# 4th Grade - Develop And Apply Generalizations

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

## Building Blocks/Prerequisites

### 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)

### Extra Help Problems

(1)

Describe and complete the pattern:

44, 48, 52, 56, ___, ___

(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? _______________

(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)