4Unit 1 – Key Ideas A quantity is a an exact amount or measurement. A quantity can be exact or approximate depending on the level of accuracy required.Examples:1 -Convert 5 miles to feet.2 -Convert 60 miles per hour to feet per minute.Unit 1 – Key Ideas
5Convert 5 miles to feet. 1 mile = 5280 feet 5 miles = 5 *5280 feet (does this need to be exact?)Convert 5 miles to feet.
7There are situations when the units in an answer tell us if the answer is wrong. For example, if the question called for weight and the answer is given in cubic feet, we know the answer cannot be correct.Tip:
8Review Examples The formula for density d is d = m/v where m is mass and v is volume.If mass is measured in kilograms and volume is measured in cubic meters, what is the unit rate for density?Review Examples
9Key Ideas: Expressions, Equations and Inequalities Arithmetic expressions are comprised of numbers and operation signs.Algebraic expressions contain one or more variables.The parts of expressions that are separated by addition or subtraction signs are called terms.The numericalfactor is called the coefficient.Key Ideas: Expressions, Equations and Inequalities
10Example: 4x2 +7xy-3 It has three terms: 4x2, 7xy, and 3. For 4x2, the coefficient is 4 and the variable factor is x.For 7xy, the coefficient is 7 and the variablefactors are x and y.The third term, 3, has no variables and is called a constant.Example: 4x2 +7xy-3
11How should we approach the solution to this equation? Example: The Jones family has twice as many tomato plants as pepper plants. If there are 21 plants in their garden, how many plants are pepper plants?
12Unit 2: Reasoning with Equations and Inequalities Understanding solving equationsSolve equations and inequalities in one variableSolve systems of equationsRepresent and solve equations and inequalities graphically.Unit 2: Reasoning with Equations and Inequalities
13Important Tips Know the properties of operations Be familiar with the properties of equality and inequality. (Watch out for the negative multiplier.)Eliminate denominators (multiply by denominators to eliminate them)Important Tips
14Solve the equation 6(x + 4) = 2(y + 5) for y. Example
15Example Karla wants to save up for a prom dress. She figures she can save $9 each week from themoney she earns babysitting.If she plans to spend up to $150 for the dress, how many weeks will it take her to save enough money?Example
16This equation can be used to find h, the number of hours it takes Flo and Bryan to mow their lawn. How many hours will it take them?Example
17A manager is comparing the cost of buying ball caps with the company emblem from two different companies.Company X charges a $50 fee plus $7 per cap.Company Y charges a $30 fee plus $9 per cap.For what number of ball caps will the manager’s cost be the same for both companies?A. 10 capsB. 20 capsC. 40 capsD. 100 capsExample
18Which graph would represent a system of linear equations that has multiple common coordinate pairs? A BC DExample
19Example Which equation corresponds to the graph shown? A. y = x + 1 B. y = 2x + 1C. y = x – 2D. y = 3xExample