math unit 1 4 th grade. problem solving jacob helps at the family flower shop in the summer. he...
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MATHUNIT 1
4TH GRADE
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PROBLEM SOLVINGJacob 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
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Use a Bar Diagram
Total: total number of bouquets he sold on
Tuesday and Wednesday.
?
Part Part
24 + 26 = ?
MONDAY 17
TUESDAY 24
WEDNESDAY 26
THURSDAY 35
FRIDAY 43
SATURDAY 48
24 26
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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?
Total: Cost of the sweatshirt
_____$32_____
32 – 13 = _____
$32$32
$13 ?
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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 ?
3 X 5 = ____
5 5 5
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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
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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
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How many ways can you make change for a quarter using dimes and nickels?
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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
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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 ___ ___ ___
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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?
Strategy: Guess and Check
Leash $8
Collar $6
Bowls $7
Bed $15
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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
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How many different ways can 4 students shake each other’s hand?
Strategy: Act it out
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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 4
1 2 3 4 5 6 7 8 9 10 11 12
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Matthew collected some shells, rocks, and beach glass.
How many of each object are in his collection?
2 rocks
3 Times as many shells as rocks
12 objects in all
Beach glass
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Olivia was in a jump rope contest. How
did her number of jumps change over the five days of the contest?
M T W T F
80
60
40
20
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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
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Writing to Explain
What will happen to the area of a rectangle if the lengths of its sides are
doubled? 2 inches
1 inch
______________________________
______________________________
______________________________
______________________________
______________________________
______________________________
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Writing to Explain
Use blocks to show 13 X 14.
Draw a picture of what you would do with the blocks.
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REVIEWdigit 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.
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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
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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
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Writing to Explain
How does using commas to separate periods help you read very large
numbers?
__ __ __, __ __ __, __ __ __, __ __ __
_________________________________
_________________________________
_________________________________
_________________________________
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Representing NumbersWhat 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.
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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
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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: __________________________
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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
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Write each number in expanded form.
764,513 23,105 219,328
85,124 806,633 75,200
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Write each number in standard form.
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Can you read this number?
.
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Write each number in Standard form.eighty-three thousand,
nine hundred twothree hundred twenty-
one thousand, two hundred fifty-three
twenty-one thousand, eight hundred
seventeen
three hundred eight thousand, twenty-nine
four hundred ninety-seven thousand, six
hundred seven
one hundred twenty-five 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
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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? _______________________________
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What is the largest 4 digit number you can make?
_____________
What is the smallest 4 digit number?
______________
Write to explain: __________________________________
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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.
_____ _____ = ______
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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?
____________
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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
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Write 217 in word form and using
hieroglyphs.
___________
___________
Write 2,523 in word form and using
hieroglyphs.
____________
____________
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Which number will take less time to write with
hieroglyphs, 9 or 100?
Explain…
Use hieroglyphs to write the greatest 5 digit number
possible.
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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.
____________
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Roman Numerals is another number system. How does it compare to the
Egyptian system?
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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.
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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
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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
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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
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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
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The vault at Fort Knox holds 147,300,000 ounces of gold. Write the number that
is one million more.
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Write the expanded form of
123,456,789 and 987,654,321.
Which digit has the same value in
both numbers?
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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.
______________
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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?
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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.
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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
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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?
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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? ______________
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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?
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How big was the King’s foot?
How do you know?
How do we use this knowledge?
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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
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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?
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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.
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How can you use the map and the known distance
between Orlando and Tampa to estimate the
distance from Orlando to Palm
Beach?
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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.
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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 ispart of the park.
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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?
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The Mote Aquarium in Sarasota, Florida,
has a 135,000 gallon shark tank.
What is the value of the 3 in this number?
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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
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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
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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
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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
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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)
264,901,835How many millions? _______
How many thousands? ___________
How many hundreds? ____________
How many tens? ________________
How many ones? ________________
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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.
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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
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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
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Write < , = , or > to compare numbers.
12,643 12,801 6,519 6,582
111,785 111,731 6,793 6,699
3,107,502 3,170,501 2,906,793 2,906,793
80,371 80,731 15,048 16,408
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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?
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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
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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
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Order the numbers on the number line.
26,000 27,000 28,000
27,505
26,905
26,950
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Order the numbers on the number line.
3,422,000 3,422,500 3,423,000
3,422,100
3,422,700
3,422,000
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Order the numbers on the number line.
7,500 7,600 7,700 7,800 7,900
7,502
7,622
7,523
7,852
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Order the numbers on the number line.
3,000 3,050
3,030
3,033
3,003
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Write the numbers in order from least to greatest.
57,535 576,945 506,495 18,764 18,761 13,490
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 77,893 274,849,551 283,940,039 230,485,903
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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?
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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.
_________________________
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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?
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Which list of numbers is in order from
least to greatest?
Which is in order form greatest to least?
1,534 1,576 1,563
18,732 18,723 18,765
234,568 234,563 234,323
383,847 383,848 383,849
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Which child has saved the most
baseball cards?
Isabella
3,424
Ethan
2,354
Samantha
3,443
Joesph
2,932
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How much greater is the land area of China than Japan?
Country Land Area
Japan 377,835
China 9,600,000
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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
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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
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Round each number to the place of the highlighted digit.
128,955 85,639
9,924 1,194,542
160,656 149,590
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In 2008, the population of the United
States was 304,691,952.
Round 304,691,952 to the nearest
hundred thousand.
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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
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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
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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?
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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?
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When rounded to the nearest ten thousand, which number would be
rounded to 120,000?
123,900
128,770
130,000
124,480
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A fruit market sold 3,849 apples,
3,498 oranges, and 3,894 pears in
one month. Which of these numbers is
the greatest?
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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.
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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
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Estimate each sum or difference.
563
+ 375
288
- 171
645
+ 253
262
- 132
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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
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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?
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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?
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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?
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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?
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During swimming practice, David swam
15 laps and Sarah swam 9 laps.
How many more laps did David
swim than Sarah?
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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
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PROBLEM SOLVING strategy: DRAW A PICTURE
The mass of a human brain is how much greater than the mass of a chimp brain?
Draw a picture and write an equation to solve.
1,350
Cat 30 grams
Chimp 420 grams
Human 1,350 grams
Dolphin 1,500 grams
420
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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
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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
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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?
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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.
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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?
?
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FLORIDA TEST
CHAPTER 1