6th Grade - Identify Relationships And Patterns

 
     
 
     
 
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6th
Reasoning
Identify Relationships and Patterns
Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
Analyze problems to find solutions. Identify relationships within problems to determine how to find a solution. Determine which information in a problem is necessary to solve it. Eliminate unnecessary information, highlight and use relevant information to find a solution. Order information by sequence or priority to solve problems. Observe patterns within a problem and use them to find a solution.
 

Sample Problems

(1)

The table shows the number of days that Fatima walks each day.

Day

1

2

3

4

5

Miles

1

1.5

2

2.5

3


If the pattern continues, how many miles will Fatima walk on Day 6?

(3.5 miles)

(2)

Monica, Christine, Tracy, David and Rick are all wearing different colored shirts (red, yellow, green, pink, and white). Tracy and Christine never wear primary colors. Christine is not wearing pink. The boys are not wearing white. None of the girls are wearing green. Only David is wearing a color that has the letter Y in it. Monica is not wearing pink or white. Find the color of shirt that each person is wearing.

(Monica – red, Christine – white, Tracy – pink, David – yellow, Rick – green)

(3)

Denise and her family are visiting an aquarium. They would like to see, each live animal show that is scheduled for the day. Each show is 1 hour and 20 minutes in duration. The family arrived at the aquarium at 11 am and plan on leaving by 4 pm. Use the table below to determine which time Denise and her family will need go to each show. Place the shows in the order in which they should attend and list the show start time. The chart shows the start time of each performance.

Sea Otters

10:30, 2:30, 5:00

Sharks

11:30, 2:00, 4:30

Bottom Dwellers

11:00, 1:00, 4:00

(Sharks 11:30, Bottom Dwellers 1:00, and Sea Otters 2:30)

(4)

Tell whether the problem below has too much, too little or just the right amount of information. Then use the relevant information to solve the problem.

Dana has 10 markers. Will has 16 markers. Thomas has 12 makers. How many more markers does Thomas have than Dana?

(Too much, we don’t need to know how many markers Will has. Thomas has 2 more markers than Dana.)

(5)

Phil is at the horse track. He peeked under the horse stalls where the horses for the next race are being held. He counted 36 horse legs. How many horses will be racing in the next round? Explain how you know. (Hint: think about the relationship between each horse and the number of legs it has.)

(9, each horse has four legs 9 x 4 = 36.)

Learning Tips

(1)

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.

(2)

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.

(3)

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

(4)

Be sure that your child understands that phase 3 of the problem solving process is just as important and the first two phases. Many children get an answer and stop there. Going back to the original problem, re-evaluating the question and problem facts and comparing them to the solution will allow students to use mathematical reasoning to determine if his/her answer is reasonable. On phase 3, children should:

Compare work to the information in the problem.

Be sure all calculations are correct.

Estimate to see if the answer seems correct.

Make sure the question(s) has/have been answered.

(5)

Many students experience anxiety when asked to use mathematical reasoning to problem solve. Often times the become overwhelmed with the amount of information in the problem and the inability to use a standard algorithm to solve a math problem. If this is the case for your child, you can help him/her to overcome these fears by breaking the problem down into smaller parts. One way to do this is to come up with a system of color-coding or note taking for the solution of these sorts of problems. For example, you may want to have your child highlight important facts from the text in yellow and then underline the question being asked in green. This will greatly benefit the visual learner. In addition, the visual learner may need to transfer the information highlighted to a table, such as the one show below. Help your child to come up with a system that he/she will be able to remember and use independently.

Sample Problem Solving Table

My Goal

(Here, I restate the question in my own words)

Problem Facts

(Use this space to write in the important numbers and information the problem gives me)

Facts I Know

(This is where I tell any information I know from personal knowledge that needs to be added to the problem. I won’t always use this space.)

Solve It

(I will use this area to show my work on the strategy I used to solve the problem.)




Check It

  • ?

  • Facts

  • Calculations

  • Estimate

(Check off each box to make sure I check my work.)

Extra Help Problems

(1)

The table shows the number of days that Don walks each day.

Day

1

2

3

4

5

Miles

1

3

5

7

9


If the pattern continues, how many miles will Don walk on Day 6?

(11 miles)

(2)

The table shows the number of days that Diane runs each day.

Day

1

2

3

4

5

Miles

2

3.7

5.4

7.1



If the pattern continues, how many miles will Diane run on Day 6?

(8.8 miles)

(3)

The table below shows the number of sides and triangles for different polygons. Identify the pattern and use it to complete the table.

sides

3

4

5

6


triangles

1

2

3


5


(6 sides = 4 triangles, 7 sides = 5 triangles)

(4)

A 4 x 4 in. rectangle has an area of 16 sq. inches. A 4 x 5 in. rectangle has an area of 20 square inches. A 4 x 6 in. rectangle has an area of 24 square inches. Make a table using the information from the problem. Identify the pattern. Then use the pattern to find the area of a 4 x 9 in. rectangle.

(Pattern – count by fours)

4 x 4

4 x 5

4 x 6

4 x 9

16

20

24

36

(5)

Identify the pattern. Use it to fill in the missing numbers.

½, ¾, 1, 1-1/4, _____, 1-3/4, _____

(pattern – add ¼, missing numbers 1-1/2, 2)

(6)

Identify the pattern. Use it to fill in the missing numbers.

11, 9-1/4, 7-1/2, _____, _____, _____

(pattern – subtract 1-3/4, missing numbers 5-3/4, 4, 2-1/4)

(7)

Chris reads for 2 minutes the first day of school. After that, he doubles his reading time each day. Make a table to show how many minutes Chris will be reading by the 7th day of school. Translate your time into hours and minutes.

(Sample Table:

1

2

3

4

5

6

7

2

4

8

16

32

64

128

2 hours, 8 minutes)

(8)

The Ross family is saving money for a family vacation. The opened a savings account with $500.00 and then began to deposit money each week. The first week they deposited $20. Each week after that, they deposited $5 more than the week before. Make a table too show how much money they will have saved by week 6.

(Sample Table:

1

2

3

4

5

6

520

545

575

610

650

695

$695 will be saved by week 6.)

(9)

Maria’s cell phone company charges $0.50 a minute for the first five minutes and $0.10 for each additional minute after that. Tammy’s cell phone company charges $0.75 a minute for the first 2 minutes and $0.12 for each minute after that. Which girl will pay less for an 8 minute phone call? Explain.

Make tables to show each girls cost for the 8 minute call.

(Tammy will pay less. She will pay $2.22, while Maria will pay $2.80.)

(10)

Ed works at a grocery story. He is building a triangular tower out of cereal boxes. The base of the display has 15 boxes. The second row form the bottom has 14 boxes. Each row after that has one less until the top only has one box. How many boxes will Ed need to finish his display? Draw a picture or use a table to show your work.

(120 boxes)

(11)

Mia, Kelly, Scott, and Nico are 11, 12, 13, and 14 years of age. Kelly is not the youngest. Scott is not the oldest. Scott is older than Mia, but younger than Kelly. Kelly is younger than Nico. How old is each kid?

(Mia – 11, Scott – 12, Kelly – 13, Nico – 14)

(12)

Leah, Tyson, Jax, and Ariana all have dogs. The breeds are Pitbull, Shephard, Chihuahua and a Retriever. Ariana does not have a Retriever. Jax has a breed that is known for retrieving items for its owner. Leah has the smallest dog. Tyson’s dog is not a Pitbull or a Chihuahua. Match each dog breed to its owner.

(Leah – Chihuahua, Tyson – Shephard, Jax – Retriever, Ariana – Pitbull)

(13)

Yolanda needs a 3 digit code for her locker. She wants to use the first 3 digits or her area code, 213. How many different combinations of using each of these digits does Yolanda have?

(6)

(14)

Francisco needs a 4 digit code for his alarm system. He wants to use the last four digits of his social security number, 1295. How many different combinations of using each of these digits doe Francisco have?

(24)

(15)

The Cyrus family has 4 children: Jessica, Tommy, Sammy, and Tori. Jessica was not born first. Tommy was born in between Tori and Sammy. Sammy is the second youngest. List the children in order from youngest to oldest.

(Jessica, Sammy, Tommy, Tori)

(16)

Tell whether the problem below has too much, too little or just the right amount of information. Then use the relevant information to solve the problem.

Dana has 15 cards. Will has 22 cards. Thomas has 24 markers. How many more markers does Thomas have than Dana?

(Too much, we don’t need to know how many cards Will has. Thomas has 9 more cards than Dana.)

(17)

Tell whether the problem below has too much, too little or just the right amount of information. Then use the relevant information to solve the problem. On Tuesday it was 75 degrees, Wednesday 76 degrees, Thursday 79 degrees. What was the average temperature for the week?

(Not enough information, we need to know the temperature everyday during the week to find the average. There is not enough relevant information to solve this problem.)

(18)

Tell whether the problem below has too much, too little or just the right amount of information. Then use the relevant information to solve the problem. On Tuesday it was 75 degrees, Wednesday 76 degrees, Thursday 79 degrees. What was the average temperature for these 3 days?

(Just right, the average temperature was about 76.7 degrees)



(19)

Tell whether the problem below has too much, too little or just the right amount of information. Then use the relevant information to solve the problem. Veronica’s sister is 20. Steven’s brother is 14. Dave’s mom is 46. Which student has the oldest sibling?

(Too much, we don’t need to know how old Dave’s mom is, because she is not his sibling. Veronica has the oldest sibling.)

(20)

Cecilia, Jaime and Natasha went to the movies. The didn’t go on a school night. They didn’t go on a Tuesday. Jaime wasn’t allowed to go to the movie on Saturday. When did the girls go to the movies?

(Sunday)

 

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