Transcript Slide 1
Let’s Review Integers (Unit 9)
http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessonshell06.swf
Learn Alberta
Add & Subtract Integers (Unit 9)
Red
Chips = +1
Blue
Chips = -1 1. Combine 2 red chips and 2 blue chips…what is their sum?
2. Make the above into an
addition statement
…use brackets.
Opposite Integers
Student Outcome: I will learn what opposite integers are.
Are integers with the same numeral, but different signs (+ or -) …they are the same distance from zero, in opposite directions.
For example: a.
(+1) and (-1) are opposite integers b.
c.
d.
(-3) and ( ) are opposite integers (+14) and ( ) are opposite integers (-659) and ( ) are opposite integers
Zero Pairs
Student Outcome: I learn about zero pairs.
Zero Pair: combining (+1) with (-1) (+1) + (-1) = 0
We can combine numerous zero pairs to solve problems:
For example: a.
(+1) + (-1) = b.
(-3) + (+3) = c.
(+11) + (-11) =
Adding
Integers
Student Outcome: I will be able to add integers using integer chips.
Grouping:
combining “positives with positives” “positives with negatives” or “negatives with negatives” to allow us to solve
Addition Statements
: (+1) + (+2) = ______ (+5) + (- 4) = ______ Your turn…apply
“integer addition”
1.
Draw the model for (-3) + (+ 4) 2. Draw the model for (+11) + (-3)
Adding Integers
GAMES
Student Outcome: I will be able to add integers using integer chips.
Using Tiles to group + and – to find the answer….(great site!) http://nlvm.usu.edu/en/nav/frames_asid_161_g_2_t_1.html
2.
Using addition equations (small to large #’s) to find the answer.
http://www.berghuis.co.nz/abiator/maths/sa/saintegeradd2.htmL
VARIETY of GAMES
: A.
http://classroom.jc-schools.net/basic/math-integ.html
Find The Addition Statement
Student Outcome: I will be able to add integers using integer chips.
SOLVE Model Expression Equation Answer
Find The Addition Statement
Student Outcome: I will be able to add integers using integer chips.
Ray spent $5 on bus fares to visit his Aunt. During the visit, her Aunt gave him $12 for doing some yard work. How much money did Ray gain from the visit?
Model the scenario and create an addition statement to find your answer…
Applying Integer Addition
Page 313: # 5 abc , 8 ab, 9ac, 12 bc Page 314: # 14, 17 acef Extend Page 315: # 18, 19
On the front
Practical Quiz #1
On the back
Using a
Number Line
to Add Integers Student Outcome: I will be able to add integers using a number line.
Start at zero and move the direction of the first number…then move the direction of the second number!
Directions: Positive (+)
and
Negative (-)
Move the
DOT
to it’s correct place using the addition statements below… 1. (+4) + (+3) 2. (-2) + (+5) 3. (+5) + (-11)
What is the
“addition statement?”
Student Outcome: I will be able to add integers using a number line.
The addition statement below is…
(+4) + (+3)
1.
2.
What do the colors of the arrows represent?
What do the length of the arrows represent?
What is the
“addition statement?”
Student Outcome: I will be able to add integers using a number line.
The addition statement below is…
(+4) + (+3)
1.
2.
3.
What do the colors of the arrows represent?
What do the length of the arrows represent?
What is the total?
What is the
“addition statement?”
Student Outcome: I will be able to add integers using a number line.
What are the “
Addition Statements
?”
What is the
“addition statement?”
Student Outcome: I will be able to add integers using a number line.
What are the “
Addition Statements
?”
What is the
“addition statement?”
Student Outcome: I will be able to add integers using a number line.
Create your own…come on up and test your classmates?
Addition Statement…
What is the
“addition statement?”
Student Outcome: I will be able to add integers using a number line.
What are the “
Addition Statements
?”
What is the
“addition statement?”
Student Outcome: I will be able to add integers using a number line.
What are the “
Addition Statements
?”
Finding Temperatures using a Number Line Number lines can also be vertical (grids). •
Top
of the “y” axis is positive and
bottom
is negative.
•
Right
side of “x” axis is positive and
left
side is negative.
What are the 2 different
addition statements
?
What is the
“addition statement?”
Create your own…
Addition Statement…
Apply Integer Addition
The temperature in Yellowknife, Northwest Territories, on morning in October was
– 4
°
C
. The temperature increased by
9
°
C
to reach the high temperature for that day. 5 °
C
0 °
C
What was the
high temperature
?
5 °
C
Apply Integer Addition
This morning it was ______ ° C and the temperature has gone up 12 ° C. 5 °
C
What is the high temperature going to be today?
0 °
C
5 °
C
Applying Integer Addition
Page 320: # 5ab, 6 bc, 7 ab, 10, 12 Page 321: # 14, 18, 20ab, 21 cd Extend Page 322: # 21ab, 22, 23
On the front
Practical Quiz #2
On the back
Explore Integer Subtraction
Student Outcome: I will be able to subtract integers using integer chips.
Subtract integers using integer chips… 1.What is the subtraction expression for the model above?
1.
Take away 4 red chips from the original 6 red chips…what do you have left?
Explore Integer Subtraction
Student Outcome: I will be able to subtract integers using integer chips.
Subtract integers using integer chips… 1.What is the subtraction expression for the model above?
2.
Take away 3 blue chips from the original 7 blue chips…what do you have left?
Model it… Subtraction
Student Outcome: I will be able to subtract integers using integer chips.
Model the equations below…
(-5) – (-2) (+8) – (+3)
Model it… Subtraction
Student Outcome: I will be able to subtract integers using integer chips.
Model the equations below…
(-5) – (-2) (+8) – (+3)
What do you notice about each equation?
Model it… Subtraction
Model the equations below…
(-5) – (+2) (+1) – (+4) CAN THESE BE SOLVED???
Model it… Subtraction
Student Outcome: I will learn different strategies to use addition to subtract integers..
STRATEGY #1 “Move in – Move out”
What if the Integer #’s are Student Outcome: I will learn different strategies to use addition to subtract integers..
different
?
Step 1
(+ 2) – (+5)
Step 2 Step 3 Step 4
Steps to follow:
1.
2.
Model the first integer
Move in
enough to model the second integer 3.
Remove
the chips asked in the subtraction statement 4. What is left
What if the Integer #’s are Student Outcome: I will learn different strategies to use addition to subtract integers..
different
?
Step 1 Step 2
(-1) – (-6)
Step 3 Step 4
Steps to follow:
1.
2.
Model the first integer
Move in
enough to model the second integer 3.
Remove
the chips asked in the subtraction statement 4. What is left
What if the Integer #’s are Student Outcome: I will learn different strategies to use addition to subtract integers..
different
?
Step 1 Step 2
(-1) – (+4)
Step 3 Step 4
Steps to follow:
1.
2.
Model the first integer
Move in
enough to model the second integer 3.
Remove
the chips asked in the subtraction statement 4. What is left
What if the Integer #’s are Student Outcome: I will learn different strategies to use addition to subtract integers..
different
?
Step 1 Step 2
(-3) – (-7)
Step 3 Step 4
Steps to follow:
1.
2.
Model the first integer
Move in
enough to model the second integer 3.
Remove
the chips asked in the subtraction statement 4. What is left
What if the Integer #’s are Student Outcome: I will learn different strategies to use addition to subtract integers..
different
?
Step 1 Step 2
(+2) – (-6)
Step 3 Step 4
Steps to follow:
1.
2.
Model the first integer
Move in
enough to model the second integer 3.
Remove
the chips asked in the subtraction statement 4. What is left
Model it… Subtraction
Student Outcome: I will learn different strategies to use addition to subtract integers..
STRATEGY #2 “Zero Pairs”
What if the Integer #’s are Student Outcome: I will learn different strategies to use addition to subtract integers..
different
?
Step 1
(+ 2) – (- 4)
Step 2 Step 3 Step 4
Steps to follow:
1.
2.
3.
Model what the question is asking
ZERO PAIRS: 2 nd integer
reversing the (+) or ( ) of number…
Remove
the chips asked in the subtraction statement 4. Then
group
the chips left over!
What if the Integer #’s are Student Outcome: I will learn different strategies to use addition to subtract integers..
different
?
Step 1
(- 2) – (- 3)
Step 2 Step 3 Step 4
Steps to follow:
1.
Model what the question is asking
2.
3.
ZERO PAIRS: 2 nd integer
reversing the (+) or ( ) of number…
Remove
the chips asked in the subtraction statement 4. Then
group
the chips left over!
What if the Integer #’s are Student Outcome: I will learn different strategies to use addition to subtract integers..
different
?
Step 1
(+5) – ( -3)
Step 2 Step 3 Step 4
Steps to follow:
1.
Model what the question is asking
2.
3.
ZERO PAIRS: 2 nd integer
reversing the (+) or ( ) of number…
Remove
the chips asked in the subtraction statement 4. Then
group
the chips left over!
What if the Integer #’s are Student Outcome: I will learn different strategies to use addition to subtract integers..
different
?
Step 1
(-4) – ( -8)
Step 2 Step 3 Step 4
Steps to follow:
1.
Model what the question is asking
2.
3.
ZERO PAIRS: 2 nd integer
reversing the (+) or ( ) of number…
Remove
the chips asked in the subtraction statement 4. Then
group
the chips left over!
Method #1: Finding the “ Student Outcome: I will learn different strategies to use addition to subtract integers..
Higher Minus Lower ”
( ) – ( )
The morning temperature is
- 5
°
C
. This afternoon it will reach a temperature of
+6
°
C
. How much
higher
is the afternoon temperature than (
difference
) the morning temperature?
1.
2.
Model it… Use the steps (
Zero Pair
,
Remove
, and then
Group
)
Method #1: Finding the “ Student Outcome: I will learn different strategies to use addition to subtract integers..
Lower Minus Higher ”
( ) – ( )
The morning temperature is
- 5
°
C
. This afternoon it will reach a temperature of
+6
°
C
. How much
lower
is the morning temperature than (
difference
) the afternoon temperature?
1.
2.
Model it… Use the steps (
Zero Pair
,
Remove
, and then
Group
)
Applying Integer Subtraction
Page 328: # 7, 9ab, 10cd, 11ac Page 329: # 14, 16
Model it… Subtraction
Student Outcome: I will learn different strategies to use addition to subtract integers..
STRATEGY #3 “Sub to Add”
Subtracting Integers
Use integer chips to find the answer to the subtraction statement below…
Zero Pair Remove Group (+4) – (+ 2)
What happens when we change the
subtraction
statement to an
addition
statement?
(+4) + (- 2) Zero Pair Remove Group NOT needed!
NOT needed!
1.The answers are ____________________.
2.Which of the two methods above are easier?
Try it again!
Zero Pair Remove (- 5) – (- 3) Zero Pair Remove (- 5) + (+ 3) NOT needed!
NOT needed!
1.The answers are ____________________.
2.Which of the two methods above are easier?
3.Do you see a pattern?
Group Group
(- 12) – (+ 5)
Try it again!
Zero Pair Remove Zero Pair (- 12) + (- 5) NOT needed!
Remove NOT needed!
1.The answers are ____________________.
2.Which of the two methods above are easier?
3.Do you see a pattern?
Group Group
Applying Integer
Student Outcome: I will learn different strategies to use addition to subtract integers..
Operations
Use a number line to
add
&
subtract
.
Subtract: (- 2) – (- 5) = ( ) + ( )
Solution
…change the above statement into an addition statement. Then use the number line below to find your answer.
Applying Integer
Student Outcome: I will learn different strategies to use addition to subtract integers..
Operations
Use a number line to
add
&
subtract
.
Subtract: (+7) – (+3) = ( ) + ( )
Solution
…change the above statement into an addition statement. Then use the number line below to find your answer.
Changing subtraction to “addition”
SUBTRACTION STATEMENT
(+4) – (+3)
SUBTRACTION CHANGED TO ADDITION
(+4) + (-3) (+2) – (- 3) (-3) – (+1) (+2) + (+3) (-4) + (- 5) (+6) + (+2) What do you notice about the signs (+ or -) when you change the subtracting statement to an adding statement?
Changing subtraction to “addition”
Find the difference of the Caspian Sea ( + 217 m) elevation from the elevation of Lake Winnipeg ( - 28 m)?
+ 245 m Steps:
1.Would you use chips or a number line?
2.Change the subtraction statement to an addition statement.
3.Model your answer.
4.You may use a calculator to help find your answer.
+ 28
m
+ 217
m
0
m
Changing subtraction to “addition”
Page 333: # 5ab, 6bc, 7a, 8b, 9cd, 14 Page 334: # 19, 22
On the front
Practical Quiz #3
Solve On the back
Applying Integer Operations
Student Outcome: I will decide when to add and subtract integers.
Use the golf score chart below to find the addition or subtraction statements.
Golf Term # of Strokes
On hole #1 Rosa made an eagle and Samantha made a bogey. 1.How many more strokes did Samantha take than Rosa?
2.Would subtract or add?
3.Find the answer!
Double Bogey Bogey Par Birdie Eagle
+2 +1 0 - 1 -2
Prize
…
what does the term “albatross” mean in a golf score?
Applying Integer Operations
Student Outcome: I will decide when to add and subtract integers.
Use the golf score chart below to find the addition or subtraction statements.
Golf Term # of Strokes
Double Bogey Rosa shot the following score…Hole #1 (par), Hole #2 (Bogey), Hole #3 (Eagle), and Hole #4 (Birdie)… 1.What is her score so far?
2.Would subtract or add?
3.Find the answer!
Bogey Par Birdie Eagle
+2 +1 0 - 1 -2
Prize
…
what does the term “albatross” mean in a golf score?
Hole #
Applying Integer Operations
Par Rosa
1 2 3 5 4 4 Par Bogey Eagle
Golf Term
Double Bogey Bogey Par Birdie Eagle
# of Strokes +2 +1 0 - 1 -2
4 3 Birdie 5 5 Par
Find out…
6 4 Birdie 7 3 Eagle
What was Rosa’s score?
8 4 Double Bogey Bogey 9 4
Applying Integer Operations
Student Outcome: I will decide when to add and subtract integers.
Use the “Wind Chill Chart” on
page 337
to answer the question below.
1.If the air temperature is – 20ºC and the wind speed is 10 km/h…then what is the “
wind chill
” temperature?
2.If the air temperature is 25ºC…and the wind speed is 50 km/h…then what is the “
wind chill
” temperature?
3. What are the
differences
between the air temperature and the “wind chill” temperatures above? (
Hint…colder!)
Applying Integer Operations
Student Outcome: I will decide when to add and subtract integers.
Use a number line to show how you could figure out the temperature as it changes throughout the day.
• The
morning
air temperature was 0ºC with a 45 km/h
wind
. • As the day went on the air temperature
changed
to 5ºC and the wind
settled
to 5 km/h.
• What is the
new temperature
?
• Write the information above into an addition or subtraction statement.
• • • • •
Applying Integer Operations
Student Outcome: I will decide when to add and subtract integers.
Use a number line to show how you could figure out the temperature as it changes throughout the day.
Applying Integer Operations
What are some words we use to know whether we should
add
or
subtract
integers?
Applying Integer Operations
What do we notice when these signs are beside each other???
- (-) =
Add/Subtract Statement…then
solve
!
- (+) = + (-) = + (+) =
Subtraction to Addition of Integers
Page 339: # 3, 4 Page 340: # 9ac, 10, 13a
Chapter Review
Page 342: # 1, 3ab, 4cd, 5, 8d, 9, 10 Page 343: # 11ab, 12bc, 13, 14a, 15a, 16, 17a, 18