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Chapter 6 Dividing & Building Expressions Ch. 6 ---------6.1.1 *I can divide quantities & represent the result in multiple ways. *I can use visual fraction models & equations to represent division. What if we had 6 Twizzlers & wanted to share them evenly amongst 5 people?: 6/5 = 1.2 pieces or 1 1/5 We could give 1 whole piece to each person & divide the remaining piece amongst the 5 people George Franklin Abe Thomas Barrack We could give 1 whole piece to each person & divide the remaining piece amongst the 5 people George Franklin Abe Thomas Barrack We could give 1 whole piece to each person & divide the remaining piece amongst the 5 people George Franklin Abe Thomas 6/5 = 1.2 or 11/2 Each person gets 1 1/5 pieces! Barrack Area of Trapezoids: Area of Trapezoids: To calculate the area of this trapezoid: Here is a video to help you: http://www.youtube.com/watch?v=pnjCyF09m2I 8 A= 8+12 * 6 2 6 Area = 60 Sq. Units 12 Ch. 6 ---------6.1.2 *I can see that a fraction can be seen as one number formed by division *I can make visual models to represent division problems. *I can make sense of long division algorithm. Ch. 6 ---------6.1.3 *I can identify problems that can be solved using division *I can use multiplication to check division. A Quick Review Of Division: -A simple way to think about division is that is REPEATED SUBTRACTION Example: What is 48/12? *Take 48 & subtract 12----you get 36 *Repeat: 36-12 = 24 *Repeat: 24-12 = 12 *Repeat: 12-12 = 0 *You had to do 4 subtractions, so 48 / 12 = 4 …but this could take a really long time for a problem like 3768 / 12--- so that is why we have to learn to use another method called ‘Long Division’ Review: Parts Of A Division Problem: Ch. 6 ---------6.1.4 *I can divide fractions by other fractions. *I can represent division problem in multiple ways. Here are a couple of videos that explain long division: http://www.youtube.com/watch?v=eIUoIhfupuA This video explains long division w/ a decimal remainder: http://www.youtube.com/watch?v=6TDLMkOCQkU Ch. 6 ---------6.2.1 *I can review the order of operations as I evaluate real-world formulas for given values. *I can evaluate expressions w/ whole-number exponents. Mathematical Rules *A rule is an equation or inequality that represents the relationship between two numerical quantities. *We often use a rule to represent the relationship between quantities in a table, a pattern, a real-world situation, or a graph. Order Of Operations *The specific order in which certain operations are to be carried out to evaluate or simplify expressions *Parentheses (or other grouping symbols) *Exponents (powers or roots) *Multiplication & Division (from left to right) *Addition and Subtraction (from left to right). Term *A term is part of an expression *It can be a single number, a variable, or numbers & variables multiplied together *It is a single number, variable, or the product of numbers & variables, Ch. 6 ---------6.2.2 *I can use variables to represent unknown lengths. *I can use algebra tiles to find area. *I can combine like terms -Algebra Tiles- Manipulatives that will help you to better understand certain concepts using algebra. x² x 1 Here is a video explaining how to use algebra tiles! Ch. 6 ---------6.2.3 *I can understand that combining like terms is a form of sorting. *I can find the lengths o the sides of algebra tiles & combine like terms as we find perimeters. Remember the definition of VARIABLE: A variable can be replaced by various numbers to represent various situations: Example: $8.00(x) = Money Earned A variable can be replaced by various numbers to represent various situations: Example: $8.00(x) = Money Earned In this example the variable X can = the number of hours worked. -…so if a person earned $8.00 per hour working, the X would help us determine how much money they would make based on how many hours they worked. -If a person worked 25 hours: $8.00(25) = $200 -If a person worked 45 hours: $8.00(45) = $360 WHAT DOES IT MEAN TO COMBINE LIKE TERMS? *LIKE TERMS- Terms that contain the same variable *COMBINING LIKE TERMS- Is a way of simplifying an expression. WHAT DOES IT MEAN TO COMBINE LIKE TERMS? *LIKE TERMS- Terms that contain the same variable *COMBINING LIKE TERMS- Is a way of simplifying an expression. Ch. 6 ---------6.2.4 *I can combine like terms to generate equivalent expressions. *I can generate equivalent expressions by finding the perimeter of complex figures composed of algebra tiles Equivalent Expressions -Two expressions are equivalent if they have the same value. -For example, 2 + 3 is equivalent to 1 + 4. 2 + 3 is equivalent to 1 + 4 3(x + 3) is equivalent to 3x + 9 2 + 3 is equivalent to 1 + 4 6( + y + 2) = 6 + 6y + 12 Coefficient -A number multiplying a variable or product of variables. -For example, -7 is the coefficient of -7xy². 4x – 7 = 5 5x² + 7x + 6 (4 is the coefficient) (5 & 7 are the coefficients) Constants -Term that does not contain variables & does not change no matter what the value of x is. -A ‘number on its own’ -For example, 7 & 5 are the constants here >>>>>>>>>>> X+5=9 6x² - 3x + 5 (5 & 9 are constants) (5 is the constant) Simplifying Expressions -Means to write an expression in the most compact or efficient way possible. -The value of the expression does not change when it is simplified. -Involves combining ‘like’ terms *Notice the 2x and the 4x were combined to make 6x *The 1 and -3 were combined to make -2 *Notice the 3a²b and the 2a²b were combined to make 5a²b Ch. 6 ---------6.2.5 *I can visually demonstrate that x can represent any number. *I can create equivalent expressions by combining like terms, & evaluating expressions, including those w/ exponents.