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Cissi Kale

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  1. Dimension 2000’sElementary Math Workshop Cissi Kale

  2. Workshop Objectives • Discuss GPS changes for grades 3-5 • Learn about the Five Stages of Teaching and Learning Math • Define and model ‘high yield’ instructional engagement strategies that address key math concepts associated with GPS standards • Investigate uses of the High Achievement Math Program

  3. What can Dimension 2000 bring to the math classroom? • High yield instructional strategies • Support materials for assessment, vocabulary, mental math, computation, and problem solving • Creative ways to motivate students and hold their interest in math and learning

  4. Contact Information • Cissi Kale • Cissikale@gmail.com • 770-356-3856 • www.dimension2k.com • Dr. Ed Thomas • Dimension2k@att.net

  5. GPS-Georgia Performance Standards • GPS Goals • 3rd Grade Standards • 4th Grade Standards • 5th Grade Standards • Performance Standards/Tasks • Concepts/Skills to Maintain

  6. Goals of GPS • Focus on ACTIVELY engaging students in development of mathematical understanding by using manipulatives • There is a shift toward APPLYING math concepts and skills in context of authentic problems and for the students to understand the concepts rather than merely follow a sequence of procedures • It is the CONNECTIONS, the reasoned, logical connections, that make math manageable.

  7. Skills to maintain: Comparison of numbers Addition and subtraction of multi-digit numbers Length and time Geometric Shapes Money Area models (arrays) of multiplication Goals: Students will understand place value. Students will use decimals and fractions to represent parts of a whole. Students will understand the four arithmetic operations for whole numbers and apply them in basic calculations, and in problem solving situations. Students will understand length, perimeter, area, and time. Students will broaden understanding of characteristics of previously studied geometric figures. Students will solve problems by collecting, organizing, displaying, and interpreting data. 3rd Grade GPS

  8. Skills to maintain: Addition and Subtraction of decimals Multiplication and division of whole numbers Area/Perimeter Place Value Weight and Length Students will MASTER the four basic operations using whole numbers. Students will add and subtract decimals and common fractions with common denominators. Students will understand how and when it is appropriate to use rounding. Student will use common measurement units to determine weight. Students will develop their understanding of measuring angles with appropriate units and tools. Students will understand the characteristics of geometric plane and solid figures. They will use tables, graphs, and charts to record and analyze data. 4th Grade GPS

  9. 4th Notes • Multiply and divide both one and two digit decimals by whole numbers • Convert and use mixed numbers and improper fractions interchangeably • Compute using order of operations, including parentheses • Properties • Draw angles • Identify types of triangles based on angle measures • Represent unknowns using symbols such and  and  • Write and evaluate expressions using symbols and different values

  10. Skills to maintain: Add/subtract decimals Whole number and decimal comparison Angle measurement Length, area, and weight Number sense Add and subtract common fractions with like denominators Data usage and representation Characteristics of 2D and 3D shapes Order of operations Students will further develop their understanding of multiplication and division of whole numbers and decimals. Students will understand and investigate algebraic expressions. Students will expand their understanding of computing area and volume of simple geometric figures. Students will understand the meaning of congruent geometric shapes and the relationship of the circumference of a circle to its diameter. Students will use circle graphs and percentages to interpret statistical data. 5th Grade GPS

  11. 5th Notes • Multiplication and DIVISION of decimals • Add/subtract common fractions and mixed numbers with unlike denominators • MODEL multiplication and division of fractions • Understand meaning of percent • Find area of triangles and parallelograms • Find the area of a circle • Computer the volume of a cube and rectangular prism using formulae • Use variables, such and n and x, for unknown quantities in algebraic expressions • Investigate simple algebraic expressions by substituting numbers for the unknown.

  12. GPS Summary • APPLICATION and UNDERSTANDING are key! • More than algorithms • Algebra is integrated into all grade levels • NEW concepts are expected to be taught and understood • Performance Based Assessments -beyond the problems in the book • HIGHER EXPECTATIONS for ALL students

  13. The Five Stages of Teaching and Learning Math

  14. 21 3/4 2 5 Stages-Knowledge Which of the following is a fraction?

  15. 5 Stages-Understanding 20 0 Graph 16/17 on the number line.

  16. 5 Stages-Understanding Explain the meaning of 3/4 3/4 refers to 3 equal parts or pieces when 4 equal pieces are needed to make one whole.

  17. 5 Stages-Proficiency Simplify without errors 1) 3/4 + 1/2 =2) 5 – 2/3 =3) 1/2 ( 1 – 1/4) = 4) 4 ÷ 3/4 =

  18. 5 Stages-Application Find the perimeter and area of: 3 1/4 in. 7/4 in.

  19. 5 Stages-Application Complete the equivalency statements. 2 1/2 gallons = ? quarts 6 3/4 days = ? hours 30.25 meters = ? centimeters

  20. 5 Stages-Inclusion Include fractions in the math we teach all year. Brainstorm Ideas

  21. Math Concept: Understanding and Applying VariablesReinforcing Math Facts Teaching Strategies: Game Competition: Developing and implementing competitive games that incorporate essential math skills and concepts Modeling and Experimentation: Using real, relevant, and tangible experiences to model abstract mathematical concepts

  22. Understanding Variables Algebra War Games: Player A: x y Player B: Winning game rule: 2x + y x + y x y

  23. Math Concept: Mental Math and Extended Facts Teaching Strategy: Mental Math Strings: Daily mental math challenges that require students to remember and manipulate numbers generated by five or six teacher lead commands.

  24. Previewing Our String 1. How many quarts are in one gallon? 2. How many pints are in a quart? 3. How do you square a number? 4. How do you cube a number? 5. What’s the first odd whole number? 6. What’s the first even whole number? 7. How do you round a number to the nearest ten? 8. How many degrees are in a right angle? 9. How many sides are in a decagon? 10. How many vertices are in a decagon?

  25. Math Strategy Mental Math Strings Start with the number of quarts in six gallons. Round your answer to the nearest ten. Subtract the number of vertices in a decagon. Square your result. Subtract the number of degrees in a right angle. Multiply by the second odd whole number. *

  26. Math Strategy Mental Math Strings Start with the number of quarts in six gallons. 24 20 Round your answer to the nearest ten. 10 Subtract the number of vertices in a decagon. 100 Square your result. 10 Subtract the number of degrees in a right angle. 30 Multiply by the second odd whole number. *

  27. Math Strategy Mental Math Strings Start with the number of quarts in six gallons. Round your answer to the nearest ten. Subtract the number of vertices in a decagon. Square your result. Subtract the number of degrees in a right angle. Multiply by the second odd whole number. *

  28. Implementing Mental Math Strings 1. Determine extended math facts you want your students to know. 2. Build your mental math strings. 3. Do one string each day. 4. Preview information in the mental math string. 5. Implement the mental math string. 6. Share results, congratulate students who succeed and encourage those who don’t. 7. Invite a student who succeeds to repeat the string in front of the class. 8. Invite students to make their own and share with the class.

  29. Math Concept: Mental Math and Math Facts Teaching Strategies: Game Competition: Developing and implementing competitive games that incorporate essential math skills and concepts

  30. Digit Products and Sums The digit sum of 24 is 6 because 2 + 4 = 6 The digit productof 24 is 8 because 2 • 4 = 8

  31. Math Concept: Proficiency with Computation, and Concepts Associated with Standards Teaching Strategy: Daily Warm ups, Gray-Band Computation Problems, and Computation Challenges

  32. Dr. Thomas’s Math Challenge #1 Find the sum of the whole number factors of 32. A) 13 B) 31 C) 63 D) 72 1. 25 + 12 = 2. 76 – 19 = 3. 23 • 11= Numbers and Operations Sixth Grade Warm-ups

  33. Problem Solving Collaboration Communication Connections Reasoning P3CR

  34. Thank you for participating in a Dimension 2000 Workshop~ www.dimension2k.comdimension2k@att.netCissikale@gmail.com