# 4th Grade - Exact Vs. Approximate Solutions

 Grade Level: 4th Skill: Problem Solving Topic: Exact vs. Approximate Solutions Goal: Indicate the relative advantages of exact and approximate solutions to problems and give answers to specified degree of accuracy. Skill Description: Decide when to estimate or use exact calculations to find solutions to problems.

## Building Blocks/Prerequisites

### Sample Problems

(1)

Tell whether we need an exact or approximate solution:

Jessie has \$25.00. If a CD costs \$11.99, a book costs \$14.50, and a bottle of water is \$1.50. Does he have enough money to buy all 3 items? (approximate)

(2)

Estimate the difference:

9.2 – 1.5 = ____ (9 – 2 = 7)

(3)

Estimate the length of the pen to the nearest inch: _______ (about 2 in.)

(4)

Round the factors and estimate the product:

749 x 48 = _____ (700 x 50 = 35,000)

(5)

Estimate to find the number of people who attended the carnival

 Group in Attendance Number Attended Adults 578 Children 867 Senior Citizens 231 Employees 132 Total _____ (1,808)

Estimated total of people that attended the carnival _______ (1,800)

### Extra Help Problems

(1)

Tell whether we need an exact or approximate solution:

Janey and Charlotte have a sticker collection. Janey has 534 stickers and Charlotte has 762 stickers. About how many stickers d o the girls have combined? _____________ (approximate- 1,300 stickers)

(2)

Tell whether we need an exact or approximate solution:

Marcy and her family went to Disneyworld. There were (4) adults and (5) kids. The adult tickets are \$49.95 each and the kid tickets are \$24.95 each. How much did they have to pay for the tickets? ___________ (exact - \$324.55)

(3)

Tell whether we need an exact or approximate solution:

On our road trip we had to travel 242.7 miles to San Francisco, 48.1 miles to Sacramento, 83.42 miles to Lake Cheris, and 309.8 miles back to Los Angeles. About how many miles did we travel? ___________ (approximate- about 630 miles {answers may vary})

(4)

Tell whether we need an exact or approximate solution:

At Teen World I bought a shirt for \$21.65 and some earrings for \$10.97. I gave the cashier \$35.00, how much change should I get back? _______ (exact- \$2.38)

(5)

Tell whether we need an exact or approximate solution:

At the graduation each student could have 2 guests attend the ceremony. There were 93 students in the graduating class. About how many guests attended the ceremony? _____________ (approximate- about 180 guests)

(6)

Tell whether we need an exact or approximate solution:

Katie wants to buy a new bike for the summer. The bike she wants is on sale for \$289.00, she has \$119.00 saved. How much does Katie need in order to buy the bike before it goes off sale? (exact- \$170.00)

(7)

Estimate the sum:

9.77 + 3.91 = ____ (10 + 4 = 14)

(8)

Estimate the difference:

17.06 – 11.4 = ____ (17 – 11 = 6)

(9)

Estimate the sum:

1.7 + 9.2 = ____ (2 + 9 = 11)

(10)

Estimate the difference:

5.93 – 5.02 = ____ (6 – 5 = 1)

(11)

Estimate the sums and compare:

12.85 + 4.32 O 15.59 + 8.9 = _____________ (17 < 25)

(12)

Estimate and compare:

82.85 + 7.30 O 92.60 – 11.40 = ____ (90 > 82)

(13)

Estimate the length of the leaf to the nearest ½ inch: _______ (about 1 ½ in)

(14)

Estimate the height of the lollipop to the nearest inch: _______ (about 2 in.)

(15)

Estimate the length of the worm to the nearest ¼ inch: _______ (about 2 ¼ in.)

(16)

Estimate the length of the book to the nearest inch: _______ (about 1 in.)

(17)

Estimate the height of the box to the nearest ½ inch: _______ (about 2 in.)

(18)

Round the factors and estimate the product:

3,332 x 47 = _____ (3,000 x 50 = 150,000)

(19)

Round the factors and estimate the product:

4,789 x 22 = _____ (5,000 x 20 = 100,000)

(20)

Round the factors and estimate the product:

\$812.15 x 7 = _____ (800 x 7 = \$5,600)

(21)

Round the factors and estimate the product:

6,322 x 296 = _____ (6,000 x 300 = 1,800,000)

(22)

Round the factors and estimate the product:

9,567 x 32 = _____ (10,000 x 30 = 300,000)

(23)

Round the factors and estimate the product:

389 x 723 = _____ (400 x 700 = 280,000)

(24)
 Grade Level Amount of candy sold Estimated amount sold Kindergarten 576 boxes □ (600) First Grade 874 boxes □ (900 Second grade 281 boxes □ (300) Third Grade 621 boxes □ (600) Fourth Grade 813 boxes □ (800) Fifth Grade 765 boxes □ (800) Total sold □ (3,930) □ (4,000)
(25)

Using the table at the top, would the estimated total be the same if you had only rounded the exact total? ________ (yes)