Transcript Common Core Standards Mathematics

IS THERE REALLY A DIFFERENCE?
Was : Mile Wide, Inch Deep
Now: Inch Wide , Mile Deep
By Marissa Sciremammano, Director of Mathematics
DESIGN AND ORGANIZATION
• Standards for Mathematical Practice
–
Carry across all grade levels
–
Describe habits of mind of a mathematically expert student
• Standards for Mathematical Content
K-8 standards presented by grade level
–
–
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Organized into domains that progress over several grades
Grade introductions give 2-4 focal points at each grade level
High School Standards presented by conceptual themes (Numbers and Quantity ,
Algebra, Functions , Modeling, Geometry , Statistics and Probability)
In mathematics, this means three major changes.
1. Teachers will concentrate on teaching a more focused set of major math
concepts and skills.
2.Students will be allowed the time to master important ideas and skills in a
more organized way throughout the year and from one grade to the next.
3.Teachers to use rich and challenging math content and to engage students
in solving real-world problems in order to inspire greater interest in
mathematics.
DESCRIBING THE K-12 STANDARDS
The 8 Standards for Mathematical Practice
–
Describe habits of mind of a mathematically expert student
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 and strategies
6. Attend to precision
7. Look for and make sense of structure
8. Look for and express regularity in repeated reasoning
DESIGN AND ORGANIZATION OF THE NEW COMMON
CORE



Content standards define what students should understand and
be able to do
Clusters are groups of related standards
Domains are larger groups that progress across grades
Grade 5 Overview
Operations and Algebraic Thinking
•
•
Write and interpret numerical expressions.
Analyze patterns and relationships.
Number and Operations in Base Ten
•
•
Understand the place value system.
Perform operations with multi-digit whole
numbers and with decimals to hundredths.
Number and Operations—Fractions
•
•
Use equivalent fractions as a strategy to add
and subtract fractions.
Apply and extend previous understandings of
multiplication and division to multiply and
divide fractions.
Measurement and Data
•
•
•
Convert like measurement units within a
given measurement system.
Represent and interpret data.
Geometric measurement: understand
concepts of volume and relate volume to
multiplication and to addition.
Geometry
•
•
Graph points on the coordinate plane to
solve
real-world and mathematical problems.
Classify two-dimensional figures into
categories based on their properties.
Accelerated Grade 6
Ratios and Proportional Relationships
• Understand ratio concepts and use ratio reasoning to solve problems.
•
Recognize and represent proportional reasoning between quantities; Identify constraints of
proportionality ( unit rate) in tables ,graphs, equations, diagrams and verbal descriptions of
proportional relationships ( scale drawings).
The Number System
• Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
• Compute fluently with multi-digit numbers and find common factors and multiples.
• Apply and extend previous understandings of numbers to the system of rational numbers
Expressions and Equations *
• Apply and extend previous understandings of arithmetic to algebraic expressions.
• Reason about and solve one-variable equations and inequalities ( one and two step equations).
• Represent and analyze quantitative relationships between dependent and independent variables .
Geometry *
•
•
Solve real-world and mathematical problems involving area, surface area, and volume.
Explore parts of circles ( circumference and area ).
Fluencies
Grade
K
1
2
3
4
5
6
7
8
Required Fluency
Add/subtract within 5
Add/subtract within 10
Add/subtract within 20
Add/subtract within 100
(pencil and paper)
Multiply/divide within 100
Add/subtract within 1000
Add/subtract within
1,000,000
Multi-digit multiplication
Multi-digit division
Multi-digit decimal operations
Solve px + q = r, p(x + q) = r
Solve simple 22 systems by
inspection
Fractions
5th Grade
Add and Subtract fractions with different denominators
Before
After
Jerry was making two different types of cookies.
3
One recipe needed cup of sugar. The other recipe called
4
for 2 cup of sugar. How much sugar did he need to make
both3recipes ?
3 2

4 3
1 cup – broken into fourths
then into twelfths
3 9

4 12
1 cup –broken into thirds
+
9 8 17
5
 
1
12 12 12
12
then into twelfths 2  8
3
17
5
or1
12
12
12
Jerry needs
of sugar to
make both recipes.
5th Grade
Multiply a fraction by a whole number or another fraction
•
Before
1
*4
2
3 2
*
5 6
After
The home builder needs to cover a small storage room floor with carpet. The storage
room is 4 meters long and half of a meter wide. How much carpet do you need to cover
the floor of the storage room?
4 meters
½ meter
5th Grade
Divide fractions by a whole number and whole numbers by fractions to
solve world problems
Before
•
5
6
7
3
9
5
After
A bowl holds 5 Liters of water. If we use a scoop that holds
1
6 of a Liter of water, how many scoops will we need to make
to fill the bowl?
6th Grade
Divide fractions by fractions using models and equations to represent the
problem. Solve word problems involving division of fractions by fractions.
Before
2 1

3 6
After
Susan has 2/3 of an hour to make cards. It takes her about 1/6 of
an hour to make each card. About how many can she make ?
Susan has 2/3 of an hour to make cards. It takes her about
1/6 of an hour to make each card. About how many can she
make?
•
What is the question asking ?
How many 1/6 are in 2/3?
•
What operation is involved ?
Division
•
What does that look like ?
2 1

3 6
2 1

3 6
Rule : When dividing a fraction by a fraction, change the division to
multiplication and “flip” the second fraction ( aka – reciprocal)
2 6
*
3 1
Now what ???
2 6
*
3 1
12
3
4
Therefore Susan can make 4 cards in 2/3 of an hour.
Susan has 2/3 of an hour to make cards. It takes her about 1/6 of
an hour to make each card. About how many can she make?
What does that really mean ?
Let’s take another look
Ann has 3 ½ lbs of peanuts for the party. She wants to put them in small
bags each containing ½ lb. How many small bags of peanuts will she
have?
1 1
3 
2 2
Pictorial
1 7
3 
2 2
There are 7 halves in
3½
Algorithm
7 1

2 2
7 2
*
2 1
14
2
7
What do you notice ?
•
Expectations are different !
•
Deeper understanding of the content is needed.
•
Deeper understanding of prerequisite knowledge is key to success.
•
Mathematics is a language, and communication is part of the
foundation of success.
•
Application! Application ! Application
!
Which approach is more meaningful to understanding ?
The algorithm ( step by step procedure) does not equate to
a deeper understanding without a foundational approach to
the relationship between concepts.
Concrete - Pictorial – Abstract
Ratios and Proportions
Granny Prix
Oliver, N. (n.d.). Granny Prix [Math Game]. Retrieved from multiplication.com
website: http://www.multiplication.com/flashgames/GrannyPrix.htm
4 girls to every 8 boys
Pictorial Introduction
Ratio of girls
to boys?
girls : boys = 4 : 8
But the simplest ratio is still 1 : 2
3 girls to every 6 boys
girls : boys = 3 : 6
But the simplest ratio is still 1 : 2
2 girls to every 4 boys
girls : boys = 2 : 4
But the simplest ratio is still 1 : 2
1 girl to every 2 boys
girls : boys = 1 : 2
This is the simplest ratio is 1 : 2
What does this look like ?
A slime mixture is made of mixing glue and liquid
laundry starch in a ratio of 3 to 2. How much glue
and how much starch are needed to make 90 cups
of slime?
Glue
PARTS
Starch
QUANTITIES
5 parts
90 cups
1 part
90/5 = 18 cups
2 parts
2x18=36 cups
3 parts
3 x18=54 cups
Technology & Project
Based Learning
• IPADS
• HANDS ON, CONCRETE
DEVELOPMENT OF CONCEPTS
• PROJECTS TO STRETCH THE MIND
AND DEEPER UNDERSTANDING.
Advice to help parents support their children:
Don’t be afraid to reach out to your child’s
teacher—you are an important part of your
child’s education.
Ask to see a sample of your child’s work or bring
a sample with you. Ask the teacher questions
like:
Where is my child excelling?
How can I support this success?
What do you think is giving my child the
most trouble?
How can I help my child improve in this
area?
What can I do to help my child with
upcoming work?
Resources
www.khanacademy.org
www.engageny.org
www.ixl.com/math
www.jmathpage.com
Math Apps for the IPAD
Math World
Math Pentagon*
Minds of Math
On the Spot
Equivalent Fractions ( NCTM)
Fill the Cup
Freddy Fractions
QUESTIONS?