Breakeven 9-20 class notes

In the button making story, we found that when you order 200 buttons, neither company gives you a better deal.  200 buttons cost $155 whether you get them from PB or from BFY.  If you get one more button over 200 from PB, you pay 15 cents more for a total of $155.15.  If you get one more button over 200 from BFY, you pay 40 cents more for a total of $155.40.  So, for an order greater than 200 buttons, PB gives you an better deal, and that is what you recommend.

In the bellringer we solved

                                       200x = 12500 +15x

The money you get from selling x buttons at 200 cents each = the cost of buying those buttons from PB.

                              x = 68

68 is the number of buttons that makes the money coming in equal the money going out.

                             $136 = $136

68 is the breakeven number of buttons.

If you sell more than the breakeven number, you make money because revenue > cost.
For 80 buttons, 200(80) = $160 and 12500 + 15(80) = $137, so you make 160 - 137 = $23

If you sell fewer than the breakeven number, you lose money because cost > revenue.

For 40 buttons, 200(40) = $80 and 12500 + 15(40) = $131, so you make 90 - 131 = negative $41 (loss)

Profit is the money you make, calculated by subtracting cost from revenue.

Homework for 9-21 is page 34, items 6 and 7.

Homework for 9-19 page 32 items 1, 2, 3, 4, 5, 6

Homework for 9-19 page 32 items 1, 2, 3, 4, 5, 6

Use any method, show your work.  You solved some of these problems in class.

Homework and class notes

Homework for Friday 9-16:  From page 31, items b, c, d, e, f, and page 32, items a, b, c, d, e, f, choose three equations to solve.  Be prepared to show your work and explain your answer in class.

Today we worked an example of solving an equation with pictures of square and rectangle shapes ("tiles").  Pairs of positive and negative tiles were erased to simplify the picture.  In our example, one rectangle (t) equals seven squares (7).

Today students presented their small dry-erase solutions to equations.

Class notes 9-14 "UNDOing" to solve equations

Undoing an equation means using inverse operations to get back to the variable (mystery number, Who Am I?)
Look at the way an equation was built.  The last operation that built the equation is the first operation to be undone.  In most cases this means using PEMDAS in the other direction.  We use SADMRP to remember this.

Work from outer to inner, towards the grouping symbols.
First, look for Subtractions and Additions to undo. Use addition and subtraction, the inverses.
Next, look for Divisions and Multiplications to undo. Use multiplication and division, the inverses.
Next, look for Exponents to undo.  We use "R" in SADMRP because the inverse of exponentiation is Root (taking the nth root, finding the nth root).
P means it's time to work inside the Parentheses (grouping symbols).

Homework is page 29, items b, d, f.
Be prepared to talk about the steps of UNDOing, similar to the right-to-left arrows and ovals on page 29.

Homework for 9-14

Homework for 9-14:  Springboard textbook, pages 27 and 28, items 4, 5, 6, 7

Class notes 9-13

Building an equation from an unknown number ("me", "what number am I?") uses the words closest to the number to suggest the first operations and grouping.  Each word phrase adds another operation or grouping.  Finally, you translate "am I" or "I am" into an equal sign.


Solving an equation for an unknown number looks at the operation farthest away from the number so you can undo it.  Remember that when you undo something, such as when typing at a computer, you affect the last thing you did.  When you undo in math, you affect the last operation used to build the equation.


To undo a math operation, you use its inverse.  Multiplication and division are inverses. Addition and subtraction are inverses.  If the equation's last piece was adding 3 (" + 3 ") to undo it so you can make the equation simpler you should subtract 3 (" - 3") from both sides.


To evaluate an expression or to build an equation, you use the order of operations PEMDAS.


To solve an equation, you use the order of undoing operations SADMRP.
We use R instead of E because Root is the inverse of Exponent.  If raising to a power/raising to an exponent was used to build an equation, tkaing the root/finding the root is used to undo the equation

Class notes 9-08 and 9-12