Math Fourth GradeBuilding Content Knowledge

Education Transformation Office

Common Board Configuration (CBC)

Exit Slip:

•Revisit Essential Question

AGENDA:

I Do:•Review focus group materials

We Do:•Teach One/Learn One Activity

They Do:•Map out how you’re going to teach the beginning of the year concepts.

You Do:•Processing Time: Answer the essential question•Homework Instruction

Vocabulary: Pacing guide, Skills Sheets,, Journal Entries , NGSSS, Item Specs

ESSENTIAL QUESTION: How can exploring the math content and resources help me to be an effective teacher?

Objective: Today we will explore the math review resources and best practices to teach the content effectively.

BENCHMARK: Math and Resources and Content.

BELL RINGER:

DATE: August 2013

Introductions: 3 – 2 - 1 Activity

3-2-1

Set 3 Goals for this school year

Write 2 actions that will assist you in

meeting your goals

Write 1 challenge that may

Encounter

Essential Question:

How can exploring the math content help me to be a more effective teacher?

What’s New and Continuing with ETO Elementary Math?

2013-2014 School Year

The ETO Website will Continue to Provide Each Grade Level with the

Following:

Pacing Guide with day-to-day breakdown

Grade Level Skills Sheets Independent Centers Binder Success Academy Lessons

Skills Sheets-Teacher Edition

What is NEW????

• GO MATH will now consist of all COMMON CORE

• Newly created Bellringers by benchmark including basic skill practice

• Teacher Led Center (TLC) packets by benchmarks

• New Dashboard for ThinkCentral

GO MATH 4th Grade “Old vs. New”

GO MATH

Go Math textbooks are all correlated to Common Core.

Schools will receive updated Common Core Teacher’s Editions

You will continue to have access to the “Old GO MATH” with the NGSSS through thinkcentral.com

GO MATH Technology Correlations

GO MATH Technology Correlations

Journal Entries

Digging Deeper Into the Math Content- 4th GradeTOPIC I: Place Value, Addition and Subtraction to One Million

New Edition Common Core TextbookMACC.4NBT. 1.1; MACC.4NBT.1.2 ; MACC.4.NBT.1.3; MACC.4NBT. 2.4Infusing the NGSSS MA.4.A.6.1-Reading, Writing and Comparing Whole Numbers

“The Standards for Mathematical Practice are unique in that they describe how teachers need to teach to ensure their students become mathematically proficient. We were purposeful in calling them standards because then they won’t be ignored.”

~ Bill McCallum

Standards for Mathematical Practices

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

Topic IMathematical Practices

MP 2: Reason abstractly and quantitatively

Mathematically proficient students can… have the ability to contextualize and decontextualize (navigate between the concrete and the abstract).manipulatives pictures symbolsunderstand and explain the computation methods they use.

Topic IMathematical Practices

MP 6: Attend to precision

Mathematically proficient students can…

use clear definitions and mathematical vocabulary to communicate their own reasoning

careful about specifying units of measure and labels to clarify the correspondence with quantities in a problem

Essential Content

A. Reading and Writing Numbers

1. Standard Form 2. Expanded Form 3. Written Form

B. Place Value, Value of Digit and Face Value1. Ones2. Tens3. Hundred4. Thousand5. Ten Thousand6. Hundred Thousand7. Million

C. Estimate

1. Rounding

a. onesb. tensc. hundredd. thousande. ten thousandf. hundred thousandg. million

2. Compatible Numbers

D. Problem Solving 1. Adding numbers through millions

2. Subtracting numbers through millions

Professional Development Podcasts

* Found on Thinkcentral.com Under Resources

MP 2 and MP 6 PD Podcast

How did you see the practice being implemented? What are some benefits by viewing the Podcasts?

(Take two minutes to discuss with your group)

Benchmark ClarificationsWhat Must Students Be Able to Do?

Students will identify, compare and/or order numbers through the millions place in real-world contexts.

Students will find the answers to real-world problems that involve adding and subtracting numbers through the millions.

Students will make estimations of numbers through the millions in real-world situations.

What Are the Content Limits?

Items may include the inequality symbols (>, <, , , ).

Items will not include decimals or fractions.

Items involving units of measure may not involve converting from one unit to another.

Front-end estimation will NOT be an acceptable estimation strategy.

Always Know Your Benchmarks Found in Your Test Item

Specifications

These are theCommon CoreStandards replacing the NGSSS

Sample Item QuestionsWhat Does it Look Like?

What is FRONT END Estimation

When using front-end estimation, use the first number without worrying about what it is closest to.

What Are Good Strategies ?

Order from least to greatest256, 162, 224

1. MAKE A PLACE VALUE CHART.2. Line numbers up ( Stack them on top of each other).3. Compare from left to right once they are lined up correctly.

4. Since the directions are least to greatest, circle the smallest number on the left. 162 would be listed first.

2 5 6

2 2 4

1 6 2

Make a Place Value Chart

5. Put a line through the number already listed. 6. The other numbers have the same digit. Circle both 2’s then compare the numbers directly behind. The number that is smallest will be listed next. 7. Have the students compare the underlined numbers to see which one is smaller. 8. Since 2 is the smaller number, 224 would be listed next and 256 is last. 9. The order would be:

162, 224, 256

Additional Strategy Have students place the numbers in

the place value chart starting in the ones place.

If there are a different amount of digits in the number, have the students place zeros in the front.

6784

3280

Comparing Strategies

The alligator always eats the larger number.

* Read it like a sentence from left to right.

6 10 6 is less than 10 10 6 10 is greater than 6

Rounding Strategies

1. Use rounding chant-

4 or less…let it rest

5 or more…raise the a score

2. When estimating, round first and then complete problem.

Example- 152 + 296

Expanded Form12,502

1. Start with the digit in the place value all the way to the left.2. Turn all of the numbers behind to zeros.3. Place a ( + ) sign between the numbers4. Repeat with each number moving from the left to the right. 12,502= 10,000 + 2,000 + 500 + 2 OR 10,000 - 1 x 10,000 = 10,000 2,000 - 2 x 1,000 = 2,000 500 - 5 x 100 = 500 2 - 2 x 1= 2

= 10,000 + 2,000 + 500 + 2

The Bar Model to Subtract

This visual bar model allows the students to see the pictorial representation. It will help them understand what DIFFERENCE means.

Suggested Activities1. Make a flip chart

3. Mystery picture – Match the standard form with the word form

2. Give students number from a chart to ORDER or COMPARE

4. Place Value GameOn long strips of paper make place value charts, making sure the commas are in place and writing the words (ones, tens, hundreds, etc.) under the blank line where a number will be placed. With a partner and a deck of cards the children shuffle the deck and then pass out the predetermined number of cards according to how far you want them to learn place value. Hundred thousands would be 6 cards, millions 7 cards, 10 millions 8 cards, etc. Cards are face down in a pile. Face cards equal 1, aces are 0, and everything else what they say. They are trying to make the largest number possible to win (or smallest). Both players turn over a card at the same time and decide where to place it. Once placed, it must stay there. You must be able to say the number you made to win the pile of cards. They learn place value and soon move on to the strategy of where to place the cards to their best advantage. They continue until all the cards are used. The winner has the largest number.

End of the Topic Group Activity Collaborative Strategy- Numbered Heads1. Each individual will receive a popsicle stick with a number.2. Everyone with the same number will group as a pair to work on an a computation problem and a word problem.3. At this time choose who will be the:

A. TeacherB. Student

4. Teachers please explicitly teach the concept and incorporate the following in your lesson:

A. Problem Solving StrategyB. Address Common Errors

Your Turn to Give It a Try(Think-Pair-Share)

# 1Estimate. Then find the difference.

# 2

Your Turn to Give It a Try(Think-Pair-Share)

# 1Estimate. Then find the difference.

# 2

How Do These Problems Relate to Mathematical Practices 2 & 6

Discuss with your partners and give at least three examples for Topic II

(Take 5 minutes to record your responses)

Digging Deeper Into the Math Content- 4th GradeTOPIC Il: Multiplication

New Edition Common Core TextbookMACC.4.NBT.2.5; MACC.4.OA.1.1; MACC.4.OA.1.2; MACC.4.OA.1.3; Infusing the NGSSS MA.4.A.1.1; MA.4.A.6.2; MA.4.A.6.4

Topic IIMathematical Practices

MP 1: Make sense of problems and persevere in solving them.

Mathematically proficient students can…

explain the meaning of the problem

monitor and evaluate their progress “Does this make sense?”

use a variety of strategies to solve problems

Topic IIMathematical Practices

MP 4: Model with Mathematics.

Mathematically proficient students can…

apply mathematics to solve problems that arise in everyday life

reflect on their attempt to solve problems and make revisions to improve their model as necessary

Essential Content

A. Multiple Representations of Multiplication and Division of Whole Numbers

1. Manipulatives

2. Drawings

3. Algorithms

4. Comparisons

B. Recall Multiplication Facts 2-9 (Daily Routine) C. Multiplication Strategies1. Partial Product2. Distributive Property3. Regrouping

D. Relate Repeated Addition to Multiplication.

E. Relate Repeated Subtraction to Division

F. Problem Solving

1.Drawings

2.Write number sentences

3.Inverse operation

These are theCommon CoreStandards replacing the NGSSS

What Does it Look Like?

Benchmark ClarificationsWhat Must Students Be Able to Do?

Students will solve real-world problems using basic multiplication and the related division facts.

Students will solve multi-digit whole-number multiplication problems or supply partial products in real-world multiplication problems.

What are the Content Limits?

Items may include whole-number multiplication facts from 0 X 0 through 12 X 12 and the related division facts.

For items that require solving multi-digit multiplication problems, the two factors may not exceed three digits by three digits or four digits by two digits.

When both factors have three digits, at least one digit must be a zero.

1. 250 (when the 0 is on the top, 123 x 123 switch it to the bottom) x 250

2. 658 2563 x 324 x 48

Three digit by Three digits

Four digit byTwo digits

What Are Good Strategies?

Teachers don’t need to stress the memorization of the property names as much as the application of what the property does.

When teaching distributive property use the grid paper to model the break apart method.

Emphasize place value when multiplying Multiplication Ladder---track students

learning their facts Multiplication with base ten blocks

Multiplication Comparisons(New with Common Core)

• This strategy will assist your students to better understand algebraic expressions.

The [bracket] = the total of

15

(3 times) draw

3 boxes of 5

(as 5)

is 5) in a single box onTop or bottom

Multiplication Comparisons

Example #1

9

9 9 9 9

n

4 936

36

Multiplication Comparisons

Example # 2

Total

Multiplication Comparisons

Example # 2

Total

Miguel n n n

6

Sara n

6 3 n

6 3 2SO, Sara has 2 rabbits

Distributive Property of Multiplication (2-Digit by 1-Digit) Using GRID PAPER

Multiply 4 x 19

10 94

4 x 10 = 40

4 x 9 = 36

40 + 36 = 76

Multiplying Using Expanded Form

100 40 3

500 + 200 + 15

7 1 5

Using Partial Products for Solving Multi-product Multiplication

45 Expand- 40 + 5 X 78 Expand- 70 + 8

40 x 70 = 2800 280040 x 8 = 320 32070 x 5 = 350 3505 x 8 = 40 + 40

3,510

Multiplication with Base-10

Blocks With Regrouping

FactorsUsing Arrays

Have the students use grid paper OR Tiles

Find the factors of 20:

2 x 10

4 x 5

• Always list the factors in order from greatest to least or least to great.

NOT IN RANDOM ORDER!

FACTORS

Multiples StrategyMake a List

Example: Find the first 5 multiples of 4 1. Skip Count 4- 4,8,12,16,20 OR 2. Multiply counting consecutively starting with 1 4 x 1= 4, 4 x 2 = 8, 4 x 3= 12, 4 x 4= 16, 4 x 5=20

Multiples StrategyMake a Number Line

Suggested Activities for Multiplication

Suggested Activities for Factors and Multiples

Your Turn to Give It a Try(Think-Pair-Share)

# 1

# 2

Your Turn to Give It a Try(Think-Pair-Share)

Your Turn to Give It a Try(Think-Pair-Share)

# 3Use the distributive property to solve.

#4

Use base-ten pictorials to show your work.

Your Turn to Give It a Try(Think-Pair-Share)

Use the distributive property to solve.

51 X 5

60 + 8 X 7

How Do These Problems Relate to Mathematical Practices 1 & 4

Discuss with your partners and give at least three examples for Topic II

(Take 5 minutes to record your responses)

Digging Deeper Into the Math Content- 4th Grade

TOPIC IlI: Multiplying Multi-Digit Numbers

New Edition Common Core TextbookMACC.4.NBT.2.5; MACC.4.OA.1.3No CC for MA.4.A.6.6Infusing the NGSSS MA.4.A.1.2; MA.4.A.6.6

Topic IIIMathematical Practices

MP 4: Model with Mathematics.

Mathematically proficient students can…

apply mathematics to solve problems that arise in everyday life

reflect on their attempt to solve problems and make revisions to improve their model as necessary

Topic IIIMathematical Practices

MP 8: Look for and express regularity in repeated reasoning

Mathematically proficient students can…

notice repeating calculations and look for efficient methods/ representations to solve a problem

evaluate the reasonableness of their results throughout the problem solving process.

Essential Content

A. Multiplication

1. Real world problem solving

2. Two, Three, Four digits by one digit

3. Two digits by two digits

4. Area Models

B. Real World Problem Solving

1. Two Step Problems

2. Number Sentences

3. Estimation

4. Rounding

a. nearest 10

b. nearest 100

C. Properties of Multiplication

1. Distributive Property

2. Associative Property

These are theCommon CoreStandards replacing the NGSSS

What Does it Look Like?

Benchmark ClarificationsWhat Must Students Be Able to Do?

Students will solve real-world problems using basic multiplication and the related division facts.

Students will solve multi-digit whole-number multiplication problems or supply partial products in real-world multiplication problems.

What Are the Content Limits?

Items may include whole-number multiplication facts from 0 X 0 through 12 X 12 and the related division facts. For items that require solving multi-digit multiplication

problems, the two factors may not exceed three digits by three digits or four digits by two digits.

When both factors have three digits, at least one digit must be a zero.

Items may include finding partial products of a multi-digit multiplication problem or finding errors in multiplication problems.

Items may include checking for reasonableness of products. Items may use properties (e.g., commutative, associative, inverse,

identity, distributive, zero) to solve problems but will not include asking students to name the specific properties.

No Common Core Standard

What Does it Look Like?

Partial Products with 2-Digit Numbers( Break Apart)

Model 13 x 181. Draw an array that shows 13 by 18.

2. Break apart 13 and 18 into smaller addends so you can multiply easier.

13 = 10 + 3 and 18 = 10 + 83.

100 80 30 244. Add all the products 100 + 80 + 30 + 24 = 234

10 x 10 10 x 8

3 x 10 3 x 8

Distributive Property of Multiplication With Larger Numbers

• When multiplying large number you can break apart the factors in order to make multiplying easier.

40 X 5020 = 40 ( 5000 + 20 )

= ( 40 x 5000) + ( 40 x 20 )

= 200,000 + 800

= 200,800

Be Sure to Show the Standard Algorithm

The answer to 213 x 58 = 12,354

***DO NOT TEACH LATTICE METHOD IN ISOLATION…STUDENTS MUST HAVE AN UNDERSTANDING OF THE STANDARD ALGORITHM

Student will not be assessed on this strategy

Commutative Property of Multiplication

You can multiply factors in any order and get the same product.

Commutative Property Activity

http://www.mathsisfun.com/activity/images/comm-assoc-dist-1.jphttp://www.mathsisfun.com/activity/images/comm-assoc-dist-1.jpgg

Associative Property of Multiplication

Associative Property Activity

Distributive Property

Your Turn to Give It a Try(Think-Pair-Share)

#1 Use the standard algorithm.

# 2

Use the strategy, partial product or break apart to solve. Show your work.

Your Turn to Give It a Try(Think-Pair-Share)

#1 Use the standard algorithm.

# 2

15 10 + 5 X 85 80 + 5

10 5

80

5

800 400 800 400 50 + 2550 25 1,275

4 4

4 6 8 +3 9 0 0 4, 3 6 8

How Do These Problems Relate to Mathematical Practices 4 & 8

Discuss with your partners and give at least three examples for Topic II

(Take 5 minutes to record your responses)

Digging Deeper Into the Math Content- 4th Grade

TOPIC IV: Algebraic Rules

New Edition Common Core TextbookNONENGSSS –MA.4.A.4.2; MA.4.A.4.3

Essential Content

A. Variables 1. Solving for an unknown

B. Algebraic Expressions 1. Determine a rule 2. Write an expression

C. Expressions with Two Operations 1. Write expressions with more than 1 operation 2. Evaluate expressions with 1 variable and two operations

D. Repeating Patterns 1. Recognize patterns 2. Describe algebraic rule

What Does It Look Like?

Benchmark ClarificationsWhat Must Students Be Able to Do?

Students will translate a written description or a graphic to an expression or equation or translate an expression or equation to a written or graphic description to solve a real-world problem.

Students will identify a missing number or element in a numeric or graphic relationship.

Students will describe or generalize the rule of a visual relationship using an expression, equation, or description of the graphic.

What Are the Content Limits?

Items must use rules or relationships that involve only one operation or a one-step function.

A relationship must be defined in words, or at least three examples of the relationship must be provided.

Relationships involving multiplication or division are limited to the multiplication facts of 0 X 0 through 12 X 12 and the related division facts.

Items may include only one variable

Algebraic Language

Algebraic Expressions Strategies

Use a model

Division Example

Algebraic Expressions Strategies

Use a model

Multiplication Example

SOME doesn’t give you an amount. A variable can be used to represent this unknown number.

Algebraic Expressions Strategies

Use a model

Addition Example

Patterns- Finding the Rule Making an Input/output Table

Strategies For Algebraic Expressions With Two Operations

Algebraic Expressions Activities

How Do These Problems Relate to Mathematical Practices 4 & 8

Discuss with your partners and give at least three examples for Topic II

(Take 5 minutes to record your responses)

Essential Question:

How can exploring the math content help me to be a more effective teacher?

QUESTIONS/CONCERNS

ETO Elementary Collaboration Website

Build, Sustain, Accelerate

You can find this presentation in addition to all curricular resources on our very

own ETO Collaboration WebsitePlease visit us at:

http://www.eto.dadeschools.net