1. Math Standards and Strategies, Grades 3-5 Gr. 3: Julie Cupp, Kelly Opiela, Cathy Vanina Gr. 4: Mary Gildea, Chris Lasher, Michelle McKee Gr. 5: Amy Isenhart and Jennifer Stapleton Shireen Fasciglione – Hillside Principal Bill Wales - District Director of Mathematics

2. Learning Standards The Common Core is: A set of instructional standards that guide our instruction. The Common Core is NOT: NYS assessments Teacher evaluation Purpose of this evening: To share our thoughts and work on the instructional standards /strategies of math instruction.

3. 6 Shifts in Mathematics Focus: Learn more about fewer topics Coherence: Build skills within and across grades Fluency: Develop speed and accuracy Deep Understanding: Really know it! Application: Use it in the real world Dual Intensity: Practice and understanding

4. Mathematics: Standards for Mathematical Practice Make sense of problems & persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.

5. Foundations of Math Number Sense - a student's understanding of the relationship of one number to another, ability to perform mental math, understanding symbolic representations, and use of numbers in real world situations Place Value - the value of a digit depending on its place in a number; using place value and a decimal point to separate whole numbers from decimal fractions. Visual Representations (e.g., model drawing) - Models give students a tangible graphic to hold onto as they compute the problem. Models also make math much clearer for struggling math students.

6. Mathematical Strategies Number bonds Ten Frames Bar models/Tape diagrams Arrays Number line Skip counting Area model Partial products

7. THIRD GRADE

8. Focus Skill - Multiplication/Division Foundation for future mathematical skills 3 rd grade: Area, fractions, measurements Future grade level concepts Efficiency- Allows them to focus on multi-step word problem understanding, not basic facts Important to focus on fluency Practicing facts frequently Understanding of fact families

9. Strategies Taught Array with Skip Counting (builds on repeated addition) 4 x 6 or 4 rows of 6 6 12 18 24

10. Number Bonds: Below shows 4 x 6 (Think of 4 groups of 6) Also shows 24 ÷ 4 = 6 Sample Number Bond (Class of 24) 24 6 6 6 6

11. Bar Model or Tape Diagram: 4 groups of 6 4 x 6 = ? 6 ?

12. Distributive Property (break apart strategy): Commutative Property: 6 x 4 or 4 x 6

13. Student Example

15. INTERMEDIATE GRADES, 4 AND 5

16. Standard Algorithm

17. Place Value Understanding

18. Area Model

19. Partial Product

20. Distributive Property of Multiplication

21. Standard Algorithm

22. Associative Property of Multiplication

23. Area Model

24. Distributive Property of Multiplication

25. Partial Product/Standard Algorithm

27. Student Example, Grade 4

31. 5 th Grade Omar is 3 times as old as Jason. Henry is 5 years older than Jason. If their total age is 80 years old, how much older is Omar than Henry? J O H x xxx x + 5 80 J = x O = 3x H = x + 5 x + 3x + x + 5 = 80 5x + 5 = 80 - 5 = - 5 5x = 75 5x ÷ 5 = 75 ÷ 5 x = 15 80 - 5 75 -5 25 -25 0 J = 15 O = 45 (15x3) H = 20 (15+5) O 45 -H -20 25 Omar is 25 years older than Henry.

34. Math is MORE than just numbers!  Make sense of problems and persevere in solving them.  Construct arguments and critique the reasoning of others.  Model with mathematics.  Look for and make use of structure.

35. Parent Tips Follow the problem solving steps. It’s the process, not the answer. Practice solving basic problems. Ask your child “why” and “how do you know” questions Always ask: Does your answer make mathematical sense? Is it reasonable? Practice facts nightly. Communicate with your child’s teacher.