P.S. 198 Parent Math Workshop

1. P.S. 198Parent Math Workshop March 20, 2013 Carol Teig

2. Common Core Standards Overview • Fewer, clearer, and higher • “What” not “How” of instruction—end year expectations, not a program • Aligned with college and work expectations • Expectations are consistent for all – and not dependent on a student’s state or zip code. • Include rigorous content and application of knowledge through higher order skills • Internationally benchmarked, so that all students are prepared to succeed in our global economy and society

3. Key differences in math • Fewer topics; more generalizing and linking of concepts • Well-aligned with the way high-achieving countries teach math • Emphasis on both conceptual understanding and procedural fluency starting in the early grades • More time to teach and reinforce core concepts from K-12 • Some concepts will now be taught later • Focus on mastery of complex concepts in higher mathematics (e.g., algebra and geometry) via hands-on learning • Emphasis on mathematical modeling in the upper grades

4. Math Standards • Mathematical Performance What students should be able to do… • Mathematical Understanding Understand is used in these standards to mean that students can explain the concept with mathematical reasoning, including concrete illustrations, mathematical representations, and example applications. • Mathematical Practices Proficient students of all ages expect mathematics to make sense. They take an active stance in solving mathematical problems. When faced with a non-routine problem, they have the courage to plunge in and try something, and they have the procedural and conceptual tools to continue. They are experimenters and inventors, and can adapt known strategies to new problems. They think strategically.” Common Core State Standards

5. Six Shifts in Mathematics Instruction Shift 1: Focus Prioritized concepts leading to strong foundational knowledge and understanding will be the focus of instruction and assessments. Other standards will be deemphasized. Shift 2: Coherence Carefully reflect the progression of content and concepts as depicted in the standards on and across grade levels. Shift 3: Fluency It is expected that students possess the required fluencies as articulated through grade 8 with building understanding and an ability to manipulate complex concepts. Shift 4: Deep Understanding Ability to access and apply concepts from a number of perspectives in both speaking and writing rather than as a right answer. Shift 5: Application Connecting content with fluency to employ to solve real-world problems. Shift 6: Dual Intensity Practice and understanding both occur with intensity.

6. Speed and AccuracyThink Fast/Solve Problems • Students must … • Be able to persevere in solving multi-step/non-routine problems…productive struggle is a good thing. • Be able to use core math facts fast • Understand and talk about why the math works—prove it! • Be able to apply math in the real world • Students must …BE PROBLEM SOLVERS!

7. How do we begin? We want your children to be problem solvers, to help them develop number sense and fluency. What is number sense? Number Sense refers to a person’s understanding of number concept, operations and applications of number and operations. It includes the ability and inclination to use this understanding in flexible ways to make mathematical judgments and to develop useful strategies for handling numbers and operations. A person with good number sense has the ability to use numbers and quantitative methods to communicate, process, and interpret information. Alistair McIntosh

8. Number Sense • It builds capacity for doing mental math • It involves the flexible decomposition of numbers (a very big idea in mathematics!)

9. Fluency • Having efficient and accurate methods for computing • Flexibility in computational methods • Understand and explain methods • Produce accurate answers efficiently • Understands base 10 number system • Understands number relationships • eg. What is the sum of 8+9=

10. Expectations of Number and Operations across the grades Kindergarten • Decompose numbers less than or equal to 10 into parts in more than one way, by using objects of drawings, and record each decomposition by a drawing or equation 1st grade • Use addition and subtraction within 20 to solve word by using objects, drawings, and equations with a symbol for the unknown number • Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction

11. Expectations of Number and Operations across the grades (con’t) 2nd grade • Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. • Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions 3rd grade • Use place value understanding and properties of operations to perform multi-digit arithmetic to fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 using strategies based on place value and properties of operations. • Develop understanding of fractions as numbers. Understand a fraction as a number on the number line; represent fractions on a number line diagram.

12. Expectations of Number and Operations across the grades (con’t) 4th grade • Generalize place value understanding for multi-digit whole numbers. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. • Use place value understanding and properties of operations to perform multi-digit arithmetic. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. • Extend understanding of fraction equivalence and ordering • Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

13. Expectations of Number and Operations across the grades (con’t) 5th Grade • Understand the place value system. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. • Use equivalent fractions as a strategy to add and subtract fractions. Add and subtract fractions with unlike denominators and apply and extend previous understandings of multiplication and division to multiply and divide fractions. 3. Interpret a fraction as division of the numerator by the denominator (a/b= a÷ b).

14. Do students need to memorize math facts? YES!!! • According to the common core standards by the end of second grade students are expected to add and subtract within 20, demonstrating fluency for addition and subtraction within 10. • Using different strategies for whole number computation allows the students to apply and extend their understanding of the different operations when asked to compute with fractions. Therefore a lot of time is spent on strategies such as • counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); • decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); • using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and multiplication and division • Creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

15. What does this look like in the classrooms? • Upstairs there will be a K-2 workshop and a 305 workshop where you will experience a lesson similar to what your children do during math lessons • (give some direction on what you want parents to do!)

16. In Summary • Each of the strategies taught allows students to make a choice. When students consider the elements in a problem and select a reasonably efficient strategy that makes sense given the numbers or the context, they are thinking like mathematicians. • Mathematics is the study of relationships. Seeing math as the study of relationships enables us to see structural logic rather than just a series of random facts and procedures.

17. What can parents do at home? • Have conversations that relate to everyday life and incorporate math questions (eg. How tall is that tree?) • Become familiar with the new math standards • Practice counting objects and money • Practice telling time everyday • Reason through questions with your children. • Play board games