3rd Grade - Exact Vs. Approximate Answers

Problem Solving
Exact vs. Approximate Answers
Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
Mathematical Reasoning: give answers, problem solving The ability to know when an approximate answer is useful and the ability to decide when a precise answer is needed instead.

Sample Problems


Would you use an approximate or precise measurement to make a new recipe for upside down cake? (answers will vary; precise, especially the first time you make a recipe)


Would you use an approximate or precise level of volume for the music at the party? (answers will vary; approximate, you would give it an “ear test” and see how it sounded)


Why would you only use an approximate number of chips to put out for the party? (answers will vary; it doesn’t matter how many chips are out, as long as people have something to eat)


Why would you use a precise measurement when measuring the length of your long jump? (answers will vary; precise measurements help to track improvement or measure performance)


Describe your process for using approximation when feeding a meter with money while going into the store? (feed the meter with more money/time than you think it will take in the store, just to be safe)

Learning Tips


Consistently give your child verbal clues that help him/her know how much accuracy is needed in a wide variety of life experiences. When you use numbers or words that suggest numbers use such modifiers as “exactly,” “about,” “a handful,” “a few,” “your choice,” and “count carefully.” Children will subconsciously absorb a lot of meaning from the words you choose.


When working in a numerical setting, as children to tell you how much precision is needed. Ask your child, “Do you think we need exactly six raisins or a small handful?”


When reducing a recipe, think out loud with your child as you determine how to re-proportion the ingredients. Talk about what items in the recipe can easily be divided up (flour, sugar, vanilla) and which can’t as easily (an egg). Explain to your child that when you re-preportion a recipe, you always look at the number of eggs and then divide the recipe accordingly—if the recipe calls for 3 eggs, then to make 1/3 of the recipe makes much more sense than to make ½ or ¼ of it. The next time you want to re-proportion a recipe, ask your child to make this determination and explain to you why this degree of precision is advisable.


Look for opportunities to explain other mathematical reasoning strategies to your child and then allow your child opportunities to practice. For example, if 20 invitations are packaged in one box and your child intends to invite 22 children, it will be necessary to purchase another box of invitations; in this instance, knowing that 22 is “about 20” will not be helpful. Similarly, if parents will be driving children to an event and each car has enough seatbelts to safely carry 4 children, then six cars will be needed to transport 21 children, even though 21 is much closer to 20 (a multiple of 4) than it is to 24 (the next multiple of 4). Or, if you have 98 chocolate chips when 100 are required in a recipe that makes 36 small cookies, 98 will be close enough and it is unlikely that anyone will notice.


Teach your child that one way to always be sure that you have enough money to purchase (in cash) what you have placed in your cart at the grocery store (exclusive of tax) is to round all prices up to the next dime. Numbers ending in 0 are easy to add and with each additional item there are likely to be additional extra pennies that won’t be needed. For example, 5 items that cost 20 cents, 54 cents, 93 cents, a dollar and 12 cents, and 81 cents will be “cart-added” (a fun term that indicates that this isn’t an “official” mathematical rounding method) would be 20+60+1.00 + 1.20 and 90 or $3.90. When one always rounds up so generously there is no possibility of finding that the cart contents total more than you think they do. (The actual value of the articles in this example is $3.60.) This is an example of a time when you want to be sure that there is an adequate disparity in the actual and estimated value to allow for unforeseen events such as a mathematical mistake, forgetting to add one item in a large order, etc. Ask your child to help you think of additional unforeseen events and to suggest times when this type of estimation is inappropriate for your family. (If you use this method to estimate how much to purchase of an item you will end up with waste; for example, if purchasing ribbon for several girls and each girl rounds her requirement up to the next-highest tens number, too much will be purchased and the excess cannot be returned.)

Extra Help Problems


Maria’s cookie recipe makes 2 dozen cookies. The recipe requires 2 cups of sugar. Maria wants to make 4 dozen cookies. How much sugar will she need? Does she need exactly this amount, or just approximately this much? (4 cups, exactly)


Jose needs 7 nails to build his wooden car model. The nails are packaged in groups of 4 to a package. Can he buy exactly as many nails as he needs? What should ask the clerk for? (2 packages of nails)


For these activities, say if you need an exact amount or an approximate amount. Choose the most reasonable choice from the listed possibilities:

Enough glue to attach 3 small hearts to a valentine.

Choices: a very small puddle on a scrap piece of paper OR 1 Tablespoon on a scrap piece of paper (puddle; approximate)


Raisins to sprinkle on your breakfast oatmeal.

Choices: ¾ cup OR a small handful (handful; approximate)


Enough rope to make a jump rope for yourself.

Choices: 2 feet of rope OR 2 yards of rope (2 yards; approximate)


Food coloring, in a dropper bottle, to color enough play-dough for one toddler to play with

Choices: 3 drops from the bottle OR the whole bottle (the bottles are very small)

(3 drops is probably sufficient; approximate)


Batteries for your flashlight

Choices: 2 batteries OR however many are in the drawer at your house (2 (or the number in the manufacturer’s specifications; exact)


Enough paper to make an origami square.

Choices: one sheet of notebook paper that you can cut to size OR one sheet of newsprint that you can cut to size

(Notebook paper size; usually origami directions call for a 6” square; exact in that each side must be the same size)


New buttons for your sweater

Choices: the number of buttonholes your sweater has OR as many buttons of that color that your mother has in her sewing box (the number of buttons equals the number of buttonholes and it is an exact number.)


Number of busses to order for a field trip; two classes will go and each class has 20 students. Each bus can seat 30 people.

(2 busses exactly; there will be seats left over but there is no such thing as ordering a half-bus)


Choose words that indicate exact measurements:

Cup, inches, handful, length of your index finger (cup, inches)


Bushel, acre, field, bucket (bushel and acre are standardized measuring units; field and bucket can be of varied sizes)


Precise or approximate? (Answers could vary under particular circumstances. These are general answers.)

Number of seconds it took to run a 100-meter race? (precise)


Amount of flour to make cookies? (precise)


Number of 2 x 4 wood planks to make the tree house in the backyard? (precise)


Number of animal crackers to put out in the bowl at the party?



Number of ink cartridges to buy so the printer will work? (precise)


Amount of sunscreen to put on at the beach? (approximate)


Number of pictures to take while our family is on vacation? (approximate)


The answers to the multiplication problems on my math homework page? (precise)


The number of songs I need to put on my ipod? (approximate)


The number of weeks I need to save to buy the new puppy? (precise)


The number of stamps I need to put on the package to mail? (precise)


The number of times I pass the mashed potatoes around the table at dinner? (approximate)


The number of words I write on my 250-word essay for the school contest? (precise)


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