The Number System8th 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. 2.58934

2.Round the decimal to the nearest tenth. 0.55

3.Round to the nearest whole number. 25.35

4.Round to the nearest thousandths. 12.57993

Procedures

• Bathroom Passes: 3 per six weeks

• Ask for permission first.

• Complete the Hall pass in the back of the agenda.

• I will initial.

Questioning:

• 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 decimalterminating decimal

Real Numbers Task (5 min.)

• Prior Knowledge Brainstorming:

• 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:

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.

Situation 2:

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 MondayAugust 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

AgendaTarget: 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 re-write 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.

AGENDAObjective: 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/SWITCHObjective: 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 WednesdayAugust 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!

AGENDAObjective: I can simplify monomials

using the laws of exponents.• 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. FridayAugust 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

AGENDAI 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 MondayAugust 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.

Write as a fraction.

3. 0.5 repeating

Terrific TuesdayAugust 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 WednesdayAugust 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. 2. 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?

Tremendous ThursdayAugust 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. 4. 5.

2nd/4th Periods AgendaI can convert numbers in standard form to scientific form.

• Opening Activity/Hook: United States Debt Clock1. 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 AgendaI 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. FridayAugust 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 AgendaI 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 × 2. 6.1 ×

 

3. 1.6 × 4. 3.46 ×

 

5. 2.91 × 6. 8.651 ×

 

7. 3.35 × 8. 7.3 ×

 

9. 1.49 × 10. 4.0027 ×

 

11. 5.2277 × 12. 8.50284 ×

 

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 meter. Write this number in standard notation.

 

4. PHYSICS The speed of light is about miles per second. Write this number in standard notation.

8th period AgendaI 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. 2. 3. 4.

 

 

5. 6. 7. 8.

 

 

 Evaluate each expression.

 

9. 10. 11. 12.

 

I can write monomials with positive exponents.

17. 18. 19. 20.

 

 

21. 22. 23. 24.

 

 

 

25. 26. 27. 28.

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. 2.

2nd/4th Periods AgendaI 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 AgendaI 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.) 4,400

• 10.) 75,000

• 11.) 69,900,000

• 12.) 575,000,000

• 13.) 0.084

• 14.) 0.0099

• 15.) 0.000000515

• 16.) 0.0000307

I can convert numbers from scientific form to standard and the reverse.

INDEPENDENT PRACTICE - Write each number in scientific notation.

13.) 34 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.) 9.03 ×

• 2.) 7.89 ×

• 3.) 4.115 ×

• 4.) 3.201 ×

•  5.) 5.1 ×

• 6.) 7.7 ×

• 7.) 3.85 ×

• 8.) 1.04 ×

I can convert numbers from scientific form to standard and the reverse.INDEPENDENT PRACTICE – Write numbers in standard form.

1.) 6.7 × 2.) 6.1 ×

 

3.) 1.6 × 4.) 3.46 ×

 

5.) 2.91 × 6.) 8.651 ×

 

7.) 3.35 × 8.) 7.3 ×

 

9.) 1.49 × 10.) 4.0027 ×

 

11.) 5.2277 × 12.) 8.50284 ×

 

Terrific TuesdayAugust 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.

Write in standard form.

3.) 2.5 x 10-8 4.) 5.356 x 105

2nd/4th AgendaI 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. 2. 3. 4.

 

 

 

5. 6. 7. 8.

 

 

 

9. 10. 11. 12.

Wonderful WednesdayAugust 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. 26. 27. 28.

2nd/4th Periods AgendaI can calculate square and cube roots.

• Fluency Practice (15 min.) – Dividing Fractions

• Remind 101

• Guided Practice

• Independent Practice

Independent Practice: Copy the following onto your paper.

Independent Practice: Find each square root or cube root.

1. 2.

 

 

3. 4.

 

 

5. 6.

 

 

7. 8.

 

 

9. 10.

 

T.G.I. ThursdayAugust 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 PracticeI can calculate square and cube roots.

ALGEBRA Solve each equation. Check your solution(s).

 

13. 14. 15.

 

 

 

16.

Guided PracticeI 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 AgendaI 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 AgendaI can find square and cube roots.

• Mini-Challenge 2-b

• Formative – Stand and Check

• Guided Practice

• Independent Practice

4th/8th Periods AgendaI 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 ThursdaySeptember 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 × pounds. The tiny krill they eat weigh only 2.1875 × pounds. How many times greater than krill are humpback whales?

 

2. MEASUREMENT One inch is equal to 1.5782 × miles. One centimeter is equal to 6.2137 × miles. How many miles greater is one inch than one centimeter?

2nd/ 4th Periods’ AgendaI 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 AgendaI can estimate non-perfect squares with

perfect squares.

• Accelerated Math (20 min.)

• Stand and Check

• Guided Practice- Lesson 9

• Independent Practice