2 3x-4=9 What is a term? A part of an equation or expression Coefficient- A number used to multiply a variableConstant- A number on its own3x-4=9CoefficientConstantsTermTermTerm
3 7y-2+9x=13 Example Terms: Coefficients: Constants: Variables: 7y , -2 , 13, 9x7, 9-2, 13Y, X
4 What EXACTLY does the same or “Like” mean? Terms with the same variable or variables and raised to the same powerSame: 5x and 12xSame: 10 and 7Same: 9z and 14zSame: 8y5x, 8y, 9z, 10, 12x, 14z, 7
5 Document cameraI couldn’t find a very fun video but I did really like the way the woman explained the concept in these videos so I think I’ll just use the document camera to do a shorter version of what she did in these following videosexpressions/simplifying-expressions-examples/like-terms-definitionexpressions/simplifying-expressions-examples/add-like-terms-example
6 What is Combining like terms If numbers have a variable, then you can combine only ones that have the same variableAlso if numbers don’t have variables they can only be combined with other numbers that don’t have variablesLike terms could be combined by adding their coefficients
7 How To Combine like Terms First, change our operators to addition by using keep- change-changeSecond, Reorder the expression so like terms are next to each otherFinally, combine like terms by adding their coefficients (simplify)
8 + – + + +( – ) + + Combine like terms –( – ) +By combining apples with apples and oranges with oranges, you get...+Emphasize equivalent equations3 apples + 2 oranges +(- 2) apples + 2 orangescoefficients1 appleoranges
9 4 + 2 -2 -1 =4 +2 +(-2 )+(-1 ) = + + + = + =2 +1 Example Good Movies = (-2 )+(-1 )=No notes= =
10 Remember: adding the opposite cancels out so Example: Simplify 2x - 3y + 5x + 3y + 12Change everything to addition2x + (-3y) + 5x + 3y + 12Reorder your terms2x+5x+(-3y)+(3y)+12Find the like terms2x +5x +(-3y) +3y +12Combine like terms7x +12Remember: adding the opposite cancels out so(-3x)+(3x)=0
11 Simplify: 4x2-13y+4x+12x2-3x+3 4x2 +(-13y) +4x +12x2 +(-3x) +3 Change all operations to addition using keep-change-change4x2 +(-13y) +4x +12x2 +(-3x) +3Reorder the termsBefore bringing up the first step ask the students where we will need to apply kccThis slide will allow me to emphasize how like terms also must include variable to the same powerHave the students do this problem on their whiteboards4x2 +12x2+ 4x +(-3x)+(-13y)+3Combine like terms (simplify)16x2 + x + (-13y) + 3
12 Combine like terms A. 14a – 5a 14a +(-5a) 9a Change any subtraction to addition14a+(-5a)Reorder TermsFor the first example I can also pose the question: what if I had 14a and just -5, would I have like terms?If I get asked why we have to apply keep change change to the first example I’ll let students know that examples are going to get more complicated so we want you to get in the habit of applying this process while the problems are easierFirst problem in their notes, second problem on the white boardsIdentify like terms.9aCombine coefficients: 14 – 5 = 9
13 Combine like terms B. 7y + 8 – 3y – 1 + y 7y +8 +(-3y) +(-1) +y Change any subtraction to additionB. 7y + 8 – 3y – 1 + yReorder Terms7y +8 +(-3y) +(-1) +yIdentify like terms ; the coefficient of y is 1, because 1y = y.7y +(-3y)+y+8 +(-1)Combine coefficients:7 – = 5 and 8 – 1 = 75y + 7
14 Combine like terms (on the boards). Change any subtraction to additionC. 4q – qReorder Terms4q +(-1q)Identify like terms ; the coefficient of q is 1, because 1q = q.3qCombine coefficients:4 +(-1) = 3.
15 Combine like terms (on the boards). D. 5c + 8 – 5c – 2Change any subtraction to addition5c + 8 +(-5c) +(–2)Reorder Terms5c +(-5c) +8 +(–2)Identify like terms ; the coefficient of q is.6Combine coefficients:4 +(-1) = 3.
16 Combine like terms (on the boards). F. 5m2 – 7m – 8 + 4Change any subtraction to addition5m2 +(-7m) + (-8) + 4Reorder Terms5m2 +(-7m) +(-8) +4Identify like terms ; the coefficient of q is.Combine coefficients:4 +(-1) = 3.5m2 – 7m – 4
17 Combine like terms (in your notes). E. 4m + 9n – 24m +9n +(-2)Change any subtraction to additionReorder Terms4m + 9n – 2Identify like terms ; the coefficient of q is.Combine coefficients.No like terms.