Mathematics for Teachers: An Interactive Approach for Grade K-8

Thomas Sonnabend

Chapter 3 Whole Numbers - all with Video Answers

Educators

Section 1

Numeration Systems

Problem 1

Write the following Egyptian numerals as HinduArabic numerals.
NUMERALS CANT COPY

Check back soon!

Problem 2

Write the following Egyptian numerals as HinduArabic numerals.
NUMERALS CANT COPY

Check back soon!

Problem 3

(a) Do both of the following Egyptian numerals represent the same number?
NUMERALS CANT COPY
(b) What difference between Egyptian and HinduArabic numerals is suggested by part (a)?

Check back soon!

Problem 4

Write the following Babylonian numerals as HinduArabic numerals.
NUMERALS CANT COPY

Check back soon!

Problem 5

Write 324 as
(a) an early Egyptian numeral.
(b) a late Egyptian numeral.
(c) a Babylonian numeral.

Check back soon!

Problem 6

Write 92 as
(a) an early Egyptian numeral.
(b) a late Egyptian numeral.
(c) a Babylonian numeral.

Check back soon!

Problem 7

Write each Mayan numeral as a base-ten numeral.
NUMERALS CANT COPY

Check back soon!

01:34

Problem 8

Write each base-ten numeral as a Mayan numeral.
(a) 14
(b) 27
(c) 60

Naomi Motes

Numerade Educator

04:31

Problem 9

What are three important characteristics of our base-ten numeration system?

Nick Johnson

Numerade Educator

00:38

Problem 10

Name three places where you might find Roman numerals.

Tiffany Tran

Numerade Educator

Problem 11

Give the Hindu-Arabic numeral for the following.
(a) XIV
(b) $\mathrm{XL}$
(c) MDCXIII
(d) MCMLXIV

Check back soon!

Problem 12

Write a Roman numeral for the following.
(a) 4
(b) 24
(c) 1998

Check back soon!

Problem 13

How many symbols would be needed to write 642 using each of the following?
(a) Tallies
(b) Early Egyptian numerals
(c) Roman numerals

Check back soon!

03:24

Problem 14

What was an advantage of the Babylonian system over the early Egyptian system?

Prabhakar Kumar

Numerade Educator

02:32

Problem 15

Write the following base-ten numbers using expanded notation.
(a) 407
(b) 3,125

Karly Williams

Numerade Educator

01:30

Problem 16

A base-ten numeral has the digits $\underline{A} \underline{A}$. The value of the $\mathrm{A}$ at the far left is $\qquad$ times the value of the A at the far right.

Noraney Ocampo

Numerade Educator

00:10

Problem 17

A base-ten numeral has the digits $\underline{A} \underline{B} \underline{C} \underline{D}$. Write this numeral using expanded notation.

Brandon Fox

Numerade Educator

00:36

Problem 18

Rewrite each of the following as a base-ten numeral.
(a) $\left(8 \times 10^3\right)+(6 \times 10)+2$
(b) $\left(2 \times 10^4\right)+\left(3 \times 10^3\right)+\left(4 \times 10^2\right)+5$

Brandon Fox

Numerade Educator

00:40

Problem 19

What number is represented in each part?
(a)
FIGURE CANT COPY
(b) 2 flats and 7 units

Ramzi Deek

Numerade Educator

01:44

Problem 20

How would you represent 380 using base-ten blocks?

Naomi Motes

Numerade Educator

Chip trading is a common place-value model that uses colored chips and a mat. In base ten, the columns on the mat represent powers of ten. For example, 4523 is represented by 4 red, 5 green, 2 blue, and 3 yellow chips.
$$
\begin{array}{c|c|c|c}
\hline \text { Red } & \text { Green } & \text { Blue } & \text { Yellow } \\
\hline 4 & 5 & 2 & 3 \\
\hline
\end{array}
$$
(a) How would you represent 372 ?
(b) Ten blue chips can be traded in for one _______ chip.
(c) Which is more abstract, chip trading or base-ten blocks? Explain why.

Check back soon!

Problem 22

What number is represented in the following picture?
FIGURE CANT COPY

Check back soon!

00:58

Problem 23

One way to represent 127 is with 12 tens and 7 ones. List three other ways.

Dading Chen

Numerade Educator

00:58

Problem 24

I have 7 base-ten blocks. Some are longs and some are units. Their value is an even number between 40 and 60 . What blocks do I have?

Dading Chen

Numerade Educator

View

Problem 25

A second grader writes "two hundred and ten" as 20010.
(a) How might this student write "three hundred and seven"?
(b) What does the student understand about place value?
(c) Give an explanation that will help the student understand why the correct notation is 210 .

Nick Johnson

Numerade Educator

00:58

Problem 26

A second grader knows that 34 is 3 tens and 4 ones. Then you ask, "How else could you represent 34? For example, it would be 2 tens and ______ ones." The student cannot answer this question. What hint would you give the student?

Dading Chen

Numerade Educator

00:39

Problem 27

Tell whether the number in each part is a count or a measure.
(a) 42 yards
(b) 42 pens
(c) 42 minutes

Ronald Prasad

Numerade Educator

Problem 28

Tell whether the number in each part is a count or a measure.
(a) 7 cats
(b) 7 days
(c) 7 meters

Check back soon!

View

Problem 29

Is money a counting unit or a unit of measure? Consider whether the definition of a unit of measure in the text would apply to 25 dollars and to 25 cents.

James Kiss

Numerade Educator

01:51

Problem 30

How can you distinguish between counting units and units of measure?

Bailey Latka

Numerade Educator

01:15

Problem 31

Round each of the following numbers to the nearest hundred.*
(a) $$\$ 625$$, the price of lunch for two at La Vielle Chaussure
(b) $$\$ 36,412$$, the one-game salary of a superstar athlete

Naomi Motes

Numerade Educator

03:43

Problem 32

According to the 2000 U.S. Census, the population of Cleveland was 478,403 . Round this number to the nearest hundred thousand.*

Charles Carter

Numerade Educator

00:58

Problem 33

Give the place to which each number has been rounded.
$$
\begin{array}{lrr}
\hline \text { Original Number } & \text { Rounded Number } \\
\hline \text { (a) } & 418 & 420 \\
\text { (b) } & 418 & 400 \\
\text { (c) } & 368,272 & 370,000 \\
\hline
\end{array}
$$

Breanna Ollech

Numerade Educator

04:02

Problem 34

Match the amount in each part with one of the following estimates.
$$
\begin{aligned}
& \begin{array}{llll}
4 & 40 & 400 & 4,000
\end{array} \\
& 4,000,000 \quad 400,000,000 \\
&
\end{aligned}
$$
(a) Number of students in a typical elementary school
(b) Population of Chicago
(c) Number of miles an adult can walk in an hour
(d) Distance, in miles, from Boston to San Diego
(e) Population of North America

Zachary Warner

Numerade Educator

04:45

Problem 35

You have $$\$ 126$$ in a checking account. The automated cash machine will give you only $$\$ 10$$ bills.
(a) What is the most money you can withdraw?
(b) Does this illustrate rounding up, rounding down, or rounding to the nearest?

Debasish Das

Numerade Educator

02:35

Problem 36

Ballpoint pens come in packs of 10 . You want 23 pens for your class.
(a) How many pens will you order?
(b) Does this illustrate rounding up, rounding down, or rounding to the nearest?

Prabhu Ramji

Numerade Educator

00:37

Problem 37

(a) About 8,000 people attended a baseball game. If this figure has been rounded to the nearest thousand, the actual attendance was between what two numbers?
(b) Tell how you found the answer.

James Kiss

Numerade Educator

08:39

Problem 38

If the quarterback in the following cartoon is right, what is the greatest number of people that could be there watching?
FIGURE CANT COPY

Derek Follett

Numerade Educator

00:24

Problem 39

Write a ten-digit numeral in which the first digit tells the number of zeroes in the numeral, the second digit tells the number of $1 \mathrm{~s}$, the third digit tells the number of $2 \mathrm{~s}$, and so on.

Brandon Fox

Numerade Educator

Problem 40

A number is called a palindrome if it reads the same forward and backward; 33 and 686 are examples. How many palindromes are there between 1 and 1,000 (inclusive)?
(a) Devise a plan and solve the problem.
(b) Make up a similar problem and solve it.

Check back soon!

02:10

Problem 41

If you have a calculator such as the TI-73 with a place-value feature, enter 1234 and find out how the calculator shows the place value of different digits.

Celine Ibrahim

Numerade Educator

02:48

Problem 42

(a) Find out what the first five digits of a zip code tell the post office.
(b) Find out what the first three digits of a Social Security number indicate.

Ankit Gupta

Numerade Educator

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42