Math Fundamentals for Statistics I (Math 52) Homework Unit ... · Is there ever a time when rounding up or down to the nearest thousand would be off by the same amount? Give an example

Math 52 – Homework Unit 2 – Page 1

Math Fundamentals for

Statistics I (Math 52)

Homework Unit 2:

Number Line and

Ordering

By Scott Fallstrom and Brent Pickett

“The ‘How’ and ‘Whys’ Guys”

This work is licensed under a Creative Commons Attribution-

NonCommercial-ShareAlike 4.0 International License

3rd Edition (Summer 2016)


Table of Contents

This will show you where the homework problems for a particular section start.

2.1: Place Values ................................................................................................................................... 2

2.2: Comparing Numbers .................................................................................................................... 4

2.3: Equality and Inequality ................................................................................................................ 5

2.4: Sorting Numbers ........................................................................................................................... 6

2.5: Placing Integers on a Number Line ............................................................................................ 7

2.6: Rounding ........................................................................................................................................ 8

2.7: Decimals ....................................................................................................................................... 10

2.8: Placing decimals on a number line ............................................................................................ 13

2.9: Negative Integers ......................................................................................................................... 14

2.10: Perfect Squares .......................................................................................................................... 16

2.11: Square Roots .............................................................................................................................. 16

2.12: Approximating Square Roots .................................................................................................. 18

2.13: Number Line Connections........................................................................................................ 19

2.14: Unit Review and Test Prep ....................................................................................................... 20

2.1: Place Values

Vocabulary and symbols – write out what the following mean:

Digits Place Value Decimal Point

Concept questions:

1. What is so special about 0?

2. Is zero really “nothing” with place value?

3. Is the decimal point really important?

4. Can you think of some examples of numbers where …

a. 0 is really not important (could write number without and keep the same value) ?

b. 0 is really important (writing without the 0 changes the value)?

Exercises:

5. Create a number line with the following characteristics:

a. From 1,000 to 2,000 by hundreds

b. From 1,200 to 1,300 by tens

c. From 1,240 to 1,250 by ones

d. From 1,243 to 1,244 by tenths

e. From 501 to 502 by tenths

f. From 500 to 510 by ones

g. From 500 to 600 by tens

h. From 0 to 1,000 by hundreds


6. Fill in the digit that is in the given place values for 56, 237.9

a. Tens

b. Thousands

c. Ones

d. Hundred Thousands

e. Tenths

f. Hundreds

g. Ten Thousands

h. Millions

7. Fill in the digit that is in the given place values for 739.106

a. Tens

b. Thousands

c. Ones

d. Hundredths

e. Tenths

f. Hundreds

g. Thousandths

h. Ten-thousandths

8. What is the place value of the “4” in…

a. 384.91

b. 4,103.923

c. 497,102,980

d. 16.2034

e. 43,091.42

f. 4,000,000,000.01

9. Look at the two numbers and determine if they have the same value or different values.

Numbers Comparison Numbers Comparison

a. 63 and 630 Same Different b. 790 and 0790 Same Different

c. 15 and 105 Same Different d. 10 and 1.0 Same Different

e. 63.5 and 63.50 Same Different f. 84 and 084 Same Different

g. 840 and 840.0 Same Different h. 11 and 11.000 Same Different

i. 1.05 and 1.005 Same Different j. 16 and 016.0 Same Different

10. Finish labeling the number lines.

a.

b.

c.

18 30

4,000 4,450

0 63


Wrap-up and look back:

11. Write in words what you learned from this first section.

12. Can we put a 0 into a number anywhere and keep the value the same?

13. Daniel says 4,103.923 has a 4 in the thousandths place value. Is he correct?

14. Did you have any questions remaining that weren’t covered in class? Write them out and bring

them back to class.

2.2: Comparing Numbers


Value Larger (of two numbers) Equal

Concept questions:

1. Are there times where you can just tell that one number is bigger than another? Give an example.

2. What method do you use to see if two numbers are equal?

Exercises:

3. Based on their size, determine the larger number.

Numbers Larger Numbers Larger

a. 237 and 253 b. 1,113 and 1,131

c. 435 and 1,200 d. 3,258 and 3,285

e. 186 and 183 f. 7,896 and 7,869

g. 13,256 and 13,256 h. 8,439 and 8,249

i. 1473 and 1478 j. 1,268 and 1,255

4. Which of the following two numbers are larger? Explain why using the words “place value” and

“digit.” The numbers are: 6,105,599 and 6,105,519.

5. Marshall, a student in Math 52, is comparing the two numbers below. He says that that (b) has

more ones so it must be the bigger number. Is he correct? Explain.

a. 6,723,894 b. 6,723,849

6. Mariam, a student in Math 52, is comparing the two numbers below. She says that that the two

numbers have the same values in the first four digits from the left, so they must be equal. Is she

correct? Explain.

a. 6,723,894 b. 6,723,849

7. Brady, a student in Math 52, is comparing the two numbers below. He tells you that (b) is

obviously bigger because it has larger values in all place values except for one. Is he correct?

Explain.

a. 5,432,718 b. 4,789,899


8. Alicia, a student in Math 52, is comparing the two numbers below. She tells you that (b) is

obviously bigger because it has more ‘tens’. Is she correct? Explain.

a. 5,432,718 b. 7,432,798


9. Write in words what you learned from this section.

10. When explaining a result, is it possible to get the correct answer for the wrong reason?


them back to class.

2.3: Equality and Inequality


Greater than

Less than

Equal to

=

Concept questions:

1. If you have two numbers, can you always put one of these symbols ( , , or = ) between them?

2. If you and I each write a 3-digit number, and we each use the same three digits to make the

number, will we have the same number? Explain.

Exercises:

3. Place the correct symbol ( , , or =) between the following numbers:

18 17

a. 72 8,236

b. 2,345 2,343

c. 42,056 42,056

d. 43 + 5 43 + 6

e. 27,438 27,439

f. 4,365 3,456

g. 39 – 5 40 – 6

h. 527 725

i. 593 590 + 3

j. 0.9 0.28

k. 207 27

l. 68 068


4. Marty says that 984 and 894 have the same value because they both have the exact same digits. Is

he correct? Explain.

5. Millie says that 58.0 is the same as 58 because they have exactly the same digits in all place

values. Is she correct? Explain.

6. Igor says that 59 is smaller than 59.0 because 59.0 has more digits. Is he correct? Explain.

7. Lucy says 40 is larger than 37 + 3 because 40 is bigger than both numbers. Is she correct?

Explain.

8. North said 2965 because 9 “ones” is bigger than 5 “ones.” What would you say to North?

9. Willie said that 0.7 is smaller than 0.43 because 43 is bigger than 7. Is this thinking correct?


10. Which number does point to… larger or smaller?

11. If a number (A) has more tens than another number (B), does that mean BA ? Explain.

12. What part of this section was the most fun for you?


them back to class.

2.4: Sorting Numbers


None

Concept questions:

1. If you have a list of numbers, how do you go about sorting them (putting them in order)? Explain

your process.

2. Consider three numbers: A, B, and C. If you start with A and you find that BA but CA , write

the three numbers in order …

a. From smallest to largest. b. From largest to smallest.

Exercises:

3. Sort the following numbers from smallest to largest.

a. 456 654 564 465 645 546

b. 2,536 2,546 2,563 2,545 2,565

c. 278 276 279 274 277

d. 2,567 2,467 4,657 4,756 4,357

e. 15.38 14.33 1.523 0.1573 154.8


4. Sort the following numbers from largest to smallest.

a. 51.869 51.868 51.876 51.896

b. 511,234 511,247 512,251 511,311

c. 9,313,496 9,313,596 9,312,497

d. 143 147 141 149 142 129 148 140 151

e. 84 9 365 4,301



them back to class.

2.5: Placing Integers on a Number Line


None

Concept questions:

1. With numbers on a number line, which one goes on the right?

Exercises:

2. Place the number in the approximate position on the number line.

a. 20, 40, 60, 80, 90, 33, 85, 10, 37

b. 30, 60, 90, 50, 15, 75, 95, 23

c. 50, 60, 70, 80, 90, 63, 78, 98, 55, 71

3. On a number line, Peeta labelled the following. Does it make sense? Explain.

0 100

0 100

18 29 65


4. On a number line, Katniss labelled the following. Does it make sense? Explain.

5. On a number line, Gale labelled the following. Does it make sense? Explain.


6. Which is a bigger mistake:

a. Writing the number 50 in a space on the number line that should have been 48 or 49.

b. Writing the number 50 in a space on the number line that should have been 20 or 21.

7. Which is a bigger mistake:

a. Writing the number 60 in a space on the number line that should have been 48 or 49 and

10 in a space that should have been 20.

b. Writing the number 60 and the number 10 on the number line so that 10 is greater than 60.


them back to class.

2.6: Rounding


Round

Conventional Rounding

Rounding Up

Rounding Down

Concept questions:

1. What determines whether we round a number up or down?

2. Is there ever a time when rounding up or down to the nearest ten would be off by the same

amount? Give an example.

3. Is there ever a time when rounding up or down to the nearest hundred would be off by the same


4. Is there ever a time when rounding up or down to the nearest one would be off by the same


0 100

42 39 65

0 200

22 49 65


5. Is there ever a time when rounding up or down to the nearest thousand would be off by the same


6. When rounding 37 to the nearest ten, why do we answer with 40?

7. When rounding 342 to the nearest hundred, why do we answer with 300?

8. Can we round 342 to the nearest thousand? Explain.

9. Can we round 342 to the nearest ten-thousand? Explain.

Exercises:

10. Round the following numbers to the nearest tens:

a. 327

b. 544

c. 275

d. 397

e. 4

f. 203

11. Round the following to the nearest hundreds:

a. 352

b. 946

c. 49

d. 2,461

e. 5,725

f. 9,350

g. 963

h. 234,567

i. 8

j. 621,549.9

12. Round 43 to the nearest:

a. tens b. hundreds c. thousands

13. Round 6,487 to the nearest:

a. tens

b. hundreds

c. thousands

d. ten thousands

e. hundred thousands

f. millions

14. Johanna rounds a number to the nearest hundred and ends with 800. Which of these numbers are

possibilities for the original (not yet rounded) number? There could be many correct options.

a. 795

b. 856

c. 733

d. 821

e. 750

f. 766



15. Desi claims that when rounding 75 to the nearest ten, both 70 and 80 would be correct answers. Is

she correct? Explain.

16. Yanni claims that when rounding 6,394 to the nearest thousand, both 6,000 and 7,000 would be

correct answers. Is he correct? Explain.

17. Isabel says that she can’t round 75 to the nearest thousand because there aren’t any. Is she correct

– why or why not?

18. Maryann rounds 493.826 to the nearest tenth and gets 490. Determine and explain her error.


them back to class.

2.7: Decimals


Integers Positive Integers

Density Property of Rational Numbers

Concept questions:

1. Which is larger – tenths or hundredths?

2. Which is larger – thousands or hundreds?

3. Which is larger – hundred millions or billions?

Exercises:

4. Write the value of the lollowing numbers: [Example: 0.045 is written 45 thousandths]

a. 0.43

b. 0.043

c. 0.0043

d. 0.521

e. 0.0521

f. 0.00521

g. 0.000521

h. 0.6475

i. 2.3

j. 23.61

k. 325.5

l. 8.8

m. 50.05

n. 4,000.0004

5. Round 45.7029824 to the nearest…

a. Tenth

b. Hundredth

c. Thousand

d. Ten thousandth

e. Hundred thousand

f. Millionth

6. Finish labeling the number line.

a.

b.

0 1 0.7

0 0.1


c.

d.

e.

7. You are going to be given two numbers. Determine the larger number.

Numbers Larger

a. 4.2 and 0.42

b. 0.0735 and 0.739

c. 8.10 and 8.01

d. 10.79 and 11.17

e. 2.81 and 2.8

f. 1037 and 103.7

g. 100.3 and 1,000.5

h. 0.049 and 0.052

i. 56.4 and 56.04


a. 3.25 32.5

b. 5.7 5.07

c. 0.345 0.354

d. 2.96384 2.96384

e. 10 – 1 10 – 0.8

f. 7.5002 7.0502

g. 25,678 25.678

h. 53.200 53,200

i. 463 466 – 32

j. 2.73 2.730

k. 1.38 1.38

0 0.01

0 0.001

0 1


9. Write a number between the two numbers given:

a. 0 and 0.1

b. 0 and the answer from part (a).

c. 0 and the answer from part (b).

d. How many numbers are there between 0and 0.1?

e. What property does this problem demonstrate?

10. Use the thinking you have developed on the size of numbers to put these positive numbers in

order from smallest to largest:

a. 6.7 9.2 8.3 1.095

b. 111 2.35 6.894 3 3.5

c. 21.1 23.7 18.5 18.45 19.74

d. 0.342 0.432 0.324 0.423 0.234

e. 345,924 345,942 345,492 345,429

11. Determine if the two numbers have the same value or different value.

Numbers Same or Different?

a. 85 850 Same Different

b. 94.0 094 Same Different

c. 17 1.7 Same Different

d. 0.17 0.017 Same Different

e. 0.44 0.440 Same Different

f. 0.44 .44 Same Different

g. 10.37 1.37 Same Different

h. 26.8 26.80 Same Different

i. 26.8 026.800 Same Different

j. 268.1 26.81 Same Different

k. 26.081 26.81 Same Different

l. 00856 0.0856 Same Different

m. 0.391 .391 Same Different


12. Are decimal numbers similar to whole numbers when sorting? Explain.



them back to class.

2.8: Placing decimals on a number line


None

Concept questions:

1. Are there similarities between putting positive integers on a number line and positive decimal

numbers?

2. Josie is putting 0.75 on a number line from 0 to 1, and Anne is putting 75 on a number line from 0

to 100. When they are done, should the locations be similar or not? Explain.

Exercises:

3. Place the number in the approximate position on the number line:

0.50, 0.25, 0.75, 0.42, 0.91, 0.02, 0.33


50, 25, 75, 42, 91, 2, 33


2.7, 4.3, 8.5, 9.2, 0.7, 1.3, 7.1


6. Which would be further to the left on a number line: 0.47 or 47?

7. Which would be further to the left on a number line: 0.47 or 4.7?

8. Which would be further to the left on a number line: 0.47 or 0.047?


them back to class.

0 1

0 100

0 10


2.9: Negative Integers


Negative Integers

Concept questions:

1. Which number is larger: 10 or 20?

2. Which number is larger: – 10 or – 20?

3. Based on the previous questions, if you knew that BA , does that mean BA ? Why or

why not?

Exercises:

4. Given the endpoints, finish labeling the number line.

a.

b.

c.

d.

5. Fill in the table by determining the larger number for each pair.

Numbers Larger

a. – 3 and –9

b. –11.2 and –112

c. – 43 and –34

d. –187 and –192

e. –2,534 and –3,256

f. –537 and 20

g. – 7.49 and –2.36

h. – 44 and –55

–120 –110

–200 –100

–115 –114

– 4.3 – 4.2



a. – 301 – 300

b. – 559 – 595

c. – 2.6 – 2.3

d. – 5,392 – 5,932

e. – 73 – 78

f. – 2.98 – 2.45

g. 596 634

h. – 596 – 634

7. Approximate the value of the number between 0 and 1 given by the letter.

a. P

b. Q

c. R

d. S

e. T

f. U

8. Approximate the value of the number between – 1 and 0 given by the letter.

a. C

b. D

c. E

d. F

e. G

f. H

9. Find three numbers between 0.5 and 0.7.

10. Find four numbers between – 0.7 and – 0.8.


11. How many integers are between 6 and 10?

12. How many integers are between – 5 and 2?

13. How many integers are between 0.8 and 2.73?

14. How many numbers (not just integers) are between 0.8 and 2.73?

15. How many numbers (not just integers) are between – 0.7 and – 0.8?


them back to class.

0 1 P Q U T S R

0 D G F E C H – 1


2.10: Perfect Squares


Perfect Squares

Concept questions:

1. What button on your calculator will create perfect squares?

Exercises:

2. Find the square for the following numbers.

Number 15 16 17 18 19 20 21 22 23 24

Square

3. Look at the numbers you wrote in. Find a pattern with these squares and explain the pattern.

4. For decimal answers, round to the nearest hundredth if necessary.

Number 31 2.1 3.1 0.3 – 5 0.8 0.75 0.43

Square

5. Is there a similarity between the square of 21 and 2.1? Explain.


6. Which number has the bigger square, 0.5 or 0.21? Why do you think that is?


them back to class.

2.11: Square Roots


Square root


Concept questions:

1. Are there two answers for 81 or just one? Explain why.

2. Marvin said that his teacher told him 636 , so there are two answers. What would you tell

Marvin?

3. Explain what 67 means in words (do not calculate a value for this).

Exercises:

4. Find the value of the following.

a. 25

b. 49

c. 1

d. 16

e. 729

f. 024,1

g. 809,2

h. 084,6

5. Put the following numbers in order from smallest to largest:

3 ,12 ,1.5 ,10 ,17 ,5 ,4 ,25

6. Put the following numbers in order from smallest to largest. Write in form. You should be

able to do this without using your calculator.

40 ,50 ,14 ,65 ,82 ,15 ,37

7. Estimate the size of the following square roots – find the whole number above and below each.

Work to not use your calculator!

a. 53

b. 89

c. 21

d. 72

e. 40

f. 33


8. Larry said 416 because 1642 . Is Larry correct?


them back to class.


2.12: Approximating Square Roots


None

Concept questions:

1. Explain how to estimate which whole numbers 42 is between without using a calculator.

Exercises:

2. Approximate the following square roots out to 6 decimal places using the calculator. Then,

with the decimal representation on screen, use the calculator to convert it to a fraction.

Square Root Decimal Approximation Fraction Representation (if possible)

87

532

280,5

17.0569

000049.0

8394.1

243

27

361

256


3. Are you able to find integers above and below a square root like 77 ? Explain how to do this to

a student in Math 52.


them back to class.


2.13: Number Line Connections


None

Concept questions:

1. Martin says – 80 is larger than 70 because 80 is bigger than 70. Is Martin correct? Explain.

2. Lisa says – 50 is bigger than – 30 because 50 is bigger than 30. Is Lisa correct? Explain.

3. Pedro says that – 50 is smaller than – 30 because – 50 is further to the left on the number line. Is

Pedro correct? Explain.

Exercises:




7. Fill in the table by determining the larger and smaller number for each pair.

Numbers Larger

a. 48 and 6.4

b. 31 and 37

c. 0.34 and 3

1

d. – 0.34 and – 3

1

e. – 65 and 0.048

f. 31 and 37

–20 30

–2 28

–2.4 2.6


8. Place the number in the approximate position on the number line (9.6 is shown):

9.6, 31 , 85 , 6.0, – 5.5, 5

13, – 0.7, 58

9. Use the thinking you have developed on the size of numbers to put these numbers in order from

smallest to largest (without using a calculator):

a. 5

25 24 6 37 5.8

b. 21 – 3.98 – 4 – 5.4 12



them back to class.

2.14: Unit Review and Test Prep

Vocabulary and symbols: All the terms and new symbols from each unit; you should have a working

knowledge of each term (knowing what it means and how to use it). These are jumbled up and not in

any order.

Digits

Place Value

Decimal Point

Value

Larger (of two numbers)

Equal

Greater than

Less than

Equal to

=

Round

Conventional Rounding

Rounding Up

Rounding Down

Integers

Positive Integers

Density Property of Rational Numbers

Negative Integers

Square root

Perfect Squares

Concept questions:

1. Thinking about place value, does the digit 0 mean “nothing”? Explain why or why not.

9.6

– 10 10


2. Consider three numbers: A, B, and C. If you start with A and you find that BA and CA , do

we know the order of the three numbers or do we need more information? Explain.

3. When rounding 96 to the nearest ten, why do we answer with 100?

Exercises:

4. Fill in the digit that is in the given place values for 89,654.23

a. Tens

b. Thousands

c. Ones

d. Hundred Thousands

e. Tenths

f. Hundreds

g. Ten Thousands

h. Millions

5. What is the place value of the “9” in…

a. 384.91

b. 4,103.7192

c. 497,102,980

d. 96.2034

e. 93,071.42

f. 4,900,000,000.01

6. Marty says that 984 and 894 have the same value because they both have the exact same digits. Is

he correct? Explain.

7. Look at the two numbers and determine if they have the same value or different values.

Numbers Comparison Numbers Comparison

a. 87 and 870 Same Different b. 79.0 and 07.90 Same Different

c. 1.9 and 19 Same Different d. 1.00 and 1.0 Same Different

e. 7.5 and 7.05 Same Different f. 13 and 013.0 Same Different

8. Based on their size, determine the larger number.

Numbers Larger Numbers Larger

a. 894 and 948 b. 2,314 and 2,341

c. 1,394 and 17 d. 6.9 and 6.09

e. – 48 and – 15 f. – 6.9 and – 6.09

g. – 0.24 and –

4

1

h. 71 and 87

i. – 35 and 0.048 j. – 0.235 and – 0.48

9. Marshall Mathers say that 23,417 is larger than 24,106 because the first number has more

hundreds, tens, and ones. Explain if he is correct or not.


10. Hannah Montana is comparing 56,384 and 57,190. She says that 57,190 is bigger because there

are more tens. Explain if she is correct or not.


a. 18 17

b. 72 8,236

c. 2,341 2,343

d. 42,056 42.056

e. 44 + 5 43 + 6

f. 1.375 1.381

g. 0.0038 0.00049

h. – 51 – 29

12. Consider three numbers: A, B, and C. If you start with A and you find that BA and CA , do

we know the order of the three numbers or do we need more information? Explain.

13. Round 9,837.261 to the nearest:

a. tens

b. hundreds

c. thousands

d. tenths

e. hundredths

f. millions

14. If a number (A) has more hundreds than another number (B), does that mean BA ? Explain.

15. (a) What is the square of 64? (b) What is the square root of 64?

16. Find the value of the following.

a. 36

b. 49

c. 481,3

d. 169,56

17. Put the following numbers in order from smallest to largest:

8

78 ,89.0 ,98 ,9 ,5.8 ,85


18. Approximate the following square roots out to 6 decimal places using the calculator. Then,

with the decimal representation on screen, use the calculator to convert it to a fraction.

Square Root Decimal Approximation

Fraction Representation

(if possible)

a. 817

b. 53

c. 000016.0

d.

369,1

561,6


20. Explain how you are able to find integers above and below a square root like 57 ? Explain how

to do this to a student in Math 52.


21. What was the most interesting part of this unit for you?

22. What concepts in this unit were the most challenging for you?

23. Do you have any additional questions?

–40 10

Documents

Math Fundamentals for Statistics I (Math 52) Homework Unit ... · Is there ever a time when rounding up or down to the nearest thousand would be off by the same amount? Give an example