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?
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 partners
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. descartess contribution Using letters
to represent numbers in mathematical statements was introduced by
Ren 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. Ren
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. 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 - ( 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 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 of the
original amount left. What is the first thing that must be done
before we express this situation using symbols? x - 6 = 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 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 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 ( x) 2 3.x - 9 = x 4.x 2 + 2x - 3 = 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? x - 21 = 15 How would you solve this? x x = 1
- 9x + 22
