4th Grade - Exact Vs. Approximate Solutions

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

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)

Learning Tips

(1)

Measurement

Review different measurement tools (ruler, measuring tape, yardstick, etc.) and practice measuring different items around your home. This will allow the child to become familiar with the different units of measurement (cm, m, in, ft. yd.), which will allow him/her to make reasonable judgments when estimating measurements.

(2)

Rules for rounding

Steps to rounding:

  1. Identify the place of the digit that you need to round

  2. Look at the digit to its right, if it is 0, 1, 2, 3, or 4, the digit you are rounding stays the same; if the digit to the right is 5,6,7,8, or 9, the digit you are rounding increases by one.

The digits after the one you have rounded become zeros

(3)

Math vocabulary

Estimate- to find an answer that is close to the exact number

Exact- the accurate solution to a problem, with no error


Approximate- An answer that is close to the exact number


Sum- the answer to an addition problem


Difference- the answer to a subtraction problem


Product- the answer to a multiplication problem

(4)

Estimate Distance

While driving on the freeway bring your child’s attention to the signs that provide information about the distance for a street exit. Have them practice estimating to the whole number (i.e. Bundy St. - 1 ¾ miles, would be estimated to 2 miles). Then, you can expand my using www.mapquest.com and type in directions to a location; have the child estimate the distances for traveling on (streets & freeways).

(5)

Compare exact and approximate

Explain exact and approximate to your child. Write a few scenarios on index cards of when you will have to provide an exact number and when you can use an approximate answer. Have the child categorize the cards and make a decision on what type of answer is necessary. Then ask why they think that.

(6)

Estimate products:

  • Round the factors to the highest place value

  • Multiply the factors in the highest place value

  • Add the number of zeros left

  • For example (300 x 400 = 120,000) I multiplied 4 x 3 = 12, and then added my remaining zeros.

Estimate Decimals

Round to the nearest whole number and eliminate the decimal.


For example, 43.7 = 44


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)

 

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