Transcript Integers Review (+, -, x, div ) - middle-school

REVIEW LESSON:
Adding, Subtracting, Multiplying,
and Dividing Integers
Warm-Up Problems
1.
8 + (-5) =
2.
‫־‬7 - ‫־‬9 =
3.
6 x ‫־‬3 =
4.
‫־‬18 ÷ ‫־‬2 =
5.
‫־‬15 ÷ 5 =
Warm-Up Problems: Answers
1.
8 + (-5) =
3
2.
‫־‬7 - ‫־‬9 =
2
3.
6 x ‫־‬3 =
‫־‬18
4.
‫־‬18 ÷ ‫־‬2 =
9
5.
‫־‬15 ÷ 5 =
‫־‬3
Any QUESTIONS?
• Share with your partner the rules for
Adding and Subtracting Integers.
(1’s start)
• Share with your partner the rules for
Multiplying and Dividing Integers.
(2’s start)
Daily Concept:
Review
• Standards:
–
–
–
–
(NS 2.3) Add positive and negative integers.
(NS 2.3) Subtract positive and negative integers.
(NS 2.3) Multiply positive and negative numbers.
(NS 2.3) Divide positive and negative integers.
• Objective:
– To review and apply the rules for adding, subtracting,
multiplying, and dividing positive and negative
integers.
Vocabulary:
Review
• Integers: Numbers that can be either
negative (‾ 1,‾ 2,‾ 3,) or positive (1, 2, 3,).
• Absolute Value: A number’s distance
from zero on a number line.
Adding Integers:
Review
• To add two integers with the same sign, add their
absolute values and write the common sign.
(6 + 7 = 13, ‾ 4 + ‾ 4 = ‾ 8)
• To add two integers with different signs, subtract the
lesser absolute value from the greater absolute value
and write the sign of the integer with the greater absolute
value. (8 + ‫־‬7 = 1, ‾ 4 + 14 = 10)
• In your own words explain this to your partner
(2’s start).
Subtracting Integers:
Review
• To subtract an integer b from an integer a, add
the opposite of b to a.
• ( a – b = a + (-b) )
• ( 3 – 6 = 3 + (-6) )
• ( a – ‫־‬b = a + b )
• ( 7 – ‫־‬10 = 7 + 10 )
• Explain subtracting integers with your
partner ( 2’s start).
Multiplying Integers:
Review
• The product of two positive integers is
POSITIVE: ( 5 x 15 = 75)
• The product of two negative integers is
POSITIVE: ( ‾ 4 x ‾ 10 = 40)
• The product of two integers with different signs
is NEGATIVE: ( 8 x ‾ 12 = ‾ 96)
• The product of an integer and zero is ZERO:
( 32 x 0 = 0)
Dividing Integers:
Review
• The quotient of two positive integers is
POSITIVE: ( 32 ÷ 8 = 4)
• The quotient of two negative integers is
POSITIVE: ( ‾ 12 ÷ ‾ 4= 3)
• The quotient of two integers with different signs
is NEGATIVE: ( 96 ÷ ‾ 12 = ‾ 8)
• The quotient of zero and a nonzero is ZERO:
(0 ÷ 8 = 0)
Think-Pair-Share
• Each of you take turns explaining to your
partner how to add, subtract, multiply, and
divide negative and positive integers.
» (30 seconds each, 1’s start)
• Share explanations with entire class.
» (Ask for volunteers)
Guided Practice
• Take notes in your journal as we do a few
sample problems:
– Copy the steps
– Copy the sample problems
– Ask questions if you don’t understand
Independent Practice
•
Work on these problems silently and independently. If you are
having difficulties use your journal as a resource.
1.
12 + (-3) =
2.
‾ 4 - ‾ 10 =
3.
‾ 12 - 25 =
4.
‾ 7 x ‾ 12 =
5.
6 x ‾ 13 =
6.
‾ 27 ÷ ‾ 3 =
7.
0 ÷ 12 =
Independent Practice: Answers
1.
12 + (-3) =
9
2.
‾ 4 - ‾ 10 =
6
3.
‾ 12 - 25 =
‾ 37
4.
‾ 7 x ‾ 12 =
84
5.
6 x ‾ 13 =
‾ 78
6.
‾ 27 ÷ ‾ 3 =
9
7.
0 ÷ 12 =
0
Mini Quiz
1.
‾ 7 + 16 =
2.
‾ 12 - ‫־‬25 =
3.
8 x ‾ 20 =
4.
‾ 64 ÷ ‾ 8 =
5.
A group of Marine scientists were measuring the distance of
the ocean floor below the surface of the water. They made 3
measurements. The first measurement was ‾ 940 feet, the
next was ‾ 910 feet, and the last was ‾ 850 feet. What was the
average distance below the water’s surface?
Mini Quiz: Answers
1.
2.
3.
4.
5.
9
13
‾ 160
8
‾ 900 feet
Order of Operations
Review
• Parenthesis
• Exponent
• Multiply
• Divide
• Add
• Subtract
Order of Operations
Review
• Evaluate expressions inside the grouping
symbols (parenthesis).
• Evaluate powers (exponents).
• Multiply and Divide from left to right.
• Add and Subtract from left to right.
Order of Operations
Guided Practice
• (‫־‬8- ‫ ־‬12) + 2² - 9 =
• Parenthesis first:
(‫־‬8 - ‫ ־‬12) + 2² - 9 =
(4) + 2² - 9 =
• Exponent next:
(4) + 2² - 9 =
(4) + 4 - 9 =
• Add and/or Subtract from left to right
(4) + 4 - 9 =
8 – 9 = ‫־‬1
Order of Operations
Independent Practice
1. (3 x 12) + (3² - 9) =
2. 16 + (4 - ‫ ־‬12) ÷ 4² =
3. 8 x 3 + (‫־‬27÷ 9) + 2² =
Order of Operations
Independent Practice: Answers
1. (3 x 12) + (3² - 9) = 36
2. 16 + (4 - ‫ ־‬12) ÷ 4² = 17
3. 8 x 3 + (‫־‬27÷ 9) + 2² = 25
Self-Reflection
• Take a few minutes to reflect upon today’s
lesson. Discuss any of the following:
– What you learned
– What helped you learn
– What you still need help with
– What changes could be made to better meet
your needs
– Anything else you feel is important related to
today’s lesson
Group Activities: Rules
• Work QUIETLY and COOPERATIVELY.
• PLEASE do not interrupt the teacher
during small group instruction. I will be
monitoring all groups and providing
feedback.
• PLEASE do your best and respect the
others around you.
• If you finish early review your journal.
Group Activities
• Group “A” work with the teacher.
• Group “B”:
– Create a poster explaining how to Add & Subtract
Integers, or how to Multiply and Divide Integers.
– Create a story problem (with illustrations) that uses
adding, subtracting, multiplying, or dividing integers.
To challenge yourself make one for each skill!
– Create a Power Point Presentation
Lesson Close
• TPS the important information you’ve
learned or practiced during today’s class.
• Any further questions, comments, or
concerns?
• Tomorrow’s homework is: