• Share
  • Email
  • Embed
  • Like
  • Save
  • Private Content
1150 day 5
 

1150 day 5

on

  • 386 views

 

Statistics

Views

Total Views
386
Views on SlideShare
294
Embed Views
92

Actions

Likes
0
Downloads
5
Comments
0

1 Embed 92

http://math1150-ss2012.blogspot.com 92

Accessibility

Categories

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

    1150 day 5 1150 day 5 Presentation Transcript

    • AlgebraicThinkingandAlgebra
    • Algebraic Thinking involves:•Recognizing patterns•Modeling situations withobjects, pictures or symbols•Analyzing the effects of change Understanding variables (letters that stand for an unknown) is key to algebraic thinking.
    • The evolution of algebraic thinking (an example) 3 + =3 1 + 2 = 3 + 2 = 3 x + 2 = 3
    • MAP released item, 2006, grade 3
    • DESE released item 2004 MAP test, grade 4
    • MAP released item, 2006, 5th grade
    • MAP released item, 2006, grade 7
    • What does an equal sign mean? 1 + 2 = 3 1 + 2 = ETA Cuisenaire
    • Model the equation using a balance scale. + 2 = 3
    • Model the equation using a balance scale. + 2 = 3 2 1
    • x + 2 = 3 -2 -2x = 1
    • http://illuminations.nctm.org/ActivityDetail.aspx?ID=26http://illuminations.nctm.org/ActivityDetail.aspx?ID=33
    • Properties of EquationsAddition Property of Equality If a = b, then a + c = b + c 4=4 4+2=4+2
    • Multiplication Property of Equality If a = b, then a · c = b · c 4=4 4·2=4·2
    • Distributive Property of Multiplication overAddition a(b + c) = a · b + a · c 2(3 + 4) = 2 · 3 + 2 · 4 5(14) = 5(10 + 4) = 5 · 10 + 5 · 4 = 50 + 20 = 70
    • Model the equation 2x + 1 = 7 using a balance scale. x +2x + 1 x = 7 1 6 3 3
    • If you triple a number and add 3, the result is 36. Findthe number. Algebra Algebraic methods 3x + 3 = 36 - 3 -3 3x = 33 3 11 36 11 33 11 3 3 3 x = 11
    • Kate bought a TV on sale for $160. If the sale was a“1/3 off” sale, what was the original price of the TV?AlgebraLet x = the original price original price - 1/3 of the original price = sale price 1 x - x 160 3 3 2 3 x 160 2 3 2 x = 240
    • Kate bought a TV on sale for $160. If the sale was a“1/3 off” sale, what was the original price of the TV?Algebraic methods $80 $80 $80 1 $160 Sale price off 3 3(80) = $240
    • Write down any three consecutive numbers.Multiply the first and third numbers.Square the middle number.What do you notice? First times last is one less than square of middle 5 6 7 36 n–1 n n+1 35 n2 (n – 1)(n + 1) 10 11 12 121 (n – 1)(n + 1) = n2 – 1 120 difference of squares
    • FunctionsA function from set A to set B is a correspondencefrom set A to set B in which every element of set Ais paired with exactly one element of set B. Input (domain) Output (range)
    • DESE sample MAP item, 3rd grade
    • Representations of Functions Table Ordered pairs Input Output {(1, 4), (2, 8), (3, 12), (4, 16)} 1 4 2 8 Domain: {1, 2, 3, 4} 3 12 Range: {4, 8, 12, 16} 4 16Arrow Diagram Function Notation 1 4 2 8 f(x) = 4x 3 12 4 16
    • Representations of Functions Graph Input Output 16 1 4 2 8 12 3 12 output 4 16 8 4 1 2 3 4 input
    • Use function notation to write a rule for the function {(1, 2), (2, 5), (3, 8), (4, 11)}Input Output Arithmetic sequence 1 a1 = 2 an = a1 + (n – 1)d 2 a2 = 5 a1 = 2 3 a3 = 8 d=3 4 a4 = 11 an = 2 + (n – 1)3 an = 2 + 3n – 3 an = 3n – 1 f(x) = 3x - 1
    • Composite Functions x f g f(x) g(f(x)) Notation: (g o f)(x) means g(f(x))
    • If f(x) = 2x – 1 and g(x) = 3x + 1, what is (f o g)(3) ? (f o g)(3) = f(g(3)) g(3) = 3(3) + 1 = f(10) =9+1 = 19 = 10 f(10) = 2(10) – 1 = 20 – 1 = 193 g f 10 19