Transcript MATH UNIT 1 - TEACHEZ

MATH
UNIT 1
4TH GRADE
PROBLEM SOLVING
Jacob helps at the family flower shop in the summer.
He keeps a record of how many flower bouquets
he sells. How many bouquets did he sell on
Tuesday and Wednesday?
MONDAY
17
TUESDAY
24
WEDNESDAY
26
THURSDAY
35
FRIDAY
43
SATURDAY
48
Use a Bar Diagram
Total: total number of
bouquets he sold on
Tuesday and
Wednesday.
?
24
26
Part Part
24 + 26 = ?
MONDAY
17
TUESDAY
24
WEDNESDAY
26
THURSDAY
35
FRIDAY
43
SATURDAY
48
Emily is saving to buy a sweatshirt from
the college her brother attends. She
has $13. How much more money does
she need to buy the sweatshirt?
$32
$32
Total: Cost of the sweatshirt
_____$32_____
$13
?
32 – 13 = _____
Tickets to a movie on Saturday cost
only $5 each no matter what age you
are. What is the cost of tickets for a
family of three?
Total cost
?
5
5
5
3 X 5 = ____
Twenty-four students traveled in 3 vans
to the zoo. The same number of
students were in each van. How many
students were in each van?
24
24 divided by 3
The race was 5 kilometers. Markers were
at the starting line and the finish line.
Markers showed each kilometer of the
race. Find the number of markers used.
What should your strategy be?
Start Line
1 km
2 km
3 km
4 km
Finish Line
How many ways can you make change
for a quarter using dimes and nickels?
Michael and Madison spent all day
Saturday at the County Fair. Michael
rode 3 rides every half hour and
Madison rode 2 rides every half hour.
How many rides had Madison ridden
after Michael rode 24 rides?
Strategy: Make a chart
The house numbers on Forest Road
change in a planned way. Describe the
pattern. Tell what the next two house
numbers should be.
3
6
10
15
___
___
___
Joshua spent $27, not including tax, on
supplies for his dog. He bought two of
one item and one of another item.
What did he buy?
Leash
$8
Collar
$6
Bowls
$7
Bed
$15
Strategy: Guess and Check
Emma’s new CD player can hold 6
discs at one time. If she has 204
CDs, how many times can the player
be filled without repeating a CD?
204 divided by 6 =
204
n
n
How many different ways can 4 students
shake each other’s hand?
Strategy: Act it out
What is the perimeter of the figure?
Each side of each triangle in the figure is one
centimeter. If there are 12 triangles in a row,
what is the perimeter of the figure shown?
Strategy: Make a table ( function chart )
3
1
4
2
3
4
5
6
7
8
9 10 11 12
Matthew collected some shells, rocks,
and beach glass.
2 rocks
3 Times as many shells
as rocks
12 objects in all
Beach glass
How many of each object are in his
collection?
Olivia was in a jump rope contest. How
did her number of jumps change over
the five days of the contest?
M
80
60
40
20
T
W
T
F
Daniel has band practice at 10:15 a.m. It
takes 20 minutes to get from his
home to practice and 5 minutes to
warm up. What time should he leave
home to get to practice on time?
Strategy: work backward
Writing to Explain
What will happen to the area of a
rectangle if the lengths of its sides are
doubled?
2 inches
______________________________
1 inch
______________________________
______________________________
______________________________
______________________________
______________________________
Writing to Explain
Use blocks to show 13 X 14.
Draw a picture of what you would do
with the blocks.
REVIEW
digit
compare
even
period
odd
number line
A group of three digits
in a number separated
by a comma is a
A ____________ is a
line that shows numbers
in order using a scale.
The number 8 is an
___________ number.
The number 5 is an
__________ number.
Compare each set of numbers using
> greater than < less than = equal to
13
10
7
7
28
29
14
5
43
34
0
1
52
52
13
65
22
33
Tell if the highlighted digit is in the
ones, tens, or hundreds place.
346
17
921
106
33
47
217
320
810
1,006
999
1,405
Writing to Explain
How does using commas to separate
periods help you read very large
numbers?
__ __ __, __ __ __, __ __ __, __ __ __
_________________________________
_________________________________
_________________________________
_________________________________
Representing Numbers
What are some ways to write numbers in the thousands?
Hannah is 4,276 feet above sea level. There are many
different ways to represent 4,276.
How do you read and write numbers in
the thousands?
Standard Form: When writing a number in
standard form you write only the digits.
5,263
Expanded Form: A number in expanded form
is written as the sum of the values of each of
the digits. 5,000 + 200 + 60 + 3
Word Form: Use periods in the place-value
chart to write the number in words.
five thousand, two hundred sixty-three
Writing to Explain
Why is the value of the 5 in 5,784 =
5,000?
Explain: __________________________
Is the expanded form for 6,348 the
same as 6,348?
Explain: __________________________
Write the word form of each.
What is the value of the red digit in
each number?
15,324
135,467
275,206
42,158
63,308
921,382
Write each number in expanded form.
764,513
23,105
219,328
85,124
806,633
75,200
Write each number in standard form.
Can you read this number?
.
Write each number in Standard form.
eighty-three thousand,
nine hundred two
three hundred twentyone thousand, two
hundred fifty-three
twenty-one thousand,
eight hundred
seventeen
three hundred eight
thousand, twenty-nine
four hundred ninetyseven thousand, six
hundred seven
one hundred twentyfive thousand, seven
hundred sixty-three
five thousand, one
hundred forty-five
twenty-three thousand,
three hundred seventy
four hundred three
thousand, eight
hundred sixty-one
Which digit is in the same place in all
three numbers?
What is the place-value position?
574,632
24,376
204,581
Write the number 403,867 in word form.
________________________________
Can you expand it?
_______________________________
What is the largest 4 digit number you
can make?
_____________
What is the smallest 4 digit number?
______________
Write to explain:
__________________________________
The city of Port Orange has 124,763
books in their Library with 3,142 DVDs
in their collection. This year they will
purchase an additional 1,500 books
and 2,000 DVDs. How many books will
the library have after the purchase?
What is the operation?
Set up and solve.
_____ _____ = ______
The Everglades National Park is the
largest national park in Florida. It was
established in 1947. What is this
number in expanded form?
___________
This is the year 2013. How long ago
was the Everglades National Park
established?
____________
The Egyptians created a number system
that used symbols, or hieroglyphs. The
chart shows the symbols and their
equivalent numbers.
Hieroglyphs are drawn with the
greater number in front of the
lesser number. 31
Hieroglyphs can be read from
left to right.
523
If the symbols are stacked,
the greater number is on
the top.
214,413
Write 217 in word
form and using
hieroglyphs.
___________
___________
Write 2,523 in word
form and using
hieroglyphs.
____________
____________
Which number will take less
time to write with
hieroglyphs, 9 or 100?
Explain…
Use hieroglyphs to write the
greatest 5 digit number
possible.
Use hieroglyphs to draw
the number one greater
than 249.
____________
It is believed that the
Egyptian number system
was created around
3000 B.C. Use hieroglyphs
to represent this number.
____________
Roman Numerals is another number
system. How does it compare to the
Egyptian system?
What are some ways to write numbers
in the millions?
Between 2001 through 2005, 356,039,763
fans attended professional baseball
games. Write the expanded form and
word form for 356,039,763.
Draw a place-value chart to help.
Write the number in word form. Then tell
the value of the red digit in each
number.
75,600,295
249,104,330
6,173,253
430,290,100
16,107,320
78,001,432
Write each number in standard form.
300,000,000 + 40,000,000 + 7,000,000 +
300,000 + 10,000 + 6,000 + 20 + 9
900,000,000 + 20,000,000 + 6,000,000 +
20,000 + 4,000 + 10
80,000,000 + 1,000,000 + 600,000 +
20,000 + 900 + 40 + 8
Tell the value of the red digit in each
number. Write each number in word
form.
7,915,878
23,341,552
214,278,216
334,290,652
7,330,968
30,290,447
133,958,840
309,603,114
In 2005, seventy-four million, nine hundred
fifteen thousand, two hundred sixty-eight
fans attended baseball games. Which
choice shows this number in standard
form?
74,015,968
74,905,268
74,900,268
74,915,268
The vault at Fort Knox holds 147,300,000
ounces of gold. Write the number that
is one million more.
Write the expanded form of
123,456,789 and 987,654,321.
Which digit has the same value in
both numbers?
Write the standard form of a 9-digit
number with a 5 in the millions place
and a 9 in the tens place.
___________________
Write a number that is ten million more
than the number you chose.
______________
Write a number that is one million less
than the number you chose.
______________
How can you estimate an unknown
distance?
Mrs. Vale asked her students to estimate
the distance around their classroom.
Is the distance closer to 50 feet, 100
feet, or 150 feet?
When trying to estimate an unknown
distance you should use a distance that
you already know. (benchmark)
You know that when you take a large step
it is about 3 feet.
Using this information you can estimate
any distance.
If it takes you 10 steps to cross the
classroom it would be about _____ feet.
Chris wanted to estimate the number of
seats in a football stadium. Is the total
number of seats in the stadium closer
to 20,000 seats, 60,000 seats or
160,000 seats?
about 5,000 seats
An unsharpened pencil is about 7 inches
long. Use your pencil to estimate the
distance around your desk. Is the
distance closer to 15 inches, 90
inches, or 300 inches?
Is the distance around your book closer
to 12 inches, 50 inches, or 100
inches?
Without using a standard measuring tool,
how can you make an educated
guess? _____________________
What else could you use as a
benchmark? ______________
How big is your thumb?
Can you use this knowledge to help you
estimate the size of objects?
How big is your arm span?
Can this knowledge help you estimate
the length of objects?
How big was the King’s foot?
How do you know?
How do we use this knowledge?
How can the known data help you
estimate how many beans are in the
jar if the jar were full?
Would the jar hold 1,500
or 3,000 or 5,000 beans?
Using data for only part
of the amount is called
a BENCHMARK.
1,000
Think about the jar of beans.
If you fill the jar with marbles to the
same level as 1,000 beans there
would be 200 marbles.
After all, marbles are bigger
than beans so they take
up more space.
Using this data how many
marbles will fill the jar?
The distance between
Orlando and Tampa is
about 85 miles. Is the
distance between
Tampa and Miami
closer to 100 miles,
300 miles, or 500
miles? Explain.
How can you use
the map and the
known distance
between Orlando
and Tampa to
estimate the
distance from
Orlando to Palm
Beach?
A parking garage has six levels. Each
level has spaces for 312 cars. Over
4,000 vehicles are expected for a large
event at the Ocean Center. Will the
parking garage be able to hold over
4,000 vehicles?
Explain your answer.
The picture of the park shows the area
of the park where trees are to be
planted.
About how much of the park will contain
trees?
Hint: The lake is
part of the park.
New park benches will be installed
every 100 yards along the path.
The total length of the walking path
is about 6,000 yards.
What is a good estimate of the number
of benches that the park will have?
The Mote Aquarium in Sarasota, Florida,
has a 135,000 gallon shark tank.
What is the value of the 3 in this
number?
The length of one year on a planet is the
total time for the planet to make one
complete trip around the Sun.
a. How many fewer days does
it take Mercury to circle
the Sun than for Earth
to circle the Sun?
b. About how many more Earth
days is a year on Mars than
a year on Earth?
c. Which planet has a digit 6 with a
value of sixty thousand in the
length of its year?
PLANET
LENGTH OF YEAR
MERCURY
88
VENUS
225
EARTH
365
MARS
687
JUPITER
4,330
SATURN
10,756
URANUS
30,687
NEPTUNE
60,190
Which planet has a year that is about six thousand
Earth days more than Jupiter’s?
a. Which two planets
have a combined year
of about 41,000 days?
b. How many fewer days
does it take Mars to
circle the Sun than
it takes Saturn?
PLANET
LENGTH OF YEAR
MERCURY
88
VENUS
225
EARTH
365
MARS
687
JUPITER
4,330
SATURN
10,756
URANUS
30,687
NEPTUNE
60,190
Which space object listed has
an average surface temperature
closest to Earth’s?
What is the average
surface temperatures
in order from least to
greatest.
SPACE
OBJECT
AVERAGE
TEMPERATURE
MERCURY
332 Degrees F
EARTH
59 Degrees F
MOON
0 Degrees F
VENUS
867 Degrees F
Abigail’s favorite
planet has at least
5 letters in its
name. The length of
its year is less than
10,000 Earth days.
List all the planets
that fit these clues.
PLANET
LENGTH OF YEAR
MERCURY
88
VENUS
225
EARTH
365
MARS
687
JUPITER
4,330
SATURN
10,756
URANUS
30,687
NEPTUNE
60,190
Interpret the value of a given digit
in a number. (Be careful – we are not talking about
place value. We are asking the actual value of each digit)
264,901,835
How many millions? _______
How many thousands? ___________
How many hundreds? ____________
How many tens? ________________
How many ones? ________________
How can you compare numbers?
Africa and Asia are the two largest
continents on Earth. The land area of
Africa is 11,608,000 square miles. The
land area of Asia is 17,212,000 square
miles.
Which continent is larger?
1 1, 6 0 8, 0 0 0
1 7, 2 1 2, 0 0 0
Compare each digit place by place.
How can you order numbers?
The area of 3 continents on Earth are
shown in the table. Write the areas in
order from least to greatest.
Continent
Area
Europe
4,010,000
N. America
9,450,000
S. America
6,890,000
Plot numbers on a number line.
4,000,000
6,000,000
8,000,000
10,000,000
Continent
Area
Europe
4,010,000
N. America
9,450,000
S. America
6,890,000
Write
< , = , or >
to compare numbers.
12,643
12,801
6,519
6,582
111,785
111,731
6,793
6,699
3,107,502
80,371
3,170,501
80,731
2,906,793
15,048
2,906,793
16,408
Order these numbers from greatest to least.
105,232,463
105,232,482
105,232,947
_____________________________
Which place did you have to look at to
order these numbers?
Compare numbers using the symbols
> < < = =
34,896 ____ 43,897
132,489 ____ 132,498
4,937 ____ 4,936
8,965,376 ____ 865,376
3,001 ____ 3,010
901,267 ____ 910,627
Writing
<, >,
or
= to compare numbers.
221,495
210,388
52,744
56,704
138,752
133,122
4,937
4,939
22,873
22,774
1,912,706
1,913,898
412,632
412,362
99,999,999
9,990,999
Order the numbers on the number line.
26,000
27,505
26,905
26,950
27,000
28,000
Order the numbers on the number line.
3,422,000
3,422,100
3,422,700
3,422,000
3,422,500
3,423,000
Order the numbers on the number line.
7,500
7,502
7,622
7,523
7,852
7,600
7,700
7,800
7,900
Order the numbers on the number line.
3,000
3,030
3,033
3,003
3,050
Write the numbers in order from
least to greatest.
57,535
576,945
506,495
18,764
18,761
25,988
25,978
25,998
877,837
37,838
878,393
43,783
434,282
64,382
723,433
72,324
72,432
58,028
85,843
77,893
274,849,551 283,940,039
13,490
230,485,903
Andrew added 57 and 20 and said the
answer is greater than 100.
Is Andrew correct?
Could you use only the millions period
to order 462,409,524 - 463,409,524
and 463,562,391?
Write three numbers that are greater
than 780,000 but less than 781,000.
___________________
Order the numbers 7,463 - 74,633 and
74,366 from greatest to least.
_________________________
In 2003, the heaviest snake living in
captivity was a Burmese python named
Baby. Baby weighed in at 403 pounds.
An average Anaconda snake
weighs 330 pounds. Which snake
weighs more?
Which list of numbers is in order from
least to greatest?
1,534
1,576
1,563
18,732
18,723
18,765
234,568
234,563
234,323
383,847
383,848
383,849
Which is in order form greatest to least?
Which child has saved the most
baseball cards?
Isabella
3,424
Ethan
2,354
Samantha
3,443
Joesph
2,932
How much greater is the land area of
China than Japan?
Country
Land Area
Japan
377,835
China
9,600,000
The Atlantic Ocean has an area of
33,420,000 square miles. This area is
between which sets of numbers?
33,400,000
33,040,000
33,400,000
33,440,000
33,100,000
33,419,000
33,430,000
33,500,000
How can you round numbers?
Round 293,655,404 to the nearest
thousand and to the nearest
hundred thousands. Use place value to
round numbers.
If the digit to the right of the rounding place is 5 or more,
add 1 to the rounding digit.
If it is less than 5, leave the rounding digit alone.
2 9 3, 6 5 5, 4 0 4
Round each number to the place of the
highlighted digit.
128,955
85,639
9,924
1,194,542
160,656
149,590
In 2008, the population of the United
States was 304,691,952.
Round 304,691,952 to the nearest
hundred thousand.
Round each number to the place of the
underlined digit.
493,295
39,230
77,292
453,280
75,254
54,846
21,679
55,560
17,909
9,049
6,668,365
3,417,547
9,511
123,900
1,666,821
9,000,985
149,999
73,065
For each zoo in the chart, round the
attendance to the nearest hundred
thousand.
Which zoo had the greatest number of
visitors?
Nashville Zoo
546,429
Philadelphia Zoo
1,244,000
Oregon Zoo
1,503,565
Brevard Zoo
328,973
Elizabeth read that about 1,760,000 people
will graduate from high school in the
next four years. She thinks this
number is rounded to the nearest ten
thousand. What would the number be
if it were rounded to the nearest
hundred thousand?
Ashley has attended class every day
since she started school as a
kindergartener. She said she has been
in school for about 1,000 days. What
could the actual number of school
days be if she is in 4th grade and the
number is rounded to the nearest ten?
When rounded to the nearest ten
thousand, which number would be
rounded to 120,000?
123,900
128,770
130,000
124,480
A fruit market sold 3,849 apples,
3,498 oranges, and 3,894 pears in
one month. Which of these numbers is
the greatest?
How can you estimate sums and
differences?
The Empire State Building was
completed in 1931. From ground to tip,
it measured 1,250 feet. At the top of
the building is an antenna and
lightning rod that measures 204 feet.
Estimate the total height of the
structure.
When estimating you usually round the
number in order to add or subtract
easily.
The Washington Monument was
completed in 1884. About how many
years after was the Empire State
Building completed?
1931
1884
Estimate each sum or difference.
563
+ 375
288
- 171
645
+ 253
262
- 132
The Statue of Liberty was completed
in 1886. About how many years later
was the Empire State Building
completed than the Statue of Liberty?
1886 - 1931
William bought a board game for $24,
a key ring for $3, and a book for $8.
How much money did he spend?
Challenge: If he gives the cashier two $20 bills
how much change will he receive?
This year, 35,658 people ran in a
marathon. Last year, 8,683 fewer
people ran in the marathon. About how
many people ran last year?
Anthony sold 86 tickets to the school’s
talent show on Thursday and 103
tickets on Friday. About how many
tickets to the talent show did he sell
in all?
Alexis was born in the year 2004.
One of her older sisters was born in
1992. Rounding to the nearest ten,
about how many years younger
is Alexis?
During swimming practice, David swam
15 laps and Sarah swam 9 laps.
How many more laps did David
swim than Sarah?
Sophia read 235 pages of a book. She
had 192 more pages to read before
she was done. How many total pages
were there in the book?
?
235
192
PROBLEM SOLVING strategy: DRAW A PICTURE
The mass of a human brain is how much greater
than the mass of a chimp brain?
Cat
30 grams
Chimp
420 grams
Human
1,350 grams
Dolphin
1,500 grams
Draw a picture and write an equation to solve.
1,350
420
Four cities are on the same road that
runs east to west. Fleming is west of
Bridgewater, but east of Clinton. Union
is between Fleming and Bridgewater. It
is 21 miles from Fleming to Union. It
is 55 miles from Clinton to Union. How
far is it from Clinton to Fleming?
W
E
There are about 200 more species of
animals in the Minnesota Zoo than in
the Phoenix Zoo. About how many
species of animals are in the
Minnesota Zoo? About how many at
the Miami Metro Zoo?
ZOO
Number of Species
Phoenix
200
Minnesota
Miami Metro
Indianapolis
360
Total Species
2,260
A parking lot had a total of 243 cars
in one day. By 6:00 a.m. there were
67 cars in the lot. In the next hour,
13 more cars joined these.
How many more cars would park
in the lot by the end of the day?
The American Kennel Club lists 17
breeds of herding dogs and 26 breeds
of terriers. Find the total number of
breeds of herding dogs and terriers.
In one week Alexandra earned $36 from
her babysitting job. She got $15 more
for doing her chores. How much
money did she earn that week?
?
FLORIDA TEST
CHAPTER 1