6th Grade - Apply What You Learned

 
     
 
     
 
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6th
Reasoning
Apply What You Learned
Apply strategies and results from simpler problems to more complex problems.
Apply strategies from simpler problems to more complex problems. Strategies may include: 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 Use the results from simpler problems to find the answer to a more complex problem. Determine how to break the problem into smaller parts in a way that makes sense. Combine the parts of the problem to find a final solution.
 

Sample Problems

(1)

Makenzie is using congruent equilateral triangles to make a trapezoid. The perimeter of each triangle of each triangle is 3 cm, each side of the triangle is 1 cm. Makenzie is fitting the triangles together with no gaps and overlapping. When she fits the first two triangles together, the perimeter is 4 cm. Three triangles have a perimeter of 5 cm. What will the perimeter be if she places 24 triangles together?

(26 cm)

(2)

Cameron is making a design with similar triangles. Each triangle is 3 times bigger than the previous. The first triangle she used had an area of 4 cm squared. What will the area of her 6th triangle be?

(972 cm squared)

(3)

Bobby has a large pizza. He gives away 1/3 of it and then he gives away half of what he has left. How much pizza did Bobby keep for himself?

(1/6 of the pizza)

(4)

Felipe is on the track team. He runs 3 miles everyday before school. On weekend days Felipe runs 7 miles. How many miles does Felipe run in 4 weeks?

(116 miles)

(5)

Tickets to an amusement park cost $42.50 for children 12 and up and adults and $25.50 for kids 12 and under. Lucia and her family are going to the amusement park. Her family includes; two sisters ages 6 and 17, two brothers ages 9 and 12, and her mom and dad. Lucia is 15. Lucia’s father has a discount coupon for $10 off. How much will it cost for Lucia and her family to get into the amusement park?

($236.50)

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.)

(6)

Sixth grade students will encounter multiple-step problems. Though, sixth graders do have the skills to solve the individual computations in the problem, they often find such problems challenging. This is why it will be crucial that your child follow all 4 phases of the problem solving process. Make sure that your child understands that in doing this, phase two will always have more than one step or operation. Multiple-step problems require students to solve the sub-problems within a problem, before answering the original problem. In solving these sub-problems, or the problems within the problem, your child may use the same operations or a variety of different operations. Hence, you and your child may want to come up with a system of color coding to help see all the different problems that need to be solved. Below, you will find a word problem and one possibility of how to color-code/underline to show all the parts of the problem that need to be addressed.

Sample Problem: Rob had 16 red marbles. He split them evenly with his brother. Then Rob bought 30 blue marbles. He gave away 1/3 of them. How many marbles does Rob have left?


Color-coding: Green-solve 1st, Blue-solve 2nd, Red-solve last

Rob had 16 red marbles. He split them evenly with his brother. Then Rob bought 30 blue marbles. He gave away 1/3 of them. How many marbles does Rob have left?

16 split evenly is 16 divided by 2 = 8 red left

30 gave away 1/3 to find this: 30 divided by 1/3= 10, now subtract the 10 from the original amount 30 – 10 = 20 blue left.

20 blue + 8 red = 28 marbles.

After solving the problem, don’t forget to go on the phase 3, check it!

Extra Help Problems

(1)

Kyle is planting a garden. So far he has planted seeds at ½ a foot from the edge, 1 foot from the edge, and 1-1/2 feet from the edge of the garden. What pattern is Kyle using to plant his seeds?

(Kyle is planting seeds every ½ a foot.)

(2)

Jake is training for a bike race. He rode 3 miles the first week, 6 miles the second week, and 9 miles the third week. If Jake continues using this pattern, how far will he be riding by the end of his third month of training?

(36 miles)

(3)

Kylie has be asked to stack cereal boxes for a store display. The manager would like the display to be in a triangle shape with one box at the top. 2 in the second row, 2 in the third and so on. If Kylie has to use 136 boxes in her display, how many boxes will be in the bottom row?

(16 boxes)

(4)

Madison is slowly increasing the time she spends reading each day. She began reading for 5 minutes the first day of school and then doubled her reading time each day for two school weeks (10 days). How long was Madison reading each day at the end of the 1st week?

(80 minutes or 1 hour and 20 minutes.)


(5)

Madison is slowly increasing the time she spends reading each day. She began reading for 5 minutes the first day of school and then doubled her reading time each day for two school weeks (10 days). What was the first day that Madison read for more than 2 hours?

(6th day)

(6)

Brendan is building a pyramid out of blocks. He has 21 blocks altogether. How many rows of blocks will be in his pyramid?

(6 rows)

(7)

Brendan used 18 blocks to build 3 steps. Each step had a width of 3 blocks. How many more blocks does he need to make 5 steps?

(15 steps)

(8)

Quarts of oil are on sale. For every 3 quarts of oil purchased, you get one free. If Kevin has 33 quarts of oil in his car, how many did he have to pay for?

(25)

(9)

Quarts of oil are on sale. For every 3 quarts of oil purchased, you get one free. How many quarts of oil will Daniel have to buy to get 6 free?

(18)

(10)

Emily is drawing polygons. She starts by drawing a triangle, then a square, followed by a pentagon. What will the 6th figure she draws be called?

(octagon)

(11)

Polygons with four or more sides can be divided into triangles by connecting vertices. A rectangle can be divided into two triangles by dividing the rectangle across opposite corners. Use the table below to determine how many triangles a 10 sided polygon can be divided into.

# sides

4

5

6

7

# triangles

2

3

4

5


(8 triangles)

(12)

Makenzie is using congruent equilateral triangles to make a trapezoid. Each side of the triangle is 2 cm. Makenzie is fitting the triangles together with no gaps and overlapping. When she fits the first two triangles together, the area is 4 cm sq. Three triangles have a area of 6 cm squared. What will the area be if she places 12 triangles together?

(24 cm sq.)

(13)

Cameron is making a design with similar octagons. Each octagon is 2 times bigger than the previous. The first octagon she used had a perimeter of 8 inches. What was the perimeter of her 5th octagon and what was the length of each side?

(40 inches, 5 inches)

(14)

During a week in the dry summer months, the water level in a lake decreased by 5 inches per day for a week, except for two days when it decreased ½ that amount. During the same week in the following year, the lake lost ½ the amount of water as the previous year. How much water was lost in the second year?

(15 inches)

(15)

Holly’s tennis class meets twice a week for 1.5 hours. Holly practices tennis on her own for 2 hours a day on the weekends and one hour on Monday and Wednesday. About how many hours does Holly practice tennis each month?

(36 hours)


 

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