Transcript Intermediate Math and Science

DATE: August 2013
BELL RINGER: Introductions:
3 – 2 - 1 Activity
BENCHMARK: Math and
Resources and Content.
Objective: Today we will
explore the math review
resources and best practices
to teach the content
effectively.
ESSENTIAL QUESTION: How
can exploring the math
content and resources help
me to be an effective teacher?
Vocabulary: Pacing guide, Skills
Sheets,, Journal Entries , NGSSS, Item
Specs
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
Exit Slip:
•Revisit Essential
Question
Set 3 Goals for this school year
Write 2 actions that will
assist you in meeting your
goals
Write 1
challenge that may
Encounter
How can exploring the
math content help me
to be a more effective
teacher?
Pacing Guide with day-to-day
breakdown
 Grade Level Skills Sheets
 Independent Centers Binder
 Success Academy Lessons

•
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 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

TOPIC I: Place Value, Addition and Subtraction to One
Million
New Edition Common Core Textbook
MACC.4NBT. 1.1; MACC.4NBT.1.2 ; MACC.4.NBT.1.3;
MACC.4NBT. 2.4
Infusing the NGSSS MA.4.A.6.1-Reading, Writing and
Comparing Whole Numbers
Standards for Mathematical Practices
“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
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
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
symbols
understand and explain the computation
methods they use.
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
A. Reading and Writing
C. Estimate
Numbers
a.
b.
1. Standard Form
2. Expanded Form
3. Written Form
c.
d.
e.
f.
g.
B. Place Value, Value of Digit
and Face Value
1.
2.
3.
4.
5.
6.
7.
Ones
Tens
Hundred
Thousand
Ten Thousand
Hundred Thousand
Million
1. Rounding
ones
tens
hundred
thousand
ten thousand
hundred thousand
million
2. Compatible Numbers
D. Problem Solving
1. Adding numbers through millions
2. Subtracting numbers through millions
* Found on Thinkcentral.com Under Resources


How did you see the practice being implemented?
What are some benefits by viewing the Podcasts?
(Take two minutes to discuss with your
group)
Students will identify, compare and/or
order numbers through the millions place
in real-world contexts.
 Students will find the answers to realworld problems that involve adding and
subtracting numbers through the millions.
 Students will make estimations of
numbers through the millions in realworld situations.


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
These are the
Found in Your Test Item
Common Core
Specifications
Standards
replacing the
NGSSS
When using front-end estimation, use the first number
without worrying about what it is closest to.
Order from least to greatest
256, 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
1
2
5 6
6 2
2 4
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

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.
4 8 7 6
0
8
2
3
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
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
12,502
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 numbers
4. 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- 2x
1=
2
= 10,000 + 2,000
+ 500 + 2
This visual bar model allows the
students to see the pictorial
representation. It will help them
understand what DIFFERENCE
means.
1.
3.
Make a flip chart
Mystery picture – Match the
standard form with the word form
2.
Give students number from a
chart to ORDER or COMPARE
4.
Place Value Game
On 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.
Collaborative Strategy- Numbered Heads
1. 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. Teacher
B. Student
4. Teachers please explicitly teach the concept and
incorporate the following in your lesson:
A. Problem Solving Strategy
B. Address Common Errors
#1
Estimate. Then find
the difference.
#2
#1
Estimate. Then find the
difference.
#2
 Discuss
with your partners and
give at least three examples
for Topic II
(Take 5 minutes to record your
responses)
TOPIC Il: Multiplication
New Edition Common Core Textbook
MACC.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
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
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
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 Strategies
1. Partial Product
2. Distributive Property
3. 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 the
Common Core
Standards
replacing
the NGSSS

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.

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
x 123
(when the 0 is on the top,
switch it to the bottom)
123
x 250
2.
658
x 324
Three digit by
Three digits
2563
x 48
Four digit by
Two digits





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
•
This strategy will assist your students to better
understand algebraic expressions.
(as 5)
is
5)
in
a single box on
Top or bottom
Example #1
9
4
9
9
9
9
9
36
n
36
Example # 2
Total
Example # 2
Total
6
Miguel
Sara
n
n
n
n
SO, Sara has 2 rabbits
6
6
3
n
3
2
Multiply 4 x 19
10
4
4 x 10 = 40
4 x 9 = 36
40 + 36 = 76
9
100
500
40
+
200
3
+
15
715
 Using
Partial Products for Solving
Multi-product Multiplication
45
X 78
Expand- 40 +
Expand70
40 x 70 = 2800
40 x 8 = 320
70 x 5 = 350
5 x 8 = 40
5
+
8
2800
320
350
+
40
3,510
Have the students use grid paper OR Tiles
Find the factors of 20:
2 x 10
4x5
• Always list the
factors in order
from greatest to
least or least to
great.
NOT IN RANDOM
ORDER!
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


#1
#2
#3
Use the distributive
property to solve.
#4
Use base-ten pictorials
to show your work.

Use the distributive
property to solve.
60 + 8
X
7
51
X 5
 Discuss
with your partners and
give at least three examples
for Topic II
(Take 5 minutes to record your
responses)
TOPIC IlI: Multiplying Multi-Digit Numbers
New Edition Common Core Textbook
MACC.4.NBT.2.5; MACC.4.OA.1.3
No CC for MA.4.A.6.6
Infusing the NGSSS MA.4.A.1.2; MA.4.A.6.6
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
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.
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 the
Common Core
Standards
replacing
the NGSSS
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.







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
1. 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 + 8
3.
100
80
30
24
4. Add all the products
100 + 80 + 30 + 24 = 234
Model 13 x 18
10 x 10
10 x 8
3 x 10
3x8
• 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
=
200,800
+
800
Student will not be assessed on this strategy
The answer to 213 x 58 = 12,354
***DO NOT TEACH LATTICE METHOD IN
ISOLATION…STUDENTS MUST HAVE AN
UNDERSTANDING OF THE STANDARD ALGORITHM

You can multiply factors in any order
and get the same product.

http://www.mathsisfun.com/activity/ima
ges/comm-assoc-dist1.jphttp://www.mathsisfun.com/activity/i
mages/comm-assoc-dist-1.jpgg
#1
Use the standard
algorithm.
#2
Use the strategy, partial
product or break apart
to solve. Show your
work.
#1
#2
Use the standard
algorithm.
4
4
15 10 + 5
X 85 80 + 5
10
468
+3 9 0 0
4, 3 6 8
80
5
5
800
400
50
25
800
400
50
+ 25
1,275
 Discuss
with your partners and
give at least three examples
for Topic II
(Take 5 minutes to record your
responses)
TOPIC IV: Algebraic Rules
New Edition Common Core Textbook
NONE
NGSSS –MA.4.A.4.2; MA.4.A.4.3
A. Variables
1. Solving for an unknown
C. Expressions with Two
Operations
1. Write expressions with more
than 1 operation
2. Evaluate expressions with 1
variable and two operations
B. Algebraic Expressions
1. Determine a rule
2. Write an expression
D. Repeating Patterns
1. Recognize patterns
2. Describe algebraic rule
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.

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


Use a model
Division
Example
SOME doesn’t give
Use
a model
you an amount. A
variable can be
used to represent
this unknown
number.
Multiplication
Example
Use a model
Addition
Example
 Discuss
with your partners and
give at least three examples
for Topic II
(Take 5 minutes to record your
responses)
How can exploring the
math content help me
to be a more effective
teacher?
You can find this presentation in addition
to all curricular resources on our very own
ETO Collaboration Website
Please visit us at:
http://www.eto.dadeschools.net
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