Math 65 Enrichment Problems

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Answers to problem sets

Activity Involves Skills Covered in Lessons 1-7

1i) If you had 3 hundreds, 1 twenty, 2 tens, and 4 ones, how much money would you have? What if you did not have the twenty? Check the box next to the correct answer.

a. $344; $324
b. $345; $325
c. $365; $345

1g) Work with a group. Write a three-digit number that has only one 3, and have the other students in the group identify the place in which the digit 3 appears. Take turns writing a number and having the others identify the place value of 3.

1f) Have your child write down as many numbers as he or she can find in your house that have two, three, or four digits. Then label the place values of the digits in each number.


Activity Involves Skills Covered in Lessons 8-14

2i) There are four piles of paper. The first pile has 13 pieces. The second pile has 5 pieces. The third pile has 21 pieces, and the fourth pile has 3 pieces. How many pieces of paper are there in all? How many would there be in all if you took 4 pieces from the first pile and placed them in the second pile? Check the box next to the correct answer.

a. 42; the same number
b. 38; four fewer
c. 36; six fewer

2g) Work with two other students. Choose a number between 2 and 9, and have the other students do the same. Have one student add his or her number to yours. Have the other student add his or her number to the previous total. Add your number to the next total. Keep going, and see how long you can continue before someone makes a mistake.

2f) Have each family member walk around the house or down the street and back, and have your child count the number of steps each person takes. Ask your child how many steps the family members took in all.


Activity Involves Skills Covered in Lessons 15-21

3i) Make a multiplication table with factors ranging from 0 to 12.

3g) Work with a group to find answers to the following problems. Check the box next to each answer you all agree is correct. Check one another's work.

  1. 9 x 6
    a. 55 b. 54 c. 53

  2. 8 x 6
    a. 48 b. 58 c. 38

  3. 5 x 7
    a. 35 b. 34 c. 45

3f) Have your child make a multiplication table with factors ranging from 0 to 12. (For an example of a multiplication table, please see Math 65, Lesson 15.) Ask your child to have family members look at and study the table for patterns. Ask your child how many patterns he or she and the family members can find in the multiplication table.


Activity Involves Skills Covered in Lessons 22-28

4i) One player scored one fourth of the 120 points in the basketball game. How many points did she score? Another scored a fifth of the total points. How many did she score? Check the box next to the correct answer.

a. 40 points; 30 points
b. 30 points; 24 points
c. 35 points; 20 points

4g) Work with a group to draw 48 dots on a piece of paper in four rows so that one fourth of the dots are in each row. How many dots are in each row? Repeat the procedure with 64 dots. Check the box next to the answer you all agree is correct.

a. 12 dots; 16 dots
b. 24 dots; 32 dots
c. 16 dots; 20 dots

4f) There are 128 ounces in a gallon. Have your child determine how many ounces are in the following:

  1. a quart (one fourth of a gallon)
  2. a pint (one half of a quart)
  3. a cup (one half of a pint)

Check the results with measuring cups.


Activity Involves Skills Covered in Lessons 29-35

5i) Solve the following problems. Check the box next to each correct answer.

  1. 173 x 600
    a. 103,800
    b. 1,038,000c. 10,380

  2. 173 x 20 x 30
    a. 1,038,000
    b. 10,380 c. 103,800

  3. 173 x 6 x 100
    a. 10,380
    b. 103,800 c. 1,038,000

How do your answers compare to one another? What similarities do you notice?

5g) Work with a group to solve the following problems. (Hint: Factor the non-zero digits of the second number into two numbers and multiply them all.) Check one another's answers.

  1. 24 x 800
  2. 32 x 1200
  3. 15 x 1500

5f) Sit down with your child and an atlas or a globe, and have your child use the atlas or globe to solve the following: A well-conditioned hiker can hike 20 miles in a day. How far could a hiker go and where could a hiker visit in:

  1. one month, or 30 days
  2. six months, or 180 days
  3. one year, or 365 days

Activity Involves Skills Covered in Lessons 36-42

6i) How many twentieths are equivalent to the following? Check the box next to each correct answer.

  1. 1/10
    a. 1/20b. 2/20c. 3/20

  2. 3/10
    a. 6/20 b. 3/20 c. 2/20

  3. 1/5
    a. 5/20b. 2/20 c. 4/20

  4. 3/5
    a. 3/20 b. 12/20 c. 5/20

  5. 1/4
    a. 5/20b. 4/20 c. 2/20

  6. 3/4
    a. 4/20 b. 18/20 c. 15/20

  7. 1/2
    a. 5/20b. 10/20 c. 16/20

6g) Work with a group. See how many of the following fractions you can divide your group into. (Calculate the numbers first; then divide the group.)

  1. 1/2
  2. 1/3
  3. 2/3
  4. 1/4
  5. 1/5
  6. 2/5
  7. 1/7
  8. 5/7

6f) Help your child cut one piece of paper into halves, another into fourths, and another into fifths. What percents of a full piece of paper are the following?

  1. one half plus two fifths
  2. one fourth plus one half
  3. three fifths plus one half

Activity Involves Skills Covered in Lessons 43-49

7i) Using short division, solve the following problems. Check the box next to each correct answer.

  1. 4256 ÷ 8
    a. 522b. 532c. 542

  2. 3652 ÷ 11
    a. 332b. 352c. 342

Explain the difference between long division and short division.

7g) Work with a group. Pick two of the following three problems and solve them using short division, and have the other students in the group do the same. Check the box next to each correct answer. Use multiplication to check one another's work.

  1. 8624 ÷ 7
    a. 1132 b. 1032c. 1232

  2. 3942 ÷ 9
    a. 438b. 418c. 428

  3. 7432 ÷ 4
    a. 1658b. 1858c. 1758

7f) Pick a one-digit number and a two-digit number and multiply them. Then give your child the one-digit number and the product. Challenge your child to figure out what the two-digit number is.


Activity Involves Skills Covered in Lessons 50-56

8i) Joe ate 5 more chicken wings than Mark. Mark ate 7 fewer chicken wings than Linn, who ate 12. How many chicken wings did Joe eat? How many chicken wings did everyone eat in all? Check the box next to the correct answer.

a. Mark ate 5 chicken wings; Joe ate 10 chicken wings; everyone ate 27 chicken wings.
b. Mark ate 10 chicken wings; Joe ate 15 chicken wings; everyone ate 32 chicken wings.
c. Mark ate 12 chicken wings; Joe ate 17 chicken wings; everyone ate 34 chicken wings.

8g) How many students are in your class? Get that many markers. Separate your desk into four sections. Before you start, calculate how many markers will be in each section of the desk after you follow the instructions. Put one third of the markers in one section of your desk. (Round to the nearest whole number.) Put two fewer markers than that in the second section of your desk. Place three more markers in the third section than are in the second. Put the rest of the markers in the fourth section. How many markers are in the third section? How many markers are in the fourth section?

8f) With your child, create a multipart word problem using family members' ages. Example: Mom is 2 years younger than Dad. Dad is 27 years older than Betty. Betty is 10 years old. How old is Mom? (Mom is 35.)


Activity Involves Skills Covered in Lessons 57-63

9i) Check the boxes next to the answers that correctly show the following numbers in words.

  1. 158423902
    a. one billion, five hundred eighty-four million, two hundred thirty thousand, nine hundred two
    b. one hundred fifty-eight million, four hundred twenty-three thousand, nine hundred two

  2. 643207873
    a. six hundred forty-three million, two hundred seven thousand, eight hundred seventy-three
    b. six billion, four hundred thirty-two million, seventy-eight thousand, seventy-three

9g) Work with a group. Choose one numeral 5 in each of the following numbers, and have each friend do the same.

  1. 834750158
  2. 569520486
  3. 835211450

Answer the following questions, and have each friend do the same: Which numeral 5 did you choose? What place is it in? Did your group identify the place values for all the fives? If not, try again.

9f) With your child, write the following numbers on separate index cards: 1, 10, 100, 1000, 10,000, 100,000, 1,000,000, 10,000,000, and 100,000,000. On the back of each card write the number in words. Use these flashcards to quiz your child by showing him or her the side with the number in digits and having him or her say the number.


Activity Involves Skills Covered in Lessons 64-70

10i) Estimate the following products by rounding the factors, then multiplying. Check the box next to the correct estimate.

  1. 42 x 19
    a. 760b. 800c. 840

  2. 23 x 52
    a. 1000 b. 1375c. 1100

Check how close each estimate is by finding the product without rounding.

10g) Work with a group. Have one friend estimate while the other friends find the exact products.

  1. 24 x 36
  2. 12 x 48
  3. 42 x 29

Compare results.

10f) With your child, pick some two-digit numbers to multiply. Have your child estimate the product while you use a calculator to find the exact product. Compare results.


Activity Involves Skills Covered in Lessons 71-77

11i) Convert the following to decimal numbers. Check the box next to each correct answer.

  1. 73/100
    a. 73b. 7.3c. 0.73

  2. 730/1000
    a. 0.73b. 7.3c. 73

  3. 531/1000
    a. 0.531 b. 5.31c. 53.1

11g) Work with a group. Sit beside one another in a line. Have one friend start by naming a fraction of one hundred. Write the fraction as a decimal number, and have the other friends do the same. Then have the next friend in line name a fraction of one hundred. Write that fraction as a decimal number, and have the other friends do the same. Repeat the process until everyone has had a chance to say a fraction of one hundred.

11f) A percent is a fraction of one hundred. Quiz your child by naming a percent (from 0 to 100) and having him or her write it as a fraction and a decimal number.


Activity Involves Skills Covered in Lessons 78-84

12i) Add the following numbers. Check the box next to each correct answer.

  1. 732.03 + 1574.42 + 10.384 + 100.4
    a. 2417.234b. 2417.874c. 2417.239

  2. 2.4 + 0.5482 + 1350 + 31.84361 + 50.46
    a. 1435.2518b. 1435.25180c. 1435.25181

12g) Work with two friends. Add the following numbers. Check the box next to each correct answer.

  1. 4.6 + 5.38 + 12.1 + 8
    a. 30.08 b. 37.08c. 30.80

  2. 10.1 + 7.9 + 6.58 + 12
    a. 35.58 b. 36.68c. 36.58

  3. 6.2 + 13.4 + 2.54 + 6.7
    a. 28.84 b. 27.88c. 28.74

Check one another's answers.

12f) Record your grocery expenses for one week. Have your child add the expenses to find the total.


Activity Involves Skills Covered in Lessons 85-91

13i) Check the box next to each correct answer.

  1. Convert 3/8 to a fraction with a denominator of 96.
    a. 39/96b. 46/96 c. 36/96

  2. Convert 1/6 to a fraction with a denominator of 96.
    a. 16/96 b. 15/96 c. 26/96

  3. Add your answers to (1) and (2). What do you get?
    a. 54/96b. 52/96 c. 72/96

13g) Work with a group. Choose and solve one of the following, and have each friend do the same. Do not tell one another which you chose.

  1. By what equivalent fraction for 1 can 2/3 be multiplied to make 48/72?
  2. Write 16/80 as a fraction with a denominator of 5.
  3. By what equivalent fraction for 1 can 1/6 be multiplied to make 12/72?

Check your answers with your group. If there are different answers to the same question, work together to determine which one is correct.

13f) With your child, write three equivalent fractions for each of the following: 1/2, 4/5, and 2/3. Then fold 81/2" x 11" pieces of paper to represent each fraction and its equivalents.


Activity Involves Skills Covered in Lessons 92-98

14i) Figure out the following fractions of whole numbers. Check the box next to each correct answer.

  1. Two thirds of a class of 27 students are girls. How many girls are in the class?
    a. 23 girlsb. 18 girlsc. 9 girls

  2. Three eighths of 336 apples are rotten. How many apples are rotten?
    a. 126 applesb. 116 applesc. 106 apples

14g) Work with a group. Ask one friend, "What is one half of 1024?" Have that friend ask another friend, "What is one half of my answer?" Take turns asking the question until the answer is no longer a whole number. How many friends got to answer? Try again beginning with one third of 729 and then one fourth of 1024.

14f) Help your child figure out answers to the following:

  1. How many months are in three fourths of a year?
  2. How many months are in five sixths of two years?
  3. How many days are in three sevenths of three weeks?

Use a calendar to check your answers.


Activity Involves Skills Covered in Lessons 99-105

15i) There are 213 bales of hay in the field. Bill can carry 12 bales of hay on his truck per trip. If he wants to carry all the bales of hay to his father's farm, how many trips will he make? How many bales of hay will he carry on the last trip? If Bill makes one trip per day, how many weeks will it take him to finish the job? Check the box next to the correct answer.

a. 18 trips with 8 bales on the last trip; 23/7 weeks
b. 17 trips with 9 bales on the last trip; 24/7 weeks
c.
19 trips with 7 bales on the last trip; 25/7 weeks

15g) Work with two friends. Name a four-digit number. Have one friend name a two-digit number less than 50. Have the other friend divide the four-digit number by the two-digit number. Agree on an answer. Repeat the activity, but switch roles. Continue until everyone has had a turn to calculate an answer.

15f) Tell your child you need to know the average number of miles you drive your car per month. Tell your child the total number of miles on your car and the number of months you have driven your car. Then ask your child to divide the number of miles by the number of months. Try it with some of your neighbors' cars, if possible.


Activity Involves Skills Covered in Lessons 106-112

16i) Find the answers to the following. Check the box next to each correct answer.

  1. three fifths divided by seven ninths
    a. 21/54b. 21/45 c. 27/35

  2. eight fifteenths divided by five eighths
    a. 40/90b. 64/75c. 40/75

16g) Work with two friends. Name a fraction. Have one friend name a number less than 20. Have the other friend divide the number by the fraction. Agree on an answer. Repeat the activity, but switch roles. Continue until everyone has had a turn to calculate an answer.

16f) Choose a whole number between 1 and 15 or a fraction with a denominator less than 10. Have your child choose a fraction. Then have your child divide your number by his or her fraction.


Activity Involves Skills Covered in Lessons 113-119

17i) Approximately 4/5 of the air is nitrogen. What percent of the air is nitrogen? Almost all of the rest is oxygen. About what percent of the air is oxygen? Check the box next to the correct answer.

a. 80% nitrogen; 20% oxygen
b. 20% nitrogen; 80% oxygen
c. 60% nitrogen; 40% oxygen

17g) Work with nine friends. What percent of your group is boys? What percent of your group is girls? What percent of your group is left-handed? What percent of your group is right-handed?

17f) Go for a drive or a walk with your child. Have your child count twenty cars or trucks and write down what color each one is. Ask your child what percent of the cars he or she saw was each color.


Activity Involves Skills Covered in Lessons 120-126

18i) The playing area of a football field is 100 yards long and 40 yards wide. Each end zone is 10 yards long and 40 yards wide. What is the total area of a football field? Check the box next to the correct answer.

a. 4400 square yards
b. 4800 square yards
c. 5800 square yards

18g) Work with a group to figure out what combinations of lengths and widths would make a rectangle with an area of 24 square feet. Measure out the possible lengths and widths on the floor. How many standing students will fit in an area of 24 square feet?

18f) Have your child measure the length and width of every room in your home to the nearest foot. Ask your child to find the area of each room and then the total area of your home. Save your child's work for Activity 20.


Activity Involves Skills Covered in Lessons 127-133

19i) Convert the following to mixed numbers of feet. Check the box next to the correct answer.

  1. 58 feet 6 inches
    a. 586/12 feetb. 582/12 feetc. 583/12 feet

  2. 31 feet 1 inch
    a. 3110/12 feetb. 311/12 feetc. 3111/12 feet

  3. 17 feet 8 inches
    a. 177/12 feet b. 178/12 feet c. 174/12 feet

  4. Find the sum of the measurements above. Simplify your answer as a mixed number. Check the box next to the correct answer.
    a. 1063/4 feet b. 1073/4 feet c. 1071/4 feet

19g) Work with two friends. Pick two of the following problems to do, and have each friend do the same. Do not tell one another which problems you picked.

  1. 125/8 + 531/4

  2. 21/3 + 51/6

  3. 73/4 - 21/2

  4. 8413/16 - 363/8

Compare answers. Was every problem solved? If not, try again.

19f) Have your child use measuring cups to pour the following amounts of water into separate containers: 11/3 cups, 11/4 cups, 2/3 cup, 1/2 cup, and 1/4 cup. Then ask your child to find the total number of cups. Have him or her check by pouring all the water into one large container and measuring the amount. Tell your child there are two cups in a pint and two pints in a quart. Then ask him or her how many pints there are and how many quarts there are.


Activity Involves Skills Covered in Lessons 134-140

20i) Multiply the following mixed numbers. Reduce your answers. Check the box next to each correct answer.

  1. Four ninths of twelve and three eighths
    a. 51/2 b. 53/8 c. 57/8

  2. Three and seven elevenths of seven and five sixths
    a. 31/3 b. 32/3c. 31/33

20g) Work in a group of four. Without arranging yourselves, figure out the following: How many friends would be in one half of two and one half groups? How many students would be in one third of one and one half groups?

20f) Have your child measure the length and width of every room in your home in feet and inches and write each measurement as a mixed number of feet. Ask your child to find the area of each room in square feet and then the total area of your home. How do the answers compare with the rounded answers from Activity 18?