Transcript The Number System

The Number System
8th Grade Math
Unit 1
Wednesday, August 7, 2013
Objective: I will convert fractions to decimals and
decimals to fractions to calculate batting averages.
• Bell Ringer: MUST HAVE DATE and OBJECTIVE listed 1st.
1. Round the decimal to the nearest hundredth.
2. Round the decimal to the nearest tenth.
3. Round to the nearest whole number.
4. Round to the nearest thousandths.
2.58934
0.55
25.35
12.57993
Procedures
• Bathroom Passes: 3 per six weeks
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•
•
Ask for permission first.
Complete the Hall pass in the back of the agenda.
I will initial.
Questioning:
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If you ask you must raise your hand!
If I ask no one raises their hand!
Be ready to answer any question.
VOCABULARY
• In your math journals, count ten pages from the end of the book and title
that page Glossary.
• We will define the following words during our lesson today. Place the word,
definition and illustration in the glossary.
• Rational numbers
repeating decimal
terminating decimal
Real Numbers Task (5 min.)
•
Prior Knowledge Brainstorming:
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What is a natural number?
What makes whole numbers different than natural numbers?
What do you know about integers?
As a team, place the following numbers in the correct category on the Real Number
Graphic Organizer:
3/5, 0, -5, 33, 0.45,
18%,
0.4 repeating
HINT: A rational number is a number that can be written as the ratio (fraction) of
two integers. The denominator CAN NOT be zero!!!!
HOT Question: Justify your classification of each number on the graphic
organizer. Ex. 1. The fraction 3/5 is a rational number because…
FRACTION to DECIMAL
EXAMPLE 1:
•
If I told you that 5/8 = 0.625, could you tell me how I “got” that answer?
EXAMPLE 2:
•
If I told you that -1 2/3 = -1.6 repeating, could you tell me how I “got” that answer?
• Show your work under notes in your Math Journal.
Thursday, August 8, 2013
• OBJECTIVE: I will convert repeating decimals into fractions and apply
conversions to find batting averages and winning percentages.
• BELL RINGER: Mrs. Frick made the following statement: A natural number
is always a rational number but a rational number is sometimes a natural
number. Do you agree or disagree with this statement? Write a sentence
justifying your decision.
Procedures
• Tutoring: Tuesdays & Wednesdays 7:15-7:50.
• I will come to the gym to let you know that I am at school.
• You need to know what it is you need help with. Questions are wonderful!
• Make arrangements with your 1st period teacher before you come to
tutoring.
Today’s Agenda
• Homework Check
• Batting average examples.
• Repeating Decimals
• Guided Practice
• Independent Practice for a grade.
Batting Averages and NASCAR
Situation 1:
Situation 2:
In a recent season, St. Louis Cardinals first baseman
Albert Pujols had 175 hits in 530 bats. To the nearest
thousandth, find his batting average.
In a recent season, NASCAR driver Jimmie Johnson won
6 of the 36 total races held. To the nearest thousandth,
find the part of races he won.
Repeating Decimals
• Example 1: 2.18
• Your Turn: 0.27, 0.135, 0.3
T.G.I.Friday, August 9, 2013
• Objective: I will convert between fractions and decimals and complete an
extended response question.
• Bell Ringer: Using complete sentences, describe the difference between 0.3
and 0.3 repeating. Convert both of them to a fraction. Show your work and
explain the process that you use.
Agenda
• Homework Check
• Mini Challenge
• Extended Response: The Field Trip
Extended Response
• An 8th grade class is going on a field trip to see a play.
• For the 27 students going on the trip, the van rentals will cost $545, gas will
cost $130, and admission to the play will be $945.
• Each student has been paying $4 per week to pay for the trip. They now
have a total of $864.
• How many more weeks does each student have to pay $4 to have enough
to pay for the entire trip?
Magnificent Monday
August 12, 2013
• Target: I can write expressions in exponential form.
• BellRinger: Complete the problems on the sheet that
you received as you walked in the door.
• Vocabulary: When you finish the bell ringer, place the
following words into your glossary:
• Power, base, exponent, expression
Agenda
Target: I can write expressions in exponential form.
• Assessment Results
• Bell Ringer
• “Double Your Money”
• Human Exponential Expressions
• Vocab.
• Foldable/Notes
• Independent Practice
Target: I can write exponential functions.
HUMAN EXPRESSIONS
1. You have a number or variable on an index card.
2. When I say “go” group yourselves without talking!
3. THINK: Are we grouped with like terms (same bases)?
How could we rewrite the groupings? When we write them with exponents, which
operation (+, -, /, x) do we use?
Notes/Vocab.
• Vocabulary is on the back white board. Copy definitions in glossary
• Notes/Examples:
Terrific Tuesday
August 13, 2013
• Objective: I can evaluate exponential expressions.
• Bell Ringer: Those who mastered need to finish their triangle
art page and those who did not need to complete the back side
of your page.
• I will collect these and for every correct answer you have, it will
replace a missed problem on Mini Challenge 1.
• This is completed independently and work must be shown.
• YOU must show ME that you have MASTERED these concepts.
AGENDA
Objective: I can evaluate exponential expressions.
• Homework Check – Stand up and Check!
• Vocabulary:
1. Order of operations: A universal order to simplify expressions so that
everyone gets the same answer.
• Switch/Switch
• Independent Practice
SWITCH/SWITCH
Objective: I can evaluate exponential expressions.
• REMEMBER PEMDAS?
• On your white boards, create an expression without variables that contains
multiple operations. Ex. 24/2 + 15 x 2
• When I say “switch” you must switch boards with someone other than in your
group and simplify their expression.
• When I say “switch” you must switch boards with someone other than in your
group and check that person’s answer. If it is NOT correct, correct it and take it
back to that person and explain.
Wacky Wednesday
August 14, 2013
• Objective: I can simplify monomials using the laws of exponents.
• BellRinger: Everyone completes Lesson 2 Problem-Solving Practice. You
have 10 minutes and you can use the calculator. SHOW YOUR STEPS!
AGENDA
Objective: I can simplify monomials using the laws
of exponents.
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•
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Small Group Homework Check
Vocabulary:
•
•
Variable – a letter that stands in the place of numbers
Monomial – A number, variable or product of numbers and variables
Foldable/Math Journal
Guided Practice w/ white boards
Independent Practice - Classwork
FYI
• Thursday – We will be doing STAR testing in the 5/6th computer lab for 2nd
period and 8th. We will be in the 7/8th computer lab for 4th period.
• Friday –You will be taking your first Challenge. You will get a list of all
vocabulary and sample problems on Thursday. We will play a head-to-head
review game on Friday before the Challenge.
T.G.I. Friday
August 16, 2013
TARGET: I can multiply and divide monomials.
• Bell Ringer:
1. Noah can run 2 ¼ miles more than Ricky. Write 2 ¼ in decimal
form.
2. The area of Mrs. Frick’s yard is 3 7 times 4. Calculate the area of
the yard.
3. Write the expression using exponents: 5x2 times 2x4
AGENDA
I can multiply and divide monomials.
I can raise a power to a power.
• Collect Homework
• Finish Foldable – Power to a Power
• Head to Head Practice
• Complete Extended Response Graphic Organizer
Extended Response
• An 8th grade class is going on a field trip to see a play.
• For the 27 students going on the trip, the van rentals will cost $545, gas will
cost $130, and admission to the play will be $945.
• Each student has been paying $4 per week to pay for the trip. They now
have a total of $864.
• How many more weeks does each student have to pay $4 to have enough
to pay for the entire trip?
Magnificent Monday
August 19, 2013
Target: I can score an 80% or above on Challenge 1 assessment.
Bell Ringer: Simplify using exponents.
1.
a • (–4) • b • a • b • (–4) • (–4)
Evaluate each expression if g = 2 and h = –3.
2. 𝑔3 + ℎ2
Write as a fraction.
3. 0.5 repeating
Terrific Tuesday
August 20, 2013
• BELL RINGER: 10 minutes
• Explain with complete sentences how to change a fraction to a decimal.
• Explain with complete sentences how to change a decimal to a fraction.
• Explain with complete sentences how to simplify using the Multiplication
Law of Exponents.
• Explain with complete sentences how to simplify using the Quotient Law of
Exponents.
• YOU MAY USE YOUR NOTES FROM YOUR GRAPHIC ORGANIZERS AND
JOURNAL.
2nd Period
• Assessment Results: You will retake the exam tomorrow!!!
• Enrichment: If you mastered you have a puzzle to complete with your
group. You will present the results to the class and explain the quote.
• Re-teach: Everyone else will join me for learning. Bring paper and pencil.
4th/8th
AGENDA
• Assessment Results: Below 70 will receive ICU.
• “WHY oh WHY do we have negative exponents.
• Notes/Math Journal
• Guided Practice
• Independent Practice
Wacky Wednesday
August 21, 2013
2nd/ 4th Periods: I can write monomials with positive exponents.
8th Period: I can convert between fractions and decimals and simplify
monomials using the Law of Exponents.
Bell Ringer:
Simplify using the Laws of Exponents
1. (𝑚5 )5
2. (ℎ6 )3
3. (𝑧 7 )3
2nd Period Agenda
• Challenge 1 Re-take – Allowed time is 30 minutes.
• Math Journal – Notes
• Guided Practice
4th Period Agenda
• Stand and Check
• Why oh Why are There Negatives?
• Zero Exponent
• Independent Practice
8th Period Agenda
• Assessment Results
• Assessment Corrections
• Why oh Why are there Negative Exponents?
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•
Tremendous Thursday
August 22, 2013
2nd/4th Period: I can convert numbers written in standard form to scientific form.
8th Period: I can convert between decimal to fraction, fraction to decimal and
simplify monomials using the Law of Exponents.
BELL RINGER: (5 min.)
Write as a fraction:
1.
0.66 repeating
2. 0.9 repeating
Using a complete sentence, explain the process to simplify the monomials.
3.
𝑚5
•
𝑚2
4.
𝑏12
𝑏5
5. (12𝑘 6 )3
2nd/4th Periods Agenda
I can convert numbers in standard form to scientific form.
• Opening Activity/Hook: United States Debt Clock
1.
If you were a newspaper or television reporter talking about the debt, how could you
modify the total to make it easier to report?
2.
Small Group
• Vocabulary:
•
•
Scientific Notation: A number written as a product of a factor and an integer power of
10.
Significant Digit: A number from 1 to 9.
2nd/4th Periods Agenda
I can convert numbers in standard form to scientific
form.
•
Notes/Journals:
• Scientific notation is in the form of 3.75 x 103
• The factor must be a significant digit.
• It is always multiplied by 10 raised to a power.
• Drop insignificant digits.
• If you begin with a number greater than zero, your exponent is positive.
• If you begin with a number less than zero, your exponent is negative.
I can convert numbers in standard form to
scientific form.
• Examples
• Guided Practice
• Independent Practice
• Closure: On a Post-it-Note, round the national debt to the nearest million
and convert to scientific notation. When I dismiss you, place your note on
the door as you leave.
T.G.I. Friday
August 23, 2013
• 2nd/4th Period: I can convert numbers written in scientific form to standard
form.
• 8th Period: I can write monomials with positive exponents.
BELL RINGER:
Write the monomial with positive exponents.
1.
x-4
2. 1 / x-5
Write with positive exponents and evaluate.
3.
8-3
4. 1/3-5
2nd/4th Agenda
I can convert numbers written in scientific form to
standard form.
• Homework Check – Dot Plot
• State Debt Clock – Rounding and scientific
notation
• Examples
• Guided Practice
• Independent Practice
I can convert numbers written in scientific notation to standard form.
Write each number in standard form.
1. 6.7 × 101
2. 6.1 × 104
3. 1.6 × 103
4. 3.46 × 102
5. 2.91 × 105
6. 8.651 × 107
7. 3.35 × 10−1
8. 7.3 × 10−6
9. 1.49 × 10−7
10. 4.0027 × 10−4
11. 5.2277 × 10−3
12. 8.50284 × 10−2
Problem Solving
1. MEASUREMENT There are
about 25.4 millimeters in one
inch. Write this number in
scientific notation.
2. POPULATION In the year 2000,
the population of Rahway, New
Jersey, was 26,500. Write this
number in scientific notation.
3. MEASUREMENT One
nanometer is 1.0 × 10−5 meter.
Write this number in standard
notation.
4. PHYSICS The speed of light is
about 1.86 × 105 miles per
second. Write this number in
standard notation.
8th period Agenda
.
I can write monomials with positive exponents
• Assessment Results
• Why oh Why Are There Negative Exponents?
• Guided Practice
• Independent Practice
• If we have time we will discuss the National Debt Clock and begin scientific
notation.
•
I
can
write
monomials
with
positive
exponents.
Write each expression using a positive exponent.
1. 4−5
5. 𝑓 −3
2. 5−7
6. (−2)−6
3. m−9
4. s −6
7. (−4)−3
8. 𝑤 −12
Evaluate each expression.
9. (−5)−5
10. 3−2
11. 8−3
12. (−9)−4
I can write monomials with positive exponents.
17. 2−6
21. 𝑦 −3
35
25. 3−3
•
23
18. 𝑠 −5
•
𝑦3
22. 𝑠 −5
𝑒 −3
26. 𝑒 −2
•
𝑠7
𝑚8
19. 𝑚−4
108
20. 109
•
𝑠7
𝑥6
23. 𝑥 −3
6−4
24. 68
𝑛−6
27. 𝑛4
𝑗 −2
28. 𝑗 −2
It’s Monday!!!!
August 26, 2013
• 2nd/4th Periods: I can multiply and divide numbers written in scientific form.
• 8th Periods: I can convert numbers from scientific form to standard form and
the reverse.
• BELL RINGER:
Write the following with exponents:
1. (−5𝑎2 𝑏 7 )7
2. (2𝑚5 𝑔11 )6
2nd/4th Periods Agenda
I can multiply and divide numbers in scientific form.
• Fluency Practice: Multiplying Fractions
• Hook - http://www.nationaldebtclocks.org/
• Journal- Notes and Examples
• Guided Practice • Independent Practice – Evens Only. If you don’t finish it is homework.
• Closure: Why is it helpful to write numbers in different ways?
I can multiply and divide numbers in scientific notation.
• GUIDED PRACTICE
8th Period Agenda
I can convert numbers from scientific form to standard form and the
reverse.
• Fluency Practice – Multiplying Fractions
• Math Journals – Vocabulary, Notes, Examples
• Guided Practice• Independent Practice –
• Closure: Round the national debt to the nearest million and write it in
scientific notation.
I can convert numbers from scientific form to standard and the
reverse.
GUIDED PRACTICE
• 9.)
• 10.)
• 11.)
• 12.)
• 13.)
• 14.)
• 15.)
• 16.)
4,400
75,000
69,900,000
575,000,000
0.084
0.0099
0.000000515
0.0000307
I can convert numbers from scientific form to standard and the reverse.
INDEPENDENT PRACTICE -
13.)
34
Write each number in scientific notation.
14.) 273
15.) 79,700
16.) 6,590
17.) 4,733,800
18.) 2,204,000,000
19.) 0.00916
20.) 0.29
21.) 0.00000571
22.) 0.0008331
23.) 0.0121
24.) 0.00000018
I can convert numbers from scientific form to standard and the reverse.
GUIDED PRACTICE
• 1.)
• 2.)
• 3.)
• 4.)
• 5.)
• 6.)
• 7.)
• 8.)
9.03 × 102
7.89 × 103
4.115 × 105
3.201 × 106
5.1 × 10−2
7.7 × 10−5
3.85 × 10−4
1.04 × 10−3
I can convert numbers from scientific form to standard and the reverse.
INDEPENDENT PRACTICE – Write numbers in standard form.
1.) 6.7 × 101
2.) 6.1 × 104
3.) 1.6 × 103
4.) 3.46 × 102
5.) 2.91 × 105
6.) 8.651 × 107
7.) 3.35 × 10−1
8.) 7.3 × 10−6
9.) 1.49 × 10−7
10.) 4.0027 × 10−4
11.) 5.2277 × 10−3
12.) 8.50284 × 10−2
Terrific Tuesday
August 27, 2013
• 2nd/4th – I can calculate square and cube roots.
• 8th – I can multiply/divide numbers written in scientific form.
• BELL RINGER:
Write in scientific form.
1.) 0.000003205
2.)
245,987,326,000.
4.)
5.356 x 105
Write in standard form.
3.) 2.5 x 10-8
2nd/4th Agenda
I can calculate square and cube roots.
• Fluency Practice: Dividing Fractions
• Stand & Check
• Vocabulary: Back white board
• Not Your Momma’s Number Line
• Math Journal: Personal Number Line
• Guided Practice:
• Independent Practice
Guided Practice
I can calculate square roots and cube roots.
Find each root.
1. 36
2. − 144
3.
121
289
5. ± 2.25
6. ±
9. – 0.49
10. – 3.24
3
27
64
7.
4. 3 2,744
−81
100
11. −
25
441
8. ± 0.0025
12. ± 361
Wonderful Wednesday
August 28, 2013
• 2nd/4th Periods – I can calculate square and cube roots.
• 8th Periods – I can multiply/divide scientific notation.
• Bell Ringer:
Simplify. Write using positive exponents.
25.
35
3−3
26.
𝑒 −3
𝑒 −2
27.
𝑛−6
𝑛4
28.
𝑗 −2
𝑗 −2
2nd/4th Periods Agenda
I can calculate square and cube roots.
• Fluency Practice (15 min.) – Dividing Fractions
• Remind 101
• Guided Practice
• Independent Practice
Independent Practice:
9.
Find each square root or cube root.
1. 16
2. − 9
3. 36
4. 3 2,744
5. 3 1,331
6. 729
7. − 0.04
8. −289
16
49
3
10.
49
100
T.G.I. Thursday
August 29, 2013
• 2nd/4th/8th Periods: I can score an 80% or above on Mini Challenge 2.
I can find square and cube roots.
Bell Ringer:
1.
Create three problems that you predict will be on the mini challenge 2.
They must represent the topics found on the white board.
2. Solve your three problems.
Guided Practice
I can calculate square and cube roots.
ALGEBRA Solve each equation. Check your solution(s).
13. ℎ2 = 121
16. 0.0196 = 𝑚2
14. 324 = 𝑎2
15. 𝑥 2 =
81
169
Guided Practice
I can calculate square and cube roots.
19.
GARDENING Moesha has 196 pepper plants that she wants to plant in
square formation. How many pepper plants should she plant in each row?
20.
RESTAURANTS A new restaurant has ordered 64 tables for its outdoor
patio. If the manager arranges the tables in a square formation, how many will
be in each row?
GEOMETRY The formula for the perimeter of a square is P = 4s, where s is the length of a side. Find the perimeter of each square.
21.
8th Period Agenda
I can multiply/divide numbers written in scientific notation.
• Fluency Practice (15 min.) – Dividing fractions
• Remind 101
• Homework Check
• Guided Practice
• Independent Practice
Wednesday, September 4, 2013
• 4th /8th: I can estimate non-perfect squares using perfect squares.
• 2nd: I can find square and cube roots.
I can score an 80% or higher on the MC 2-b
Bell Ringer: Write each decimal as a fraction.
1.) -0.25
2.) 0.35
3.) -0.456
4.) 0.7
2nd Period Agenda
I can find square and cube roots.
• Mini-Challenge 2-b
• Formative – Stand and Check
• Guided Practice
• Independent Practice
4th/8th Periods Agenda
I can estimate non-perfect squares with perfect
squares.
• Formative: Stand and Check
• Accelerated Math Guidelines
• Guided Practice
• Independent Practice
Accelerated Math
• You will be assigned 40 objectives for each 6-weeks.
• You can choose no more than 3 objectives for each diagnostic.
• Rewards:
• 10 objectives met – homework pass or candy
• 20 objectives met – computer time – math games
• 30 objectives met –
• 40 objectives met -
Terrific Thursday
September 5, 2013
• 2nd/4th – I can compare and order real numbers.
• 8th – I can estimate non-perfect squares with perfect squares.
Bell Ringer:
1. OCEAN Humpback whales are
known to weigh as much as 8 ×
104 pounds. The tiny krill they
eat weigh only 2.1875 × 10−3
pounds. How many times
greater than krill are humpback
whales?
2. MEASUREMENT One inch is
equal to 1.5782 × 10−5 miles.
One centimeter is equal to
6.2137 × 10−6 miles. How many
miles greater is one inch than
one centimeter?
2nd/ 4th Periods’ Agenda
I can compare and order real numbers.
• Accelerated Math (20 min.)- Leaders should distribute folders with journals.
• Vocabulary Pictionary –You can use your glossary for help.
• Stand and Check
• Hook – Major League Baseball Field
• Guided Practice – Worksheet
• Independent Practice -
8th Period Agenda
I can estimate non-perfect squares with perfect
squares.
• Accelerated Math (20 min.)
• Stand and Check
• Guided Practice- Lesson 9
• Independent Practice