Presentation on theme: "Are you smarter than a fifth grader? 1. The ratio of children to pet dogs in Brian’s neighborhood is 4:1. There are 11 dogs in the neighborhood; how many."— Presentation transcript:
Are you smarter than a fifth grader? 1. The ratio of children to pet dogs in Brian’s neighborhood is 4:1. There are 11 dogs in the neighborhood; how many children live there? 2. Deana packages tiles in a factory. Tiles are packed 8 per package, and shipped in boxes containing 12 packages per box. There are 100 tiles at her station. Can she fill a shipping box? Yes, with 4 left over. 44 children
Back to Basics Presented by Mrs. Phyllis Prestamo Supervisor of Applied Sciences Roxbury Public Schools
New Jersey Core Curriculum Content Standards - 2004 4.1 Number and Numerical Operations 4.2 Geometry & Measurement 4.3 Patterns & Algebra 4.4 Data Analysis, Probability, & Discrete Math 4.5 Mathematical Processes
New Standards due out January 2010 NJ is participating along with 48 other states/territories in drafting a “Common Core of K-12 Math Standards” February
Fundamental Premise All students must have a solid grounding in mathematics to function effectively in today’s world. from Memo dated 7/10/09 from Willa Spicer, Deputy Commissioner & Sandra M. Alberti, Director, Office of Math and Science Education
Areas of Agreement: Automatic recall of basic facts: Computational fluency in whole number arithmetic is vital. Computational fluency requires automatic recall of addition and multiplication facts from 0-12 and an understanding of the underlying mathematical ideas. Calculators: Calculators can have a useful role even in the lower grades, but must be used judiciously so as not to impede the acquisition of fluency with basic number facts and computational procedures. Learning Algorithms: Students should be able to fluently and accurately use basic algorithms to add, subtract, multiply and divide whole numbers. Fractions: Understanding the number meaning of fraction is critical. Teaching Mathematics in “real-world” contexts: Applied problems can motivate and introduce mathematical ideas. from Memo dated 7/10/09 from Willa Spicer, Deputy Commissioner & Sandra M. Alberti, Director, Office of Math and Science Education
It’s a Fact Permanent learning of basic facts is stored in long term memory and can be later retrieved quickly when needed without much thought. Students who automatically know their basic facts are better able to master more complex operations and are better equipped to tackle math applications in all subjects. Research has shown (D. Klein, 2005) that progress in Mathematics in students who do not know their basic number facts often grinds to a halt by the end of elementary school. Youngsters who have not mastered whole number arithmetic by the end of 4 th grade are at risk of later becoming remedial students in mathematics. (T. Loveless 2003) All children are able to master the basic facts through drill once they have constructed a strategy for a particular set of facts. Mastering of the basic facts requires frequent rehearsal and practice and should occur on a daily basis.
The Goal The goal for mastery of the basic facts is automaticity. A student is considered to have achieved automaticity when he or she can give an answer to a basic fact in less than 3 seconds without using finger counting.
Building Understanding Practice activities developed around how the brain makes and stores long- term memories should precede drill and should be designed to build students’ conceptual understanding.
Teaching Sequence Mathematics is a discipline of connected ideas. Knowledge of a single concept or skill is often the foundation for many aspects within the discipline. New concepts cannot be formed if the prerequisite concepts and skills are not well established. Curriculum is organized into a careful sequence of clustered strategies.
GRADE 1Addition & Subtraction Facts to 18 1 st quarter - Count on 1, 2, 3 addition 2 nd quarter - Count back 0, 1 subtraction 3 rd quarter - Doubles/doubles +1, +2, +3 addition 3 rd quarter - Count back 0, 1, 2 subtraction Make a “10” GRADE 2Addition & Subtraction Facts to 18 Review – count on 1, 2, 3 addition Review – doubles/doubles +1, 2, 3 addition Review – count back 1, 2, 3 subtraction Review – make “10” Fact Families Skip counting x2, x5, x10 GRADE 3Addition & Subtraction Facts to 18 Review – addition/subtraction to 18 Multiplication 0-10 & Division 1-10 Doubling = x2 1 st quarter – x0, x1, x2, x5 2 nd quarter – x0, x1, x2, x3, x4, x5 and ÷1, 2, 5 3 rd quarter – x0-10 and ÷1, 2, 3, 4, 5, 10 End of year – Multiplication 0-10 & division 1-10 GRADE 4Multiplication 0-12 & Division 1-12 Review – Multiplication 0-10 & division 1-10 2 nd quarter x11 & ÷11 3 rd quarter x12 & ÷12 End of Year - Multiplication 0-12 & division 1-12 GRADE 5 & 6Multiplication 0-12 & Division 0-12 Review all facts 0-12
X0123456789 00000000000 10123456789 2024681012141618 30369121518212427 404812162024283236 5051015202530354045 6061218243036424854 7071421283542495663 8081624324048566472 9091827364554637281 TEN FACTS TO MEMORIZE
4 Stages of Teaching & Learning Example: “Use tens multiplication strategy for the fives facts”
Introduce the strategy Hands on activities - manipulatives are used to model a strategy 4 x 10 = 40 10 x 4 = 40 4 x 5 = 5 x 4 = “I know ten fours are forty, so five fours must be half of that--–twenty.”
Reinforce the strategy These activities are designed to make links between the concrete/pictorial and symbolic representations. 8 x 10 = _____ ____ x ____ = _____ 80 8 5 40
Practice the facts At this stage students should use mental computation only and fast recall is stressed. 10452520 35154525 30351540 The player rolls a “four” and says “four tens are forty, so four fives are twenty” and covers the twenty.
Extend the strategy Once mastered, the strategies and skills can be applied to new contexts and new situations. Students are encouraged to go beyond. 10 x 18 = ______ so 5 x 18 = _______ 10 x 26 = ______ so 5 x 26 = _______ 10 x 22 = ______ so 5 x 22 = _______ 10 x 15 = ______ so 5 x 15 = _______ 150 260 90 130 220110 180 75 Later students will then vary this strategy by halving and doubling other factors: e.g. 14 x 35 has the same answer as 7 x 70 which is much easier to calculate mentally.
References Adding It Up: Helping children learn mathematics, National Research Council, 2001 Book on the web: http://books.nap.edu/openbook.php?record_id=9822&page=R1 http://books.nap.edu/openbook.php?record_id=9822&page=R1 Math Fluency: Scholastic Research Foundation Paper www2.scholastic.com/browse/article.jsp?id=324&print=1 Trends in Math Achievement: The Importance of Basic Skills – Tom Loveless, Brown Center on Educational Policy, The Brookings Institute www.brookings.edu/speeches/2003/0206education_loveless.aspx www.brookings.edu/speeches/2003/0206education_loveless.aspx Bloom, B. (1986, Feb.) Automaticity: the hands and feet of genius. Educational Leadership, 43 (5), 70-77. Burnett, James (2008) Developing the Essential Strategies for Computation. Origo Education. www.origomath.com Klein, D. (2005). The state of math standards. Thomas B. Fordham Foundation Washington, DC www.edexcellence.netwww.edexcellence.net