Try...Check....Revise (Math 1512)

I am infamous for the saying "If at first you don't succeed, try...and then try again!"  I have worked with children in childcare settings for 12 of the last 13 years and my goal was to always make the best big people out of the little people I blessed to share time with.  Part of achieving this goal was to make them independent thinkers.  While it often seems easier to just "do it for them," in the long run kids do not benefit from this.  Children need to learn that with success comes failure and many times there will be several failures before finally succeeding.  The most basic situation I can think of is completing puzzles with toddlers.  Little kids LOVE to dump out puzzles, and then when the pieces do not easily go back into place chances are they will walk away.  I loved to sit with my little ones and "coach" them through reassembling the puzzle.  "Turn this piece...oops! , try again, ok...now try this piece here, wow...good job! "  Now, how does any of this pertain to our math lesson???
Try...Check....Revise!
*Use the given facts to try and check one answer. Then revise and try again until you solve the problem.  "If at first you don't succeed, try...and then try again!"  

-Solving Linear Equations (equations where the value of y is known, they can be associated with linear functions)  Try-Check-Revise is relatively efficient when the numbers in the equation are integers.  The equation 12x + 35 = 131 can be solved using try-check-revise.

To begin, use number sense to estimate the solution.  For this particular problem one may estimate the solution to be 10.  Substitute 10 for x,

12(10) + 35= 155, since 155 is greater than 131, the actual solution must be less than 10. "Try again!"  

After a couple more attempts the solution proves to be 8.... 12(8) + 35 = 96 + 35 = 131 

A spreadsheet can also be used to solve linear equations, and it provides a high-speed application of the try-check-revise strategy.  This approach also starts by using number sense and estimation to think of a reasonable range for the solution.  This independent thinking gives students the opportunity to "attempt" to solve the equation based off of their number sense and then be willing to continue problem solving until the correct solution is found.  This was a fun web site that I found dealing with linear equations....lots of opportunity to Try-Check-Revise! Cool Math- Linear Equations

 

Estimation....Math 1510

Just Guess, Guess-timate, Close Enough!  These are all common terms associated with Estimation.  To estimate means to approximately calculate.  Common examples of estimations can be costs of items, measures, quantities and values.  The skill of estimation can be very useful in everyday life.  Probably the most used estimation of cost is done while grocery shopping.  Before the days of credit cards it was essential to know that if you went into the store with $50.00, you would have enough money to purchase all the items you placed into your cart.  I remember "keeping track" for my mom as we paced up and down the aisles many times.  Of course in an effort to avoid the embarrassing event at the check out of not having enough money, I was told to round-up when estimating.
I found this neat website that has all sorts of ideas for teaching children various estimation skills at the grocery store.  Math at the Grocery Store

Computational estimation is a process for finding a number reasonably close to the exact answer for a calculation.  There are four computational estimation techniques: rounding, substitution of compatible numbers, front-end estimation, and clustering. 
*Rounding- the process of replacing a number or numbers in a calculation with the closest multiple of 10,100, 1000 etc... 

How to round numbers

Make the numbers that end in 1 through 4 into the next lower number that ends in 0. For example 74 rounded to the nearest ten would be 70.
Numbers that end in a digit of 5 or more should be rounded up to the next even ten. The number 88 rounded to the nearest ten would be 90.

*Substitution of compatible numbers- involves replacing some or all of the numbers in a computation with numbers that are easy to compute mentally

Compatible Number Strategy
Compatible numbers are number pairs that go together to make “friendly” numbers.  That is, numbers that are easy to work with.  To add 78 + 25 for example you might add 75 + 25 to make 100 and then add 3 to make 103.

*Front end estimation- involves calculating with the leftmost, or front-end, digit of each number as if the remaining digits were all zeros

Front-End Estimation
This strategy involves adding from the left and then grouping the numbers in order to adjust the estimate.  For example 5239 + 2667 might be calculated in the following way: Seven thousand (5000 + 2000), eight hundred (600 +200) – no, make that 900 (39 and 67 is about another hundred).  That’s about 7900

*Clustering- involves looking for the number about which the addends cluster and then multiplying by the number of addends

Clustering in Estimation
Clustering involves grouping addends and determining the average.  For example, when estimating 53 + 47 + 48 + 58 +52, notice that the addends cluster around 50.  The estimate would be 250 (5 x 50)

As you can tell when it comes to estimation there are several options to help guess-timate. The approximate answer you are looking for can easily be found as long as the situation allows for "close enough" to be good enough!