Grade 5 Practice Problems: Numbers
Examples from Standards Revision and GLEs
5N-25) Answer: 75 cards
George had 75 football cards. He gave 3-for-1 in four trades. Then he received 5-for-1 in two trades. How many cards does he have now? Write to help explain your best thinking using words, numbers, or pictures.
5N-24) Answer: 34 or 94
I am a number less than 100. My units digit is a 4. The sum of my digits is an odd number. My tens digit is a multiple of 3. Who am I? Write to help explain your best thinking using words, numbers, or pictures.
5N-23) Answer: 1/3 vinegar
One jar is half full of vinegar and another jar twice its size is one quarter full of vinegar. Both jars are filled with water and the contents are mixed in a third container. What part of the mixture is vinegar? Write to help explain your best thinking using words, numbers, or pictures.
5N-22) Answer: 543
Monica is thinking of a number. Can you guess her number using these clues? It is a three digit number. Its digits are in descending order. It is divisible by three. The hundred's digit is two more than the one's digit. Add the the three digits will give you a dozen. Write to help explain your best thinking using words, numbers, or pictures.
5N-21) Answer: 21 marbles
Jeff has less than 30 marbles. When he puts them in piles of 3 he has no marbles left over. When he puts them in piles of 2 he has 1 left. When he puts them in piles of 5 he has 1 left. How many does he have? Write to help explain your best thinking using words, numbers, or pictures.
5N-20) Answer: 4 axles
A large truck, a 14-wheeler, has 2 wheels on its front axle. Each of the other axles has 4 wheels. How many axles does the truck have? Write to help explain your best thinking using words, numbers, or pictures.
5N-19) Answer: 16 golf balls
Jesse was out playing golf last Thursday On the first six holes, he lost 4 golf balls. On the next six holes, he lost one-half of the number of golf balls he had then. On the last six holes, he only lost 2 more golf balls. He finished with 4 golf balls. How many did he start with? Write to help explain your best thinking using words, numbers, or pictures.
5N-18) Answer: 41 cans
The Girl Scouts were collecting tin cans to recycle. Helen collected the most cans. Amanda collected 7 cans less than Helen. Alex collected 4 more cans than Amanda. Alex collected 14 cans. How many cans did the three girls collect altogether? Write to help explain your best thinking using words, numbers, or pictures.
5N-17) Answer: 8 dozen
Mrs. Green is buying cookies for the class party. She expects that each pupil will eat 4 cookies. How many dozen will she need if there are 24 pupils in the class? Write to help explain your best thinking using words, numbers, or pictures.
5N-16) Answer: 4 feet
Jean needs to cut a board into two 3.5 foot pieces. She starts with an 11 foot board. How much of the board will she have left after she makes the cuts? Write to help explain your best thinking using words, numbers, or pictures.
5N-15) Answer: 1st-Moe; 2nd-Curly; 3rd-Larry
Larry, Curly, and Moe decided to race up the stairs which have 24 steps. Larry takes the steps 2 at a time while Curly takes the steps 3 at a time while Moe takes the steps 4 at a time. If all three start at the bottom at the same time, who will finish lst? 2nd? 3rd? Write to help explain your best thinking using words, numbers, or pictures.
5N-14) Answer: Larry 12 and Curly 6
Larry, Curly, and Moe decided to race up the stairs that have 24 steps. Larry takes the steps 2 at a time while Curly takes the steps 3 at a time while Moe takes the steps 4 at a time. If Moe starts at the bottom, what step should Larry and Curly start on so all three finish in a tie? Write to help explain your best thinking using words, numbers, or pictures.
5N-13) Answer: 44 pencils
At the end of the school lday Mr. Howard had 30 pencils in the pencil box. In the morning, he gave 12 pencils to students. At lunch time, he got 6 of them back. He then gave 8 pencils to other students in the afternoon. How many pencils did he start with? Write to help explain your best thinking using words, numbers, or pictures.
5N-12) Answer: 3 girls got 10 cents, 1 girl got 15 cents, and the dog owner saved 5 cents
The four girls washed the neighbor's dog for 50 cents. They didn't know how to divide the money, so the dog owner said: "I will give the four of you 4/5 of the total amount. To the first one to tell me how much that is, I will give 1/2 of the other 1/5" . If someone gave the dog owner the right answer, how did the money get divided up? Write to help explain your best thinking using words, numbers, or pictures.
5N-11) Answer: Lisa-8 1/2 minutes; Angie-4 1/4 minutes
Angie and Lisa were taking gymnastics together. One day each of them ran to class from where they lived. Together it took them 12 3/4 minutes. It took Lisa twice as much time as it took Angie. How many minutes did it take each of them to run to class? Write to help explain your best thinking using words, numbers, or pictures.
5N-10) Answer: 147 kids were interviewed, 3 liked tennis, 9 liked basketball, 45 liked baseball or softball, and 90 liked soccer best
At school they did a survey of everyone's favorite sport. The survey showed that one third as many kids liked tennis as liked basketball. There were one fifth as many kids who said they liked basketball as said they liked baseball or softball. Then one half as many kids liked baseball or softball as liked soccer. There were 90 kids who liked soccer the best. How many kids did they interview, and how many liked each sport the best? Write to help explain your best thinking using words, numbers, or pictures.
5N-9) Answer: 40 hot dogs, 10 ribs, 2 chicken
Sue's great-grandfather was 100! They were celebrating with a big family cookout and Sue was taking orders. She found one fifth as many people wanted chicken as wanted ribs, one fourth as many people wanted ribs as wanted hot dogs, and one half as many people wanted hot dogs as wanted hamburgers. Sue gave her brother, the chef, an order for 80 hamburgers. How many people asked for chicken, how many people asked for ribs, and how many asked for hot-dogs? Write to help explain your best thinking using words, numbers, or pictures.
5N-8) Answer: 308
Danielle was the 100th runner across the finish line. Lots of runners finished after Danielle. Here are some clues for the number of runners who finished the race: it is more than 280; it is less than 316; if you count by 4s you say its name; it can be divided evenly by 7. How many runners crossed the finish line? Write to help explain your best thinking using words, numbers, or pictures.
5N-7) Answer: 3 pkg. forks; 2 pkg. knives
A package of plastic forks contains 8 forks. A package of plastic knives contains 12 knives. What is the fewest number of packages you would have to buy to have exactly the same number of forks as knives? Write to help explain your best thinking using words, numbers, or pictures.
5N-6) Answer: 85 pennies
Sarah has between 50 and 100 pennies in her collection. When she divides them into groups of 2, of 3, or of 7, there is always 1 penny left. How many pennies does Sarah have in her collection? Write to help explain your best thinking using words, numbers, or pictures.
5N-5) Answer: 40 students
The number of students on the field trip is greater than 30 but less than 50. When seated 2 in a seat on the bus, no student has to sit alone. When placed in groups of 5 for a tour, all groups are the same size. How many students are on the field trip? Write to help explain your best thinking using words, numbers, or pictures.
5N-4) Answer: how many groups of three are in 4
What does 4 divided by 3 mean? Write to help explain your best thinking using words, numbers, or pictures.
5N-3) Answer: 3/8
What fraction of the letters in the word multiply are also in the word product? Write to help explain your best thinking using words, numbers, or pictures.
5N-2) Answer: 10 handshakes
There are 5 people at a meeting. If each person shakes hands with each of the other once, how many handshakes are exchanged? Write to help explain your best thinking using words, numbers, or pictures.
5N-1) Answer: 20 times
How many times would the digit, 2, be written if you wrote down all the whole numbers from 1 to 100? Write to help explain your best thinking using words, numbers, or pictures.
Expectations & Examples of Numbers from the 2008 Math Standards Revision (draft) - Grade 5
Given a pair of fractions, rewrite them with common denominators. The given pair of fractions could have denominators with or without common factors. Factors, multiples, greatest common factors, and least common multiples are used here.
Use divisibility concepts to classify numbers as prime or composite. Use prior knowledge of common factors and multiples to find the greatest common factor and least common multiple of two or more whole numbers. (Use the least common multiple (LCM) to find common denominators for pairs of fractions.) (Use the greatest common factor (GCF) to simplify fractions.) |
Expectations and Examples of Operations from the 2008 Math Standards Revision (draft) – Grade 5
Represent multi-digit division, with and without a remainder, using words, numbers, pictures, physical materials, or equations. Find quotients for multiples of 10 and 100 by applying knowledge of place value and properties of operations. Divide three- or four-digit numbers by two digit numbers, with and without remainders, using the standard algorithms. Estimate quotients in problems involving up to two-digit divisors to predict results or determine reasonableness of answers. Use multiples of 10, 100, and compatible numbers to mentally estimate quotients. For example, to estimate 419 ÷ 68, one might use 420 ÷ 70. 420 and 70 are close to the original numbers and they are compatible—that is, they are easily divided mentally. Solve problems requiring multi-digit division, and interpret and communicate solutions. Problems include those with and without remainders. Represent addition and subtraction of fractions and mixed numbers using words, numbers, pictures, or physical materials, and translate among representations. Numbers include fractions with and without common denominators. Representations may include number lines, fraction pieces, and fraction bars. Represent addition and subtraction of decimals using words, numbers, pictures, or physical materials, and translate among representations. Representations may include base ten blocks, number lines, and grid paper. Add and subtract fractions, decimals, and mixed numbers using the standard algorithms. Fractions can be in either proper or improper form. Estimate sums and differences of fractions, decimals, and mixed numbers to predict results or determine reasonableness of answers. Solve word problems involving addition and subtraction of fractions, mixed numbers, and decimals and explain solutions using words, numbers, pictures, physical materials, or equations. Use parentheses to write and evaluate expressions. This reinforces students’ understanding of the distributive property and helps them understand the order of operations. 3 x 12 = 3 x (10 + 2) = (3 x 10) + (3 x 2) (5 + 3) x (7 – 4) = 24 |
Examples of Number Sense from the 2006 GLEs – Grade 5
Represent mixed numbers, proper and improper fractions, and decimals using words, pictures, models, and/or numbers. Make a model when given a symbolic representation or write a fraction or decimal when given a number line, picture, or model. Explain how the value of a fraction changes in relationship to the size of the whole. Explain the value for a given digit and/or show how to read and write decimals to at least the thousandths place. Represent improper fractions as mixed numbers and mixed numbers as improper fractions. Order decimals, proper and improper fractions, and/or mixed numbers with denominators 2, 3, 4, 5, 6, 10, 12, and/or 15 using symbolic representations, number lines, or pictures. Identify and/or explain the relationship among equivalent decimals and fractions. Explain why one fraction is greater than, less than, or equal to another fraction. Explain why one decimal is greater than, less than, or equal to another decimal. Show how factors and multiples can be used to name equivalent fractions. Use the concepts of odd and even numbers to check for divisibility. Illustrate prime or composite numbers by creating a physical model. Identify prime or composite numbers between 1 and 100 and explain why a whole number is prime or composite. Explain how to find the least common multiple (LCM) and greatest common factor (GCF) of two numbers. Use factors, multiples, and prime and composite numbers in a variety of situations. Factor a number into its prime factorization or into factor pairs. Explain or show whether one number is a factor of another number. Explain or demonstrate why a number is prime or composite. Represent addition and subtraction of fractions with denominators of 2, 4, 8 or 2, 3, 6, 12 or 2, 5, 10. Represent or explain addition and subtraction of non negative decimals through thousandths using words, pictures, models, or numbers. Explain a strategy for adding and subtracting fractions. Select and/or use an appropriate operation(s) to show understanding of addition and subtraction of non negative decimals and/or fractions. Explain the relationship between addition and subtraction of non negative decimals and fractions. Translate a picture or illustration into an equivalent symbolic representation of addition and subtraction of non negative fractions and decimals. Add and subtract non negative decimals and like denominator fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and/or 15. Find sums or differences of decimals or like denominator fractions in given situations. Calculate sums of two numbers with decimals to the thousandths or three numbers with decimals to hundredths. Calculate difference of numbers with decimals to thousandths. 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 strategy or tool is more efficient or more appropriate than another strategy or tool for a situation. Describe strategies for mentally adding or subtracting non negative decimals and/or like denominator fractions. Explain when an estimation or exact answer is or is not appropriate. Use a variety of estimation strategies to predict an answer prior to computation Use estimation to verify the reasonableness of calculated results. Compute to check the reasonableness of estimated answers for a given situation. Explain an appropriate adjustment when an estimate and a computation do not agree. Explain or describe a strategy used for estimation involving addition and subtraction of non negative decimals and like denominator fractions. |