relationships

• Decontextualize• Contextualize• Represent symbolically (ie. Equations,

expressions)

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3c

Page 16: Elementary Common Core Team Training Math Lesson Summer 2013

What does MP 2 look like in a classroom?

I had two pencils. My mom gave me some more. Now I have five pencils. How many pencils did my mom give me?

Decontextualize the problem:

2 + □ = 516

Page 17: Elementary Common Core Team Training Math Lesson Summer 2013

What does MP 2 look like in a classroom?

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2 + □ = 5Contextualize the problem:

I had two pencils. My mom gave me some more. Now I have five pencils. How many pencils did my mom give me?

Page 18: Elementary Common Core Team Training Math Lesson Summer 2013

What does MP 2 look like in a classroom?

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How many buses are needed for 99 children to go on a field trip if each bus seats 44 students?

99÷44

Is the answer: 2r11 or 2¼ or 2.25?

Recontextualize to get the answer: 3 buses

Page 19: Elementary Common Core Team Training Math Lesson Summer 2013

MP 3 - Construct Viable Arguments and Critique the Reasoning of Others

• Use mathematical terms to construct arguments

• Use definitions and previously established solutions in their arguments

• Engage in discussions about problem-solving strategies

• Recognize and discuss reasonableness of strategies

• Recognize and discuss similarities and differences between strategies

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2a, 3b, 3c

Page 20: Elementary Common Core Team Training Math Lesson Summer 2013

What does MP3 look like in a classroom?

I can make a plan, called a strategy, to solve the problems and discuss other students’ strategies too.

http://insidemathematics.org/index.php/classroom-video-visits/public-lessons-proportions-a-ratios/205-proportions-a-ratios-problem-3-part-d?

Page 21: Elementary Common Core Team Training Math Lesson Summer 2013

MP 4 - Model with Mathematics.

• Model with manipulatives and much more• Model with a number sentence or equation• Check to make sure the number sentence

matches the context of their problem• Model with concrete manipulative

representations• Model with pictorial representations• Have matching equations for their

representations

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2e, 3c

Page 22: Elementary Common Core Team Training Math Lesson Summer 2013

What does MP 4 look like in a classroom?

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I have three cars. My friend gives me some more cars. Now I have seven cars. How many toy cars did my friend give me?

Model with Pictures

Model with Tools

Model with Symbols

3 + □ = 7

Model with Words

I have three cars. I get four more. Now I have seven cars.

Page 23: Elementary Common Core Team Training Math Lesson Summer 2013

Break

Page 24: Elementary Common Core Team Training Math Lesson Summer 2013

MP 5 - Use Appropriate Tools Strategically

The purpose is to move students toward a deeper understanding of these tools.

• Have access to a variety of tools (counters, place value blocks, hundred boards, number lines, geometric shapes, paper/pencil, etc…)

• Need to express in their own words the “what, why, and how” to help them clarify, perfect, and organize their thinking.

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2c, 2e

Page 25: Elementary Common Core Team Training Math Lesson Summer 2013

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What does MP 5 look like in a classroom?

• Students have easy access to math tools.

• Students select their own tools.

Page 26: Elementary Common Core Team Training Math Lesson Summer 2013

MP 6 – Attend to Precision

• Communicate precisely with teachers and peers (written and verbal)

• Clearly define terms• Identify the meanings of mathematical

symbols and use them appropriately• Specify units of measure

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2b

Page 27: Elementary Common Core Team Training Math Lesson Summer 2013

What does MP 6 look like in a classroom?

How might a student explain their solution to the subtraction problem shown below?

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413-168

Page 28: Elementary Common Core Team Training Math Lesson Summer 2013

MP 7 - Look for and Make Use of Structure

• Look for patterns • Recognize mathematical structures• Generalize to other problem situations• Simplify complex problems

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3c

Page 29: Elementary Common Core Team Training Math Lesson Summer 2013

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1 2 543 6 7 10981112 151413 1617 2019182122 252423 2627 3029283132 353433 3637 4039384142 454443 4647 5049485152 555453 5657 6059586162 656463 6667 7069687172 757473 7677 8079788182 858483 8687 9089889192 959493 9697 10

09998

53 + 23 = ?53 + 23 = 76

82 - 14 = ?

82 - 14 = 68

What does MP7 look like in a classroom?

Page 30: Elementary Common Core Team Training Math Lesson Summer 2013

MP 8 - Look for and Express Regularity in Repeated Reasoning

• Look for regularity in problem structures when solving mathematical tasks

• Maintain oversight

• Check for reasonableness during and after task

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3b

Page 31: Elementary Common Core Team Training Math Lesson Summer 2013

What does MP 8 look like in a classroom?

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Doubles Plus One

Decompose 7

Add the double

Add one more

13

6 + 7

6 1

12+1=

=13

Page 32: Elementary Common Core Team Training Math Lesson Summer 2013

Identify Mathematical Practices

Try to identify as many examples of the mathematical practices in action as possible as you view this video of a kindergarten class.

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Page 33: Elementary Common Core Team Training Math Lesson Summer 2013

“If the Standards for Mathematical Practice are not in place, well

then, you’re not really using the Common Core.”

– Phil Daro, Common Core author - Mathematics

Page 34: Elementary Common Core Team Training Math Lesson Summer 2013

Let’s take a Break…

Page 35: Elementary Common Core Team Training Math Lesson Summer 2013

Do You Know The Mathematical

Practices?

Rate YourselfTake a moment and jot down the

Mathematical Practices on the sticky note provided.

Place your sticky on the scale.

Page 36: Elementary Common Core Team Training Math Lesson Summer 2013

Handouts

Observing Mathematical Practices in a Classroom

Questions to Develop Mathematical Thinking correlated to the SMP

SMP in Student Friendly LanguageSMP Unpacked by Grade LevelDepth of Knowledge Chart3rd Grade Quarter 1 PlacematUnpacking Documents

Page 37: Elementary Common Core Team Training Math Lesson Summer 2013

Question to Ponder

What does it mean to “really understand”?

What are indicators of knowledge without understanding?

What are concrete indicators of really understanding something?

What can the person with understanding do that the person with only knowledge cannot do?

Page 38: Elementary Common Core Team Training Math Lesson Summer 2013

Be able to KNOW and UNDERSTAND

What we want students to know

Vocabulary Definitions Concepts Key facts Critical details Laws, formulas

What we want students to understand

Decoding Computation Communication skills –

listening, speaking, writing

Thinking skills – compare, confer, analyze

Research – inquiry, investigate

Page 39: Elementary Common Core Team Training Math Lesson Summer 2013

Unpacking Standards

Why unpack?• Standards require a close read and analyze

for meaning

• Standards are rarely taught in isolation

• Not all standards are equal in rigor

1c

Page 40: Elementary Common Core Team Training Math Lesson Summer 2013

Student Friendly

LanguageStudents Will

Be able ToWhat Students

Need to Understand

What Students Need to Know

MACC.5.NBT.2.6Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division, illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Standard

Page 41: Elementary Common Core Team Training Math Lesson Summer 2013

Student Friendly

LanguageStudents Will

Be able ToWhat Students

Need to Understand

Whole-number quotientsFour-digit dividendsTwo-digit

divisorsStrategies

Place valueProperties of

operations Multiplication

Division Equations

Rectangular Arrays

Area Models

What Students Need to Know

MACC.5.NBT.2.6Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division, illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Standard

Page 42: Elementary Common Core Team Training Math Lesson Summer 2013

Student Friendly

LanguageStudents Will

Be able To

Find

Use

Illustrate

Explain

What Students Need to

Understand

Whole-number quotientsFour-digit dividendsTwo-digit

divisorsStrategies

Place valueProperties of

operations Multiplication

Division Equations

Rectangular Arrays

Area Models

What Students Need to Know

MACC.5.NBT.2.6Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division, illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Standard

Page 43: Elementary Common Core Team Training Math Lesson Summer 2013

Student Friendly

Language

Use various strategies to

divide

Interpret remainders

Explain the strategy used

Students Will Be able To

Find

Use

Illustrate

Explain

What Students Need to

Understand

Whole-number quotientsFour-digit dividendsTwo-digit

divisorsStrategies

Place valueProperties of

operations Multiplication

Division Equations

Rectangular Arrays

Area Models

What Students Need to Know

MACC.5.NBT.2.6Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division, illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Standard

Page 44: Elementary Common Core Team Training Math Lesson Summer 2013

I can solve division

problems using

different strategies.

I can explain my strategy.

Student Friendly

Language

Use various strategies to

divide

Interpret remainders

Explain the strategy used

Students Will Be able To

Find

Use

Illustrate

Explain

What Students Need to

Understand

Whole-number quotientsFour-digit dividendsTwo-digit

divisorsStrategies

Place valueProperties of

operations Multiplication

Division Equations

Rectangular Arrays

Area Models

What Students Need to Know

MACC.5.NBT.2.6Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division, illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Standard

Page 45: Elementary Common Core Team Training Math Lesson Summer 2013

Your turn!

Form groups with 3-5 participants in each group.

Each group will be given five 3rd grade standards from chapter1.

Each group member should unpack at least one standard.

Share your unpacked standards with your group members.

Look for similarities and/or differences in these standards.

Groups should share their discoveries.

Page 46: Elementary Common Core Team Training Math Lesson Summer 2013

Break

Page 48: Elementary Common Core Team Training Math Lesson Summer 2013

Model for Instructional Planning

Course Descriptions

• “Chunk” the standards to identify 10 to 12 critical areas of focus or big ideas.

• Integrate standards across content areas as appropriate.

Learning Goals

• Define 10 to 12 major learning goals based upon the “chunks” of integrated standards from the course description.

• Develop learning progression scales to describe the steps students will take to attain each learning goal as well as what success looks like at each step.

Lesson Plans

• Use the learning progressions to guide lesson development; include formative assessment tasks as part of the instructional plan, identify resources in advance, and incorporate the use of technology as a tool for learning when applicable.

• Use the formative assessment data to revise and/or differentiate instruction as appropriate to meet the needs of ALL students.

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Page 49: Elementary Common Core Team Training Math Lesson Summer 2013

MACC.4.NBT.1.1: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

MACC.4.NBT.1.2 : Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

MAACC.4.NBT.1:3 Use place value understanding to round multi-digit whole numbers to any place.

Content Standards

Page 50: Elementary Common Core Team Training Math Lesson Summer 2013

Learning Goal:

Students will be able to solve problems using place value understanding to read, compare, and round multi-digit numbers by:• Recognizing a digit in one place represents ten

times what it represents in the place to its right. • Reading and writing whole numbers using base-

ten numerals, number names, and expanded form.

• Comparing two numbers based on the meaning of the digits in each place.

• Using symbols to record comparisons.• Rounding whole numbers to any place using

place value understanding.

1c

Page 51: Elementary Common Core Team Training Math Lesson Summer 2013

Wrap – Up

Exit Pass: How are you going to share with your school the MP, Unpacking the Standards, and Learning Goals?