Transcript Document

6 Grade math
resource lesson
plan
April 28-2,2014
Standards
6th grade
6.ee.1 write and evaluate numerical
expressions involving whole-number exponents.
6.ee.2A/b/c write, read, and evaluate
expressions in which letters stand for numbers
6.ee.6 use variables to represent numbers and
write expressions when solving a real-world
or mathematical problem; understand that
variable can represent an unknown number, or,
depending on the purpose at hand, any number
ina specified set.
FYI
PASS Testing
APRIL 6-9,2014
7 Grade math
resource lesson
plan
April 28-2,2014
Standards
7th grade
6.ee.6 use variables to represent numbers and
write expressions when solving a real-world
or mathematical problem; understand that
variable can represent an unknown number, or,
depending on the purpose at hand, any number
in a specified set.
7.ns.3 solve real-world and mathematical
problems involving the four operations with
rational numbers.
FYI
PASS Testing
APRIL 6-9,2014
A variety of methods will be used to
accommodate the needs of individual learners
such as:
o IEP’s and 504 Plans are followed
o hands-on activities
o discussions through whole group and
shoulder buddies
o informational text strategies (steps to
problem solving)
o note taking
• CFU throughout the lesson and in closure. I
will be looking for at least 80% skill
mastery daily.
• Homework and classwork will be graded
on the following scale: 100 -All Completed,
75- if 75% is completed, 60- if 60% is
completed or less.
“getting into shape classroom
project”
“getting into shape classroom
project”
Directions
 These pictures must be mounted on the
paper provided in your packet, using glue
sticks. Please trace or outline the shape
within the picture with a black marker.
 You will also write the word and its’
definition on the page (Please Write NEAT).
“getting into shape”
Page Example
Parallel Lines -lines that are in the
same plane and never intersect.
PASS Review
Unit 1-Number and Operations
 Compare and order integers
The Number Line
Negative Numbers (-)
Positive Numbers (+)
(The line continues left and right forever.)
Bell Work
Monday, April 28,2014
On a map, 1 inch = 52 miles. If the
distance between two cities
measures 2 &1/2 inches. How
many miles apart are they.
Agenda
• Bell Work
• Review Instructions for “Getting into Shapes”
Project
• Review Essential Question
• Relevance
• Prior learning
• Modeling (I Do)
• Guided Practice (We Do)
• Closure/CFU
• Reflection
• Independent Practice ( You Do)(CFU)
• Early finishers- work on math project
• HAVE A GREAT DAY!
Essential Question
How do I compare and order integers?
Comparing and Ordering Integers
Relevance
Integers are whole numbers and their
opposites (positive numbers, zero, and
negative numbers). Negative numbers are
numbers less than zero. The opposite of a
number is the number that is the same
distance form 0 on a number line, but on the
opposite side of 0.
For example, 4 and -4 are opposites.
Comparing and Ordering Integers
Real Life Application:
Integers can be used in real-life situations. Some
keywords that indicate positive integers are
gained, increased, rose, above, more, and up.
Some keywords that indicate negative integers are
lost, decreased, dropped, below, less, and down.
Comparing and Ordering Integers
Integers are compared almost in the same way as whole numbers, but
with addition of some rules.
Steps for comparing integers:
1.If we compare numbers with different signs, then negative number is
less than positive.
2.If numbers are both positive then this is the case when we compare
whole numbers.
3.If numbers are both negative then we compare numbers without
signs. The bigger positive number, the smaller negative. For example, if
we compare -3 and -5, then we compare 3 and 5 (numbers without
signs). Since 3<5 then −3>−5 .
Comparing and Ordering Integers -- I Do
 Example 1. Compare 4567 and -12345.
Numbers are with different signs. Negative number is always less than
positive. Therefore, 4567>−12345 .
 Example 2. Compare -300 and 0.
0 is always bigger than any negative number, so −300<0 .
 Example 3. Compare -12 and -234.
Compare numbers without signs: 12 and 234.
Since 12<234 then −12>−234 .
Comparing and Ordering Integers- We Do
 Example 4. Compare -234 and -123.
Compare numbers without signs: 234 and 123.
Since 234>123 then −234<−123 .
 Example 5. Compare -2345 and -2346.
Compare numbers without signs: 2345 and 2346.
Since 2345<2346 then −2345>−2346 .
 Example 6. Compare -456 and 12.
 Answer: −456<12 . Hint: numbers are with different
signs.
Comparing and Ordering Integers- Reflection
Which did you move from to compare fractions on
the number line?
Left to Right
What is the first step to ordering integers using a
number line?
Find the integers on a number line to see exactly
where they are located.
Comparing and Ordering Integers
Independent Practice/ You Do
Ordering Integers Skill Sheet
*You may work with a partner to complete
skill. Teacher will circulate classroom to
provide extra assistance if needed.*
Tuesday, April 29,2014
Bell work
Lesson6: Expressions, equations,
and inequalities
How can the following
expression be written
using the distributive
property?
8(5+12)
Agenda
Bell Work
Review Instructions for “Getting into Shapes” Project
Review Essential Question
Relevance
Prior learning
Modeling (I Do)
Guided Practice (We Do)
Closure/CFU
Reflection
Independent Practice ( You Do)(CFU)
Early finishers- work on math project
HAVE A GREAT DAY!
Essential Question
How do I distinguish between the Number
Properties: Associative,
Commutative, and Distributive ?
Relevance
Why not learn about number properties?
Because every math system you've ever worked
with has obeyed these properties! You have
never dealt with a system where a×b did not in
fact equal b×a, for instance, or where (a×b)×c
did not equal a×(b×c). Which is why the
properties probably seem somewhat pointless to
you.
is easy to remember, if you recall that
"multiplication distributes over addition". Formally,
they write this property as "a(b + c) = ab + ac". In
numbers, this means, that 2(3 + 4) = 2×3 + 2×4. Any
time they refer in a problem to using the
Distributive Property, they want you to take
something through the parentheses (or factor
something out); any time a computation depends on
multiplying through a parentheses (or factoring
something out), they want you to say that the
computation used the Distributive Property.
Why is the following true? 2(x + y) = 2x + 2y
Since they distributed through the parentheses, this
is true by the Distributive Property.
Use the Distributive Property to rearrange: 4x – 8
The Distributive Property either takes something
through a parentheses or else factors something out.
Since there aren't any parentheses to go into, you
must need to factor out of. Then the answer is "By
the Distributive Property, 4x – 8 = 4(x – 2)"
The word "associative" comes from "associate" or
"group"; the Associative Property is the rule that
refers to grouping. For addition, the rule is "a + (b +
c) = (a + b) + c"; in numbers, this means
2 + (3 + 4) = (2 + 3) + 4. For multiplication, the rule is
"a(bc) = (ab)c"; in numbers, this means 2(3×4) =
(2×3)4. Any time they refer to the Associative
Property, they want you to regroup things; any time a
computation depends on things being regrouped, they
want you to say that the computation uses the
Associative Property.
Rearrange, using the Associative Property: 2(3x)
They want you to regroup things, not simplify things. In other
words, they do not want you to say "6x". They want to see the
following regrouping: (2×3)x
Simplify 2(3x), and justify your steps.
In this case, they do want you to simplify, but you have to tell
why it's okay to do... just exactly what you've always done.
Here's how this works:
2(3x) original (given) statement
(2×3)x by the Associative Property
6x simplification (2×3 = 6)
Why is it true that 2(3x) = (2×3)x?
Since all they did was regroup things, this is true by the
Associative Property.
The word "commutative" comes from "commute" or
"move around", so the Commutative Property is the
one that refers to moving stuff around. For addition,
the rule is "a + b = b + a"; in numbers, this means 2 +
3 = 3 + 2. For multiplication, the rule is "ab = ba"; in
numbers, this means 2×3 = 3×2. Any time they refer
to the Commutative Property, they want you to move
stuff around; any time a computation depends on
moving stuff around, they want you to say that the
computation uses the Commutative Property.
Use the Commutative Property to restate "3×4×x" in
at least two ways.
They want you to move stuff around, not simplify. In
other words, the answer is not "12x"; the answer is
any two of the following:
4 × 3 × x,
4 × x × 3,
3 × x × 4,
x × 3 × 4, and x × 4 × 3
Why is it true that 3(4x) = (4x)(3)?
Since all they did was move stuff around (they didn't
regroup), this is true by the Commutative Property.
Number Properties: I Do
Write the property that is represented by the given
equation:
6 x 11=11 x 6 Commutative Property
2(x+3) – 2x+6 Associative Property
(14 x 3) x 8= 14 x (3 x 8) Distributive Property
Associative Property/Commutative
Property/Distributive Property
Number Properties:
We Do
3a + 7a – 5b Commutative Property
(3a + 7a) – 5b Associative Property
a(3 + 7) – 5b Distributive Property
Write the property that is
represented by the given
equation:
Number Properties: Reflection
Any time they refer to the Commutative Property
what do they want you to do with the numbers?
“Move them around”
Any time they refer to the Associative Property, what
od they want you to do with the numbers?
They want you to regroup things
Any time they refer in a problem to using the Distributive
Property, what do they want you to do with the numbers?
They want you to take something through the parentheses
(or factor something out)
Number Properties:
Independent Practice
BUCKLE DOWN PASS Skill Sheets
Pages 60-63
*You may work with a partner to complete
skill. Teacher will circulate classroom to
provide extra assistance if needed.*
Wednesday, April 30,2014
PASS Review
Lesson6: writing Expressions
What is the value of t
in the equation
below?
13t=143
Agenda
• Bell Work
• Review Instructions for “Getting into Shapes”
Project
• Review Essential Question
• Relevance
• Prior learning
• Modeling (I Do)
• Guided Practice (We Do)
• Closure/CFU
• Reflection
• Independent Practice ( You Do)(CFU)
• Early finishers- work on math project
• HAVE A GREAT DAY!
Essential Question
How do I write an expression using variables,
symbols, and/or numbers?
Relevance
Knowing how to evaluate algebraic expressions
can help you determine the amount of your
paycheck.
A variable is a letter that represents an unknown
number. Variables are used in expressions and
equations.
2n + 4
C = 2F – 7
When you multiply a number by a variable, you do
not need a multiplication sign between them. You
can write the number directly in front of the
variable. Above, 2n is the same as 2 x 4
An expression is a mathematical phrase made of
variables, symbols, and/or numbers and operations.
To translate a written phrase into an algebraic
expression, you need to identify the operations.
The operations link the individual terms; they are
addition, subtraction, multiplication, and division.
For Example
Write and algebraic expression to
represent “four plus three times a
number.”
Let n = the number.
What is the main operation? The word
plus indicates addition.
What the terms to be added? 4 and 3n
Four plus three times a number
4 +
3n
The algebraic expression can be written as
4 + 3n or 3n + 4.
When the main operation is subtraction or division,
the order in which the terms are written does matter.
Example
Write an algebraic expression to represent “six less
than twice a number.” Let z=the number.
The phase less than indicates subtraction.
The two terms in the expression are 6 and 2z.
You may be asking yourself which of the following
expressions is correct: 6-2z or 2z-6?
The word than in less than indicates that you have
to switch the order of the terms in the expression
from how they appear in the description.
The algebraic expression can be written as 2z-6.
Writing Expressions: I Do
Underline the part of the phrase that indicates the main
operation, then write an expression.
1. Sixteen more than a number____________________
2. The product of a number and eleven______________
16 + n
N x 11
Writing Expressions :
We Do
Nine increased by a number 9 + n
Twenty –five decreased by a number 25 - n
A number doubled by ten n(10)
Writing Expressions: Reflection
Tell in your own words, the
difference between numbers and
variables.
Writing Expressions:
Independent Practice
Writing Expressions PASS Skill Sheet
*You may work with a partner to complete
skill. Teacher will circulate classroom to
provide extra assistance if needed.*
Pages 65-68
Thursday, may 1,2014
PASS Review
Lesson 6: equations and inequalities
Sara own 23 fewer CDs than
Kathy. Kathy owns k CDs. Write
an expression for the situation.
Agenda
• Bell Work
• Review Instructions for “Getting into Shapes”
Project
• Review Essential Question
• Relevance
• Prior learning
• Modeling (I Do)
• Guided Practice (We Do)
• Closure/CFU
• Reflection
• Independent Practice ( You Do)(CFU)
• Early finishers- work on math project
• HAVE A GREAT DAY!
Essential Question
How do I solve equations?
Relevance
Knowing how to solve equations mentally can
help you solve problems in science.
To solve an equation, you need to
isolate the variable (get it alone on
one side of the equation). Use inverse
operations to find the value of the
variable.
Remember that addition and subtraction are inverse operations;
one “undoes” the other. To undo addition, use subtraction. To
undo subtraction, use addition.
Example: Solve the following equation for x.
7+x=30
Use inverse operations to get the variable alone on one side of the
equation.
7+ x=30
7+x-7=30-7
X=23
The solution to the equation is x=23.
Solve the following equation for s.
S – 9 = 18
Use inverse operations to get the variable alone on one
side of the equation.
S – 9 = 18
S – 9 + 9 = 18 + 9
S = 27
The solution to the equation is s= 27.
Solve the following equation for y.
12 x y = 84
Use inverse operations to get the variable alone on one
side of the equation.
12 x y =84
12 x y / 12= 84/12
Y= 7
The solution to the equation is y=7.
Solve the following equation for n.
N/8=6
Use inverse operations to get the variable alone on one
side of the equation.
n / 8 =6
n / 8 x 8= 6 x 8
n=48
The solution to the equation is n=48.
When writing equation to represent and solve realworld problems, you do the following.
1. Find all the information you need to know.
2. Now you can write an equation.
3. There may be more than one way to write and
equation to represent the situation.
4. Use inverse operations to get the variable alone on
one side of the equation.
5. Solve the equation.
Writing Equations: I Do
Look at the example on page 72 and read along
Check to see if I followed the correct steps
1. Underline my key information.
2. Write my equation.
3. Remember Mrs. Toomer, there may be more than one
way to write and equation to represent the situation.
4. Did I Use inverse operations to get the variable alone
on one side of the equation.
5. Did I solve the equation.
Writing Equations :
We Do
A tour bus holds 84 passengers. Each seat holds 3
people. How many passenger seats are on the bus?
(Let x = the number of passenger seats.)
There are ___passenger seats on the bus.
Writing Equations: Reflection
Tell in your own words, the steps for
solving equations.
Writing Expressions:
Independent Practice
Writing Equations PASS Skill Sheet
*You may work with a partner to complete
skill. Teacher will circulate classroom to
provide extra assistance if needed.*
Pages 72=73
Friday, may 2,2014
Students will work on
regular education
assignments and tests
that requires extra
assistance
If a student does not have any
regular education assignments,
they will work on their geometry
projects for resource.