Grade 4 Practice Problems: Numbers
Examples from Standards Revision and GLEs
4N-29) Answers vary
Place any of the four operation signs between the nine figures so that they equal 100. 1 2 3 4 5 6 7 8 9 = 100 Write to help explain your best thinking using words, numbers, or pictures.
4N-28) Answer: 9 people
The city bus left the terminal and picked up 5 people at the first stop. At the second stop, 2 people got off and 4 people got on. At the third stop, 3 people got off and 5 got on. How many passengers were now on the bus? Write to help explain your best thinking using words, numbers, or pictures.
4N-27) Answer: 5,481 traffic lights
The new city of Graphville is laid out on a grid. There are 87 avenues that all run from north to south. There are 63 streets that all run from east to west. The avenues intersect the streets, and there is a traffic light at each intersection. How many traffic light are there? Write to help explain your best thinking using words, numbers, or pictures.
4N-26) Answer: 20
How many times does the digit nine appear in the numbers from 1 to 100? Write to help explain your best thinking using words, numbers, or pictures.
4N-25) Answer: 23
Julie was reading a book that had 128 pages in it. Figure out how many number sixes there were in all the page numbers. Write to help explain your best thinking using words, numbers, or pictures.
4N-24) Answer: 6 pages
Briana was looking through her math book and discovered that after page 44 the next page was 51. How many pages were torn out of the book? Write to help explain your best thinking using words, numbers, or pictures.
4N-23) Answer: 17, 26, 35, 44, 53, 62, 71, 80
What numbers less than 100 make eight when the digits are added together? (example 17 is a solution because 1+7=8) Write to help explain your best thinking using words, numbers, or pictures.
4N-22) Answer: (several answers)
Farmer Ruth raises cows and geese. One day she looks out into her field and sees some of each kind of animal. Altogether she sees 20 feet. How many cows and how many geese does she see? Give all possible answers. Write to help explain your best thinking using words, numbers, or pictures.
4N-21) Answer: 16
Richard was collecting shells on the beach. He gave 5 shells to Robin and 3 shells to Sarah. He has 8 shells left. How many did he collect? Write to help explain your best thinking using words, numbers, or pictures.
4N-20) Answer: the 12th and 24th children are boys with red shirts wearing glasses, the 18th child is a boy with a red shirt
There are 30 children standing in a straight line in Mrs. Johnson's third-grade class. Every 4th child is wearing glasses. Every 3rd child is a boy. Every 2nd child is wearing a red shirt. What can you say about the 12th, 18th, and 24th children? Write to help explain your best thinking using words, numbers, or pictures.
4N-19) Answer: 7
Linda wants to clean her fish tank. She is putting her fish into a bowl. She picked up three fish in a net, but one jumped back into the tank. She put the two fish into the bowl. Then she put the remaining five fish into the bowl. How many fish does Linda have? Write to help explain your best thinking using words, numbers, or pictures.
4N-18) Answer: smallest number of coins is 6 (5 dimes and 1 nickel); largest number of coins is 10 (1 dime and 9 nickels)
Tanya has 55 cents in her pocket in nickels and dimes. What is the smallest number of coins she can have? What are they? What is the largest number of coins she can have? What are they? Write to help explain your best thinking using words, numbers, or pictures.
4N-17) Answer: 270
Stuart's dog Barney wagged his tail. Barney had never seen so many dogs at once. Stuart counted up all the dogs at the dog show: the number is greater than 195; the number is less than 300; if you count by l0s you say its name; it can by divided evenly by 3 and 9. How many dogs did Stuart count? Write to help explain your best thinking using words, numbers, or pictures.
4N-16) Answer: 315
Conrad was scared as he knocked on the door. A low voice said, "Before I open the door you must name the secret number." Here are some clues: it is greater than 275; it is less than 325; if you count by 5s you say its name; it can be divided evenly by 3 and 9. What is the secret number? Write to help explain your best thinking using words, numbers, or pictures.
4N-15) Answer: 60
Yolanda and Mary are playing a game with a timer and three dice. Each player rolls three dice and uses the three numerals rolled to make 3-digit numbers. A numeral can only be used once in a number. Each number is worth 10 points. Mary rolls 3, 6, and 5. How many points can she earn? Write to help explain your best thinking using words, numbers, or pictures.
4N-14) Answer: 16 banners
The magic show was almost over. Mario was getting ready to do his famous banner trick. He pulled banners made out of flags from a top hat. First he pulled out a banner made up of 14 flags. Next he pulled out a banner made up of 23 flags. The third banner was made up of 18 flags, and the fourth banner was made up of 27 flags. The fifth banner was made up of 22 flags. Mario stopped his banner trick when there were more than 50 flags in the banner. How many banners did Mario pull out of the hat? Write to help explain your best thinking using words, numbers, or pictures.
4N-13) Answer: on a calendar
Sara asked, "Where do you see the fraction 23/30 most often?" Can you answer Sara's question? Write to help explain your best thinking using words, numbers, or pictures.
4N-12) Answer: 6 numbers
How many three-digit numbers contain only the digits 5 and 6? What are they? Write to help explain your best thinking using words, numbers, or pictures.
4N-11) Answer: 9 students
There are 23 students in the class. All but 9 went outside for recess. How many students stayed inside? Write to help explain your best thinking using words, numbers, or pictures.
4N-10) Answer: least 11; greatest 17
Use the numbers 2, 5, and 3. What is the least number you can get if you multiply two of the numbers and add the third to the product? What is the greatest number you can get? Write to help explain your best thinking using words, numbers, or pictures.
4N-9) Answer: How many legs on seven insects?
Make up a word problem that has 42 as its solution. Explain how someone could solve the problem. Write to help explain your best thinking using words, numbers, or pictures.
4N-8) Answer: 36
I am a number between 31 and 41. I am a multiple of 3. I am an even number. What number am I? Write to help explain your best thinking using words, numbers, or pictures.
4N-7) Answer: $9 left
Sam had $12. Then he spent one fourth of the money on a book. How much money did Sam have left? Write to help explain your best thinking using words, numbers, or pictures.
4N-6) Answer: How many bicycles can be made with 45 wheels?
Write a word problem that can be solved by finding 45 divided by 2. Then solve your problem. Write to help explain your best thinking using words, numbers, or pictures.
4N-5) Answer: 2/3 of the panes
A window in Helen's house is made up of 12 small panes of glass. While playing baseball, she accidentally broke 4 of the panes. What fraction of the panes were not broken? Write to help explain your best thinking using words, numbers, or pictures.
4N-4) Answer: 16 grapes
Jim bought a bunch of grapes. He ate one half of the grapes. Then his friend Gary ate one fourth of the remaining grapes. There were 6 grapes left. How many grapes were in the bunch to begin with? Write to help explain your best thinking using words, numbers, or pictures.
4N-3) Answer: no - not enough flour to bake the cookies
Judy needs 5 pounds of flour to bake some cookies. She has three partially filled bags of flour. They contain one and one fourth pounds, two and one fourth pound, and three fourths pound. Does Judy have enough flour to bake the cookies? Write to help explain your best thinking using words, numbers, or pictures.
4N-2) Answer: Mary gives Kim 2 dollars; Judy gives Kim 1 dollar
Kim, Judy, and Mary decided to equally share the cost of a present for their friend. Kim spent $7, Judy spent $3, and Mary spent $2. How much did each person pay the others so that everyone spent the same amount? Write to help explain your best thinking using words, numbers, or pictures.
4N-1) Answer: 12 days from now
Ed jogs every third day, Ned jogs every 4th day, and Fred jogs every 6th day. If they all jogged today, when will they all jog on the same day again? Write to help explain your best thinking using words, numbers, or pictures.
Expectations & Examples of Numbers from the 2008 Math Standards Revision (draft) - Grade 4
Identify factors and multiples of a number. (The factors of 12 are 1, 2, 3, 4, 6, 12.) (The multiples of 12 are 12, 24, 36, 48, . . .) Apply knowledge of place value and properties of addition and multiplication to find products for multiples of 10 and 100. (Example: 40 times 30 is (4 times 10) times (3 times 10) = (4 times 3) times (10 times 10)) Represent decimals through hundredths with physical materials, pictures, numbers, or words, and translate among representations. Representations may include base ten blocks, place value charts, and number lines. Use place value to read, write, compare, and order decimals through hundredths. Decimals may be compared using benchmarks, such as 0, 0.5, 1, 1.5, etc. Convert between mixed numbers and improper fractions using words, numbers, pictures, or physical materials.
Compare mixed numbers, fractions, and decimals. Examples follow: Use common factors to find equivalent fractions or to simplify fractions. Solve problems that involve fractions, decimals, and mixed numbers in a variety of contexts, and explain solutions using words, numbers, pictures, physical materials, or equations.
|
Convert between decimals and fractions that are equivalent to fractions with denominators of 10 or 100, using words, numbers, pictures, or physical materials. (An example is at the right.)
Expectations and Examples of Operations from the 2008 Math Standards Revision (draft) – Grade 4
Demonstrate mastery of multiplication and related division facts through 10 x 10 and use them to solve problems. Represent multiplication of up to three-digit by two-digit numbers using words, numbers, pictures, physical materials, or equations. Apply knowledge of place value and properties of addition and multiplication to find products for multiples of 10 and 100.
Multiply up to three-digit by two-digit numbers using the standard algorithms. Estimate products of factors less than 100 in order to predict results or determine reasonableness of answers. Examples:
Solve word problems involving multiplication of up to three-digit by two-digit numbers, and explain solutions using numbers, words, or equations. Problems could include two-step problems that use other operations as well; problems can either be in traditional word problem or more complex problem-solving contexts. Solve word problems involving division with one-digit divisors and up to three-digit dividends using numbers, pictures, physical materials, or inverse relationships. Problems should allow students to reinforce connections between multiplication and division. Note that division algorithms, including long division, are developed in fifth grade. |
Examples of Number Sense from the 2006 GLEs – Grade 4
Represent parts of a whole or parts of a set as fractions with common denominators. Represent decimals (money) in multiple ways including symbols, pictures, and physical models. Illustrate fractions as parts of a whole object, number, or set. Explain or show how a fraction can be decomposed as a sum of smaller fractions. Describe or show equivalent fractions using models, including pictures, paper folding, geoboards, and parallel number lines. Approximate halves, thirds, and fourths in relationship to whole units on a number line. Order fractions with like denominators using numbers, pictures, and objects. Explain or show equivalent relationships between decimals and fractions. Explain how to order fractions and/or decimals related to money. Explain why one fraction is greater than, less than, or equal to another fraction. Explain the commutative property of multiplication and give examples. Explain the identity property of addition and multiplication and give examples. Explain why equations are true or false based on one of the properties of addition or multiplication. Illustrate and demonstrate the use of the commutative, associative, or identity property of addition or multiplication using words, pictures, numbers, or objects. Use addition or multiplication properties to replicate a computational strategy when given an example. Illustrate and demonstrate the use of the zero property of multiplication on whole Represent addition and subtraction of fractions with like denominators using numbers, pictures, and models including everyday objects, fraction circles, number lines, and geoboards. Use joining, separating, part part whole, and comparison situations to add and subtract like denominator fractions. Translate a given picture or illustration into an equivalent symbolic representation of addition and subtraction of like denominator fractions. Select and/or use an appropriate operation to show understanding of addition and subtraction of like denominator fractions. Select and develop strategies that help with recall of multiplication and division through 12s. Select and test algorithms used in computational situations that involve multiplication and division of whole numbers and explain strategies. Compute with whole numbers using a combination of any two operations in a given situation. Explain and apply strategies or use procedures to multiply 2 digit numbers by 3 digit numbers and/or divide 3 or 4 digit numbers by 2 digit numbers without remainders. Appropriately apply and explain the concept of remainder in a given context. Select and use appropriate tools from among mental computation, estimation, calculators, manipulatives, and paper and pencil to compute in a given situation. Explain why a selected tool is most efficient for a situation. Explain when an estimation or exact answer is or is not appropriate. Apply a variety of estimation strategies, including multiples of 10 and 100, rounding, and compatible numbers, to predict an answer prior to computation. Use estimation to check the reasonableness of calculated results. Explain an appropriate adjustment when an estimate and a calculation don’t agree. |