Grade 6 Practice Problems: Algebra
Examples from Standards Revision and GLEs
6A-18) Answer: 2.5 feet
A ball is dropped from a height of 80 feet, and rebounds one-half the height each time it hits the ground. How high will it rebound after it hits the ground for the fifth time? Explain in detail how you found your answer using words, numbers, and/or pictures.
6A-17) Answer: bag $22; ball $66
A bowling ball and a bag together cost $88. The ball costs three times as much as the bag. How much does each cost? Explain in detail how you found your answer using words, numbers, and/or pictures.
6A-16) Answer: 16
A chocolate bar is separated into several equal pieces. If one person eats one quarter of the pieces and a second person eats one half of the remaining pieces, there are six pieces left over. Into how many pieces was the original bar divided? Explain in detail how you found your answer using words, numbers, and/or pictures.
6A-15) Answer: 8 grapes
A man ate a total of 100 grapes in five days, each day eating six more than on the previous day. How many grapes did he eat on the first day? Explain in detail how you found your answer using words, numbers, and/or pictures.
6A-14) Answer: There are two answers: 1 four-wheeled cart and 7 three-wheeled carts; or 4 four-wheeled carts and 3 three-wheeled carts
At the caddy shack on the local golf course, the golf carts have either three wheels or four wheels. Jamie checked the air in all 25 wheels. How many 3-wheeled carts and how many 4-wheeled carts did he check? Is there more than one possible answer? Explain in detail how you found your answer using words, numbers, and/or pictures.
6A-13) Answer: sandwich-$3; milk-$1
At the zoo, Michelle paid $7.00 for two sandwiches and a container of milk. Her brother, Ralph, paid $5.00 for one sandwich and two containers of milk. How much would one sandwich and one container of milk cost? Explain in detail how you found your answer using words, numbers, and/or pictures.
6A-12) Answer: less than 4 inches of rain
During the monsoon, there were two inches of rain on Thursday. On Friday, there was twice as much rain as on Thursday. On Saturday, there was just a little less rain than on Friday. How much rain was there on Saturday? Explain in detail how you found your answer using words, numbers, and/or pictures.
6A-11) Answer: beetles-7; spiders-5
Jill's bug collection contains 12 beetles and spiders. Beetles are worth 10 cents and spiders are worth 20 cents. Jill's whole collection is worth $1.70. How many beetles and how many spiders does Jill have? Explain in detail how you found your answer using words, numbers, and/or pictures.
6A-10) Answer: 84 grapefruits
Jose works in the produce department of the supermarket. He is arranging grapefruits in the shape of a triangle. When he has finished, the first (or top) row had 1 grapefruit, the second row had 3 grapefruits, the third row had 6 grapefruits, the fourth row had 10 grapefruits, and so on for a total of 7 rows. How many grapefruits did Jose use in the display? Explain in detail how you found your answer using words, numbers, and/or pictures.
6A-9) Answer: 4x15 feet
Last year Jan's rectangular garden had an area of sixty square feet. This year her garden is one foot wider and three feet shorter than last year's garden but it has the same area. What were the dimensions of the garden last year? Explain in detail how you found your answer using words, numbers, and/or pictures.
6A-8) Answer: Josh-14; Marissa-8
Marissa and Josh were picking up golf balls that had been hit into the woods. They picked up 22 golf balls in all, and Josh picked up 6 more than Marissa. How many did each of them pick up? Explain in detail how you found your answer using words, numbers, and/or pictures.
6A-7) Answer: 87 total (10 rust; 14 yellow; 56 brown; 7 gray)
Mr. Jackson is taking inventory of the scarves in his store. He has 1/8 as many gray scarves as brown ones. He has four times as many brown ones as yellow ones. There are 24 that are either rust or yellow. There are 10 rust-colored scarves. How many scarves does he have in his inventory? Explain in detail how you found your answer using words, numbers, and/or pictures.
6A-6) Answer: day 11
Nick has $40 and spends $1.50 each day. Bob has only $9 but he saves $1.50 each day. In how many days will Bob have more money than Nick? Explain in detail how you found your answer using words, numbers, and/or pictures.
6A-5) Answer: $450
On a string of 15 opals, the center stone is the largest and the most expensive. Starting from one end, including the center stone, each opal is worth $50 more than the previous one. Starting from the other end and including the center stone, each opal is worth $25 more than the previous one. The total value of the 15 opals is $4,650. What is the value of the center opal? Explain in detail how you found your answer using words, numbers, and/or pictures.
6A-4) Answer: 1092
Scotty's Supermarket is having their sale next week. On Monday, Scotty called 3 people to tell them about the sale. He asked them to each call 3 of their friends on Tuesday, and ask each of them to call 3 friends. Everyone who is called will call 3 different friends the next day When the campaign ends on Saturday, how many people will have been called? Explain in detail how you found your answer using words, numbers, and/or pictures.
6A-3) Answer: 3
The 20 children in Mrs. Chan's science class planted 40 lima beans. Of every 4 they planted, 3 grew a shoot. How many shoots were there? Explain in detail how you found your answer using words, numbers, and/or pictures.
6A-2) Answer: 22 miles
The distance between Exit 1 and Exit 20 on the turnpike is 130 miles. If any two exits must be at least 6 miles apart, what is the largest number of miles between any two consecutive exits? Explain in detail how you found your answer using words, numbers, and/or pictures.
6A-1) Answer: no
The fourth-grade wants to collect 50 cartons of food for the needy in the next 6 weeks. They collect 2 cartons the first week, 5 cartons the second week, and 8 cartons the third week. If the pattern continues in this way, will they meet their goal in the 6 weeks? Explain in detail how you found your answer using words, numbers, and/or pictures.
Expectations and Examples of Algebra from the 2008 Math Standards Revision (draft) – Grade 6
Use variables to write mathematical expressions or equations from information in tables or contextual situations. Examples:
Draw first-quadrant graphs from a contextual situation or a table of values. Evaluate mathematical expressions when values for each variable are given. Evaluate 6a + 5b when a = 1/3 and b = 0.3 Apply the commutative, associative, and distributive properties, and use the order of operations to evaluate mathematical expressions. Examples:
Solve one-step equations using number sense, models, or properties of equality. Example:
Write and use a mathematical expression or equation to solve a problem from a given context and verify the reasonableness of the solution. |
Examples of Algebraic Sense from the 2006 GLEs – Grade 6
Create a pattern and explain what makes it a pattern. Select or create a pattern that is equivalent to a given pattern. Identify and describe a number pattern for a given table, graph, rule, or words, Use technology to generate patterns based on two arithmetic operations. Extend a pattern by supplying missing elements in the beginning, middle, and/or end of the pattern. Describe or write a rule for a pattern with combinations of two different arithmetic operations in the rule. Identify, describe, or write a rule for a given pattern involving two different alternating operations. Create a pattern that uses the same rule as a given pattern. Determine a rule in order to supply missing elements in the beginning, middle, or end of a pattern or sequence. Create a pattern involving two alternating operations using a given rule. Express relationships between quantities including non negative fractions, decimals, percents, and integers using =, ≠, <, >, ≤, and ≥. Describe a situation represented by an equation or inequality involving non negative fractions, decimals, percents, and/or integers. Write a simple equation or inequality using non negative fractions, decimals, percents, and integers to represent a given situation. Translate a situation involving two arithmetic operations into algebraic form involving variables and using =, ≠, >, <, ≥, or ≤. Describe a situation involving two arithmetic operations that matches a given equation with variables. Write an equation, expression, or inequality using a variable to represent a given situation and explains the meaning of the variable. Describe a situation that corresponds to a given expression, equation, or inequality that includes variables. Explain the meaning of variables in a formula, expression, or equation. Determine the value of simple expressions and formulas using pictures and/or symbols. Determine the value of an expression or formula by substituting non negative values for variables. Write an expression with a variable that represents a given situation and determine the value of the expression given a value for the variable. Solve one step equations involving non negative rational numbers using manipulatives, pictures, and/or symbols. Solve one step single variable equations. Write and solve one step single variable equations for a given situation. Explain or show the meaning of the solution to an equation. |