Topic A Identities

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Announcements 3/5
• Homework
– Decimals Test Corrections due Friday
New late policy for 6th grade:
-1 day late = -10
-after 1 day late = 50%
Warm Up - Wednesday
a) Every week, Hannah has to walk 0.35 miles to
get to her local grocery store and back. How
far does she walk to do her shopping over 15
weeks? (Answer in complete sentence)
b) Lucila used a stair-climbing machine for
15.25 minutes and was able to climb set to 93
flights of stairs. How many flights did Lucila
climb per minute? Round to hundredths place
(Answer in complete sentence)
Review
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Sum
Product
Factor
Difference
Quotient
variable
Manipulatives
• Cut out the 30 squares and put them in your
baggie
• Write your name with a Sharpie on your
baggie
• Objective: Understand relationships of
operations and use them to generate
equivalent expressions
Addition and Subtraction
Identity
Opening Exercise
a. Draw a tape diagram to represent the
following expression : 5 + 4
b. Write an expression for each tape diagram
i.
ii.
Addition and Subtraction Identity Discussion
• Take out 10 of your squares and place them
on your desk
• If each square represents 1 unit, represent the
number 3 using the squares
• Add two more squares to your tape diagram
• Draw AND Write an expression to represent
how we created a tape diagram with 5 squares
Discussion
• Remove two squares from your tape diagram
• Alter our original expression, 3 +2, to create
an expression that represents what we just did
with the tape diagram
• Evaluate the expression
Discussion
• Clear your desk
• This time, create a tape diagram with six
squares
• Use your tiles to demonstrate 6 + 4
• Draw AND Write an expression to represent
this tape diagram
Discussion
• Remove four squares from your tape diagram
• Alter our original expression, 6 +4, to create
an expression to represent the tape diagram
• How many tiles are left on your desk?
• Evaluate the expression
• How many tiles did we start with?
Discussion
• What effect did adding four tiles then
subtracting the four tiles have on the number
of tiles?
• What if I asked you to add 215 tiles to the six
tiles we started with and then subtract 215
tiles?
• Do you need to actually add and remove these
tiles to know what the result will be? Why?
Discussion
• What do you notice about the expressions we
created with the tape diagrams?
• Write a number sentence, using variables, to
represent what we just demonstrated with
tape diagrams. Remember that a variable is a
letter that represents a number.
• Why do you think this is called an identity?
Announcements 3/6
• Homework
– Addition and Subtraction identity practice
– Decimals Test Corrections due Friday
New late policy for 6th grade:
-1 day late = -10
-after 1 day late = 50%
Warm Up – Thursday
a) The sand pit for the long jump has a width of
2.75 meters and a length of 9.54 meters. Just in
case it rains, the principal wants to cover the
sand pit with a piece of plastic the night before
the event. How many square meters of plastic
will the principal need to cover the sand pit?
b) A book is ½ of an inch thick. How many of these
books will fit into a shelf that is 5 and ¾ inches
wide?
Discussion
• Write a number sentence, using variables, to
represent what we just demonstrated with
tape diagrams. Remember that a variable is a
letter that represents a number.
• w + x – x = w AND w - x + x = w
• Why do you think this is called an identity?
Exercises
• What if we rearrange the number sentence:
x+w–x=?
-x + x + w = ?
x–x+w=?
-x + w + x = ?
Closing Discussion
• In every problem we did today, why did the final
value of the expression equal the initial
expression?
• Initially, we added an amount and then
subtracted the same amount. Later in the lesson,
we subtracted an amount and then added the
same amount. Did this alter the outcome?
• Why were we able to evaluate the final
expression even when we did not know the
amount we were adding and subtracting?
Addition and Subtraction Identity:
w+x–x=w
w–x+x=w
Homework
Multiplication and Division
Identity
Opening Exercise
• Draw a pictorial representation of the division
and multiplication problems using a tape
diagram.
a. 8 ÷ 2
b. 3 · 2
Review
• Variable
• Number sentence
Discussion
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Need 10 squares
Build a tape diagram to represent 9 units
Divide the 9 units into 3 equal groups
Write an expression to represent the process
you modeled
• Evaluate the expression
• Use your squares to demonstrate what it
would look like to multiply 3 by 3
• Alter our original expression to represent
what we just did
Discussion
• What do you notice about the expression of
the tape diagram?
• Write a number sentence, using variables, to
represent the identities we demonstrated
with the tape diagram.
Discussion
Create a model to represent your number sentence
Exercises
• With your partner come up with another
number sentence to show the relationship
between multiplication and division. The
number sentence should include variables and
an identity.
• Model it in your notes
Closing Discussion
• What did you determine about the
relationship between multiplication and
division?
Multiplication and Division Identity:
a·b÷b=a
a÷b·b=a
Homework
Announcements 3/7
• Homework
– */+ and ÷/- identity practice
– Study for Identity quiz on Monday
New late policy for 6th grade:
-1 day late = -10
-after 1 day late = 50%
Warm Up - Friday
a) Matt is running for student council. His
friends are going to help him give out 15
posters and 6 banners. Matthew plans to pack
all of the posters and the same number of
banners in each box. What is the greatest
number of boxes Matthew can pack?
b) A pie recipe requires 2/3 lbs of apples. How
many apples are needed for 4 whole pies and
a mini pie (1/2 of whole pie)
**Have homework on desk
Review Homework
Review Homework
Multiplication and Addition
Identity
Opening Exercise
• Write two different expressions that can be
depicted by the tape diagram shown. One
expression should include addition, the other
multiplication
Discussion
• Need 20 squares
• Partner 1 : build a tape diagram to represent the
expression 2 + 2 + 2 + 2
• Partner 2 : build a tape diagram to represent the
expression 4 x 2
• What do you notice about the 2 tape diagrams?
• Why are they the same?
• What does the say about the value of the expressions?
(use your elevated diction)
• 2+2+2+2=4x2
• Is there an advantage to using one over the other?
Discussion
• Partner 1 : Represent 3 x 4
• Partner 2 : Represent 4 + 4 + 4
• Are they equivalent?
Discussion
• Use variables to create a number sentence to
show the relationship between addition and
multiplication
• g + g + g = 3·g or 3g (multiplication implied)
• Is this an identity?
Exercises
Multiplication and Addition
Identity:
3·g=g+g+g
Homework
Division and Subtraction Identity
Discussion
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Need 30 squares
Build a tape diagram with 20 units
Divide it into 4 equal sections
How many squares are in each section?
Write a number sentence to demonstrate
what happened.
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Discussion
Build your tape diagram with 20 units again
Subtract 4 units from your tape diagram
Write an expression to demonstrate what happened.
Subtract 4 more units from your tape diagram
Add to your previous expression to demonstrate what
happened.
Subtract 4 more units from your tape diagram
Add to your previous expression to demonstrate what
happened.
Subtract 4 more units from your tape diagram
Add to your previous expression to demonstrate what
happened.
Subtract 4 more units from your tape diagram
Add to your previous expression to demonstrate what
happened.
Discussion
• Evaluate your expression
• What is the relationship between 20 ÷ 4 = 5
and 20 – 4 – 4 – 4 – 4 – 4 = 0?
Discussion
• Let’s switch the quotient and the divisor:
• 20 ÷ 5 = 4
• 20 ÷ x = 5
Announcements 3/10
• Homework
– Weekly math Corrections
– Properties worksheets
New late policy for 6th grade:
-1 day late = -10
-after 1 day late = 50%
Warm Up – Monday
a) Alisha is putting cheese cubes and crackers onto
small plates. She has 24 cubes of cheese and 40
crackers. She wants both cheese and crackers on
each plate and each plate must have the same
number of cheese cubes and the same number
of crackers. What is the greatest number of
plates she can make using all the cheese and
crackers?
b) Create the number line below, fill in the boxes,
and draw lines to 3 opposites:
-7
-4
0
3
6 7
Review
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Variable
Number sentence
Identity
Addition and subtraction
Multiplication and division
Multiplication and addition
Division and subtraction
Review Homework
Exercises
Division and Subtraction Identity:
12 ÷ x = 4 means
12 – x – x – x – x = 0
Closing Discussion
Properties Homework
• 3 worksheets over Commutative and
Associative Properties of Addition
Announcements
• Homework
– Weekly math Corrections
– Properties worksheets
New late policy for 6th grade:
-1 day late = -10
-after 1 day late = 50%
Identities Quiz
Warm Up - Tuesday
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