Welcome Back to Math January 25, 2016 Today you will need:a pencil and eraser, your notebook, your tablet Math Message: Write an expression using letters and/or numbers: 1) The sum of m and n divided by 2 2) A number x decreased by 6 and then the difference is doubled. 3) Bill had d more than 3 times the number of baseball cards as Frank. Frank has f cards.

Do you agree? 1.(m + n) ÷ 2 2.(x - 6) 2 3.3f + d

Laila tells Julius to pick a number between one and ten. “Add three to your number and multiply the sum by five,” she tells him. Next she says, “Now take that number and subtract seven from it and tell me the new number.” “Twenty-three,” Julius exclaims. Can you figure out what Julius’ number was? Write down a guess that is too low. Write down a guess that is too high. How did you know? Working with a partner, record your operations that Julius used. What was his number? In the next round, Leila is supposed to pick a number between 1 and 10 and follow the same instructions. She gives her final result as 108. Julius immediately replies: “Hey, you cheated!” What might he mean?

can you write what you did algebraically? Add three to your number and multiply the sum by five. Now take that number and subtract seven from it and tell me the new number.

Create your own to share with your partner… 1. Write in words steps for your partner to follow. start with a number between one and ten. 2. Pass your notebook/whiteboard to your partner. 3. Your partner will write the steps algebraically and give you their final result. 4. Figure out what your partner’s number was based on only their final result.

How are these related? Which do you prefer? The number 1,157 is the sum of the squares of two consecutive odd integers divided by the difference between the two consecutive odd integers.

descartes’s contribution Using letters to represent numbers in mathematical statements was introduced by René Descartes in the 1600s. In that era, people used only words to describe mathematical statements. The use of letters, or symbols, to represent numbers not only brought clarity to mathematical statements, it also expanded the horizons of mathematics. René Descartes The reason we want to learn how to write a mathematical statement using symbols is to save time and labor. Imagine having to write the sentence: “The number 1157 is the sum of the squares of two consecutive odd integers divided by the difference between the two consecutive odd integers.”

What would the equation be? A whole number has the property that when half the number is added to 15, we get the number itself.

What would the equation be? A whole number has the property that when half the number is added to 15, we get the number itself. ½ x + 15 = x

What would the equation be? A whole number has the property that when the square of half the number is subtracted from five times the number, we get the number itself.

What would the equation be? A whole number has the property that when the square of half the number is subtracted from five times the number, we get the number itself. 5x - (½ x) 2 = x

can you write it another way?

What would the equation be? Paulo has a certain amount of money. If he spends 6 CHF, then he has ¼ of the original amount left. What is the first thing that must be done before we express this situation using symbols?

Begin all word problems by defining your variables. State clearly what you want each symbol to represent. Written mathematical statements can be represented as more than one correct symbolic statement. Break complicated problems into smaller parts, or try working them with simpler numbers. Remember...

What would the equation be? Paulo has a certain amount of money. If he spends 6 CHF, then he has ¼ of the original amount left. What is the first thing that must be done before we express this situation using symbols? x - 6 = ¼ x

can you write it another way?

what is this in words? 3 (d + 2) ÷ 10

what is this in words? (5x) 2 = x + 3

What would the equation be? The sum of three consecutive integers is 372.

What would the equation be? The sum of three consecutive integers is 372. x + x x + 2 = 372

What would the equation be? The sum of three consecutive odd integers is 93.

What would the equation be? The sum of three consecutive odd integers is 93. x + x x + 4 = 93

home learning: complete the practice worksheet

Welcome Back to Math January 26, 2016 Today you will need:a pencil and eraser, your notebook, your tablet Math Message: Write one of the word problems at your table as an equation. Pass your equation to your partner to have them check your work.

Write as algebraic equations 1.The sum of four consecutive even integers is A number is four times larger than the square of half the number. 3.Steven has some money. If he spends 9 CHF, then he will have ⅗ of the amount he started with. 4.The sum of a number squared and three less than twice the number is Miriam read a book with an unknown number of pages. The first week, she read five less than ⅓ of the pages. The second week, she read 171 more pages and finished the book. Write an equation that represents the total number of pages in the book.

Write as algebraic equations 1.x + x x x + 6 = x = 4 (½ x) 2 3.x - 9 = ⅗ x 4.x 2 + 2x - 3 = ⅓ x = x

sort the expressions into groups… Be ready to explain your reasoning…

linear expressions Linear expressions in x are special types of expressions. Linear expressions are expressions that are sums of constants and products of a constant and x raised to a power of 0, which simplifies to a value of 1, or a power of 1. Nonlinear expressions are also sums of constants and products of a constant and a power of x. However, nonlinear expressions will have a power of x that is not equal to 0 or 1.

4 + 3x 5 How many terms are there? Is there a constant? Is there a coefficient? Is it a linear or nonlinear expression? Why?

7x x How many terms are there? Simplify this expression... Is there a constant? Is there a coefficient? Is it a linear or nonlinear expression? Why?

94 + x + 4x Is it a linear or nonlinear expression? Why?

x 1 + 9x - 4 Is it a linear or nonlinear expression? Why?

these are linear equations. Why?

Which are true? Why? = = = = 1

Is this true if x = 2? Why or why not? x = 49

Is this true? Why or why not? x = 49 What if x = 2?

Is x = 5 a solution to... 8x - 19 = x ?

Is x = 5 / 4 a solution to... 3(x + 9) = 4x x ?

Is x = 6 a solution to... -2x x = 5 - 6x ?

expressions and equations practice... Please complete your work in your notebook. The answers are provided. Check your work only once you are done. Let Ms. Powell know if you have any questions.

Welcome Back to Math January 28, 2016 Today you will need:a pencil and eraser, your notebook, your tablet Math Message: Be ready to explain the home learning assignment # 14 and 15. Combine the like terms:

How would you solve this? 4x + 1 = 13

would you use the same technique to solve this? 3(4x - 9) + 10 = 15x x

Is this true? = 7 - 2

the 4 properties of equations If A = B then… A + C = B + C A - C = B - C A ∙ C = B ∙ C A = B C

How would you solve this? 2x - 3 = 4x

How would you solve this? ⅗ x - 21 = 15

How would you solve this? ⅕ x x = 1 - 9x + 22