Grade 4 Practice Problems: Algebra
Examples from Standards Revision and GLEs
4A-32) Answer: 3 possible combinations (1 stool + 7 tables, 5 stools + 4 tables, 9 stools + 1 table)
In my carpenter shop I make only 3-legged stools and 4-legged tables. One day I looked at my day's output and counted 31 legs. How many different answers can you find for this problem? Write to help explain your best thinking using words, numbers, or pictures.
4A-31) Answer: 5 cents for the cap; $1.05 for the bottle
Julie bought some "Sensational Suntan Lotion". The bottle and the cap together cost $1.10, but the bottle cost $1 more than the cap. How much does each cost? Write to help explain your best thinking using words, numbers, or pictures.
4A-30) Answer: frame $5 and picture $105
A picture and a frame cost $110 together. The picture costs $100 more than the frame. How much does the frame cost? Write to help explain your best thinking using words, numbers, or pictures.
4A-29) Answer: 6 times
Sharon, Sally, and Shelia and Sara all decided to take up horseback riding. Shelia went twice as many times as Sally and Sharon went four more times than Sara but three less times than Shelia. Sara went 5 times altogether. How many times did Sally go? Write to help explain your best thinking using words, numbers, or pictures.
4A-28) Answer: 17, 19, 21, 23
Find four consecutive odd numbers which add to 80. Write to help explain your best thinking using words, numbers, or pictures.
4A-27) Answer: 32
Linda had 2 snails in her tank at the end of the first week. At the end of the second week, she had 4 snails. At the end of the third week, she had 8 snails. If this pattern continues, how many snails will she have at the end of the fifth week? Write to help explain your best thinking using words, numbers, or pictures.
4A-26) Answer: 13 ducks and 7 beaver
Farmer Matt raises ducks and beavers. The animals have a total of 20 heads and 54 feet. How many ducks and how many beavers does farmer Matt have? Write to help explain your best thinking using words, numbers, or pictures.
4A-25) Answer: 16
Jaime is building a sand castle by placing buckets of wet sand in the shape of a triangle. He places 1 bucket on the top, 4 buckets in the row beneath it (row 2), 7 buckets in row 3, and so on. If the castle contains 6 rows, how many buckets of sand are in the bottom row? Write to help explain your best thinking using words, numbers, or pictures.
4A-24) Answer: $12.00
At Pizza Hut 2 small and 1 large pizzas cost the same as 5 small pizzas. If one small pizza costs $4, then what does one large pizza cost? Write to help explain your best thinking using words, numbers, or pictures.
4A-23) Answer: 12 cans
Rick is packing two sizes of boxes. Three size A boxes and one size B box holds the same number of cans as 7 size A boxes. If size A box holds 3 cans, then what does size B box hold?
4A-22) Answer: 36 ounces
One large bowl and one small bowl hold the same amount of soup as 5 small bowls. If one small bowl holds 9 ounces of soup, then how much soup does one large bowl hold? Write to help explain your best thinking using words, numbers, or pictures.
4A-21) Answer: $24
Five model cars cost the same as two model cars and one model plane. If one car costs $8, then how much does one plane cost? Write to help explain your best thinking using words, numbers, or pictures.
4A-20) Answer: 21 centimeters
Four comic books are as thick as one comic book and my math book. If one comic book is 7 centimeters thick, how thick is my math book? Write to help explain your best thinking using words, numbers, or pictures.
4A-19) Answer: 12 pounds
At the dime store 6 cats and 1 dog statues weigh the same as 9 cat statues. If a cat statue weighs 4 pounds, then what does a dog statue weigh? Write to help explain your best thinking using words, numbers, or pictures.
4A-18) Answer: 134
Astronauts saw one third as many strange objects as moons. They saw 4 fewer moons than UFOs. They saw one fourth as many UFOs go by as stars. They saw 88 stars out the window of their spacecraft. How many things did they see altogether in that hour? Write to help explain your best thinking using words, numbers, or pictures.
4A-17) Answer: 14 weeks
Barbara and Janet were collecting Terrible Willy stickers. Barbara had 8 stickers and Janet had 4. Barbara collected a new one each week and Janet collected 2 new ones each week. How many weeks would it take for Janet to have exactly 10 more stickers than Barbara? Write to help explain your best thinking using words, numbers, or pictures.
4A-16) Answer: 85
James noticed that each day he was in the sun he got new freckles. On Friday he counted 31 new freckles, and the day before he had gotten 7 fewer new freckles. Beginning on Tuesday he had gotten 7 more new freckles each day than he had gotten the day before. During the five days, how many new freckles did James get? Write to help explain your best thinking using words, numbers, or pictures.
4A-15) Answer: 245 north of Main St., 139 south of Main St.
I needed to deliver all 384 papers by myself last week. I needed to deliver 106 more papers north of Main Street than south of Main Street. How many papers did I deliver north of Main Street and how many papers did I deliver south of Main Street? Write to help explain your best thinking using words, numbers, or pictures.
4A-14) Answer: 27
Arbie, a wind-up robot, hops when you clap your hands. If you clap your hands once, Arbie makes 5 hops. If you clap twice, the robot makes 7 hops. Clap three times, and Arbie makes 10 hops. Clap four times, and Arbie makes 12 hops. Clap five times, and the robot makes 15 hops. Arbie's hops keep increasing in the same way. How many hops does Arbie make when you clap ten times? Write to help explain your best thinking using words, numbers, or pictures.
4A-13) Answer: 10
Nancy and Nicole bought a book of tickets for rides at Mystery Mountain Park. In the book there were 5 more green tickets than red tickets, and one-third as many red tickets as yellow tickets. The girls used up the 15 yellow tickets first. How many green tickets were still in the book? Write to help explain your best thinking using words, numbers, or pictures.
4A-12) Answer: 7
Donna stopped picking peaches. She sat down under the tree and fell asleep. A family of raccoons discovered the 42 peaches in Donna's sack. When the first raccoon finished eating, there were only 37 peaches left in the sack. When the second raccoon finished nibbling, there were 32 peaches left in the sack. Then the third raccoon ate until there were exactly 27 peaches left in the sack. If the raccoons kept eating the peaches in that way, how many peaches did Donna find in the sack after the seventh raccoon had eaten? Write to help explain your best thinking using words, numbers, or pictures.
4A-11) Answer: the rooms for cats
There are 19 rooms for cats and 19 rooms for dogs in Kenny's Pet Hotel. On Monday 1 cat room and 1 dog room were full. On Tuesday 4 cat rooms and 2 dog rooms were full. The next day 6 cat rooms and 6 dog rooms were full. On Thursday 9 cat rooms and 7 dog rooms were full. If pets keep coming to Kenny's Pet Hotel in the same way, which rooms will all be full first, the ones for the cats or the ones for the dogs? Write to help explain your best thinking using words, numbers, or pictures.
4A-10) Answer: 32 Proceratops buttons, 18 Iguanadon buttons
Gene and Ruth bought a bag of 50 buttons that had pictures of dinosaurs on them. The label on the bag showed Iguanadons and Proceratops. When Gene and Ruth took the buttons out of the bag, they found that there were 14 fewer Iguanadon buttons than Proceratops buttons. How many of the buttons showed Iguanadons and how many showed Proceratops? Write to help explain your best thinking using words, numbers, or pictures.
4A-9) Answer: 3 squids and 7 octopuses; or 7 squids and 2 octopuses
The squids and octopuses are gathering seaweeds, and their arms are loaded. Squids have 10 arms and octopuses have 8 arms. There are 86 arms loaded with seaweed. How many squids and how many octopuses are gathering seaweeds? Write to help explain your best thinking using words, numbers, or pictures.
4A-8) Answer: 70 legs
Joan went to a pet store. She saw 6 puppies, 25 fish, 4 kittens, and 15 birds. How many legs did those animals have? Write to help explain your best thinking using words, numbers, or pictures.
4A-7) Answer: 6 and 9
The sum of two numbers is 15. The difference between the same two numbers is 3. What are the numbers? Write to help explain your best thinking using words, numbers, or pictures.
4A-6) Answer: 20 children
If there were 4 more children on a school bus, there would be two dozen children on the bus. How many children are on the bus? Write to help explain your best thinking using words, numbers, or pictures.
4A-5) Answer: $4.50
At her fruit stand, Vicki sells oranges for 10 cents each. One day she sold three-fourths of her oranges and had 15 oranges left. How much money did she make on the oranges she sold? Write to help explain your best thinking using words, numbers, or pictures.
4A-4) Answer: 9 and 18
When two numbers are added, the sum is 27. One of the numbers is half of the other. What are the two numbers? Write to help explain your best thinking using words, numbers, or pictures.
4A-3) Answer: $2.75
Suppose that tickets for a rock concert cost 5 cents for the first ticket, 10 cents for the second ticket, 15 cents for the third ticket, and so on. If you bought 10 tickets, how much would you pay altogether? Write to help explain your best thinking using words, numbers, or pictures.
4A-2) Answer: 126 girls
Two hundred thirty-five students go to Camp Fir Tree. There are 17 more girls than boys. How many are girls? Write to help explain your best thinking using words, numbers, or pictures.
4A-1) Answer: 6,2,8,4,0,6,2,8,4,0…
Add 6 to itself over and over again. What is the pattern in the ones-place digits of the sums? Write to help explain your best thinking using words, numbers, or pictures.
Expectations & Examples of Algebra from the 2008 Math Standards Revision (draft) - Grade 4
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. Example:
Use letters, boxes, or other symbols to represent an unknown quantity in simple expressions, equations, or inequalities. Example:
Locate and name points in the first quadrant of a coordinate grid using ordered pairs of whole numbers. An interesting way to reinforce this basic graphing skill is to have students construct a figure with vertices at given points on a coordinate grid, perhaps generating a design or character. |
Examples of Algebraic Sense from the 2006 GLEs – Grade 4
Extend, describe, or construct patterns of numbers, using addition, subtraction, or multiplication, based on a single operation between terms. Extend, describe, or construct patterns of shapes or objects. Extend and represent patterns using words, tables, numbers, physical models, and/or pictures. Construct a number pattern and explain what makes it a pattern. Determine missing elements in the beginning, middle, and/or end of a pattern. Identify or generate a rule for a pattern with a single arithmetic operation in order to extend or fill in parts of the pattern. Show growing patterns using objects or pictures and explain the rule. Determine the operation that changes the elements of one set of numbers into the elements of another set of numbers such as using a function machine. Explain why a given rule fits a pattern based on a single arithmetic operation in the rule. Explain inequality and the use of ≠, >, or < in inequalities. Use the symbols >, <, and ≠ to show the relevant value of multiplication or division expressions. Identify or describe a situation that represents a given expression, equation, or inequality using =, ≠, <, or >. Express relationships between quantities using =, ≠, <, or >. Read formulas, expressions, and equations involving a single variable. Use mathematical symbols including a single variable to write expressions and equations to represent a given situation. Describe a situation that represents a given expression or equation that includes a single variable. Explain the meaning of a single variable in a formula, expression, or equation. Illustrate expressions using manipulatives, physical models, pictures, and/or symbols. Substitute a numeric value for a symbol in an expression or formula and compute as indicated. Solve a simple equation using addition, subtraction, multiplication, or division. Write and solve a one step equation for a given situation. Explain the meaning of the solution for an equation. |