COMMON CORE STANDARDS

MATHEMATI

CS

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 – 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 them2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning of others4. Model with mathematics5. Use appropriate tools and strategies6. Attend to precision7. Look for and make sense of structure8. 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 Required Fluency

K Add/subtract within 51 Add/subtract within 10

2Add/subtract within 20Add/subtract within 100 (pencil and paper)

3 Multiply/divide within 100Add/subtract within 1000

4 Add/subtract within 1,000,000

5 Multi-digit multiplication

6Multi-digit divisionMulti-digit decimal operations

7 Solve px + q = r, p(x + q) = r

8 Solve simple 22 systems by inspection

Fractions

5th Grade Add and Subtract fractions with different denominators

Before After

32

43

Jerry was making two different types of cookies. One recipe needed cup of sugar. The other recipe called for cup of sugar. How much sugar did he need to make both recipes ?

43

32

1 cup – broken into fourths

then into twelfths

1 cup –broken into thirds

then into twelfths

129

43

128

32

+

1251

1217

128

129

Jerry needs of sugar to make both recipes.

1251

1217 or

5th Grade Multiply a fraction by a whole number or another

fraction•

4*21

62*

53

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?

Before

4 meters

½ meter

5th Grade Divide fractions by a whole number and whole numbers by

fractions to solve world problems •

675

Before

539

After A bowl holds 5 Liters of water. If we use a scoop that holds of a Liter of water, how many scoops will we need to make to fill the bowl? 61

6th Grade Divide fractions by fractions using models and equations to represent the problem. Solve word problems involving division of fractions by fractions.

Before

61

32

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 ?

61

32

61

32

Rule : When dividing a fraction by a fraction, change the division to multiplication and “flip” the second fraction ( aka – reciprocal)

16*

32

Now what ???

16*

32

312 4

Therefore Susan can make 4 cards in 2/3 of an hour.

Old way

What does that really mean ? 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?

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?

There are 7 halves in 3 ½

21

213

27

213

21

27

12*

27

214 7

Let’s take another look

PictorialAlgorithm

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

1 girl to every 2 boys

2 girls to every 4 boys

3 girls to every 6 boys

4 girls to every 8 boys

girls : boys = 4 : 8

girls : boys = 3 : 6

girls : boys = 2 : 4

girls : boys = 1 : 2

But the simplest ratio is still 1 : 2

But the simplest ratio is still 1 : 2

But the simplest ratio is still 1 : 2

This is the simplest ratio is 1 : 2

Pictorial Introduction

Ratio of girls to boys?

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 Starch

PARTS QUANTITIES 5 parts 90 cups 1 part 90/5 = 18 cups

2 parts 2x18=36 cups3 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.orgwww.engageny.orgwww.ixl.com/math www.jmathpage.com

Math Apps for the IPAD Math World Math Pentagon*Minds of Math On the SpotEquivalent Fractions ( NCTM)Fill the Cup Freddy Fractions

QUESTIONS?