4th Grade - Develop And Apply Generalizations

 
     
 
     
 
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4th
Problem Solving
Develop and Apply Generalizations
Develop generalizations of the results obtained and apply them in other circumstances.
Draw conclusions of solutions in math problems and relate the information to solve other problems.
 

Sample Problems

(1)

Describe and complete the pattern:


1, 2, 4, 8, 16, ___, ___


(Double the number; 32, 64)

(2)

Write the coin value as a fraction of a dollar and solve the problem:


2 quarters + one dime = _____________


(2/4 + 1/10 =10/20 +2/20 = 12/20 (12 nickels = $0.60)

(3)

Multi-step problems:

Matt paid $20.00 for lunch. He bought pasta, salad and dessert. The pasta cost 3 times the amount of the salad and dessert. The salad and dessert cost the same amount. How much was each item? _________


(4)

Sarah’s science scores for the month of April are 86, 90, 83, 82, 79. What is her average score for April? What can you generalize about Sarah’s grade for science?


(Sarah’s average score is 84; I can generalize that she will get a good grade in science, a B)

(5)

Perimeter

If the area of a rectangle is 12. Identify three different perimeters it can have. _______________________

(4 x 3; 6 x 2; 12 x 1)

Learning Tips

(1)

Practice skip counting using a number line in order to help your child find patterns in a list of numbers.


When you are using a number line, it will be best to color code the numbers (counting by 2s (place a blue dot above each number).

You can also identify prime and composite numbers on a number line. Color code the prime numbers one color and composite numbers another color.

(2)

Money and fractions

The value of coins as fractions of a dollar

Quarter = ¼

Dime = 1/10

Nickel = 1/20

Pennies = 1/100


Add the fractions of coins with your child and count out the number of coins (i.e. 3/10 = 3 dimes) that it is equivalent to so they can understand the concept of coins and fractions.


Add unlike denominators: Make the denominators the same by finding the common multiple. Multiply the denominator by the factor to make the multiple. Multiply the numerator by the same factor. Then, add the numerators, do not add the denominators.


For example:

1 + 2

3 4


Find the lowest common multiple to make the denominators the same (multiply by factors up to 9):

3: 3, 6, 9, 12, 15, 18, 21, 24, 27

4: 4, 8, 12, 16, 20, 24, 28, 32, 36

The lowest common multiple is 12

Multiply the denominators by the factor that will make 12, and multiply the numerator by the same factor.


1 x 4 + 2x 3 = 4 + 6 = 10

3x4 4x3 12 12


Make to simplest form:


10 ÷2 = 5

12 ÷2 = 6





(3)

Choose the operation:

Write math word problems. Have your child underline the clue words that let tem know what operation to use. Then, have them identify the operation. Have them complete this task for all the problems without finding the answer. You want them to focus on the process of solving the problem, not getting the correct answer.

(4)

Perimeter- The distance around a figure; measured in linear units


Perimeter = 2 x width + 2 x length (P = 2W x 2L)

P = (addition of # of sides)

P = (2 x 5) + (2 x 4)

P = 18


Geo-board/ Dot Paper

Have the child practice drawing rectangular figures that have the same perimeter, but different area. Have them label the length, width, area, and perimeter. Discuss the differences on how they look.

Remind them that the number of squares it covers is the area in square units. The number of squares on that outlines the shape is the perimeter

(5)

Calculate the mean:

Mean- the average of a set of numbers. You can find the mean by dividing the sum of a set of numbers by the amount of numbers.

Addend- the number that is added to another in an addition problem


For example, 2 + 1 + 3 = 6

Divide 6 by the amount of numbers or addends (3).

6 ÷ 3 = 2

The mean for the amount is 2.


Practice finding the mean.

Use the newspaper and look up scores for various sporting events and have them find the averages in scores and players’ points.

Extra Help Problems

(1)

Describe and complete the pattern:


44, 48, 52, 56, ___, ___


(add 4; 60, 64)

(2)

Describe and complete the pattern:


1, 3, 5, 7, 11, 13, ___, ___


(Prime numbers in order from least to greatest; 17, 19)

(3)

Describe and complete the pattern:


8; 40; 200; 1,000; 5,000; ___, ___


(Multiply product by 5; 25,000;125,000)

(4)

Describe and complete the pattern:


0, 1/4, 1/2, ___, ___


(adding by fourths; ¾ , 1)


(5)

Describe and complete the pattern:


1, 12, 24, 36, 48, ___, ___


(Multiply by 12)

(6)

Write the coin value as a fraction of a dollar and solve the problem:


3 nickels + 3 pennies = _____________


(3/20 + 3/100 = 15/100 + 3/100 = 18/100 ($0.18)

(7)

Write the coin value as a fraction of a dollar and solve the problem:


1 quarter + 3 nickels = _____________


(1/4 + 3/20 = 5/20 + 3/20 = 8/20 ($.040)

(8)

Write the coin value as a fraction of a dollar and solve the problem:


5 dimes + 8 dimes = _____________


(5/10 + 8/10 = 13/10 ($1.30)

(9)

Write the operation and solve the problem:

There was a pizza with 10 slices. If Julie at ½ and John ate 2 slices, how many slices of the pizza are left? _________

(subtract; 3 slices left)

(10)

Write the operation and solve the problem:

Mark spent 1/6 of his time doing homework; 2/6 of his time doing chores; and 1/6 of his time reading a book. How much time did he have left to ride his skateboard? _______________

(add; 2/6 or 1/3)

(11)

Use the table to answer the question below:


Snack Shack at Bouncing Baseball Field

Food Item

Price

Pizza

$2.00

Hot dog

$1.50

Nachos

$3.00

Fries

$1.00

Capri-Sun

$0.50

Water

$1.00


If the Snack Shack sold pizza and Capri-Suns to each baseball team playing on Saturday and there are 15 players on each team. How much money was made? ________________


(15 x $2.00 + 15 + $0.50= $30.00 + $7.50= $37.50)


(12)

Use the table to answer the question below:

Snack Shack at Bouncing Baseball Field

Food Item

Price

Pizza

$2.00

Hot dog

$1.50

Nachos

$3.00

Fries

$1.00

Capri-Sun

$0.50

Water

$1.00


Would the Snack Shack make more money selling 15 pizzas and 15 Capri Suns or 20 hotdogs and 10 waters? ____________

(More money will be made selling 20 hot dogs and 10 waters)

(13)

Multi-step problem:

Joey has $500 to spend on art work for his apartment. The price of photographs are $75.00 each; paintings are $125.00 each, and sculptures are $100.00 each. If Joey bought two photographs, 2 paintings and one sculptures. Would he have enough money? _______


(Yes, he will spend $500.00 exactly)

(14)

Multi-step problem:

Mr. Jackson needs to buy new equipment for his woodshop class. He needs 20 yd. of wood, 3 boxes of nails, 10 tool packs and 20 rulers. The wood is $2.50 per yard; nails are $1.50 each box, the tool packs are $6.79; and the ruler are $1.00 each. How much would all his items cost to purchase? ____________

($50.00 + 4.50 + 67.90 + 20 = $142.40)

(15)

Scores for Top 5 Basketball Stars

Player

Game 1

Game 2

Game 3

Game 4

Jonah

10

17

18

22

Bob

15

16

16

18

Kayden

18

20

23

19

Nick

14

15

19

20

Austin

12

21

20

17


What is the average score for the players in Game 1? _______

(16)

Scores for Top 5 Basketball Stars

Player

Game 1

Game 2

Game 3

Game 4

Jonah

10

17

18

22

Bob

15

16

16

18

Kayden

18

20

23

19

Nick

14

15

19

20

Austin

13

21

20

16


Compare the average scores for game 1 and game 4? Did they make improvement? _________

(Game 1 =14 pts Game 4 19 pts—Yes, they made improvement)

(17)

Scores for Top 5 Basketball Stars

Player

Game 1

Game 2

Game 3

Game 4

Jonah

10

17

18

22

Bob

15

16

16

18

Kayden

18

20

23

19

Nick

14

15

19

20

Austin

13

21

20

16


Who is the leading scorer for the team? ____________ (Kayden)

What is his average score? ________ (16)

(18)

Scores for Top 5 Basketball Stars

Player

Game 1

Game 2

Game 3

Game 4

Jonah

10

17

18

22

Bob

15

14

16

18

Kayden

18

17

23

19

Nick

14

15

19

20

Austin

13

21

20

16


Find the average number of points for Jonah and Bob. _________


(26 pts)

(19)

Scores for Top 5 Basketball Stars

Player

Game 1

Game 2

Game 3

Game 4

Jonah

10

17

18

22

Bob

15

14

16

18

Kayden

18

17

23

19

Nick

14

15

19

20

Austin

13

21

20

16

Which game was the average score for the players the highest?


(Game 3)

(20)

If the area of a rectangle is 30. Identify three different perimeters it can have. _______________________

[(2 x3) +(2 x 10) = 26;(2 x 5) + (2x6) = 22; (2 x2) + (2 x 15)= 34)]

(21)

If the area of a rectangle is 40. Identify three different perimeters it can have. _______________________

[(2x4) + (2 x 10) = 28; (2 x8 ) +(2 x 5) = 26;(2 x 2) + (2 x 20= 44)]

(22)

If the area of a rectangle is 18. Identify three different perimeters it can have. _______________________

[(2x 2) + (2 x9) = 22;( 2x3) +(2 x 6)=18;(2x 1) +( 2 x 18)= 38]


(23)

Find the perimeter of the rectangle below. Choose the perimeter that is the same, but has a different area.


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


(P = 2 x4 + 2 x 5 = 18 units—same perimeter measurements will vary, must =18)

(24)

Find the perimeter of the rectangle below. Choose the perimeter that is the same, but has a different area.



 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(P= 4 x 6 = 24 units—same perimeter measurements will vary, must = 24)

(25)

Find the perimeter of the rectangle below. Choose the perimeter that is the same, but has a different area.


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


(P= 2 x8 + 2 x 2 = 20—same perimeter measurements will vary, must = 20)

 

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