Basic Pre Algebra Intervention Program

Transcription

1 Basic Pre Algebra Intervention Program This 9 lesson Intervention Plan is designed to provide extra practice lessons and activities for students in Pre Algebra. The skills covered are basics that must be mastered in order to ensure success in Pre Algebra. These lessons are not meant to be 90 minute full class lessons (although some could be used that way and some might last that long). Intervention works best when students work in small, targeted groups with a teacher. This is a small piece of a larger, 35 lesson, full Pre Algebra Intervention Plan. Created by: Lindsay Perro 20

2 Basic Pre Algebra Intervention Program LESSON TOPIC PLAN A B C D E Order of Operations No Calculator Order of Operations with Decimals No Calculator Expanded Form No Calculator Rules of Exponents No Calculator Review Expanded Form & Laws of Exponents No Calculator Warm-up A Notes on Order of Operations Order of Operations Notes & Practice Independent Practice Order of Operations Bingo Students solve the problems independently. Bingo can be played if time permits. Exit ticket A Warm up B Decimal Operations Notes & Review Puzzle with partners Exit Ticket B Warm up C Expanded Form Notes Independent Practice - Form is Important Worksheet Exit Ticket C Warm up D Review of Exponents Exponents Practice Worksheet Rules of Exponents Notes & Practice Exponents Versa Tiles Activity - Independent (Must have Versa Tiles for students to use) Exit Ticket D Warm up E Expanded Form with Decimals and Fractions Worksheet Exponents Matching Game Should be played like the game Memory. Exit Ticket E 2

3 LESSON TOPIC LESSON F G H I Fractions, Decimals & Percents No Calculator Percent of a Number Proportions and Unit Rates Proportions and Scale Warm up F Fractions, Decimals and Percents Guided Practice and Pairs Practice Silly Face Worksheet Independent Practice Exit Ticket F Warm up G Percent of a Number Guided Practice Percent of a Number Coloring Sheet Independent Practice Exit Ticket G Warm up H Proportions and Unit Rate Notes and Guided Practice Proportions and Unit Rate Coloring Sheet Independent Practice Exit Ticket H Warm up I Candy Bar Scale/Proportions Activity Exit Ticket I 3

4 Warm Up A Name List as many words as you can that signal each operation. ) Addition 2) Subtraction 3) Multiplication 4) Division Name KEY Warm Up A List as many words as you can that signal each operation. ) Addition 2) Subtraction Sum, more than, increased, plus Less than, difference, decreased 3) Multiplication Of, product, per 4) Division Quotient, per, divided by/into 4

5 Lesson A Notes Give the students notes on the order of operations. Feel free to use PEMDAS, however stress to them that Multiplication and Division are done from left to right same with Addition and Subtraction. Have them copy down the following graphic organizer, or have it copied for them. ORDER OF OPERATIONS PARENTHESIS EXPONENTS MULTIPLICATION OR DIVISION ADDITION OR SUBTRACTION 5

6 Lesson A Notes and Practice Name: Date: Order of Operations Notes & Practice P ( ) E 3 M/D x / A/S + / - Remember Multiplication and Division are solved from left to right Addition and Subtraction are solved from left to right Solve each problem. Show your work for each step. EX. 0 2 x x (5 6) x (8 4) 5. 6( 2-4 ) x x 0 6

7 (5 4) x x (4 x 2) 7. 2 x x 2 Bonus! ( ) x 8 2 7

8 Name: KEY Date: Order of Operations Notes & Practice P PARENTHESIS ( ) E EXPONENTS 3 M/D_MULTIPLICATION / DIVISION x / A/S_ADDITION / SUBTRACTION + / - Remember Multiplication and Division are solved from left to right Addition and Subtraction are solved from left to right Solve each problem. Show your work for each step. a. 0 2 x x (5 6) x (8 4) x ( 2-4 ) x x 0 6(8)

9 (5 4) x () x x x x (4 x 2) 7. 2 x x x (4 x 2) x Bonus! ( ) x 8 2 ( ) x 8 2 (5 2) x x x

10 Lesson A Independent Practice / Game Name Date Order of Operations BINGO! Solve each problem. When you are finished, Bingo will be played! B I N G O x (9-7) 3(7-5+) 5(3) - 3(4) 42 (5-3) 2 x x 3+ 4 x (8-4) 2 x 2 - (6 x 2) x x 4 x (3) + 3 3(3) - 3 (2-3) x 2 6(5) - 3(5) 6(6) + 3 x 2 0 x 4 4 x (2) 7(4-3) 5 2 x (2) + 4 x 3 2(3 + 6) 2 x 3 (3 x 4 x 5) - 4(5) 3(4 + 2) 3 x 3 5(7-4) 2[2 + (0-4) 3] 0[ 3( + 4) - 6(2) ] 0

11 Name KEY Date Order of Operations BINGO! Solve each problem. When you are finished, Bingo will be played! B I N G O x (9-7) 3( ) 7(3) - 3(4) 42 (5-3) x x 3+ 4 x (8-4) x 2 - (6 x 2) x x 4 x (3) + 3 6(2) (2-3) x 2 6(5) - 3(5) 6(6) + 3 x 2 0 x 4 4 x (2) 7(4-3) 5 2 x (2) + 4 x 3 2(3 + 6) 2 x (3 x 4 x 5) - 4(5) 5(4 + 2) (7-4) 2[2 + (0-4) 3] 0[ 3( + 4) - 6(2) ]

12 Exit Ticket A Name ) ( 3 ) 2) 3 x 3 4 x 2 3) 5 5 x ) 4 x Name KEY Exit Ticket A ) ( 3 ) 3 2) 3 x 3 4 x 2 3) 5 5 x ) 4 x

13 Use < or > to make each statement true. Warm Up B Name ) ) 3-3) ) 0-9 5) ) ) ) 3-3 Use < or > to make each statement true. Warm Up B Name KEY ) -6-8 > 2) 3 - > 3) -7-5 < 4) 0-9 > 5) < 6) > 7) -3-2 < 8) 3-3 > 3

14 Lesson B Notes and Review Name DECIMAL OPERATIONS REVIEW Complete the following table about decimal rules. Put a check mark in the box to show a rule applies to the given operation. Line up the decimals Drop down the decimal into your answer (Or Float it up) Count the number of decimal places for your answer Move the decimal so you have a whole number Practice! Adding Decimals Subtracting Decimals Multiplying Decimals Dividing Decimals. 4.5 x x ,

15 Word Problems - Read each problem carefully. These are REAL LIFE situations you need to know how to set up and solve each of these!. Morgan purchased $30.46 worth of groceries. She paid the cashier with a $50 bill. How much change should she receive? 2. Aileen worked 35.5 hours last week. She earns $7.75 per hour. How much money did she make last week? 3. Reggie has a piece of lumber that is 9 feet long. He needs to cut it into.75 foot sections. How many pieces will he have after he makes his cuts? 4. Aralynn is making a quilt. She has used 5.5 balls of yarn and will need 8 more. How many balls of yarn will she have used when she s finished? 5. Coffee costs $3.59 per pound. How much would 5.7 pounds of coffee cost? 6. Carl ran the 00 meter dash in seconds. Jeremy ran it in 6.05 seconds. How much faster did Carl run than Jeremy? 5

16 DECIMAL OPERATIONS REVIEW Name KEY Complete the following table about decimal rules. Put a check mark in the box to show a rule applies to the given operation. Line up the decimals Drop down the decimal into your answer (Or Float it up) Count the number of decimal places for your answer Move the decimal so you have a whole number Practice! Adding Decimals Subtracting Decimals Multiplying Decimals Dividing Decimals You can t have a decimal divisor. 4.5 x 0.56 = x 4.6 = = = = = = , =

17 Word Problems - Read each problem carefully. These are REAL LIFE situations you need to know how to set up and solve each of these!. Morgan purchased $30.46 worth of groceries. She paid the cashier with a $50 bill. How much change should she receive? $ Aileen worked 35.5 hours last week. She earns $7.75 per hour. How much money did she make last week? $ Reggie has a piece of lumber that is 9 feet long. He needs to cut it into.75 foot sections. How many pieces will he have after he makes his cuts? 2 pieces 4. Aralynn is making a quilt. She has used 5.5 balls of yarn and will need 8 more. How many balls of yarn will she have used when she s finished? 3.5 balls of yarn 5. Coffee costs $3.59 per pound. How much would 5.7 pounds of coffee cost? $ Carl ran the 00 meter dash in seconds. Jeremy ran it in 6.05 seconds. How much faster did Carl run than Jeremy?.596 seconds 7

18 (5.5 x ) (2.3 x 3.6) ( 4 3.5) (4 2) (4.2 x 2.6) ( ) Lesson B Activity Puzzle. Pre Cut! x x (4 3 x 0.2) x (9 3.5) 6[5.2 (4. 3.6)] x x 4 8

19 Exit Ticket B Name ) ( ) 2) 3.2 x 3 4. x 2 3) x ) 2.4 x Exit Ticket B Name KEY ) ( ) 2) 3.2 x 3 4. x ) x ) 2.4 x

20 Warm Up C Name ) Order the following numbers from least to greatest. 0.43, 0.5, 0.57, ) Order the following numbers from least to greatest. 5, 2 3, 3 8, 4 3) Order the following numbers from greatest to least. 2, 8, 3 5, 3 4 4) Order the following numbers from least to greatest. 0.5, 3 5, 0.35, 3 0 Warm Up C Name KEY ) Order the following numbers from least to greatest. 0.43, 0.5, 0.57, , 0.43, 0.5, ) Order the following numbers from greatest to least. 2, 8, 3 5, , 3 5, 2, 8 2) Order the following numbers from least to greatest. 5, 2 3, 3 8, 4,, 3, ) Order the following numbers from least to greatest. 0.5, 3 5, 0.35, , 0.35, 0.5,

21 Lesson C Notes Name Date Expanded Form Notes There are TWO different ways to write numbers in expanded form. One way is to use place value, and the other is to use fractions. You need to be familiar with both ways. Place Value Guided Practice Write in expanded form. Step : Identify the place value of each number. The 3 is in the place. The 2 is in the place. The is in the place. The 4 is in the place. Skip any zeros. Step 2: Multiply each number by the decimal for its place value. (3 x 0) + ( x ) + (2 x 0.0) + (4 x 0.00) Independent Practice Write 5.06 in expanded form. Step : Identify the place value of each number. The 5 is in the place. Skip any zeros. The is in the place. The 6 is in the place. Step 2: Multiply each number by the decimal for its place value. Write in expanded form. Write in expanded form. 2

22 Place Value Using Fractions Guided Practice Write in expanded form. Step : Identify the place value of each number. The 3 is in the place. The 2 is in the place. The is in the place. The 4 is in the place. Skip any zeros. Step 2: Multiply each number by the fraction for its place value. Independent Practice Step : Identify the place value of each number. (3 x 0) + ( x ) + (2 x 00 ) + (4 x 000 ) Write 5.06 in expanded form. The 5 is in the place. Skip any zeros. The is in the place. The 6 is in the place. Step 2: Multiply each number by the fraction for its place value. Write in expanded form. Write in expanded form. Bring it all together. Write each of the following numbers in expanded form using place value and fractions. Write in expanded form. Write in expanded form. 22

23 Name KEY Date Expanded Form Notes There are TWO different ways to write numbers in expanded form. One way is to use place value, and the other is to use fractions. You need to be familiar with both ways. Place Value Guided Practice Write in expanded form. Step : Identify the place value of each number. The 3 is in the TENS place. The 2 is in the HUNDREDTHS place. The is in the ONES place. The 4 is in the _THOUSANDTHS place. Skip any zeros. Step 2: Multiply each number by the decimal for its place value. (3 x 0) + ( x ) + (2 x 0.0) + (4 x 0.00) Independent Practice Write 5.06 in expanded form. Step : Identify the place value of each number. The 5 is in the ONES place. Skip any zeros. The is in the TENTHS place. The 6 is in the _THOUSANDTHS place. Step 2: Multiply each number by the decimal for its place value. ( 5 X ) + ( X 0.) + ( 6 X.00) Write in expanded form. Write in expanded form. ( X 00) + (5 X 0) + (2 X ) + (2 X.0) + (6 X.00) (2 X 0) + (5 X ) + (6 X.0) + (3 X.000) 23

24 Place Value Using Fractions Guided Practice Write in expanded form. Step : Identify the place value of each number. The 3 is in the TENS place. The 2 is in the HUNDREDTHS place. The is in the ONES place. The 4 is in the _THOUSANDTHS place. Skip any zeros. Step 2: Multiply each number by the fraction for its place value. Independent Practice Step : Identify the place value of each number. (3 x 0) + ( x ) + (2 x 00 ) + (4 x 000 ) Write 5.06 in expanded form. The 5 is in the ONES place. Skip any zeros. The is in the TENTHS place. The 6 is in the _THOUSANDTHS place. Step 2: Multiply each number by the fraction for its place value. ( 5 X ) + ( X 0 ) + ( 6 X 000 ) Write in expanded form. Write in expanded form. ( X 00) + (5 X 0) + (2 X ) + (2 X ) + (6 X ) (2 X 0) + (5 X ) + (6 X ) + (3 X. ) Bring it all together. Write each of the following numbers in expanded form using place value and fractions. Write in expanded form. Write in expanded form. ( 7 X.0) + ( 5 X.00) ( X 00) + (2 X 0) + ( 5 X.00) (7 X 00 ) + ( 5 X 000 ) ( X 00) + ( 2 X 0) + ( 5 X 000 ) 24

25 Lesson C Independent Practice Name Form Is Important Date Write the given decimal in standard form, and expanded form using decimals. Written Form Standard Form Expanded Form using Decimals EX: Three and fifteen hundredths 3.5 (3 x ) + ( x 0.) + (5 x.0) Four and ninety three thousandths Eighty six hundredths One hundred twenty and four tenths Six and one thousandth One thousand four and sixteen hundredths Ninety and five tenths Complete the table by writing each decimal in the missing form. Written Form Standard Form Expanded Form using Decimals (4 x,000) + (2 x 0) + (6 x 0.00) 3.07, (9 x ) + (4 x.0) + (5 x.00) (5 x 0,000) + (3 x 00) + (4 x.) 25

26 Name KEY Form Is Important Date Write the given decimal in standard form, and expanded form using decimals. Written Form Standard Form Expanded Form using Decimals EX: Three and fifteen hundredths 3.5 (3 x ) + ( x 0.) + (5 x.0) Four and ninety three thousandths (4 x ) + (9 x.0) + (3 x.00) Eighty six hundredths 0.86 (8 x.) + (6 x.0) One hundred twenty and four tenths 24.4 ( x 00) + ( 2 x 0) + (4 x ) + (4 x.) Six and one thousandth 6.00 (6 x ) + ( x.00) One thousand four and sixteen hundredths,004.6 ( x,000) + (4 x ) + ( x.) + (6 x.0) Ninety and five tenths 9.5 (9 x ) + (5 x.) Complete the table by writing each decimal in the missing form. Written Form Standard Form Expanded Form using Decimals One hundred forty two and six hundredths ( x 00) + (4 x 0) + (2 x ) + (6 x.0) Four thousand twenty and six thousandths 4, (4 x,000) + (2 x 0) + (6 x 0.00) Three and seven hundredths 3.07 (3 x ) + (7 x.0) One thousand six and eight hundredths, ( x,000) + (6 x ) + (8 x.0) Nine and forty five thousandths (9 x ) + (4 x.0) + (5 x.00) Seven hundred and seven thousandths (7 x 00) + (7 x.00) Fifty thousand, three hundred and four tenths 50,300.4 (5 x 0,000) + (3 x 00) + (4 x.) 26

27 Exit Ticket C Name ) Write in expanded form using place value. 2, ) Write in expanded form using fractions ) Write in expanded form using place value ) Write in expanded form using fractions Exit Ticket C Name KEY ) Write in expanded form using place value. 2, (2 x,000) + (2 x ) + (4 x.00) 3) Write in expanded form using place value (5 x 00) + (5 x ) + (5 x.0) 2) Write in expanded form using fractions (5 x ) + (2 x 0 ) + (7 x 00 ) + (6 x,000 ) 4) Write in expanded form using fractions (2 x 0) + (3 x ) + (2 x 0 ) + (3 x 00 ) 27

28 Warm Up D Name ) Simply. Write your answer as an exponent ) Simply. Write your answer as an exponent ) Simply. Write your answer as an exponent ) Simply. Write your answer as an exponent Warm Up D Name KEY ) Simply. Write your answer as an exponent ) Simply. Write your answer as an exponent ) Simply. Write your answer as an exponent ) Simply. Write your answer as an exponent

29 Lesson D Review Name Date Exponents Practice Fill in the missing parts of the table. Words Expanded Form Standard Form Three cubed Six to the 2 nd power Four squared Seven to the 4 th power Three to the 4 th power Three squared plus 2 cubed Two squared plus ten squared

30 Name KEY Date Exponents Practice Fill in the missing parts of the table. Words Expanded Form Standard Form Three cubed Four to the 4 th power Six to the 2 nd power Four squared Seven to the 4 th power ,40 Two to the 6 th power Three to the 4 th power Three squared plus 2 cubed Five cubed plus four squared Two squared plus ten squared Two squared plus six to the fourth power ,300 30

31 Lesson D Notes Name Date Rules of Exponents Notes Rule Definition Example What is an Exponent? An exponent tells us how many times we multiply a number by itself. We never multiply the base by the exponent! 8³ = 8 x 8 x 8 (not 8 x 3) Product Rule When multiplying two powers that have the same base, you can add the exponents. 5³ x 5² = = 5 5 Quotient Rule We can divide two powers with the same base by subtracting the exponents = 97 5 = 9 2 Zero Rule Any nonzero number raised to the power of zero equals. x 0 = Product Rule - Let s try some! Write each answer as an exponent.. 3³ x 3¹ x x x m x n 3

32 Quotient Rule - Let s try some! Write each answer as an exponent BCR Practice Part A: Reduce the given fraction. Write you answer as an exponent. Part B: Use what you know about the laws of exponents to explain why your answer is correct. Use words, numbers and/or symbols in your explanation. 32

33 Name KEY Date Rules of Exponents Notes Rule Definition Example What is an Exponent? An exponent tells us how many times we multiply a number by itself. We never multiply the base by the exponent! 8³ = 8 x 8 x 8 (not 8 x 3) Product Rule When multiplying two powers that have the same base, you can add the exponents. 5³ x 5² = = 5 5 Quotient Rule We can divide two powers with the same base by subtracting the exponents = 97 5 = 9 2 Zero Rule Any nonzero number raised to the power of zero equals. x 0 = Product Rule - Let s try some! Write each answer as an exponent.. 3³ x 3¹ x x x m x n m +n x 33

34 Quotient Rule - Let s try some! Write each answer as an exponent = = = = 04 BCR Practice Part A: Reduce the given fraction. Write you answer as an exponent. 9 6 Part B: Use what you know about the laws of exponents to explain why your answer is correct. Use words, numbers and/or symbols in your explanation. 34

35 Lesson D Independent Practice Name Date Exponents & Square Roots VersaTiles Activity Solve each problem by following the given directions. Find your answer in the box below. Using the VersaTiles, place the problem number over the letter that corresponds to your answer below. WRITE YOUR ANSWER ON THIS SHEET AS WELL! Simplify. Write your answer using exponents = 9? = 5? ? = = 7? Write in standard form Simplify Answer Box A 8 B 25 C 4 D E 2 F 64 G 5 H 5 I 9 J 27 K 8 L 6 35

36 Name KEY Date Exponents & Square Roots VersaTiles Activity Solve each problem by following the given directions. Find your answer in the box below. Using the VersaTiles, place the problem number over the letter that corresponds to your answer below. WRITE YOUR ANSWER ON THIS SHEET AS WELL! Simplify. Write your answer using exponents = 9? = 5? ? = = 7? Write in expanded form Simplify Answer Box 36

37 Exit Ticket D Name ) Solve ) Write using exponents ) Simplify using exponents ) Simplify using exponents Exit Ticket D Name KEY ) Solve ) Write using exponents ) Simplify using exponents ) Simplify using exponents

38 Warm Up E Name 5) Write in expanded form using place value ) Write in expanded form using fractions ) Solve ) Write using exponents Warm Up E Name KEY ) Write in expanded form using place value ( x 00) + (5 x 0) + (4 x ) + (4 x.00) 2) Write in expanded form using fractions (2 x 00) + (3 x ) + (7 x 0 ) + (4 x,000 ) 3) Solve ) Write using exponents

39 Lesson E Worksheet Name Date Expanded Form with Decimals and Fractions Use the digits in the given number to fill in the place value chart. Then write each number in expanded form using decimals and expanded form using fractions. Example: hundreds Tens Ones Tenths Hundredths Thousandths / 0.0 / / ,000 (3x00) + (5 x ) + (4 x.0) + (7 x.00) (3x00) + (5 x ) + (4 x ) + (7 x ) 00,000 Your Turn! hundreds Tens Ones Tenths Hundredths Thousandths / 0.0 / /, hundreds Tens Ones Tenths Hundredths Thousandths / 0.0 / /,000 39

40 Example: Each number is given in expanded notation. Break it down by using the given table. Then write each number in standard form. (5 x 0) + (4 x 0 ) + (6 x,000 ) hundreds Tens Ones Tenths Hundredths Thousandths / 0.0 / / Fill in the empty spaces with zeros ,000 Your Turn! (9 x 00) + (6 x 00 ) + (8 x,000 ) hundreds Tens Ones Tenths Hundredths Thousandths / 0.0 / /,000 (8 x 0 ) + (4 x 0 ) + (5 x,000 ) hundreds Tens Ones Tenths Hundredths Thousandths / 0.0 / /,000 40

41 Independent Practice Write each number in expanded form using decimals Write each number in expanded form using fractions , Write each number in standard form. 9. (5 x 0) + (9 x 0 ) + (6 x,000 ) 0. (7 x 0 ) + ( x 00 ) + (3 x,000 ). (9 x,000) + (5 x 00) + (6 x 00 ) 2. (2 x 00) + (9 x 0) + (3 x 0 ) + (4 x 00 ) 4

42 Name KEY Date Expanded Form with Decimals and Fractions Use the digits in the given number to fill in the place value chart. Then write each number in expanded form using decimals and expanded form using fractions. Example: hundreds Tens Ones Tenths Hundredths Thousandths / 0.0 / / ,000 Your Turn! (3x00) + (5 x ) + (4 x.0) + (7 x.00) (3x00) + (5 x ) + (4 x ) + (7 x ) 00, hundreds Tens Ones Tenths Hundredths Thousandths / 0.0 / /,000 ( 4 x 0 ) + ( 8 x ) + ( 6 x 0. ) + ( 5 x 0. 0) ( 4 x 0 ) + ( 8 x ) + ( 6 x 0 ) + ( 5 x 00 ) hundreds Tens Ones Tenths Hundredths Thousandths / 0.0 / /,000 ( 7 x 0 ) + ( 5 x ) + ( 8 x 0. 0) ( 7 x 0 ) + ( 5 x ) + ( 8 x 00 ) 42

43 Example: Each number is given in expanded notation. Break it down by using the given table. Then write each number in standard form. (5 x 0) + (4 x 0 ) + (6 x,000 ) hundreds Tens Ones Tenths Hundredths Thousandths / 0.0 / / Fill in the empty spaces with zeros ,000 Your Turn! (9 x 00) + (6 x 00 ) + (8 x,000 ) hundreds Tens Ones Tenths Hundredths Thousandths / 0.0 / / 9 6 8, (8 x 0 ) + (4 x 0 ) + (5 x,000 ) hundreds Tens Ones Tenths Hundredths Thousandths / 0.0 / / 8 4 5,

44 Independent Practice Write each number in expanded form using decimals ( 6 x 00) + ( 2 x 0) + ( 5 x ) + ( 3 x.0) ( x 00) + ( 5 x.00) ( 4 x 0) + ( 5 x ) + ( 7 x. ) + ( 6 x.0) ( x 00) + ( 9 x 0) + ( 4 x. ) + ( 5 x.00) Write each number in expanded form using fractions ( x 0 ) + ( 4 x ) + ( 7 x 0 ) 6., ( x,000 ) + ( 5 x 0 ) + ( 6 x,000 ) ( 5 x 0 ) + ( 5 x ) + ( 9 x 0 ) + ( 8 x 00 ) ( 2 x 00 ) + ( x 0 ) + ( 6 x Write each number in standard form.,000 ) 9. (5 x 0) + (9 x 0 ) + (6 x,000 ) (7 x 0 ) + ( x 00 ) + (3 x,000 ) (9 x,000) + (5 x 00) + (6 x ) 9, (2 x 00) + (9 x 0) + (3 x 0 ) + (4 x 00 )

45 Lesson E Worksheet Rules of Exponents Memory Pre -cut the cards. To ensure students cannot see through the back, print on cardstock or darker paper

46 Exit Ticket E Name ) Write in expanded form using place value ) Write in expanded form using fractions ) Simplify using exponents ) Simplify using exponents Exit Ticket E Name KEY ) Write in expanded form using place value (2 x 00) + (6 x.00) 3) Simplify using exponents ) Write in expanded form using fractions (7 x ) + (7 x 4) Simplify using exponents.,000 )

47 Warm Up F Name ) Put the following numbers in order from least to greatest. 3, 4, 0.04, 3% Use what you know about rational numbers to explain how you found your answer. Use words, numbers, and/or symbols in your explanation. Warm Up F Name KEY ) Put the following numbers in order from least to greatest. 3, 4, 0.04, 3% 3%, 0.04, 4, 3 Use what you know about rational numbers to explain how you found your answer. Use words, numbers, and/or symbols in your explanation. Students should demonstrate their ability to convert the four numbers to all be in the same form, and then compare them. They can show their work in this section to get credit if they wish and if all work is shown. 47

48 Lesson F Guided & Group Practice Name Fractions, Decimals and Percents Date Use the chart below to help you convert among fractions, decimals and percents. You will need this to change and compare these three forms of numbers! 48

49 Use the chart to help you complete the following problems.. The annual amount of rainfall in a given city is inches. Convert to a decimal. 2. Put the following numbers in order from least to greatest. 4, 0.202, 30% 3. You scored an 80% on your math test. Express this number as a fraction and as a decimal. 4. A new car loan comes with a 3.49% interest rate. Express this number as a decimal. 5. Which number has the greatest value? 3 5, 0.35, 35%,

50 Directions: Cut up the cards before giving them to students. The students (working individually or with partners) will pick 5 cards from the pile. They must use a white board or sheet of paper to order the numbers from least to greatest. If they are working with a partner, they must both agree on the answer before they can pick 5 more cards

51 % 95% 5% 4.5% 72% 4% 5% 7.5% 55% 0%

52 Lesson F Independent Practice 52

53 53

54 Lesson F Exit Ticket Name Exit Ticket F SHOW YOUR WORK!. In Megan s Science class there are 35 students. Fourteen are girls. What is the ratio of girls to boys? 2. The ratio of number of cats to dogs in the pound was 2:36. How is this ratio represented as a fraction in simplest form? 3. On a day it snowed, three-tenths of the students wore snow boots. Write a ratio to represent the number of students who did wear boots compared to the number of students who did not. 4. Which of the following does not represent 75%? A. 75 B D. C Carleigh took a survey of the students in her art class to see what their favorite color was. 5 students chose 25 blue. What is 5 written as a percent? Rewrite 0.5 as a fraction in simplest form. 54

55 Name KEY Exit Ticket F SHOW YOUR WORK!. In Megan s Science class there are 35 students. Fourteen are girls. What is the ratio of girls to boys? 4 : 2 Reduced to 2 : 3 2. The ratio of number of cats to dogs in the pound was 2:36. How is this ratio represented as a fraction in simplest form? 3 3. On a day it snowed, three-tenths of the students wore snow boots. Write a ratio to represent the number of students who did wear boots compared to the number of students who did not. 4. Which of the following does not represent 75%? A. 75 C B D. 3 : 7 5. Carleigh took a survey of the students in her art class to see what their favorite color was. 5 students chose 25 blue. What is 5 written as a percent? Rewrite 0.5 as a fraction in simplest form % 55

56 Name Warm Up G ) Re-write as a decimal and a percent ) Re-write as a fraction and a percent ) Re-write as a decimal and a fraction. 5% 4) Re-write as a fraction in simplest form Warm Up G Name KEY ) Re-write as a decimal and a percent % 2) Re-write as a fraction and a percent % 3) Re-write as a decimal and a fraction. 5% ) Re-write as a fraction in simplest form

57 Lesson G Notes and Practice Name Date Percent of a Number Guided Practice To determine the percent of a number you need to remember two key points: ) The word of means Multiply! 2) Percents must be changed to decimals before you can multiply with them. Example: What is 70% of 50? Step : Change the percent to a decimal by moving the decimal two places to the left. Remember, the decimal in a whole number is at the end just like a period is at the end of a sentence. 70% = 0.70 Step 2: Multiply the percent (which is now a decimal) by the given number x Try these: What is 40% of 20? Step : Change the percent to a decimal by moving the decimal two places to the left. Remember, the decimal in a whole number is at the end just like a period is at the end of a sentence. 40% = Step 2: Multiply the percent (which is now a decimal) by the given number. x What is 60% of 70? Step : Change the percent to a decimal by moving the decimal two places to the left. Remember, the decimal in a whole number is at the end just like a period is at the end of a sentence. 60% = Step 2: Multiply the percent (which is now a decimal) by the given number. x 57

58 On Your Own: ) What is 30% of 250? = Show your work here! 2) What is 40% of 55? = Show your work here! 3) What is 0% of 780? = Show your work here! 4) What is 20% of,300? = Show your work here! 5) What is 90% of 800? = Show your work here! 6) The Smith family went out to dinner and received great service. They decided to leave a 20% tip for their waitress. If their dinner bill totaled $90, how much was the tip? Think: You need to find what percent of what number? Show your work! 7) Carlos just took a 40 question math test. He scored a 75%. How many questions did he get correct on his test? Show your work! 8) Marge ordered $320 worth of photographs from a website. She has to pay a 0% shipping and handling fee. How much will the fee cost her? Show your work! 9) April made $440 in tips last night waitressing. She had to give 20% of her tips to the boys who clean the tables. How much money did she have to give them? Show your work! 0) You purchase a $,500 television. You have to pay 6% sales tax. How much will the tax be on your new television? Show your work! 58

59 Name KEY Date Percent of a Number Guided Practice To determine the percent of a number you need to remember two key points: 3) The word of means Multiply! 4) Percents must be changed to decimals before you can multiply with them. Example: What is 70% of 50? Step : Change the percent to a decimal by moving the decimal two places to the left. Remember, the decimal in a whole number is at the end just like a period is at the end of a sentence. 70% = 0.70 Step 2: Multiply the percent (which is now a decimal) by the given number x Try these: What is 40% of 20? Step : Change the percent to a decimal by moving the decimal two places to the left. Remember, the decimal in a whole number is at the end just like a period is at the end of a sentence. 40% = 0.40 Step 2: Multiply the percent (which is now a decimal) by the given number x What is 60% of 70? Step : Change the percent to a decimal by moving the decimal two places to the left. Remember, the decimal in a whole number is at the end just like a period is at the end of a sentence. 60% = 0.60 Step 2: Multiply the percent (which is now a decimal) by the given number x

60 On Your Own: ) What is 30% of 250? 0.30 x 250 = 75 Show your work here! 2) What is 40% of 55? 0.40 x 55 = 22 Show your work here! 3) What is 0% of 780? 0.0 x 780 = 78 Show your work here! 4) What is 20% of,300? 0.20 x,300 = 260 Show your work here! 5) What is 90% of 800? 0.90 x 800 = 720 Show your work here! 6) The Smith family went out to dinner and received great service. They decided to leave a 20% tip for their waitress. If their dinner bill totaled $90, how much was the tip? Think: You need to find what percent of what number? Show your work! 0.20 x 90 $8 tip 7) Carlos just took a 40 question math test. He scored a 75%. How many questions did he get correct on his test? Show your work! 0.75 x questions correct 8) Marge ordered $320 worth of photographs from a website. She has to pay a 0% shipping and handling fee. How much will the fee cost her? Show your work! 0.0 x 320 $32 fee 9) April made $440 in tips last night waitressing. She had to give 20% of her tips to the boys who clean the tables. How much money did she have to give them? Show your work! 0.20 x 440 $88 0) You purchase a $,500 television. You have to pay 6% sales tax. How much will the tax be on your new television? Show your work! 0.06 x,500 $90 sales tax 60

61 Lesson G Independent Practice Name Percent of a Number Date Solve each problem. Find your answer in one of the two answer boxes. Find the problem number on the coloring page and color each section with the number the color that corresponds to your answer. # Problem Answer Answer 2 Answer 3 2 What is 0% of 47? 470 DARK GREEN What is 20% of 82? 6.4 BLACK 4.7 LIGHT GREEN 62 ORANGE 37 YELLOW 64 BLUE 3 What is 50% of 50? 7.5 ORANGE 00 RED 75 YELLOW 4 What is 50% of 30? 5 ORANGE 80 YELLOW 60 RED 5 What is 0% of 9? 90 PINK 9 PURPLE 0.9 RED 6 A $400 TV is on sale for 25% off. What is the sale price of the TV? $00 GREEN $300 BLUE $375 YELLOW 7 A $65 purse is on sale for 0% off. How much money will you save if you buy it? $55.00 BLACK $0.00 RED $6.50 DARK GREEN 8 The cost of a movie ticket increased by 5%. The old price was $8. How much are they now? $23.00 LIGHT BLUE $9.20 GRAY $9.50 PINK 9 A $75 jacket is 50% off. How much does the jacket cost now? $37.50 PURPLE $40.00 GREEN $25.00 RED 0 You leave a 20% tip on your $70 dinner bill. How much was the tip? $5.00 ORANGE $4.00 PINK $90.00 YELLOW 6

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63 Name KEY Percent of a Number Date Solve each problem. Find your answer in one of the two answer boxes. Find the problem number on the coloring page and color each section with the number the color that corresponds to your answer. # Problem Answer Answer 2 Answer What is 0% of 47? 470 DARK GREEN What is 20% of 82? 6.4 BLACK What is 50% of 50? 7.5 ORANGE What is 50% of 30? 5 ORANGE 4.7 LIGHT GREEN 62 ORANGE 00 RED 80 YELLOW 37 YELLOW 64 BLUE 75 YELLOW 60 RED 5 What is 0% of 9? 90 PINK 9 PURPLE 0.9 RED 6 A $400 TV is on sale for 25% off. What is the sale price of the TV? $00 GREEN $300 BLUE $375 YELLOW 7 A $65 purse is on sale for 0% off. How much money will you save if you buy it? $55.00 BLACK $0.00 RED $6.50 DARK GREEN 8 The cost of a movie ticket increased by 5%. The old price was $8. How much are they now? $23.00 LIGHT BLUE $9.20 GRAY $9.50 PINK 9 A $75 jacket is 50% off. How much does the jacket cost now? $37.50 PURPLE $40.00 GREEN $25.00 RED 0 You leave a 20% tip on your $70 dinner bill. How much was the tip? $5.00 ORANGE $4.00 PINK $90.00 YELLOW 63

64 Name Exit Ticket G SHOW YOUR WORK!. Daniel is shopping for a new TV. He found one on sale for 25% off the original price, which is $650. Write an expression (don t solve it) to find out how much money he saved. 2. Corrine ordered a $20 couch and needs to pay a 0% shipping charge. How much will the shipping charge be? 3. Stephanie s test score was 50% lower than Jonathan s. If Jonathan scored a 96 on his test, what did Stephanie score? 4. Amber s soccer team has scored 40 goals this season. Amber scored 0% of the goals by herself. How many goals has she scored? 5. Heather is reading a 450 page book. She is 0% finished with the book. How many pages has she read? 6. Kevin is jogging 20 miles today. He is 25% finished. How many miles has he completed? 64

65 Name KEY Exit Ticket G SHOW YOUR WORK!. Daniel is shopping for a new TV. He found one on sale for 25% off the original price, which is $650. Write an expression (don t solve it) to find out how much money he saved. 650 x Corrine ordered a $20 couch and needs to pay a 0% shipping charge. How much will the shipping charge be? $2 3. Stephanie s test score was 50% lower than Jonathan s. If Jonathan scored a 96 on his test, what did Stephanie score? Amber s soccer team has scored 40 goals this season. Amber scored 0% of the goals by herself. How many goals has she scored? 4 goals 5. Heather is reading a 450 page book. She is 0% finished with the book. How many pages has she read? 6. Kevin is jogging 20 miles today. He is 25% finished. How many miles has he completed? 45 pages 5 miles 65

66 Warm Up H Name ) You just purchased a $50 television. The sales tax is 6%. How much will you pay in sales tax? 2) How much will you pay all together for the television in problem #? 3) You are planning to go to a theme park. Admission is $45. You have a coupon for 0% off your admission fee. How much money will you save by using the coupon? 4) What will your new cost of admission be in problem #3? Warm Up H Name KEY ) You just purchased a $50 television. The sales tax is 6%. How much will you pay in sales tax? $9.00 2) How much will you pay all together for the television in problem #? $ ) You are planning to go to a theme park. Admission is $45. You have a coupon for 0% off your admission fee. How much money will you save by using the coupon? $4.50 4) What will your new cost of admission be in problem #3? $

67 Lesson H Notes and Practice Name Proportions and Unit Rate PROPORTIONS NOTES Date When setting up a proportion, first decide what two units you are comparing miles to minutes, degrees to hours, etc. o Write your units as a proportion of their own. Example: You just traveled 40 miles in 30 minutes. How far will you travel in 45 minutes? We are comparing miles to minutes, therefore: miles minutes o Usually you will be given a ratio in the problem. Above we are told You just traveled 40 miles in 30 minutes. This can be written as a ratio. Be sure to set it up the same was as the unit ratio. miles 40 miles = minutes 30 minutes o Next, look at the information you have left in the problem, and look to see WHAT you are trying to find. We want to find out how far we will travel in 45 minutes. We know two things:. We are trying to find out how far (distance miles) 2. We know the minutes, 45. Substitute what you KNOW into the proportion. Since we know the minutes, we must make sure to put the 45 on the bottom of the fraction bar. miles minutes = 40 miles 30 minutes = N miles 45 minutes To solve the proportion you cross multiply, and divide. 40 miles 30 minutes = N miles 45 minutes o Multiply the 30 and N to get 30 N, and multiply the 40 and 45 to get Set this up as an equation. o 30 N = Solve as you would a regular equation o 30 N =, o N = 60 miles 67

68 Guided Practice You just paid $30 for 2 gallons of gas. How much will it cost you to get an additional 4 gallons of gas? o We are comparing cost to gallons. Write this as it s own ratio. o We know we paid $30 for 2 gallons. Write this as a ratio, set equal to the ratio from above. o We know we are looking for the cost of 4 gallons. Write this as a ratio set equal to the proportion you just wrote above. o Now cross multiply and solve! Independent Practice. It takes you 25 minutes to drive the 35 miles from school to your house. How long will it take you to drive the 70 miles from your house to the beach if you travel at the same rate of speed? SHOW YOUR WORK! 2. You used 4 cups of chocolate chips to bake 90 batches of cookies. How many cups do you need if you are planning to only bake 2.5 batches of cookies? SHOW YOUR WORK! 68

69 UNIT RATE NOTES: Determining Unit Rate is nothing more than finding the cost/mileage/etc. for ONE unit. o Most unit rate questions will be given you information for more than one thing. Example: You can purchase 6 boxes of tissues for $5. How much does each box cost? o Write the information you have been given as a ratio. 6 boxes $5 o Next, set up a proportion to determine the cost of just one box of tissues. Don t forget to write a ratio using words first. We are comparing boxes to cost. boxes cost 6 boxes = $5 = box $N o To solve the proportion you cross multiply, and divide. 6 boxes box $5 = o Multiply the 6 and N to get 6 N, and multiply the 5 and to get 5. Set this up as an equation. o 6 N = 5 Solve as you would a regular equation o 6 N = o N = $2.50 $N o You will see that you end up dividing the cost by the number of units. When you get better at finding unit rate, you can solve that way. Guided Practice You just paid $45 for 2 gallons of gas. How much did each gallon of gas cost you? o You paid $45 for 2 gallons of gas. Write this as a ratio. $45 2 gallons o We want to find the cost of ONE gallon. We write this as another ratio. cost = $45 = $N gallons 2 gallons gallons o Now cross multiply and solve! 2 N = 45 2 N = N = $

70 INDEPENDENT PRACTICE. A pack of 5 books costs $8.75. A pack of 3 books $2.75. Which pack has the lowest cost per book? (hint find the unit rate for each pack, then compare) SHOW YOUR WORK! 2. You found CDs on sale! Eight CDs would cost you $ What is the cost per CD? SHOW YOUR WORK! 3. You have the option of buying 20 tickets at the fair for $5 or 45 tickets for $27. Which is the best deal? SHOW YOUR WORK! 4. You can buy 30 cans of soda for $6. What is the cost per can? SHOW YOUR WORK! 70

71 Name KEY Date Proportions and Unit Rate PROPORTIONS NOTES When setting up a proportion, first decide what two units you are comparing miles to minutes, degrees to hours, etc. o Write your units as a proportion of their own. Example: You just traveled 40 miles in 30 minutes. How far will you travel in 45 minutes? We are comparing miles to minutes, therefore: miles minutes o Usually you will be given a ratio in the problem. Above we are told You just traveled 40 miles in 30 minutes. This can be written as a ratio. Be sure to set it up the same was as the unit ratio. miles 40 miles = minutes 30 minutes o Next, look at the information you have left in the problem, and look to see WHAT you are trying to find. We want to find out how far we will travel in 45 minutes. We know two things: 3. We are trying to find out how far (distance miles) 4. We know the minutes, 45. Substitute what you KNOW into the proportion. Since we know the minutes, we must make sure to put the 45 on the bottom of the fraction bar. miles minutes = 40 miles 30 minutes = N miles 45 minutes To solve the proportion you cross multiply, and divide. 40 miles 30 minutes = N miles 45 minutes o Multiply the 30 and N to get 30 N, and multiply the 40 and 45 to get Set this up as an equation. o 30 N = Solve as you would a regular equation o 30 N =, o N = 60 miles 7

72 Guided Practice You just paid $30 for 2 gallons of gas. How much will it cost you to get an additional 4 gallons of gas? o We are comparing cost to gallons. Write this as it s own ratio. cost gallons o We know we paid $30 for 2 gallons. Write this as a ratio, set equal to the ratio from above. cost = $30 gallons 2 gallons o We know we are looking for the cost of 4 gallons. Write this as a ratio set equal to the proportion you just wrote above. cost = $30 = N cost gallons 2 gallons 4 gallons o Now cross multiply and solve! 2 N = N = N = $0 Independent Practice 3. It takes you 25 minutes to drive the 35 miles from school to your house. How long will it take you to drive the 70 miles from your house to the beach if you travel at the same rate of speed? SHOW YOUR WORK! minutes miles = 25 minutes 35 miles 35 N = N =, N = 50 minutes N minutes = 70 miles 4. You used 4 cups of chocolate chips to bake 90 batches of cookies. How many cups do you need if you are planning to only bake 2.5 batches of cookies? SHOW YOUR WORK! cups = 4 cups = N cups batches 90 batches 2.5 batches 90 N = N = N = 5 cups 72

73 UNIT RATE NOTES: Determining Unit Rate is nothing more than finding the cost/mileage/etc. for ONE unit. o Most unit rate questions will be given you information for more than one thing. Example: You can purchase 6 boxes of tissues for $5. How much does each box cost? o Write the information you have been given as a ratio. 6 boxes $5 o Next, set up a proportion to determine the cost of just one box of tissues. Don t forget to write a ratio using words first. We are comparing boxes to cost. boxes cost 6 boxes = $5 = box $N o To solve the proportion you cross multiply, and divide. 6 boxes box $5 = o Multiply the 6 and N to get 6 N, and multiply the 5 and to get 5. Set this up as an equation. o 6 N = 5 Solve as you would a regular equation o 6 N = o N = $2.50 $N o You will see that you end up dividing the cost by the number of units. When you get better at finding unit rate, you can solve that way. Guided Practice You just paid $45 for 2 gallons of gas. How much did each gallon of gas cost you? o You paid $45 for 2 gallons of gas. Write this as a ratio. $45 2 gallons o We want to find the cost of ONE gallon. We write this as another ratio. cost = $45 = $N gallons 2 gallons gallons o Now cross multiply and solve! 2 N = 45 2 N = N = $

74 INDEPENDENT PRACTICE. A pack of 5 books costs $8.75. A pack of 3 books $2.75. Which pack has the lowest cost per book? (hint find the unit rate for each pack, then compare) SHOW YOUR WORK! books cost 5 books book = = $8.75 $N books cost 3 books book = = $2.75 $N 5 N = N = N = N = N = $3.75 per book N = $4.25 per book Lowest cost per book 2. You found CDs on sale! Eight CDs would cost you $ What is the cost per CD? SHOW YOUR WORK! CDs cost 8 CDs CD = = $79.92 $N 8 N = N = N = $9.99 per CD 3. You have the option of buying 20 tickets at the fair for $5 or 45 tickets for $27. Which is the best deal? SHOW YOUR WORK! tickets 20 tickets cost = $5 = ticket $N tickets cost = 45 tickets $27 = ticket $N 20 N = 5 45 N = N = 5 45 N = N = $0.75 per ticket N = $0.60 per ticket Best Deal 4. You can buy 30 cans of soda for $6. What is the cost per can? SHOW YOUR WORK! cans cost = 30 cans $6 = can $N 30 N = 6 30 N = N = $0.20 per can 74

75 Lesson H Independent Practice Name Proportions & Unit Rates Date Solve each problem. Find your answer in one of the two answer boxes. Find the problem number on the coloring page and color each section with the number the color that corresponds to your answer. # Problem Answer Answer 2 It takes you 45 minutes to drive the 30 miles from your house to the mall. How long will it take you to drive the 75 miles to the beach? 50 minutes RED 2.5 minutes BLACK 2 A box of 6 matchbox cars costs $.94. A box of 4 matchbox cars costs $8.2. Which box has the lowest cost per car? Box of 6 DARK GREEN Box of 4 LIGHT GREEN 3 You were able to purchase 5 gallons of gas for $9.85. How many gallons did you buy if you spent $ gallons GRAY 2 gallons BLUE 4 You used 5 cups of flour to bake 80 cookies. How many cups do you need if you are planning to bake 44 cookies? 6 cups BLACK 9 cups BROWN 5 You found DVDs on sale! Six DVDs would cost you $ What is the cost per DVD? $ PINK $7.99 RED 6 You have the option of downloading 2 songs online for $0.68 or 9 songs for $7.38. Which is the best deal? 9 songs YELLOW 2 songs ORANGE 7 You are taking a trip at the same time as another family. Your family traveled,900 miles in 2 days, their family traveled 2,700 miles in 3 days. Who is traveling faster? Your family GRAY Their family BROWN 8 Carla purchases 4 books for $0. Amy purchases 9 books. How much did Amy spend if her books cost the same as Carla s? $3.60 BLUE $22.50 PURPLE 9 You can buy a 20 pound bag of dog food for $35. What is the cost per pound? $5 RED $.75 PINK 0 Amy used 3 gallons of paint to cover 2,00 ft² of wall space inside her house. How much wall space can she paint with 7 gallons? 4,900 ft² ORANGE 00 ft² YELLOW 75

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77 Name KEY Proportions & Unit Rates Date Solve each problem. Find your answer in one of the two answer boxes. Find the problem number on the coloring page and color each section with the number the color that corresponds to your answer. # Problem Answer Answer 2 It takes you 45 minutes to drive the 30 miles from your house to the mall. How long will it take you to drive the 75 miles to the beach? 50 minutes RED 2.5 minutes BLACK 2 A box of 6 matchbox cars costs $.94. A box of 4 matchbox cars costs $8.2. Which box has the lowest cost per car? Box of 6 DARK GREEN Box of 4 LIGHT GREEN 3 You were able to purchase 5 gallons of gas for $9.85. How many gallons did you buy if you spent $ gallons GRAY 2 gallons BLUE 4 You used 5 cups of flour to bake 80 cookies. How many cups do you need if you are planning to bake 44 cookies? 6 cups BLACK 9 cups BROWN 5 You found DVDs on sale! Six DVDs would cost you $ What is the cost per DVD? $ PINK $7.99 RED 6 You have the option of downloading 2 songs online for $0.68 or 9 songs for $7.38. Which is the best deal? 9 songs YELLOW 2 songs ORANGE 7 You are taking a trip at the same time as another family. Your family traveled,900 miles in 2 days, their family traveled 2,700 miles in 3 days. Who is traveling faster? Your family GRAY Their family BROWN 8 Carla purchases 4 books for $0. Amy purchases 9 books. How much did Amy spend if her books cost the same as Carla s? $3.60 BLUE $22.50 PURPLE 9 You can buy a 20 pound bag of dog food for $35. What is the cost per pound? $5 RED $.75 PINK 0 Amy used 3 gallons of paint to cover 2,00 ft² of wall space inside her house. How much wall space can she paint with 7 gallons? 4,900 ft² ORANGE 00 ft² YELLOW 77