Grade 6 Math. Oak Meadow. Coursebook. Oak Meadow, Inc. Post Office Box 1346 Brattleboro, Vermont oakmeadow.

Transcription

1 Grade 6 Math Oak Meadow Coursebook Oak Meadow, Inc. Post Office Box 1346 Brattleboro, Vermont oakmeadow.com Item #b064010

2 Grade 6 Contents Introduction... ix Lessons... Lesson Multiplication with Carrying Multiplication with Large Numbers Multiplying by 10, 100, and 1,000 Lesson Division of Whole Numbers Division Signs Creating Fractions with Remainders Lesson Two-Digit Divisors Estimating with Large Divisors Lesson Common Fractions Adding Fractions with Common Denominators Subtracting Fractions with Common Denominators Improper Fractions and Mixed Numbers Lesson Adding Mixed Numbers Subtracting Mixed Numbers Reducing Fractions Reducing Fractions to Lowest Terms iii

3 Contents Grade 6 Math Lesson Subtracting Mixed Numbers from Whole Numbers Borrowing with Mixed Numbers Lesson Common Denominators Finding the Lowest Common Denominator Lesson LCDs in Mixed Numbers Borrowing with Mixed Numbers and LCDs Lesson Multiplying Simple Fractions Multiplying Whole Numbers by Fractions Multiplying by Fractions in Word Problems Lesson Multiplying Fractions and Mixed Numbers Multiplying Two Mixed Numbers Lesson Multiplying Whole and Mixed Numbers Canceling Fractions Lesson Dividing Fractions Dividing Whole Numbers and Fractions Lesson Dividing with Fractions and Mixed Numbers Dividing Whole Numbers and Mixed Numbers Dividing with Two Mixed Numbers Lesson Decimal Fractions Decimal Fractions to Two Places (Hundredths) Decimal Fractions to Three Places (Thousandths) iv Oak Meadow

4 Grade 6 Math Contents Lesson Comparing Decimals Adding Decimals Lesson Subtracting Decimals Subtracting Decimals and Whole Numbers Subtracting Hundredths and Thousandths from Tenths Lesson Adding and Subtracting Money The Sign Lesson The Metric System Meters and Kilometers Lesson Multiplying Decimals Multiplying Larger Decimals Multiplying Decimals and Whole Numbers Multiplying Decimals by 10, 100, and 1,000 Lesson Dividing Decimals by Whole Numbers Dividends with Three or More Decimal Places Lesson Dividing with Dividends Less than 1 Dividing Decimals with Remainders Dividing by 10, 100, and 1,000 Lesson Dividing Decimals by Decimals Dividing Whole Numbers by Decimals Oak Meadow v

5 Contents Grade 6 Math Lesson Percentages Finding a Percent of a Number Using Percentages in Word Problems Lesson Converting Common Fractions to Decimals Converting Decimals to Percentages Finding Percentages in Word Problems Lesson Finding Averages Ratios Lesson Probability Chance Lesson Finding the Square of a Number Square Roots Lesson Measuring Weight Using the Metric System Measuring Liquid Using the Metric System Lesson Calculating Perimeter of Squares and Rectangles Calculating Perimeter of Triangles Calculating the Radius and Diameter of a Circle Lesson Figuring Area Parallel and Perpendicular Lines Finding Area of Irregular Rectangular Shapes vi Oak Meadow

6 Grade 6 Math Contents Lesson Determining Sales Tax Making Change Lesson Reading an Inch Ruler Reading a Centimeter Ruler Lesson Finding Missing Numbers in Addition Finding Missing Numbers in Subtraction Lesson Factors of Whole Numbers Prime Numbers Lesson Missing Numbers in Multiplication and Division Problems Parentheses in Mathematical Equations Lesson Final Exam Appendix Answer Key B-Tests for Enrolled Students Oak Meadow vii

7 Grade 6 3 Lesson MATH INSTRUCTION Two-Digit Divisors Every division problem has three main parts, and there are specific math terms used to describe these parts. Look at the following example: 238 Example 1: In this example, we ve left out the part of the solution that lies below the division bracket so we can focus on the main parts, which are called the divisor, the dividend, and the quotient. In the example above, 3 is the divisor, 714 is the dividend, and 238 is the quotient. The names of these three parts remain the same, even if the problem is presented like this: = 238 The divisor is always the number that you are dividing by, the dividend is always the number you are dividing into, and the quotient is always the answer. In all of the examples and problems we ve presented so far, we ve used 1-digit divisors, but it is possible to divide by larger divisors. In this lesson, we ll practice dividing by 2-digit divisors. Example 2: When we divide by 2-digit divisors, we follow the same four-step process as with 1-digit divisors, but we just use the entire 2-digit divisor for each step. Step 1: Start with the divide step. Ask yourself, How many times does 10 go into 3? Since 10 doesn t go into 3, ask How many times does 10 go into 32? 10 times 2 is 20, 10 times 3 is 30, and 10 times 4 is 40. Since 40 is too much, you go back to 30, so 10 goes into 32 three times. Write 3 as the quotient above the bracket, directly above the 2 in the dividend. ASSIGNMENT SUMMARY Skill Practice A Skill Practice B Lesson 3 Review 21

8 Lesson 3 Grade 6 Math Step 2: Continue with the multiply step, by saying, 10 times 3 is 30. Write 30 under the 32. Step 3: Next, proceed with the subtract step. Say, 32 minus 30 equals 2. Draw a line under the 30 and write 2 underneath the line. Step 4: The final step in the four-step process is bring down, so bring down the next number in the dividend, the 5, to make 25. When you ve completed this last step in the four-step process, the problem looks like this: To complete the problem, start again with step 1 of the four-step process: Step 1: Begin again with the divide step by asking, How many times does 10 go into 25? Since the correct answer is 2, write a 2 in the quotient, next to the 3. Step 2: Then go to the multiply step again, say 2 times 10 is 20, and write the number 20 underneath the 25. Step 3: Next, draw a line under the 20, subtract 20 from 25, and write 5 underneath. Step 4: This is the last step of the four-step process, but there is nothing left in the dividend to bring down, so we put the remainder over the divisor to create the fraction 5, and the problem is finished Estimating with Large Divisors You can divide by a number with any number of digits using the same four steps you have learned, but with larger numbers you have to follow those steps carefully and pay very close attention to keep from getting confused Oak Meadow

9 Grade 6 Math Lesson 3 You especially have to remember to keep each digit in a straight line above and below the others, so that you bring down the correct digit. When you are working with large divisors, one approach that can help you solve the problem more quickly is to estimate the quotient before you divide. Consider the following example: Example 1: Step 1: Start with the divide step, but instead of trying to determine how many times 21 goes into 49, estimate the quotient by asking yourself how many times the first digit of the divisor goes into the first digit of the dividend. Ask yourself, How many times does 2 go into 4? Since 2 x 2 is 4, try 2 as the quotient. Write 2 as the quotient directly above the 9 in the dividend. Step 2: Continue with the multiply step, by saying, 2 times 21 is 42. Write 42 under the 49. Here is where you find out if your estimate was correct. If you discovered that your estimate was too large, then you would decrease it by 1 and multiply again. If it was too small, then increase it by 1 and multiply again. Step 3: Next, proceed with the subtract step by saying, 49 minus 42 equals 7. Draw a line under the 42 and write 7 underneath the line. Step 4: The final step in the four-step process is bring down, so bring down the next digit in the dividend, the 4, to make 74. When you ve completed this fourth step in the four-step process, the problem looks like this: Step 1: Now start the four-step process over again with the divide step by estimating the quotient again. Ask yourself, How many times does 2 go into 7? Since the correct answer is 3, write a 3 in the quotient, next to the 2. Step 2: Then go to the multiply step again, say 3 times 21 is 63, and write the number 63 underneath the 74. Once again, if your estimate was either too high or too low, you would correct it at this point. Oak Meadow 23

10 Lesson 3 Grade 6 Math Step 3: Next, draw a line under the 63, subtract 63 from 74, and write 11 underneath. Step 4: Finally, bring down the next digit in the dividend, the 3, and put it next to the 11 so it makes 113. At this point, the problem looks like this: Step 1: Now start the four-step process again with the divide step by estimating the quotient again. Ask yourself, How many times does 2 go into 1? 2 doesn t go into 1, so include the next digit and ask yourself How many times does 2 go into 11? The answer is 5, so write 5 in the quotient next to the 23, to make 235. Step 2: Then multiply 5 times 21 and get 105. Write it underneath the 113. Again, here is where you can correct your estimate, if necessary. Step 3: Next, draw a line under the 105 and subtract 105 from 113. Write the answer, 8, under the line. Step 4: Now we are at the final step of the four-step process, but since there is nothing left in the dividend to bring down, we put the remainder 8 over the divisor 21 to make the fraction We add this next to the whole numbers in the quotient, and the problem is finished Oak Meadow

11 Grade 6 Math Lesson 3 Estimating quotients using the first digit of the divisor will work fairly well in many cases. But for greater accuracy in estimating two-digit divisors, it s best to round the divisor to the nearest ten before estimating. To do this, follow the standard rule for rounding: Look one place to the right of the place you want to round to. If the digit in that place is 5 or more, round up, if it s less than 5, round down. So if the divisor is 18, you would round it to 20 and use 2 to estimate the quotient. Likewise, if the divisor is 35, you would round it to 40 and use 4 to estimate the quotient. But if the divisor is 53, you would round it to 50 and use 5 to estimate the quotient. Even if you round divisors before estimating, you will still find some problems in which this gives you an estimate that is not correct. In this case, just adjust the estimate in the multiply step of the four-step process. Assignments Complete the following assignments. Show all your work. Skill Practice A Skill Practice B Lesson 3 Review For Enrolled Students At the end of the next lesson, you will be submitting work to your Oak Meadow teacher. Please help your student score the practice sheets and make corrections before completing the lesson 3 review. After you score the lesson 3 review, place the score at the top of the page and then have your child talk you through the process for each incorrect problem. Help your child make corrections as necessary. Check to make sure your student is showing all work, using complete sentences in word problems, and expressing remainders as fractions. Continue documenting your student s process with the assignment summary checklist, weekly planner, and the learning assessment form. Feel free to contact your teacher if you have any questions about the assignments or the learning process. Oak Meadow 25

12 Lesson 3 Grade 6 Math Learning Assessment Use these assessment rubrics to track student progress throughout the year and to make notes about the learning the student demonstrates or skills that need work. MATH Performs long division with single-digit divisors Uses estimating when solving long division with multi-digit divisors Performs multiplication involving large numbers Multiplies by 10, 100, and 1000 Not Yet Evident Developing Consistent Notes Adds and subtracts multi-digit numbers with carrying and borrowing Adds columns of numbers Translates word problems into numeric equations involving the four processes Uses unit labels and complete sentences when writing solutions to word problems Shows all work when solving problems Checks work using inverse operations Expresses remainders in division as fractions 26 Oak Meadow

13 Grade 6 Math Lesson 3 Skill Practice A Oak Meadow 27

14 Lesson 3 Grade 6 Math Skill Practice B Oak Meadow

15 Grade 6 Math Lesson 3 Lesson 3 Review , , , , , ,3 8 7 Oak Meadow 29

16 Lesson 3 Grade 6 Math Lesson 3 Review continued , Joan s father is 42 years old today. How many days old is he? (Note: don t add any days for leap year; just count each year as 365 days.) 30 Oak Meadow

17 Grade 6 4 Lesson MATH INSTRUCTION Common Fractions So far we have been working with whole numbers such as 23 or 568. They are called whole numbers because each number represents one whole unit, whatever it may be. Whether it s apples, cars, or flowers, each whole number represents one whole unit. Fractions are numbers that are less than 1, so they represent parts of 1 whole unit. For example, if we have 1 whole pie and we cut it into 6 pieces, each piece is a part of the pie. If there are 6 equal pieces, each piece is 1 part out of 6 parts of the pie. We can write this relationship between the part and the whole like this: 1 6 This is called a common fraction. The number below the line is called the denominator, and this is the number of parts in the whole. In our example, there are 6 pieces in the whole pie, so 6 is the denominator. The number above the line is called the numerator, and it is the number of parts that we are talking about in whatever problem we re discussing. In the example, we are talking about 1 piece of the pie, so 1 is the numerator. If we were talking about 3 pieces of the pie, we would call it 3 6, and if we talked about 5 pieces, we d call it 5 6. Sometimes common fractions are written on a slant, like 5/6, instead of above and below as we ve written it. In this case the numerator is on the left and the denominator on the right. But however it s written, every common fraction has these two parts: a numerator and a denominator. Remember these names, because we ll be referring to them often. ASSIGNMENT SUMMARY Skill Practice A Skill Practice B Lesson 4 Test 31

18 Lesson 4 Grade 6 Math Adding Fractions with Common Denominators Sometimes common fractions will have different denominators. We ll explain how to add those at a later time, but for now we ll talk about how to add fractions that have the same denominator. When we add fractions that have the same denominator, we can simply add the numerators to get the total, as in the following example: Example 1: Since both denominators are the same, you just add the numerators. When we do that, you find that = 4, so the answer is 4. Notice that 8 you do not add the denominators, because the total number of parts in the whole does not change. Example 2: = Example 3: Oak Meadow

19 Grade 6 Math Lesson 4 Subtracting Fractions with Common Denominators As you can see from the previous examples, adding common fractions that have the same denominator is very easy. Subtracting common fractions that have the same denominators is also easy. If common fractions have the same denominators, you can subtract one fraction from another by simply subtracting numerators, as in the following example: 7 Example 1: Both denominators are the same, so you just subtract the numerators. Since 7-5 is 2, the answer is 2. As with addition, remember that you only 9 subtract the numerators. You don t subtract the denominators. Example 2: = 1 7 Example 3: Practice these skills with Skill Practice A. Oak Meadow 33

20 Lesson 4 Grade 6 Math Improper Fractions and Mixed Numbers Fractions usually have a numerator that is smaller than the denominator, and these are called proper fractions. But when the numerator is larger than the denominator, this is called an improper fraction. This often happens when you add two proper fractions. When you solve a problem and the answer is an improper fraction, you have to change that into a mixed number a combination of a whole number and a proper fraction. 5 Example 1: Step 1: Add the numerators together: = Step 2: Determine if the fraction is improper is an improper fraction, because the numerator (11) is larger than the denominator (8). Step 3: Divide the numerator by the denominator: 11 divided by 8 is 1, with a remainder of 3. Step 4: Write the whole number (1), then put the remainder (3) over the denominator (8) to make a proper fraction. The whole number and the fraction together make the mixed number The solution to the complete problem looks like this: = 11 = The horizontal line that separates the numerator from the denominator in a fraction actually means divided by. So 11 means 11 divided by 8, just 8 the same as 8 11 or is just another way of showing the same 8 relationship. If you divide the numerator by the denominator and there is no remainder, then the answer is just a whole number without a fraction. Example 2: = = 2 34 Oak Meadow

21 Grade 6 Math Lesson 4 Assignments Complete the following assignments. Show all your work. Skill Practice A Skill Practice B Lesson 4 Test For Enrolled Students At the end of this lesson, you will be sending your second batch of work to your Oak Meadow teacher. Include any additional notes or questions with your documentation your teacher is eager to help. Please make sure your submission is organized and labeled well, and that all reviews and tests are scored by you and corrected by the student. Include the lesson 4 B-test (which your teacher will score). Send only the lesson 3 review, the lesson 4 test, and the lesson 4 B-test (please do not send any skill practice worksheets) along with your documentation notes. Learning Assessment Use these assessment rubrics to track student progress throughout the year and to make notes about the learning the student demonstrates or skills that need work. Oak Meadow 35

22 Lesson 4 Grade 6 Math Learning Assessment MATH Adds fractions with common denominators Not Yet Evident Developing Consistent Notes Subtracts fractions with common denominators Converts between mixed numbers and improper fractions Performs long division with single-digit divisors Uses estimating when solving long division with multi-digit divisors Performs multiplication involving large numbers Multiplies by 10, 100, and 1000 Adds and subtracts multi-digit numbers with carrying and borrowing Translates word problems into numeric equations involving the four processes Uses unit labels and complete sentences when writing solutions to word problems Shows all work when solving problems Checks work using inverse operations Expresses remainders in division as fractions 36 Oak Meadow

23 Grade 6 Math Lesson 4 Skill Practice A Oak Meadow 37

24 Lesson 4 Grade 6 Math Skill Practice B Solve these problems. Change improper fractions to mixed numbers Oak Meadow

25 Grade 6 Math Lesson 4 Lesson 4 Test 1. 1, , , , Oak Meadow 39

26 Lesson 4 Grade 6 Math Lesson 4 Test continued 17. Harry plans to save $65 a month. If he saves this much each month for a year (12 months), how much will he have saved? 18. The Springfield Community Association raised $6,500 to feed homeless people in their community. If 50 homeless people sign up for this program, how much can Community Service spend on each person? 19. Jackson Fishing Tools makes fishing rods. In April they manufactured 1,279 rods, in May they made 1,426, and in June they created 1,612. How many fishing rods did they make during April, May, and June? 20. Farmville library had 1,816 books in the children s section. A retired schoolteacher donated another 145 children s books to the library. How many children s books did the library have after the new donation? 40 Oak Meadow

27 Grade 6 23 Lesson MATH INSTRUCTION Percentages We might read in a newspaper article that Steve Forbes received 20 percent of the vote in the election. Or we might hear a TV announcer say, 60 percent of children ages 12 to 14 say they would like to spend more time with their parents. What does the word percent mean? We know that common fractions and decimal fractions both represent parts of a whole. For example, if a pie is cut into 10 pieces and 3 pieces have been eaten, we would say that 3 10 of the pie has been eaten. If we express this as a decimal fraction, we would say that 0.3 of the pie has been eaten. Since the pie was divided into 10 pieces, we say that the fractions and 0.3 are based upon ten. The whole was divided into 10 parts A percent is another way of expressing a fraction. The word percent means of a hundred. The symbol for percent is %. In percents, the whole is divided into 100 parts, so every percent expresses the number of parts of a hundred. For example, if we divided the pie above into 100 (very small) pieces, and 30 of those pieces had been eaten; we would say that 30 percent of the pie had been eaten. We would write this as 30%. Since a percent is based upon one hundred, we could express the value of a percent as either a common fraction or a decimal fraction, and the value would remain the same. For example, if we wrote 30% as a common fraction, we would call it , because we re talking about 30 parts out of 100. If we wrote it as a decimal fraction, we would write it as.30. All of these forms express the same value: 30 parts out of a hundred. Example 1: Write 75% as a common fraction. 75% means 75 parts out of a hundred, so we could express this as ASSIGNMENT SUMMARY Skill Practice A Skill Practice B Skill Practice C Lesson 23 Review 205

28 Lesson 23 Grade 6 Math Example 2: Write 18% as a decimal. 18% means 18 parts out of a hundred, so we could express this as.18. We could also put a zero in front to indicate that there is no whole number, so it would be Either way, the value is the same. Usually it is written without the zero. Example 3: Write as a percent. means 50 parts out of a hundred, so we could express this as 50%. Finding a Percent of a Number Since percents express values as parts of a hundred, we know that 80% means 80 out of 100. But suppose we want to find the value of 80% of 30? To do this, we have to multiply by the percent, as follows: Example 1: How much is 80% of 30? Step 1: Convert 80% into a decimal. 80% expressed as a decimal is.80. Step 2: Multiply the total number by the decimal Since there are only zeros after the decimal, we can drop the zeros. This means that 80% of 30 is 24. Example 2: 25% of 1,200 is how much? Step 1: Convert 25% into a decimal. 25% expressed as a decimal is.25. Step 2: Multiply the total number by the decimal Since there are only zeros after the decimal, we can drop the zeros. This means that 25% of 1,200 is Oak Meadow

29 Grade 6 Math Lesson 23 Using Percentages in Word Problems We can apply the skills we just learned to solve word problems that involve percents. Example 1: There were 20 people at the birthday party, and 60% of them were girls. How many girls were at the party? Step 1: Convert 60% into a decimal. 60% expressed as a decimal is.60. Step 2: Multiply the total number by the decimal Since there are only zeros after the decimal, we can drop the zeros. This means that 60% of 20 is 12. There were 12 girls at the party. Example 2: 1,500 people voted in the election, and 45% voted for Bill Jackson. How many people voted for Bill Jackson in the election? Step 1: Convert 45% into a decimal. 45% expressed as a decimal is.45. Step 2: Multiply the total number by the decimal Since there are only zeros after the decimal, we can drop the zeros. This means that 45% of 1,500 is 675. There were 675 voters who chose Bill Jackson in the election. Oak Meadow 207

30 Lesson 23 Grade 6 Math Assignments Complete the following assignments. Show all your work. Skill Practice A Skill Practice B Skill Practice C Lesson 23 Review For Enrolled Students Please contact your teacher if any questions arise. Learning Assessment Use these assessment rubrics to track student progress throughout the year and to make notes about the learning the student demonstrates or skills that need work. 208 Oak Meadow

31 Grade 6 Math Lesson 23 Learning Assessment MATH Converts between decimals, fractions, and percentages Not Yet Evident Developing Consistent Notes Calculates percentages Divides decimals by whole numbers and decimals Multiplies decimals Adds and subtracts decimals Converts between different metric units of measurement Converts between decimal fractions and simple fractions Correctly writes decimal fractions in words Divides using fractions, whole numbers, and mixed numbers Multiplies fractions with whole and mixed numbers Identifies lowest common denominator Adds and subtracts mixed numbers Performs long division with two-digit divisors Performs multiplication involving large numbers Translates word problems into numeric equations involving the four processes with whole numbers, mixed numbers, and fractions Shows all work when solving problems Oak Meadow 209

32 Lesson 23 Grade 6 Math Learning Assessment MATH Reduces fractions to lowest terms Not Yet Evident Developing Consistent Notes Reduces fractions before multiplying by canceling Converts between whole numbers, mixed numbers, and improper fractions 210 Oak Meadow

33 Grade 6 Math Lesson 23 Skill Practice A 1. Write 16% as a decimal. 2. Write 23% as a common fraction. 3. Write as a percent. 4. Write as a percent. 5. Write 82% as a common fraction. Do not reduce. 6. Write as a percent. 7. Write 7% as a common fraction. 8. Write 49% as a decimal. 9. Write as a percent. 10. Write as a percent. 11. Write 15% as a decimal. 12. Write as a percent. Oak Meadow 211

34 Lesson 23 Grade 6 Math Skill Practice B 1. How much is 25% of 300? 2. How much is 14% of 300? 3. 30% of 90 is how much? 4. 15% of 500 is how much? 5. 16% of 50 is how much? 6. 80% of 350 is how much? 7. How much is 20% of 75? 8. How much is 10% of 450? 9. How much is 50% of 250? % of 320 is how much? 212 Oak Meadow

35 Grade 6 Math Lesson 23 Skill Practice C 1. There were 400 people at the game between Centerville and Dayton. 70% of the fans were from Dayton. How many fans at the game were from Dayton? 2. 70% of the members of the Cloverdale Rotary Club voted for Dan Darrow for president. If there were 80 members in the club, how many members voted for Dan? 3. Elise goes to a Tai Chi class every Monday night. 65% of the students in the class are men. If there are 20 students in the class, how many men are in Elise s Tai Chi class? 4. Dale bought a washing machine for $250. The salesman said if Dale would make a down payment of 20%, he could pay the rest in monthly payments over one year. If he wants to make monthly payments, how much money does Dale have to give for a down payment? 5. Sabina found a stereo system on sale at Cheap Stereo Warehouse. The system normally sells for $425, but it was on sale for 20% off the regular price. How much will Sabina save off the regular price if she buys during the sale? Oak Meadow 213

36 Lesson 23 Grade 6 Math Notes 214 Oak Meadow

37 Grade 6 Math Lesson 23 Lesson 23 Review Reduce all common fractions to lowest terms Oak Meadow 215

38 Lesson 23 Grade 6 Math Lesson 23 Review continued 13. The sales tax in Jim s state is 6%. How much sales tax will he have to pay on a wool scarf that costs $20? 14. It s 14.7 miles from Bill s house to his office. How many miles does he travel each day driving to and from his office? 15. Joan had dinner at Mama Mia s Italian restaurant. Her check came to $ How much change will she receive from a $20 bill? 16. Susan is buying a sofa for her living room, and she has to pay $58.62 per month for a year. When she finishes all her payments, how much will she have paid for her sofa? 216 Oak Meadow

39 Grade 6 24 Lesson MATH INSTRUCTION Converting Common Fractions to Decimals As we learned previously, we can convert common fractions to decimals, but so far we ve only converted common fractions with a denominator of 10, 100, or 1,000. For example, we know that we can change 7 into.7, 10 that is the same as.38, and that equals.425. But what about common fractions that don t have a denominator of 10, 100, or 1,000? For the purpose of converting common fractions to decimals, the line that separates the numerator from the denominator in a common fraction has the same meaning as a division sign. So we can say that 5 means 5 divided 8 by 8, and that 2 is 2 divided by 3. In this way, all common fractions can be 3 easily converted to decimal fractions by simply dividing the numerator by the denominator, as in the following example: Example 1: Write 3 as a decimal. 4 Step 1: Write the fraction as a division problem, using the division bracket. Put the numerator under the bracket and the denominator outside the bracket. 43 Step 2: Place a decimal to the right of the number under the bracket and add two zeros. You may not need two, or you may need more than two, but start with two zeros ASSIGNMENT SUMMARY Skill Practice A Skill Practice B Skill Practice C Lesson 24 Test 217

40 Lesson 24 Grade 6 Math Step 3: Divide as usual, until the answer comes out evenly and there is no remainder To convert some fractions, you may need to add more zeros to the dividend to make the answer come out evenly. Continue to add as many zeros as necessary, until there is no remainder. Example 2: Write 5 as a decimal. 8 Step 1: Write the fraction as a division problem. 8 5 Step 2: Place a decimal to the right of the number under the division bracket and add two zeros to start Step 3: Divide as usual, adding more zeros if necessary until the answer comes out evenly and there is no remainder Oak Meadow

41 Grade 6 Math Lesson 24 Converting Decimals to Percentages Now that you know how to convert a common fraction into a decimal, it s easy to change that decimal into a percent. We simply move the decimal point 2 places to the right and add a percent sign. Look at the following example: Example 1: Write.75 as a percent. We move the decimal 2 places to the right and add a percent for an answer of 75%. Why do we move the decimal 2 places to the right? Remember, percents are based upon one hundred; so moving the decimal 2 places to the right is the same as multiplying by = 75% In the previous example, the decimal was in hundredths (.75), so when we moved the decimal over 2 places it became a whole number. But what happens if the decimal is not in hundredths? Suppose it s in tenths? Look at the following example: Example 2: Write.2 as a percent. To convert a decimal to a percent, we always move the decimal point 2 places to the right. But since.2 doesn t have 2 decimal places, we have to create another decimal place. We do this by adding a zero, since we learned in a previous lesson that we can add zeros at the end of a decimal without changing its value. We add a 0 to the end of.2 to make it.20, then we move the decimal 2 places as usual, for a final answer of 20%..2 =.20 = 20% This works fine if the decimal is in tenths, but what if it s in thousandths, as in the following example? Example 3: Write.375 as a percent. We always move the decimal point 2 places to the right when we re converting a decimal to a percent, even if there are more places..375 = 37.5% Oak Meadow 219

42 Lesson 24 Grade 6 Math Finding Percentages in Word Problems We can apply the skills we have learned to find percents in word problems. Example 1: There are 8 blocks in a box, and only 2 of them are green. What percent of the blocks are green? Step 1: Write the problem as a common fraction. Remember, a common fraction is always the part over the whole. The numerator is the number of items in the part, and the denominator is the number of items in the whole. In this example, the part is the 2 green blocks, and the whole is the 8 blocks, so the common fraction is 2 8. Step 2: Write the fraction as a division problem, using the division bracket. Put the numerator under the bracket and the denominator outside. 8 2 Step 3: Place a decimal to the right of the number under the division bracket and add two zeros. You may not need two, or you may need more than two, but always start with two zeros Step 4: Divide as usual, until the answer comes out evenly and there is no remainder Step 5: Move the decimal point two places to the right and add a percent sign. The decimal is.25, so when we move the decimal point 2 places to the right, the decimal becomes 25%. So we can say that 25% of the blocks in the box are green. 220 Oak Meadow

43 Grade 6 Math Lesson 24 Example 2: There are 16 boys in John s scout troop. 10 of them are going on the 50-mile hike. What percent of the boys are going on the hike? Step 1: Write the problem as a common fraction, with the part over the whole Step 2: Write the fraction as a division problem, using the division bracket, and add a decimal and two zeros to the dividend Step 3: Divide as usual, adding more zeros if necessary, until the answer comes out evenly and there is no remainder Step 4: Move the decimal point two places to the right and add a percent sign. The decimal is.625, and when we move the decimal point 2 places to the right the decimal becomes 62.5%. We can say that 62.5% of the boys in John s scout troop are going on the 50-mile hike. Example 3: There are 5 kittens in the litter. 4 kittens are black and 1 is brown. What percent of the kittens in the litter are black? Step 1: Write the problem as a common fraction, with the part over the whole. 4 5 Step 2: Write the fraction as a division problem, using the division bracket, and place a decimal and two zeros after the dividend Oak Meadow 221

44 Lesson 24 Grade 6 Math Step 3: Divide as usual until the answer comes out evenly and there is no remainder Step 4: Move the decimal point two places to the right and add a percent sign. The decimal is.8, so we add another 0 after the.8 to make it.80. Then we move the decimal point 2 places to the right and add the percent sign for a final answer of 80%. That means 80% of the kittens in the litter are black. Assignments Complete the following assignments. Show all your work. Skill Practice A Skill Practice B Skill Practice C Lesson 24 Test For Enrolled Students When lesson 24 is complete, please send your student s work to your Oak Meadow teacher. Include your weekly planner, assignment checklists, and learning assessment forms from each lesson. Learning Assessment Use these assessment rubrics to track student progress throughout the year and to make notes about the learning the student demonstrates or skills that need work. 222 Oak Meadow

45 Grade 6 Math Lesson 24 Learning Assessment MATH Converts between decimals, fractions, and percentages Not Yet Evident Developing Consistent Notes Calculates percentages Divides decimals by whole numbers and decimals Multiplies decimals Adds and subtracts decimals Converts between different metric units of measurement Converts between decimal fractions and simple fractions Correctly writes decimal fractions in words Divides using fractions, whole numbers, and mixed numbers Multiplies fractions with whole and mixed numbers Identifies lowest common denominator Adds and subtracts mixed numbers Performs long division with two-digit divisors Performs multiplication involving large numbers Translates word problems into numeric equations involving the four processes with whole numbers, mixed numbers, and fractions Shows all work when solving problems Oak Meadow 223

46 Lesson 24 Grade 6 Math Learning Assessment MATH Reduces fractions to lowest terms Not Yet Evident Developing Consistent Notes Reduces fractions before multiplying by canceling Converts between whole numbers, mixed numbers, and improper fractions 224 Oak Meadow

47 Grade 6 Math Lesson 24 Skill Practice A Change the following common fractions to decimals. When dividing, add as many zeros as necessary to the dividend until there is no remainder Oak Meadow 225

48 Lesson 24 Grade 6 Math Skill Practice B Convert the following decimals to percents. Remember to add the percent sign Oak Meadow

49 Grade 6 Math Lesson 24 Skill Practice C 1. There were 12 girls on the basketball team. 3 of them scored over 10 points in the game. What percent of the girls on the team scored over 10 points in the game? 2. Fred has 8 dogs. 3 of the dogs are males and 5 are females. What percent of Fred s dogs are males? 3. There are 5 trees in Melinda s front yard. 2 of them are maples and 3 are oaks. What percent of the trees in Melinda s front yard are maples? 4. Frank s been traveling a lot lately as part of his job. During the past 30 days, he s been out of town 18 days. What percent of the past 30 days has Frank been out of town? 5. Jan went to the mall with $20. She spent $5 at the mall. What percent of her $20 did she spend at the mall? Oak Meadow 227

50 Lesson 24 Grade 6 Math 228 Oak Meadow

51 Grade 6 Math Lesson 24 Lesson 24 Test Reduce all common fractions to lowest terms Oak Meadow 229

52 Lesson 24 Grade 6 Math Lesson 24 Test continued 13. Oak Ridge Medical Supply has 16 employees. 2 of those employees just started working last week. What percent of all the employees just started last week? % of the voters in Pinchville voted for Martin French for mayor. If there are 1,300 voters in Pinchville, how many of them voted for Martin French? 15. Cindy has 30 CDs in her collection, and 6 of those are country music CDs. What percent of Cindy s CD collection is country music? 16. The sales tax in Judy s state is 5%. How much sales tax will she have to pay on a stereo system that sells for $799? 230 Oak Meadow