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

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.

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

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.

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.

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

THIRD GRADE

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

Strategies Taught Array with Skip Counting (builds on repeated addition) 4 x 6 or 4 rows of

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

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

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

Student Example

INTERMEDIATE GRADES, 4 AND 5

Standard Algorithm

Place Value Understanding

Area Model

Partial Product

Distributive Property of Multiplication

Standard Algorithm

Associative Property of Multiplication

Area Model

Distributive Property of Multiplication

Partial Product/Standard Algorithm

Student Example, Grade 4

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 J = x O = 3x H = x + 5 x + 3x + x + 5 = 80 5x + 5 = = - 5 5x = 75 5x ÷ 5 = 75 ÷ 5 x = J = 15 O = 45 (15x3) H = 20 (15+5) O 45 -H Omar is 25 years older than Henry.

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.

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.