Meeting the Goals of an Integrated Mathematics Curriculum. Ed Thomas Dimension 2000

Transcription

1 Meeting the Goals of an Integrated Mathematics Curriculum Ed Thomas Dimension 2000

2 Ed Thomas Dimension

3 Integrated Math I and Integrated Math II Achieve and Succeed Program Order Form Program Cost $ SREB Price $ Mental Math Strings Function Analysis Activities Integrated Algebra and Geometry Activities Weekly Integrated Math Challenges Monday- Wednesday- Friday Dimension Hwy. 92 South Fayetteville, GA Dr. Ed Thomas Daily Problem-Solving Warmups Name School Street City - Zip Phone Date PO# Math I Integrated Program Quantity Math II Integrate Program Quantity Total $149 = Shipping and Handling 10% Visa/Master Card Expiration Date Total Cost Fax your order today

4 Word Scramble 1. Find the average of 2, 3, 6, 6, and Evaluate 2ab c where a= 3, b= 4, and c= Find the number that is one more than the cube of two. 4. Find the square root of Find the hypotenuse of a right triangle with leg measures 12 and Find f(5.5) when f(x)= 2x Find one more than twice ten. 8. Find the GCF between 16 and 48. a b c d e 1-5 f g h i j 6-10 k l m n o p q r s t u v w x y z 26

5 Math Concept: Sums and Reasoning Teaching Strategies: Five Stages of Learning: Accounting for knowledge, understanding, skill proficiency, applications, and retention

6 Five Stages Knowledge What s the mathematical term for: n? arithmetic series What s the formula for finding the sum? n ( n + 1) 2

7 Five Stages Understanding For any sum of the form: n? Why does the formula work? Sum = n ( n + 1) 2

8 Five Stages Understanding Let s look deeper = (n+1) the sum of each pair 10 = n 2 = the number of pairs n ( n + 1) 2

9 Five Stages Understanding n ( n + 1) 2 20 ( 21) 2 = = 210

10 Five Stages Proficiency Find the following sum: / 2 = = 20,100

11 Five Stages Proficiency Peer Problem Solving Challenge Make 2 summation problems of the form n On separate paper, solve the two problems you made Exchange problems with a partner and solve your partner s problems Swap back and evaluate each other s work

12 Five Stages Application If ten people are in a room, how many handshakes would take place if each person shook hands with every other person exactly once?

13 Connecting the Handshake Problem to Geometry

14 Connecting the Handshake Problem to Geometry 1 2 Sides + Diagonals n + n(n 3)

15 n + n(n 3) 2 = 2n + n(n 3) 2 2 = n 2 n 2

16 Connecting the Handshake Problem to Geometry (n 1) + n (n 1)n 2 = n2 n 2

17 Teaching Integrated Math Monday - Wednesday - Friday Warmups The following samples are part of Dimension 2000 s Integrated I and Integrated II Achieve and Succeed Programs.

18 Dimension 2000's Integrated Math Challenge #1 Which value represents the square of five less than twice the value of x if x=10? A) 5 B) 125 C) 150 D) 225 Mental Challenge: Find 250% of 40. Problems from Dr. Thomas s Math Challenges Series, Dimension Algebra and Number Sense Level 1

19 Dimension 2000's Integrated Math Challenge #2 Line m is parallel to line n. Find the equation of line n. m B( 8, 4.5 ) A) y = 2x + 4 B) y = (1/2) x - 4 A( 4, 2.5 ) n C) y = (1/8) x 4 D) y = ( 1/2) x + 4 S( 4, 2 ) Mental Challenge: Multiply Problems from Dr. Thomas s Math Challenges Series, Dimension Geometry and Measurement Level I

20 Dimension 2000's Integrated Math Challenge #3 Use algebraic notation to represent the square of four less than three times a number. A) 4 3x 2 B) (3x 4) 2 C) 4 2 < 3x D) (3x 4 2 ) Mental Challenge: Find 250% of 60. Problems from Dr. Thomas s Math Challenges Series, Dimension Algebra and Number Sense Level I

21 Dimension 2000's Integrated Math Challenge #4 Isosceles trapezoid ABCD with median EF is given. Find the measure of angle CEF. A) 120 degrees B) 110 degrees C) 105 degrees D) 205 degrees C Mental Challenge: E A Add B F 60 D Problems from Dr. Thomas s Math Challenges Series, Dimension Geometry and Measurement Level I

22 Dimension 2000's Integrated Math Challenge #5 The width of rectangle ABCD is five more than half its length. The length is 42cm. Find the perimeter of the rectangle. A) 63 cm. B) 136 cm. C) 110 cm. D) 120 sq. cm. Mental Challenge: A D 42 Simplify 4 ½ ¼. B C Problems from Dr. Thomas s Math Challenges Series, Dimension Geometry and Measurement Level I

23 Dimension 2000's Integrated Math Challenge #5 Find the midpoint of the points shown. A) i B) 10 2i C) i D) 1 + 3i Mental Challenge: Find the sum i R Problems from Dr. Thomas s Math Challenges Series, Dimension Complex Numbers and Geometry Level II

24 Dimension 2000's Integrated Math Challenge #36 Find the area of the figure below. L= (3x + 1) W= (2x 1) Check your answer using x= 6. Mental Challenge: Multiply Problems from Dr. Thomas s Math Challenges Series, Dimension Polynomials, Quadratic Expressions, and Geometry Level II

25 Dimension 2000's Integrated Math Challenge #50 n(n + 1) Use the formula to solve the problem below. 2 Twenty people in a room shake hands with each other once and only once. How many total handshakes take place? Mental Challenge: Subtract: Problems from Dr. Thomas s Math Challenges Series, Dimension Arithmetic Series and Algebra Level II

26 Dimension 2000's Integrated Math Challenge #75 The circle below is divided into 60 and 30 degree sectors. Find the area of the blue portion of the circle. Note, r= 9. A) 9π sq. units B) 27π sq. units C) 18π sq. units D) 81π sq. units Mental Challenge: Solve for x: 8x 32 = 128 Problems from Dr. Thomas s Math Challenges Series, Dimension Algebra and Geometry Level II

27 Dimension 2000's Integrated Math Challenge #87 The diameter of a typical billiard ball is 2.25 inches. Find the surface area of a sphere with diameter 2.25 inches to approximate the surface area of a billiard ball. A) (81/16)π sq. in. B) (9/4)π sq. in. C) (3/2)π sq. in. D) 4π sq. in. Mental Challenge: Find the sum of the even numbers between 10 and 20. Problems from Dr. Thomas s Math Challenges Series, Dimension Algebra and Geometry Level II

28 Teaching Integrated Math Function Analysis Activities The following samples are part of Dimension 2000 s Integrated I and Integrated II Achieve and Succeed Programs.

29 Dimension 2000 Function Analysis Activity Function rule: Base Graph Modified Graph Domain Range X-intercepts Y-intercepts Interval of increase Interval of decrease Maximum value Minimum value Lines of symmetry Even, odd, neither Dr. Thomas s Math Challenges Dimension

30 Dimension 2000 Function Analysis Activity Function? yes or no Piecewise Graph 10 Piecewise Equation Domain Range 5 X-intercepts Y-intercepts Interval of increase Interval of decrease Maximum value Minimum value -5 Lines of symmetry 2-10 Dr. Thomas s Math Challenges Dimension

31 Teaching Integrated Math Integrated Algebra and Geometry Activities A Sample was provided at the workshop.

32 Teaching Integrated Math Integrated Math Challenges The following samples are part of Dimension 2000 s Integrated I and Integrated II Achieve and Succeed Programs.

33 Dr Thomas s Integrated Math I Challenge

34 Dr Thomas s Integrated Math II Challenge #5: Equations, Area, Perimeter Dr Thomas s Integrated Math II Challenge #6: Equations, Area, Exponents 1. Find the value of x if 2(x - 6) - 10 = 5(x -2). a) 4 b) - 4 c) 2 d) 3 e) 6 1. If 4x + 2y - 6 = 4, find the value of 6x + 3y - 9. a) 4 b) 8 c) 5 d) 6 e) 9 B 2. Using the given measures, find the value of the area of triangle ABC. A C 6 2. An isosceles triangle is inscribed in a square with side length = 1. Find the area of the isosceles triangle. 1 a) 84 b) 94 c) 86 d) 36 e) The Wilsons have a rectangular vegetable garden which is 25 feet longer than it is wide. They used exactly 222 feet of fence to enclose the garden. Find the width of the garden. a) 43ft b) 50ft c) 68ft d) 33ft e) 107 ft a) 1 b) 1 c) 1 d) 2 e) If a = 2b, find the value of (7a - 2b) (8b - 4a) a) 0 b) 1 c) 4 d) 8 e) 12 Extra for experts: Use the definition of a circle to argue that no portion of the edge of a circle can contain a line segment, even if it is infinitesimally small. Extra for experts: Given! n = n(n+1)/2, find!

35 Teaching Integrated Math Mental Math Strings The following samples are part of Dimension 2000 s Integrated I and Integrated II Achieve and Succeed Programs.

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37 Start with the number of lines of symmetry associated with a square Cube your answer Add the digits of your answer together Cube your answer Multiply by the number of sides on a hexagon Add the digits of your answer together