Transcript 7th Grade Math

th
7
Grade Math
9/22/14
Monday: Bell work
• Jimmy was diving in the ocean. He dove 6.2
miles. Then he found a shark. He darted
upward 2 miles then fought him off. He then
dived 5.12 miles again. How many miles is he
below sea level?
(Mitch Crockett)
Solve
–7.5t + 4 = -26
TURN IN ANY LATE HOMEWORK!!
Lesson
• ... solve real-world problems involving the
addition, subtraction, multiplication, and/or
division of rational numbers? (7.NS.3)
Word Wall Quiz
• Match and/or Fill in the blank for each term
• Words are only used one time.
• For the matching – write the letter beside the
number
Remember
Multiplying Fractions
N
D
x
6 X
7
•
N
D
8
11
=N
D
= 48
77
Multiply straight across
Dividing Fractions
N
÷ N
=N
D
D
D
*multiply the reciprocal
N
x
D
=N
D
N
D
6 ÷ 8
= 48
7
11
77
6 x 11 = 66
7
8
56
Multiplying / Dividing Mixed Numbers
• Change to mixed numbers to improper
fractions and then multiply or divide.
Multiplying Fractions using Area
Model
• http://www.libertyunion.org/userfiles/1039/C
lasses/3543/Unit%202%20Lesson%203.pdf
• http://www.cpm.org/pdfs/skillBuilders/MC/M
C_Multiplication_of_Fractions.pdf
Exit / Closure
• Tommy said that 4 + 2 x = -24
x is 14.
• Justify whether Tommy is incorrect or correct.
• ***Be ready to explain your answer to a
partner.
Tuesday: Bell Work
1. Can you relate fractions to the
real world?
2. Where have you used or seen
fractions, specifically the
multiplication of fractions ?
Vocabulary
Looking the word wall.
Pick 1 word that you can apply to
fractions.
Be prepared to justify why you
choose that word.
Essential Question
• Can I solve real-world problems involving the
addition, subtraction, multiplication, and/or
division of rational numbers? (7.NS.3)
Multiplying Fractions using Area
Model
Garden Task
• 1. Work on the task individually in the indicated
corner.
• 2. Combine and work as a group of 4 to solve and
model the garden task in the middle of the 4-corner
poster.
• 4. At least two groups will present. While a group is
presenting, write down questions you can ask the
group.
EQ: Can I solve real-world problems involving the
addition, subtraction, multiplication, and/or division
of rational numbers? (7.NS.3)
Student 1
Student 2
Group Work
Student 4
Student 3
Exit Ticket
Solution
12
60
•Essential Question: CAN I solve real-world problems
involving the addition, subtraction, multiplication, and/or
division of rational numbers? (7.NS.3)
Wednesday: Bell Work
1) a + 5.8 = 26.6
4.5
2) X + 2.4 = 15.4
2
Solve the equations
Have homework on desk ready to check
Adding Fractions
• Adding Fractions
• There are 3 Simple Steps to add fractions:
• Step 1: Make sure the bottom numbers (the
denominators) are the same
• Step 2: Add the top numbers (the
numerators), put the answer over the
denominator
• Step 3: Simplify the fraction (if needed)
Subtracting Decimals
• Follows the same pattern as adding except
you subtract the numerators.
Exit / Closure
In math, why is it important to have the same
denominator when adding and subtracting
decimals?
Thursday: Bell Work
•
Joey, Keith, and Eli have a combined height
of 7 meters. If Joey is 2.31 meters tall and Eli
is 2.6 meters tall, how tall is Keith?
•
*Write and solve the equation. The variable
cannot be in the answer.*
Lesson
• ... solve real-world problems involving
the addition, subtraction, multiplication,
and/or division of rational numbers?
(7.NS.3)
•
•
Critical Thinking Activity
Dan worked as a volunteer for a total of 103
hours in 21 days. He worked about the same
number of hours each day. Which is the best
estimate of the number of hours Dan
worked as a volunteer each day?
–
–
–
–
a) 3
b) 4
c) 5
d) 6
• Constructed Response
• Amy is in charge or ordering new computers for her
classroom. If each computer costs $1256.33 and
Amy needs to order 5 computers, about how much
money will Amy need?
• Amy says she will need about $5,000.00 for her new
computers. She shows her work:
• $1256.33 rounds to $1000.00 and 1000.00 times 5 =
$5,000.00
• Did Amy round correctly for this situation? Defend
you answers using words and examples.
Adding / Subtracting Mixed Numbers
Subtracting Mixed Numbers
Solving Equations with Fractions
My.hrw.com
Exit / Closure
• What is the purpose of converting mixed
numbers to improper fractions?
Friday: Bell Work
1) James
works at an Indian sweet shop. He needs
to fill boxes with 0.3 kilograms of coconut candy
each. If he has 8 kilograms of coconut candy, how
many boxes can he fill?
Write and solve the equation. The variable
cannot be in the answer.*
Lesson
• ... solve real-world problems involving
the addition, subtraction, multiplication,
and/or division of rational numbers?
(7.NS.3)
Exit / Closure
• What is the importance of checking your work
in math?
• Discuss with a partner
Wednesday: Bell Work
Problem Solving with Scientific
Notation
• You know that a number is in scientific notation when it is
broken up as the product of two parts. The first part, the
coefficient, is a number between 1 and 10. The second part is
a power of ten. For example, 3 500 is expressed in scientific
notation as
• 3 500 = 3.5 x 10^3
•
↑
↑
• coefficient
power of ten
• How can you do calculations with numbers expressed in
scientific notation? First consider addition and subtraction,
then multiplication and division.
Addition and Subtraction
• Like Exponents: If two numbers have like
exponents, simply add or subtract the
coefficients and keep the same power of ten.
Convert the sum or difference to scientific
notation if needed. For example:
• a. (9.0 x 10^3) + (2.5 x 10^3) = 11.5 x 10^3 =
1.15 x 10^4
• b. (4.4 x 10^5) - (2.2 x 10^5) = 2.2 x 10^5
• Unlike Exponents: If two numbers have unlike
exponents, they must be made the same before the
numbers can be added or subtracted. Move decimal
points as needed to compensate for changes you
make to the exponents. For example:
• a. (3.0 x l0^5 m) + (2 x 10^4 m) = (30 x 10^4 m) + (2 x
10^4 m) = 32 x 10^4 m = 3.2 x l0^5 m
• b. (6.0 x 10^6 kg) - (4 x 10^7 kg) = 6.0 x 10^6 kg - 0.4
x 10^6 kg = 5.6 x 10^6 kg
• Unlike Units: To add and subtract numbers in
scientific notation with unlike units, you need to
know about metric prefixes. (Look in your text for a
list of them.) To begin, convert measurements to a
common metric unit. Then make powers of ten the
same. Finally you can add or subtract. For example:
• a. 6.1m + 24km = 6.1m + 2400m = 2406.1 m
• b. (4.62 x 10^2 L) + (2.1 mL) = 46.2 mL + 2.1 mL =
48.3 mL = 4.83 x 10^1 mL
Multiplication and Division
• Numbers expressed in scientific notation don't
need to have the same exponents to be
multiplied or divided. Just use the following
rules.
• Multiplication: To multiply two or more
numbers in scientific notation, multiply the
coefficients and add the exponents. Units are
multiplied. For example:
• a. (4 x 105 m)(2 x 106 m) = 8 x 1011 m2
• b. (2 x 10-2 m)(4 x 106 m) = 8 x 104 m2
• c. (3 x 103 kg)(5 x 106 m) = 15 x 109 kg. m =
1.5 x 1010 kg. m
• Division: To divide two or more numbers in
scientific notation, divide the coefficients and
subtract the exponent of the denominator
from the exponent of the numerator. Units
are divided. For example:
• a. (9 x 106 m) / (3 x 102s) = 3 x 106-2m/s = 3 x
104m/s
• b.(4 x 103g) / (2 x 10-2L) = 2 x 103-(-2)g/L = 2 x
105g/L
Try These: Exit Ticket
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1. (3 x 103) + (2 x 103)
2. (2 x 10-7 m) + (3 x 10-7 m)
3. (8 x 10-8 m2) – (3 x 10-8 m2)
4. (3.8 x 10-7 m2) – (2.8 x 10-7 m2)
5. (5.0 mm) + (2 x 10-4 m)
6. (6.2 km) – (3 x 102 m)
7. (2 x 105 m)(3 x 106 m)
8. (5 x 10-4 m)(4 x 10-2 m)
9. (1.50 x 10-7 m)(2.50 x 1015 m)
10. (9 x 108 kg)/(3 x l04 m2)
11. (2.4 x 105 kg)(3 x 104 m) / (4 x 10-2 s2)