1. 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

2. 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)

3. 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.

4. 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

5. 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

6. 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.

7. 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 ).

8. Fluencies GradeRequired Fluency KAdd/subtract within 5 1Add/subtract within 10 2 Add/subtract within 20 Add/subtract within 100 (pencil and paper) 3 Multiply/divide within 100 Add/subtract within 1000 4 Add/subtract within 1,000,000 5Multi-digit multiplication 6 Multi-digit division Multi-digit decimal operations 7Solve px + q = r, p(x + q) = r 8 Solve simple 2  2 systems by inspection

9. Fractions

11. 5 th Grade Add and Subtract fractions with different denominators Before After 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 ? 1 cup – broken into fourths then into twelfths 1 cup –broken into thirds then into twelfths + Jerry needs of sugar to make both recipes.

12. 5 th Grade Multiply a fraction by a whole number or another fraction 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

13. 5 th Grade Divide fractions by a whole number and whole numbers by fractions to solve world problems Before 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?

14. 6 th Grade Divide fractions by fractions using models and equations to represent the problem. Solve word problems involving division of fractions by fractions. Before 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 ?

15. What is the question asking ? How many 1/6 are in 2/3? What operation is involved ? Division What does that look like ?

16. Rule : When dividing a fraction by a fraction, change the division to multiplication and “flip” the second fraction ( aka – reciprocal) Now what ??? 4 Therefore Susan can make 4 cards in 2/3 of an hour. Old way

17. 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?

18. 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 7 Let’s take another look Pictorial Algorithm

19. 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 !

20. 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

21. Ratios and Proportions

22. Granny Prix Oliver, N. (n.d.). Granny Prix [Math Game]. Retrieved from multiplication.com website: http://www.multiplication.com/flashgames/GrannyPrix.htmhttp://www.multiplication.com/flashgames/GrannyPrix.htm

23. 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 This is the simplest ratio is 1 : 2 Pictorial Introduction Ratio of girls to boys?

24. 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 PARTSQUANTITIES 5 parts90 cups 1 part90/5 = 18 cups 2 parts2x18=36 cups 3 parts3 x18=54 cups

25. Technology & Project Based Learning IPADS HANDS ON, CONCRETE DEVELOPMENT OF CONCEPTS PROJECTS TO STRETCH THE MIND AND DEEPER UNDERSTANDING.

26. 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?

27. 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

28. QUESTIONS?