6th Grade - Develop Strategies To Help You

 
     
 
     
 
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6th
Problem Solving
Develop Strategies to Help You
Develop generalizations of the results obtained and the strategies used and apply them in new problem situations.
Develop general idea about how to solve a problem. Use generalizations to solve new, unrelated problems.
 

Sample Problems

(1)

Parker runs a mile in 8 minutes. At this rate, how long will it take him to run a 26-mile marathon? Which of the following problems can be solved using the same arithmetic operations that are used above?

  1. A doctor has 1,300 patients in two offices. He wants each office to house the same number of patients. How many patients should be invite to visit at the new office?

  2. A cereal box weighs 100 grams. What is the weight of 2 boxes?

  3. Ron walks 4 miles in 30 minutes. How long will it take him to walk one mile?

(B)

(2)

Which two problems use the same operations and strategies to obtain a result. Identify the strategies used.

  1. Bill can type 90 words in 30 seconds. At that rate, how long will it take him to type 200 words?

  2. Ron walks 4 miles in 30 minutes. How long will it take him to walk two miles?

  3. Chad is making 2 quarts of lemonade. Each quart will serve 4 people. How many servings is Chad making?

(A and B both use multiplication and division.)

(3)

Mia’s room is in an L shape. She found the area of her room by dividing it into two rectangles, finding the area of each and then adding the areas together. What other room shape would this work for?

(Answers will vary. It will work for any room that can be broken into rectangles without overlapping or gaps.)

(4)

True or False. Explain.

The problems can be solved using the same strategies.

  1. Tessa completed 144 problems in 60 minutes. How many problems can she solve in 2 hours?

  2. Jack has driven 234 miles in 2 hours. At what rate is he driving?

(False, the first problem requires multiplication, while the second uses division.)

(5)

True or False. Explain.

The problems below cannot be solving using the same strategy.

  1. Dave bought a pizza with 12 slices. He ate 4/5 of the pizza. How many slices did he eat?

  2. Shana has 4 pink hats and 7 blue hats. How many hats doe she have in total?

(True, even though the same operation is used for both problems, multiplication, problem one needs division also to finish the solution.)

Learning Tips

(1)

It is important for sixth graders to relate what they know about how a solution is obtained and apply that knowledge to new problem situations. Children naturally make generalizations through experiences in the everyday world. For example, if a child touches a hot pan on the stove, he or she should be able to make the generalization that a bowl sitting over the same flame will also be hot. Children simply need to be reminded to relate problem to problem in math. When they are able to make generalizations from other problems they have solved, they will succeed more in mathematical reasoning, because they’ve applied background knowledge.

(2)

Generalizations can be made easily by seeking out key words and phrases that help determine how to derive at a solution. Here are a few.

Add: altogether, combined, add, both, in all, sum, total

Subtract: difference, fewer, how many more, how much more, left, less, minus, remains

Multiply: product, times, every, at this rate, of

Divide: each, divide, quotient, split evenly

These key words can help your child determine which operation was performed in solving a problem. He or she will also be able to look for these words in solving similar problems.

(3)

Mathematical reasoning is needed for problem solving. In general, sixth grade students should be able to problem solve by using 3 phases of a problem solving process. These phases allow children to think thorough a problem logically to determine a solution. The first phase of problem solving is to be sure to read and understand the problem. The second phase is to plan and solve the problem. The last phase is to look back at the problem and check work. The more children practice working through each of these phases, they better they will become at using mathematical reasoning to problem solve. Phases one and two will be most important for this skill.

(4)

Work with your child to help him/her successfully complete phase one of the problem solving process. Be sure that your child reads the problem a few times before attempting to solve it. In phase one, read and understand, sixth graders should be sure to identify and determine each of the following:

What exactly is being asked?

Children should underline the sentence or command in the problem and write a problem goal in their own words.

What do I know from the problem?

Children should highlight important, relevant facts that will help them to meet his/her goal from question one.

What do I know from personal knowledge?

When necessary, children will apply personal knowledge to add important facts to a problem.

This step can be used in this skill to look for similar questions.

(5)

A strong understanding of phase 2 is most important to this skill. Your child will have to look problems he/she has completed, as well as problems that others have completed to determine how the problem was solved. This information will then be used to solve similar problems.

In phase two of the problem solving process, 6th graders will use the information obtained in phase one to evaluate relationships and determine how to solve the problem. After choosing a strategy to solve a problem, children will use that strategy to find a solution. There are several strategies that can be used to solve problems. Help your child to use the list of all the options below to determine which could be used to reasonably solve each problem he/she encounters.

Problem Solving Strategies

Choose an operation: + , - , x,

Make an organized list

Make a table

Draw a picture

Make a graph

Look for a pattern

Guess and test

Write an equation

Work Backward

Solve a simpler problem

Act it out or use objects

Once your child can identify which strategy was used to solve a problem, he/she will be able to determine if this would also work for a new problem situation.

Extra Help Problems

(1)

Find the problem that can be solved using the same arithmetic operation(s) as the problem below.

Tyler wanted to combine 2 ½ cups of juice with 3 2/3 cups of lemon soda. He had a punch bowl that holds 6 1/2 cups of liquid. Tyler determined that the bowl was large enough to hold his punch.

  1. Shyla had 4 ½ cups of juice. Her brother drank ½ a cup. How much does she have left?

  2. 1/5 of Jordan class has no pets. There are 30 kids in the class. How many students have not pets?

  3. James ran 12.4 miles on Saturday and 8.2 miles on Sunday. How far did James run over the weekend?

(C)

(2)

Find the problem that can be solved using the same arithmetic operation(s) as the problem below.

Jimmy is eating at his favorite restaurant. His bill comes to 12.50. He’d like to tip the waitress 20%. How much money will his lunch end up costing him?

  1. Addison is buying a new video game for $20. She must pay 5% sales tax. What will the total cost of her game be after the tax is added in?

  2. Matt is shopping for shoes. The basketball shoes are on sale for 20% off. If the regular price of the shoe is $50, how much will they be with the discount?

(A)

(3)

Find the problem that can be solved using the same arithmetic operation(s) as the problem below.

Gracie saves $15 a week. If she does this for 12 weeks, how much money will she have saved?

  1. Judd is calculating the discount of a fishing rod that is on sale for 40% off. How much will it cost him, if the regular price is $45.00?

  2. Tammie saves $40 in May, $50 in June and $60 in July. How much money has she saved altogether?
    (A)

(4)

Find the problem that can be solved using the same arithmetic operation(s) as the problem below.

Bananas are on sale for 8 for $5. How much will one banana cost?

  1. How much are 5 apples, if they’re .50 each?

  2. Write 3/8 as a decimal.

(B)

(5)

Find the problem that can be solved using the same arithmetic operation(s) as the problem below.

What is the least number that is divisible by both 5 and 12?

  1. Hotdog buns come in packs of 10. Hotdogs come in packs of 6. What is the least number of hotdogs and buns that will need to be purchased to have equal amounts?

  2. What is the greatest common factor of 12 and 4?

(A)

(6)

True or False. Explain.

The problems can be solved using the same strategies.

1. A bakery has a choice of three frostings: chocolate, vanilla or lemon, three choices of cake flavors: chocolate, chocolate swirl, and white, and two style choices: cupcake or sheet cake. How many different combinations are there?

2. Jake has 3 times the amount of marbles than Dave. Dave has 12 marbles. Stacy has twice as many marbles as Dave. If they put all their marbles together, how many will they have?

(True, both problems require multiplication by 3 numbers to find a solution.)

(7)

True or False. Explain.

The problems can be solved using the same strategies.

  1. Dan ran 5 miles in June, 25 miles in July and 50 miles in August. If Dan continues this pattern, how far will he run in October?

  2. Veronica saved $40 in June, $60 in July and $80 in August. How much money has she saved in all?

(False, the first problem should be solved by looking for a pattern. The second problem needs to be solved using addition.)

(8)

True or False. Explain.

The problems can be solved using the same strategies.

  1. Amanda split her sticker collection into fifths to share with her friends. She had 3,000 stickers to begin with. How many stickers did each girl get?

  2. Jayden has 13 baseball cards. His dad bought him twice that amount for his birthday. How many cards does Jayden have now?

(False, the first problem requires division and the second multiplication and addition.)


(9)

True or False. Explain.

The problems must be solved using different strategies.

  1. On the night before a big test, Jen studies twice as long as usual. Solve the problem, for Jen usually studying for 1.5 hours.

  2. Haley had five less than 3 times an amount of dollars, d. Express your solution for $10.

(True, they both do require multiplication and the use of an expression, however, the second problem also needs to subtraction.)


(10)

True or False. Explain.

The problems must be solved using different strategies.

  1. A triangle has three angles; a, b, and c. Angle a measures 40 degrees and angle b measures 70 degrees. Show how you would find the measure of angle c.

  2. A supplementary angle has two angles that measure 90 degrees and 45 degrees. What is the measure of the third angle?

(False, these problems are solved by using the same strategies, addition of the known angles, followed by subtraction from 180.)


(11)

Mia’s room is in an L shape. She found the area of her room by dividing it into two rectangles, finding the area of each and then adding the areas together. Could she use this strategy to find the area of regular octagonal room? Explain.

(No, an octagon should be split into triangular shapes, not rectangles.)


(12)

Mia has an octagonal room that she’s split into 8 triangles that meet at a vertex in the center of the octagon. How could she find the area of the room?

(Mia needs to measure the base and height of one triangle. Then she needs to multiply the base times the height and divide by two to find the areas of that one triangle. Then she needs to multiply the area she finds by 8.)

 

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