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
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