Pre Algebra chapter 1 notes
- 1. 1.1 Bar Graphs and Line Graphs Bar Graph- uses bars to represent data (usually compares different categories) Line Graph – shows a line relationship between two data sets (usually shows changes over time) Fish Dog Snake Cat 4 3 2 1 0 20 30 1988 1989 1990 1991 1992 1993 1994 Number of Postmasters Postmasters years Kids Pets Favorite Pets
- 2. 1.1 Histograms Frequency Table- shows classes of things, a tally, and the frequency at which they occur Example – Hours watching TV 0, 1, 5, 4, 0, 1, 4, 1, 3 Histogram – are useful when displaying intervals 0-1 2-3 4-5 Hours Students Hours watching TV 6 5 4 3 2 1 Hours Tally Frequency 0-1 IIII 5 2-3 I 1 4-5 III 3
- 3. 1.2 Order of Operations Order of Operations: PEMDAS P arenthesis first E xponents M ultiply and D ivide from left to right at the same time A dd and S ubtract from left to right at the same time M8A3.3.1 M8A2.1.1
- 4. 1.3 Writing Algebraic Expressions Examples : 6 more than a number -> 6 + n 8 less than twice a number -> 2t – x M7D2.2.1; M8D2.2.1; M8D2.2.2 addition subtraction multiplication division Plus Minus Times Divided by Sum Difference Product Quotient More than Less than Double Half of Increased by Decreased by By Separate equally Gain of Less of per
- 5. 1.3 Algebraic Expressions and Equations Algebraic expression – an expression that contains a variable. Ex . T+5 ; 6n; y Evaluate – substitute the value in and simplify (do it) Equation – when two quantities are equal (has an equal sign) Solve – find the value of the variable (do it) Solution – the answer Examples: Evaluate 8y +4 for y=10 8y + 4 = 8(10) + 4 = 80 + 4 = 84 Solve m - 3 = 15 m = 18 M7D2.1.2, M7D2.1.1; M8D2.1.3; M8D2.1.2
- 6. 1.4 Powers and Exponents 5 3 is a way to show repeated multiplication. 5 - is the base 3 - is the exponent , or the power 5 3 = 5 x 5 x 5 = 125 -2(9-6) 2 + 15 = -2(3) 2 +15 = -2(9)+15 = -18 + 15 = -3 Expanded form Evaluated form M8A1.1.1 M8A1.1.2 M8A2.1.1 M7A2.1.1
- 7. Variable – a letter that represents a number or numbers Substituting – replacing a variable with a number Example : x+5 = 12, does x = 9 work? 9 + 5 = 12? 14 = 12? NO! Solve 5x = 45 Do the opposite so 45/ 5 = 9 WATCH FOR THE SWITCHERO!!!!! In Division and subtraction when the variable is second! 10 – c =4 do switchero 10-4 = 6 20 = 5 do switchero 20 / 5 = 4 y 1.5 Equations and Solutions
- 8. 1.6 Perimeter and Area