Transcript Ex - Alliance Gertz-Ressler High School

DO NOW
Use the following to answer parts a –d.
7x + 4 – 2x + 8 = 32
a. Put a circle around all the variables.
b. Put a triangle around all the
constants.
c. Put a box around all the terms.
d. Underline all of the coefficients.
Objective
The student will be able to:
• Translate verbal phrases into
algebraic expressions and
• demonstrate 100%
understanding of properties by
correctly matching them to
complete the square.
Standard 1.0 Students identify and use the
arithmetic properties of subsets of integers and
rational, irrational, and real numbers, including
closure properties for the four basic arithmetic
operations where applicable.
Standard 1.1 Students use properties of numbers to
demonstrate whether assertions are true or false.
Standard 25.0 Students use properties of the
number system to judge the validity of results, to
justify each step of a procedure, and to prove or
disprove statements.
Vocabulary
Algebraic expression- an expression
consisting of one or more numbers &
variables along with one or more arithmetic
operations.
Ex: 4x + 3
Variable- symbols used to represent unknown
numbers.
Equation- a mathematical sentence that
contains an equals sign, =. It may contain
numbers, variables, or algebraic expressions
Ex: 2x + 13 = 15
Activity # 1
In your notes create this graphic
organizer.
Addition Subtraction Multiplication Division Equals
(+)
(-)
(x)
(÷)
(=)
Activity # 1
On your own put the words below under
the operation you believe they are
describing. You have 3 minutes.
More than
Plus
Increased by
Sum of
Less than Subtracted by
Difference of Decreased by
Times
Product of Twice Divided by
Half of
Quotient of Total
Here are some more words to
add to your graphic organizer….
Addition
Subtraction
Multiplication
Division
Equals
added to
subtracted from
multiplied by
divided by
sum of
difference of
product of
quotient of equal
plus
more than
increased
by
minus
less than
decreased by
times
double, triple,
quadruple
of
divided into
ratio of
per
total
is, results
in
yields
is the
same as
Example 1
a) Seven more than a number
x+7
b) Eight less than a number
x–8
c) Half of a number
½ x or x ÷2
d) Twice a number
2x
Example 2
a) One half of a number increased by 7.
½x+7
b) The difference of a number squared
and 5.
x² - 5
• Identify the
operations
c) 8 less than twice a number
• What
happens to
2x - 8
the variable
first?
Misconceptions
Describe
error:
Seventeen less than a Error: order
number
is switched.
17 – n
This says “a
number less
than 17.”
Example
Why is this error
What’s the
made
correct answer?
Why? They took the n – 17
order that the words
were written in and
copied that for the
algebraic expression.
They ignored the fact
that we need 17 less
than the unknown
amount, meaning we
start with an
unknown amount
and then take 17
away from it.
Misconceptions
Example
The quotient of 5
and a number
n/5
Describe the
error:
Error: the order
is incorrect. If
we’re finding the
quotient of two
numbers, the
order they’re
stated in tells us
the order in
which to divide:
first number
divided by
second number.
Why is this What’s the
error made correct answer?
Why: it’s
5/n
confusing to
remember
when order
in the
expression
is the same
as the order
in the verbal
phrase.
Misconceptions
Example
10 less
than half
of a
number
10 – ½ n
Describe the error:
Why is this error What’s the
made
correct answer?
Error: the expression Why: they just
½ n – 10
was written in the
wrote down the
wrong order. This
expression as he
says “10 subtracted
read it: first 10,
by half of a number,” then subtract, then
or “half of a number half of a number.
less than 10.” We had We should read the
half of a number, and entire expression
we need 10 less than and determine
that quantity.
what’s happening
before writing
anything down.
CFU 1: Write an algebraic expression to
represent each verbal phrase.
Verbal Phrase
a) A number increased by 5
b) Seventeen less than a number
c) A number times 10
d) The quotient of 9 and a number
e) Eleven more than a number
f) A number squared
g) 5 times a number
Algebraic Expression
Vocabulary
Commutative Property of Addition - the
order in which two numbers are added does not
change their sum.
Ex: 5 + 7 = 7 + 5
Commutative Property of Multiplication –
the order in which two numbers are multiplied
does not change their product.
Ex: 3 ∙10 = 10 ∙3
Vocabulary
Associative Property of Addition – the way
in which three numbers are grouped when
they are added does not change their sum
Ex: (24 + 8) + 2 = 24 + (8 +2)
Associative Property of Multiplication – the
way in which three numbers are grouped when
they are multiplied does not change their
product.
Ex: (9 ∙ 4) ∙ 25 = 9 ∙ (4 ∙ 25)
Vocabulary
Distributive Property – for any numbers a, b, & c:
2(5x + 3) = (2 ∙5x) + (2 ∙ 3)
= 10x + 6
Additive Identity- for any number a the sum of a
and 0 is a.
a +0 = a & 0 + a = a
5+0=5 & 0+5=5
Multiplicative Identity- for any number a the
product of a and 1 is a.
a·1=a & 1·a=a
12 · 1 = 12 & 1 · 12 = 12
Ex 1:
Identify the property shown:
(5 + 3) + 7 = 5 + (3 +7)
Ex 2:
Identify the property shown:
(4 ∙ 3) ∙ 9 = 4 ∙(3 ∙9)
Ex 3:
Identify the property shown:
2+9 =9+2
Ex 4:
Identify the property shown:
5 ∙ 4x = 4x ∙ 5