MATH UNIT 1 4 TH GRADE PROBLEM SOLVING

MATH UNIT 1 4 TH 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 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 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 + 40, 000 + 7, 000 + 300, 000 + 10, 000 + 6, 000 + 20 + 9 900, 000 + 20, 000 + 6, 000 + 20, 000 + 4, 000 + 10 80, 000 + 1, 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 6, 000 8, 000 10, 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 9, 990, 999

Order the numbers on the number line. 26, 000 27, 505 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, 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 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, 100, 000 33, 040, 000 33, 419, 000 33, 430, 000 33, 500, 000

How can you round numbers? Round 293, 655, 404 to the nearest thousand 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 4 th 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 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?