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
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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.
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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 Operations4.2 Geometry & Measurement4.3 Patterns & Algebra4.4 Data Analysis, Probability, & Discrete Math4.5 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 4th 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 1 Addition & Subtraction Facts to 181st quarter - Count on 1, 2, 3 addition2nd quarter - Count back 0, 1 subtraction3rd quarter - Doubles/doubles +1, +2, +3 addition3rd quarter - Count back 0, 1, 2 subtractionMake a “10”
GRADE 2 Addition & Subtraction Facts to 18Review – count on 1, 2, 3 additionReview – doubles/doubles +1, 2, 3 additionReview – count back 1, 2, 3 subtractionReview – make “10”Fact FamiliesSkip counting x2, x5, x10
GRADE 3 Addition & Subtraction Facts to 18Review – addition/subtraction to 18Multiplication 0-10 & Division 1-10Doubling = x21st quarter – x0, x1, x2, x52nd quarter – x0, x1, x2, x3, x4, x5 and ÷1, 2, 53rd quarter – x0-10 and ÷1, 2, 3, 4, 5, 10End of year – Multiplication 0-10 & division 1-10
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
•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
•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.net