4 Enrichment

11

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EnrichThink of It

Read each riddle and write the answer in the form requested. 1. It is a three-digit number whose tens digit is 3. Its hundreds digit is 4 more than its ones digit, which is an odd number less than 5. No two digits are the same. Write it in standard form:

2. It is the greatest even two-digit number. The product of its digits is 72. Write it in word form:

3. It is the least four-digit number that can be rounded up to the nearest hundred as 4,100.Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Write it in expanded form:

4. It is a four-digit number greater than 7,000. None of its digits are the same and all of them are even numbers. Its ones digit is 6 and the sum of its digits is 20. Write it in standard form:

5. Both the sum and the product of its three digits are 6. The least digit is in the hundreds place and the greatest digit is in the ones place. Write it in word form:

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Chapter 1

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Telephone Fun

Use what you know about place value and telephone numbers to complete this chart.Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Telephone Number

Standard Form

Expanded Form

Word Form Two million, six hundred thirty-seven thousand, four hundred twenty

905-9618

7,000,000 + 300,000 + 10,000 + 5,000 + 800 + 80 + 2Write your telephone number in standard form:

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Chapter 1

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EnrichBig Time

One million is a big number, and these are big questions. A good problem-solving plan and a calculator will help you find the answers. 1. About how many years old were you by the time you had lived a million minutes?

2. About how old would you be if you lived a million hours?

3. About how old would you be if you lived a million days?

4. About how old would you be if you lived a million weeks?

5. About how many months is a million weeks?

6. About how many years is a million months?

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More or LessRead each question. Then write your answers on the lines provided. 1. How many different three-digit numbers can you make using 1, 2, and 3 as digits?

2. From least to greatest, write the 6 three-digit numbers you can make using the digits 1, 2, and 3.

3. How many different three-digit numbers can you make using 4, 5, and 6 as digits?

Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

4. From least to greatest write the 6 three-digit numbers you can make using the digits 4, 5, and 6.

5. Write the greatest and least numbers you can make using all four of these digits: 0, 3, 5, 7 Use the signs >, or < to show which package weighs more. Then multiply to check your answers. 37 tons 42 56 tons 21


78 pounds 11

42 pounds 98

87 ounces 84

65 ounces 33

57 kilograms 59

84 kilograms 29

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Chapter 7

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EnrichAsked and Answered

Almost 2,000 kids went to Camp Guthrie last summer884 boys and 965 girls. Most of them bought clothes at the Guthrie Gift Shop. Write three questions you can ask and answer by multiplying. 1.


2.

3.

Add 3 items to the Guthrie Gift Shop price list. Create two more questions that you can ask and answer by multiplying. Be sure to use the new items in your questions! 4.

5.

Trade with a partner to check each others work.

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Fill the GridUse a number cube to roll the top two numbers for each multiplication problem in the grid. Trade with a partner to check each others work.

14

35

62


53

89

71

27

94

56

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75

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EnrichDigit Detective

Fill in the missing digits in the multiplication problems below. 1.

83 4 2 1674 33 351 8 4 14 5 5484 4570 5 184 4 7 2430 3 02 36450 6

2.

6

2

3 8 5376 2 01 24.

536Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

3.

5

5 25

7 1 3675 376.

75 95 8

5.

3160 790 11 60

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Napiers BonesIn the 17th century, John Napier invented a simple calculator that multiplied by adding. Use Napiers Bones to find 49 37. 1. Cut out the ten strips below. Place the 4, 9, and index strips next to each other. 2. Fold the strips so that rows 3 and 7 of the index are next to each other. See how the diagonal lines form a pattern of diagonal columns. 3. To find the product, add the numbers along the diagonal columns starting from the bottom right. The first diagonal (3) is the ones digit. The next diagonal (7 + 6 + 8 = 21) is the tens. Write 1 under the tens column and regroup 2 to the next diagonal. Add the next diagonal, 2 + 2 + 2 + 2 = 8, for the hundreds. The last diagonal (1) is the thousands. So, the product of 49 37 is 1,813. Use the strips to find each product.Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

1. 57 34 = 4. 32 33 =

2. 61 76 = 5. 94 65 =

3. 85 29 = 6. 56 48 =

91 8 2 7 3 6 4 5 5 4 6 3 7 2 8 1

81 6 2 4 3 2 4 0 4 8 5 6 6 4 7 2

71 4 2 1 2 8 3 5 4 2 4 9 5 6 6 3

61 2 1 8 2 4 3 0 3 6 4 2 4 8 5 4

51 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5

48 1 2 1 6 2 0 2 4 2 8 3 2 3 6

36 9 1 2 1 5 1 8 2 1 2 4 2 7

24 6 8 1 0 1 2 1 4 1 6 1 8

12 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8 9

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EnrichEight Million or More

Using the digits 3, 4, 5, 6, 7, 8, and 9, write at least 5 multiplication problems with a product of eight million or more. You may not use the same digit more than once in the same problem. Multiply to check your answers.

Using the same digits (3, 4, 5, 6, 7, 8, and 9), write at least 5 numbers that round to six million. Round to check your answers.


Now, create a problem for a partner. Choose seven digits. ___ ___ ___ ___ ___ ___ ___ Create a question. For example, write at least 5 addition problems with a sum less than four million.

Trade with a partner, and complete each others problems.

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Chapter 7

81

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EnrichDivision Rules

Work across each row of problems to discover a division rule. 36 2 = 42 2 = 12 2 = 54 3 = 48 3 = 30 3 = 3= 3= 3= 2= 2= 2= 36 6 = 42 6 = 12 6 = 54 6 = 48 6 = 30 6 =


Complete this statement: If a number can be divided evenly by 2 and by 3, then it is also divisible by .

Keep in mind 1. All even numbers are divisible by 2.

2. If the sum of the digits in a number is divisible by 3, then the number is divisible by 3.

Circle the numbers that are divisible by 6. 432 746 330 895 546

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Chapter 8

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Timed Ten

Use a stopwatch or a second hand, to see how quickly you can complete these division chains using mental math. Ready, set, GO! 1. 3,500 70 = 2. 420 6 = 3. 81,000 900 =Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

10 = 7= 3=

5= 2= Rate Yourself: 5= 5= 90 seconds or less: Mental Mathemagician! 91 119 seconds: Magnificent Multiplier! Two minutes or more: Dawdling Divider! 10 = 10 = 4= 3= 5=

4. 50,000 50 = 5. 560 7 = 6. 64,000 80 = 7. 2,400 8 = 8. 48,000 10 = 9. 5,400 2 = 10. 32,000 80 = 4=

10 = 2=

20 = 6=

60 = 30 = 10 =

Grade 4

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Chapter 8

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EnrichThe Bike Path

The Tollivers live on a bike path. Last Saturday morning, in just five minutes, they counted eleven riders and 26 wheels passing by. There were no unicycles just bicycles and tricycles with one rider each. How many bicycles and tricycles did the Tollilvers see? Use the space below to draw, guess and check, or make a table to find the answer.


Explain your thinking.

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Estimate QuotientsEstimate. Check your estimate. 1. 7 428 2. 3 605 3. 4 316

4. 9 8,140

5. 5 5,165

6. 8 3,999

7. 6 3,546

8. 2 196

9. 4 85

10. 9 98

11. 8 725

12. 5 5,620


Use the problems above to spell the name of the treasure state. Write the estimated quotient from above beside the matching problem number below. The first one, problem 11, is done for you. Cross out the letters above the quotients with two digits. Circle the letters above the quotients with three or more digits.

H11. 9.

15.

A10.

D

N2. 4.

N6.

T8.

M

O7. 1.

B3.

P12.

A

Use the circled letters. Unscramble the letters to spell the name of the treasure state, where valuable ore is mined.

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85

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EnrichTricky Tracking


Write and solve a division problem for each set of clues. 1. The quotient is 7. There is no remainder. The dividend is a square number less than 50. 2. The remainder is 2. The quotient is 4. The quotient equals the divisor. 3. The divisor is 3. The quotient is 2 2 2. The remainder is 2. 4. The quotient is 5. The dividend is 48. The remainder is an odd number. 5. The dividend is 65. The remainder is 1. The quotient is between 5 and 10.Grade 4

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Puzzling Pennies

1. Start with 27 pennies. Divide them into three equal piles. Now move just six pennies so that one pile has nine more than the other two.


Prove your answer.

2. Place six pennies in two rows as shown: Now move one penny so that you have two rows with four pennies in each row.

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Chapter 8

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Watch for patterns as you solve these division problems. 1. 9 189 2. 6 144 3. 7 189

What is one way the first three quotients are similar?

4. 2 486

5. 3 486

6. 6 486


What is one way problems 4, 5, & 6 are similar?

7. 9 108

8. 5 65

9. 8 112

What pattern do you see in problems 7, 8 & 9?

10. 5 248

11. 5 722

12. 3 244

What pattern do you see in problems 10, 11 & 12?

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Strategic DivisionUse one-digit divisors to create 20 division problems. Choose divisors carefully to earn points as follows: Zeros in the quotients hundreds place are not worth any points. Zeros in the quotients tens place are worth 2 points. Zeros in the quotients ones place are worth 1 point.

1.

604

2.

781

3.

852

4.

509

5.

619

6.

775

7.

423

8.

170

9.

875

10.

181

11.Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

363

12.

725

13.

211

14.

321

15.

354

16.

104

17.

545

18.

323

19.

906

20.

806

Zeros in the 10s Place = _____ 2 = _____ Zeros in the 1s Place = _____ 1 = _____ Total Points Earned = _____

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EnrichTic-Tac-Toe

Play division tic-tac-toe. First, solve all the division problems.

4 81,332

6 60,624

3 30,737

5 15,102

9 72,275

2 61,279Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

8 16,726

4 32,364

7 42,284

How many ways can you make tic-tac-toe by finding three problems in a row that all have remainders?

Grade 4

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Chapter 8

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EnrichThree-Dimensional Figures

Look at the net below. What three-dimensional figure can you make from the net on this page? List two ways to name this three-dimensional figure.

Predict which numbers will be on opposite faces of the solid threedimensional. Use these as factors to write three multiplication sentences and three addition sentences.

Cut out the net and create a three-dimensional figure to check your answers!6


4

8

5

7

9

Challenge: Renumber the faces of the three-dimensional figure so the product of each set of opposite faces is 36.

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Chapter 9

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Polygon Challenge

Use the figure above to follow the directions below. 1. Shade the part of the figure that is not a polygon.Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

2. Name the largest polygon that appears in the figure.

3. Count all the triangles. How many?

4. Name the polygon that appears inside the square.

5. Draw a pentagon inside one of the large triangles. Hint: You can use the sides of the triangle for some of the sides of the pentagon.

6. Count all the rectangles. How many?

Grade 4

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Chapter 9

9-3

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EnrichPentadots

5 dots

10 dots

15 dots

Pentadots are made with dots in the shape of a regular pentagon. It takes 5 dots to make a pentadot with 2 dots per side. It takes 10 dots to make a pentadot with 3 dots per side, 15 dots to make a pentadot with 4 dots per side, and so on. 1. Describe the pattern you see:Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

2. How many dots will be on each side if the total number of dots is 40? dots

3. How many dots does it take to make a pentadot with 17 dots per side? dots

4. Draw a hexadot, a hexagon with 2 dots per side.

5. How many dots does it take to make a hexadot with 3 dots per side? dots

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Time for Angles11 12 1

10 9 8

2 3 4

7 6

5

Imagine how the hands of the clock would appear at each time listed below. Think about each angle the hands would form as the minute hand moves in a clockwise direction away from the hour hand. Classify each angle by making a checkmark in one of the columns.

AnglesCopyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Time 9:00 1:30 4:30 11:00 12:15

Acute

Obtuse

Right

Now fill in a time when the clock is at each given angle.

Time

Angles Acute

Obtuse

Right

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EnrichTri This!

Triangles may be classified according to their interior angles: right, acute or obtuse. Triangles may also be classified according to their sides: Scalene triangles have no equal sides. Isosceles triangles have two equal sides. Equilateral triangles have three equal sides. Draw and label at least one of each kind by connecting dots on this grid. (Your triangles may overlap, so use different colors.)


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Some or AllQuadrilaterals

Rect. Square

Reg. Polygon

Choose the word some or all to make each statement true. 1.Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

quadrilaterals have two parallel sides. parallelograms are rectangles. quadrilaterals are polygons. polygons are squares. rectangles have four right angles. squares are rectangles. trapezoids are quadrilaterals. rhombuses are squares. squares are parallelograms. trapezoids have four interior angles.

2. 3. 4. 5. 6. 7. 8. 9. 10.

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97

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F

N

U

I

P

V

L

T

W

X

Y

Z


Pentominoes are special figures made of five squares. They are named for letters in the alphabet that they look like. There are 12 different pentominoes that can be flipped and rotated. Cut out the pentominoes pictured above and use them to completely cover the squares in the grid below. There are more than 1000 ways to solve the puzzle following these rules: Use all twelve pentominoes. Do not overlap any of the pentominoes. Do not leave any squares uncovered.

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Chapter 9

101

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EnrichInfinite Possibilities

Does the number line represent the data well? If not, how could you improve it? 1.1,000 J KL 5,000 10,000

2.130

A

B 430

3. How would you make this number line better?

L 283

M

N 383 483Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

This timeline shows you some of the major events in Dr. Martin Luther King Jr.s lifetime.Gives I have a Dream Speech

Graduate Morehouse Collage

1929

1948

1953 1958 1955

Publishes Stride Toward Freedom

Earns Doctoral Degree

Marries Corretta Scott

Born in Atlanta, GA

1963 1968 1964

4. How many years passed between Martin Luthar King Jr.s birth and death? 5. If Martin Luther King Jr. had been born in 2008 and lived to be the same age, what year would it be when he died? 6. His wife, Corretta, was born in 1927. How old was she when Dr. Martin Luther King Jr. was 19?Grade 4

12

Assassinated in Memphin, TN

Awarded Nobel Peace Prize

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Line up

A E F

B

C G

D H


Lines can be straight, curved, parallel, perpendicular, horizontal, or vertical. Line segments and rays have end points, and sometimes lines intersect. Read this sentence and decide whether it is true: BF is not parallel to any other line in the figure. Thats true. Now write five more statements that describe the figure. You may use the words in italics and other math vocabulary words that you know.

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Chapter 10

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EnrichPrincipals Office

The principal keeps a dish of mints on her desk. She offered a piece to Sebastian when he turned in $3 he found on the playground. Half of the mints in the bowl had red wrappers. Without looking he grabbed a piece with a yellow wrapper. His chances of doing that again were 3 out of 23. Use the information above to write a reasonable description of the principals bowl of mints.


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Chapter 10

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Enrichy AChapter Resources

Points and Polygons12 11 10 9 8 7 6 5 4 3 2 1 0

y 8 7 6 5 G 4 3 F 2 1 0Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

y 7 6 5 4 3 2 1 0 A F E B C D

H

A B C

B

C

E

D

x 1 2 3 4 5 6

1 2 3 4 5 6 7

x

1 2 3 4 5 6

x

Name the polygon that appears on the grid. Then give the ordered pair for each of its vertices.

1.

A E

B F

C G

D H

2.

A

B

C

3.

A E

B F

C

D

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EnrichTesselations

Color the tessellation accordingly. Should some parts be 2 or more colors? Color each piece every color it can be.


Tessellations are repeating shapes placed side by side. Use triangles, squares, and/or hexagons to make your own tessellation and color it.

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Likely or UnlikelyPlay this game with a partner. Player A chooses a secret 4-digit number and writes it on a separate sheet of paper. Player B guesses a 4-digit number and writes it in the first row of the guess chart. Player A looks at the guess and then fills in the second chart. Player A tells the number of digits that are correct, AND how many are in the correct position. (For example, the secret number is 1093. The first guess is 6198. The number of correct digits is 2. The number of digits in the correct position is 1.) Based on that information, Player B makes a second guess. Continue playing until the secret number is guessed, or until 10 guesses have been used. Players then switch roles.Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

After playing a couple of games compare the strategies you used for guessing with your partner.

Guess

Number of Correct Numbers 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.37

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Numbers of Digits in the Correct Position

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EnrichCut Ups

Look at the figures below. How can you cut along the grid lines to make two congruent pieces from each figure? Cut out the pieces to test whether each piece is the same size and shape. Or, draw lines where you would cut the figures.


Grade 4

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Chapter 10

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Natural Symmetry

Have you ever wondered why kite strings attach to the kite where they do? One of the reasons it is easy to fly a kite, is that kites have bilateral symmetry. This makes them easier to balance and control. Many things in nature have symmetry too. Think about animals that fly. Name three that have natural bilateral symmetry:Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

1.

2. 3. Draw a picture of two things found in nature that have rotational symmetry.

Grade 4

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Chapter 10

111

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EnrichMathematical Reasoning

How long is your finger? 1. Estimate the length of your index finger without using a ruler.

2. Estimate the length of each of your other fingers.

1 3. If 1 inch is about 2__ centimeters, how many centimeters long is 2 each finger? Use your estimations to calculate this. Estimate the length in centimeters of your index finger.


4. Now use your ruler to find the exact length of your index finger and your other fingers. How close were your estimations?

5. Was there a larger gap between your estimation and the real length when you measured in inches or centimeters? Why?

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Mathematical ReasoningWalking and Running 1. Andrea went for a walk with her dog. They walked 330 feet east, 40 yards south, 15 yards west, 171 feet south, 285 feet west, and 129 feet north. How many more feet does she need to walk to end in her original position? 2. There are 12 inches in a foot, 3 feet in a yard, and 5,280 feet in a mile. What do all of these numbers have in common?

3. Macie went for a walk and counted her steps. She took 2,030 1 steps. If each of her steps was 2__ feet, how far did she walk in 2 yards?Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Try It! How many feet are in one of your steps?

4. Dani, Christi, Mark, and Matteo went for a run together. At different points, each person took a break to walk. Dani ran 15,840 feet, Christi ran 4,400 yards, Mark ran 7,920 feet, and Matteo ran 7,040 yards. Draw a diagram to represent how far each person ran before he or she started to walk.

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113

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EnrichConcrete Squares

1. Three congruent squares of concrete are placed next to each other to form a rectangular walkway. The perimeter of the concrete path is 24 feet. A. What are the dimensions of the rectangular walkway? B. How much area does it cover?

2. Centered inside each of the concrete squares is a circle that has a diameter of 2 feet. The circumference of the circle is marked with a wavy line. A. About how long is each wavy line?

B. How close to the edge of the concrete square does the wavy line ever get?


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Chapter 11

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Mathematical ReasoningWhat Am I? 1. I am bigger than a millimeter, but smaller than a kilometer, what am I? 2. I am measured in meters and am known for my long neck. I live in Africa, what am I? 3. I am measured in kilometers. People practice and practice to be able to complete me. I occur all over the world, but am especially well known in Boston, Massachusetts. What am I?

4. I am pretty small. You could use millimeters or centimeters to measure me. I grow on your body and some people paint me.Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

What am I? 5. I am found in the kitchen and am used to cook things quickly. I am perfect for popcorn. Measure me in centimeters.

6. I am measured in centimeters and grow on the side of your head.

7. I am long and thin. Use me to water the flowers in the garden. Measure me in meters.1. 5. 6. 4. 7. 3. 2.

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115

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EnrichPerimeter Puzzles

Each square at the right is divided into three regions. Each region has a perimeter of 8 units. The square at the right is divided into two regions. Each region has a perimeter of 10 units. Divide each square below into the number of regions with the perimeter given. Try to do this in two different ways. 1. Number of regions: 4 Perimeter of each region: 10


2. Number of regions: 5 Perimeter of each region: 12

3. Number of regions: 6 Perimeter of each region: 12

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Dive In

Jeremys family has a square swimming pool. A rope runs from the middle of one side to the middle of the opposite side to divide the shallow half from the deep half. One side of the pool is 30 feet long. 1. What is the perimeter of the swimming pool?Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

2. What is the surface area of the deep end?

3. What is the surface area of the entire pool?

4. What is the perimeter of the shallow end?

Katies family also has a swimming pool. Her familys pool has a shallow end that is twice as long as the shallow end of Jeremys pool. 5. What is the perimeter of Katies pool?

6. What is the surface area of Katies pool?

7. What is the perimeter of the shallow end of Katies pool?

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Chapter 11

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EnrichThree-Dimensional Drawings

You can draw a picture of a cube by lightly drawing two squares that overlap, and connecting the corners with diagonal lines.

1. On the left below draw a picture of a cube that would have a surface area of 6 square inches. Use a ruler to measure the line segments to make your drawing as accurate as possible. 2. On the right below, draw a cube that would have four times as much surface area.Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

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EnrichChapter Resources10 0 10 70 60 50

Mathematical ReasoningSwapping Units There is a specific calculation to change a degrees Fahrenheit temperature into degrees Celsius. There is also a simple way to estimate the conversion. To Estimate: If you are changing from Celsius to Fahrenheit, double the number and add 30. C 2 + 30 = F If you are changing from Fahrenheit to Celsius, subtract 30 and divide by 2. (F 30) 2 = C This estimation works well for some temperatures, but not all. Determine whether or not the estimation technique is reliable for the following temperatures. 1. 44C170 160 150 140 130 120 50 60 70


2. 5C

60 50 40 30 20

170

3. 70 F

60 50 40 30 20 10 0 10

4. 350 F

160 150 140 130 120

5. What relationship do you notice between the numbers and the reliability?

Grade 4

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EnrichHow Much Water Do You Use?

Here is a chart that shows Catalinas familys water bills for the past year. Catalinas Water Bills Month January February March April May June July August September October November December Price of Bill $18.25 $19.75 $18.00 $17.20 $19.90 $21.05 $18.15 $19.50 $16.75 $17.80 $20.50 $19.30Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

1. There are 4 people in Catalinas family. If each person uses the same amount of water, how much is Catalinas portion of the water bill in March? 2. If a gallon of water costs a penny, how many gallons of water did Catalinas family use in July? 3. If a gallon of water costs half a penny, how many gallons of water did Catalinas family use in November? 4. Use the chart above to estimate the gallons of water Catalinas whole family would use in a month. Do you think the price of water is closer to a penny or half a penny per gallon?

5. Did Catalinas family use more water in the first or second half of the year?

Grade 4

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Chapter 12

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Fill It Up!Describe about how much the amount given would fill up the container shown.

1. 48 cups

2. 1 cup

5 gal fish tank

16 oz shampoo bottle

3. 120 fluid ouncesCopyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

4. 30 pints

Paint 5 gal. 1 gal milk jug 5 gal can of paint

5. 4 cups

6. 100 cups

4 quart pot

20 gal barrel

Grade 4

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Chapter 12

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EnrichThe Price is Right

Pete is having a big party and wants to be sure to get the best deal on the drinks he is buying. Help him figure out what is the best deal. Arrange the sets of items from least to most expensive PER LITER to find the secret message. 1. $1.50 for 2 L Soda 2. $1.10 for 1 L apple juice 3. $2.50 for 2 L water 4. $1.50 for 1 L water 5. $3.50 for 4 L soda 6. $2.50 for 3 L apple juice 7. $4.50 for 6 L fruit punch 8. $5.00 for 8.5 L soda 9. $3.00 for 2 L fruit punch Soda t , u , | r c Apple Juice , | j f Water , | i i Fruit Punch , u e 9 8 2 7 4 6 1. 2. 3. 4. 5. 6. 7. 8. 9.Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Americans consume 42.8 liters of 3 5 1 per person, per year.

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Pumping IronThe origins of modern weightlifting can be dated back to the 18th and 19th centuries. Today, some professional weightlifters can lift barbells over 1,000 pounds. 1. Chris has decided to start lifting weights. He begins by lifting 22 pound weights. About how much more does he have to lift to reach 1,000 pounds? 2. In three years, Chris plans to be lifting 100 more pounds than he is now. If he follows his plan, how far will he be from 1,000 pounds? 3. When professional weightlifters train, they lift a smaller amount of weight multiple times (called reps, which is short for repetitions). This increases their muscle mass more quickly. Below is a weightlifters training plan. Fill in the table.Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Training Plan Goal Weight (X) 5 reps (X - 125) 2 reps (X - 75) 1 rep (X - 25) Week 1 650 Week 2 Week 3 Week 4 715 Week 5 705 550 625

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EnrichMissing Information?

Here are two different tables. Write 2 problem solving questions for each table. The questions may or may not be written with the idea that those solving them would not have all the information provided in the tables.

Baseball Practice Monday Throw and Catch Hitting Fielding Running1.

Tuesday 25 min 5:205:55 35 min 6:307:05

Wednesday 1:402:00 2:002:45 2:453:00 15 min

Thursday 4:155:15 25 min 20 min 30 min

Friday 20 min 30 min 2:052:45 2:453:15

2:152:45 2:453:15 3:154:00 4:004:15


2.

Rock, Paper, Scissors Rock Peter Ada Renee1.

Paper

Scissors

2.

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Converting WeightsAlita and John were in a race to see which team could collect more water in a bucket. To play, each team lined up next to the first bucket. One at a time, each player dipped the sponge into the bucket, raced to the other bucket, and squeezed the water into it. The team with more water in the second bucket, after 2 minutes of playing, won. They played 5 times.

The results looked like this every time:

Because it was so close, they decided to measure the weight of the water. Which team won each round?

Alitas Team Johns TeamCopyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Who Won? 1. 2. 3. 4. 5.

Round 1 Round 2 Round 3 Round 4 Round 5

4 lb 3 lb 67 oz 3 lb 74 oz

66 oz 55 oz 4 lb 50 oz 4 lb

6. If they determined who won by totaling the weight of all the water collected, would the results change? Why?

7. Change the weights of the water collected so that Alitaa team still wins 3 out of 5, but Johns team wins the total.

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EnrichMathematical Reasoning

Use what you know to convert grams to kilograms. Animal Giraffe Elephant Hippopotamus Blue whale Salmon Mountain lion Goldfish Fly 6. 7. 2g 8. 4. 5,500 g 5. 45 kgCopyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Mass in Grams 1. 2,300,000 g 2,000,000 g 2. 3.

Mass in Kilograms 1,000 kg

120,000 kg

0.01 kg

9. Order these animals from greatest mass to least mass.

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Estimate and Measure VolumeMake your own paper cube where the edges are 2 inches long.

1. If you made cubes where the edges were 1 inch long, how many would fit inside the 2 inch cube?1 2. If you made cubes where the edges were __ inch long, how many 2 would fit inside the 2 inch cube?

3. If your 2 inch cube was 4 inches instead, how many 2 inch cubes would fit inside the 4 inch cube?Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

4. How many 1 inch cubes would fit inside the 4 inch cube?

1 5. How many __ inch cubes would fit inside the 4 inch cube? 2

6. Explain how you solved Exercise 5.

7. Explain a pattern you see in these numbers.

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EnrichGraphs That Curve

Many graphs have straight lines. But graphs can also be made up of points that make curved lines. Look for a pattern in these ordered pairs. (2, 18) (3, 12) (6, 6) (9, 4) The numbers in each ordered pair have the same product. When you multiply the numbers you get 36. 1. Find ten different ordered pairs with a product of 36. You may use whole and decimal numbers. 2. Mark a dot for each ordered pair on the grid. Then connect the dots. You will make a curved line graph. The dots for (1, 36) and (36, 1) wont fit on this grid, but you can imagine them.20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


3. Explain why the ordered pair (3.6, 10) belongs on this graph.

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Elapsed TimeJames, Jamal, and Josie were in a jalapeno eating contest. How did they compare to the professionals also participating in the contest? Number of Jalapenos Eaten Each Minute 1 2 3 4 5 6 7 8 16 11 5 12 12 12 15 3 10 12 12 35 43 8 20 30 35 6 11 25 33 4 13 22 36 12 7 25 35 15 15 30 10 10 18 40 4

James Jamal

Total 86 77 104 243 236

Josie 8 Professional 1 36 Professional 2 40

1. If the contest started at 4:25, what time did it finish? 2. If the contest started at 5:23, by what time had Jamal finishedCopyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

40 jalapenos? 3. In the third minute, how many seconds did it take Josie to eat each jalapeno? 4. In the third minute, how many seconds did it take Professional 1 to eat each jalapeno? 5. In the third minute, how many seconds did it take James to eat each jalapeno? 6. Find the median number of jalapenos James ate each minute. If he ate at this rate for all 8 minutes, how many jalapenos would he have eaten? How many would he have eaten each second?

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EnrichStained Glass Door

An artist decided to use stained glass panes in his front door. Read all the color clues first. Then use a colored pencil or a crayon to color the panes.Color Clues

One-eighth of the panes are red. Four-eighths of the panes are blue, and none of them are in the top half. Two-eighths of the panes are yellow. They have no sides in common. The whole door contains eight stained glass panes: red, yellow, green, or blue.


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Name That PartWrite the fraction represented by each idea below.2

For example, two stars on the American flag is _ or _. 50 251

1. One day a week

2. Three months in a year


3. Eight toes on two feet

4. Two legs on a spider

5. Ten minutes in an hour

6. The left shoe of a pair

7. One flat tire on a car

8. Twelve inches of a yard

9. Three arms on an octopus

10. The color yellow on a traffic light

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EnrichFor the Birds

Use the information to answer the questions. - An eagle can fly 40 miles to her home in the woods in one hour. - A robin can cover a quarter of the distance in the same amount of time. 2 - An eagle flies __ as fast as a falcon. 3 - A falcon flies at twice the speed of an owl. 3 - A crow covers __ as much distance as an eagle does in one hour. 4

1. How far can a robin fly in sixty minutes?

2. Which two birds travel at half the speed of a falcon?


3. How fast does the falcon fly?

4. How many miles can a crow fly in half an hour?

5. What fraction tells how fast the robin flies compared to the crow?

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Matching ModelsWrite a fraction that names the shaded part of each figure. Draw lines to connect the equivalent fractions.


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EnrichJust Five

Use only the numbers 1, 2, 3, 4 and 5 to fill in as many circles as you can to make each number sentence true.

1.

3.

=

4.

>


5.

=

6.

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4 Enrichment