Common Core Math Front-End Estimation

The Common Core Standards include estimation skills for every grade level. We’re interested in using language with children that includes such words and phrases as about, close, just about, a little more (or less) than, and between. From a 10,000 foot view, we want our students to be able to do the following mathematically: 

Make sense of problems and persevere in solving them. 
Reason abstractly and quantitatively. 
Construct viable arguments and critique the reasoning of others. 
Model with mathematics. 
Use appropriate tools strategically. 
Attend to precision. 
Look for and make use of structure. 
Look for and express regularity in repeated reasoning. 


For students, estimating is an important skill. First and foremost, we want students to be able to determine the reasonableness of their answer. Without estimation skills, students aren’t able to determine if their answer is within a reasonable range. This inability to reason causes them to make computational errors without it even being on their radar. For example, if a student is asked to multiply 523 x 34 and they arrive at a product of 177,820, we want students to independently recognize that 177,820 couldn’t possibly be a reasonable answer. If they use the estimation of 500 x 30 to arrive at 15,000, they quickly realize that their place value is way off and that their work needs to be redone. 

Second, we want students to be able to use mental math to more quickly arrive at a reasonable ballpark solution. When I worked as a talent development and learning specialist at Time Warner, I remember sitting in meetings with marketers and finance executives as they kicked around cost estimates for various projects. The leaders in the room could compute estimates quickly and mentally. They didn’t need calculators to find reasonable percentages or cost ranges. They could look at the data and mentally compute estimates that were sufficient for moving the agenda forward. It was only afterwards that they would build their Excel models and determine exact costs and time lines. If we want to teach our children to be successful in business, we need to promote strong estimation skills. 

Third, we want students to use estimation beyond adding, subtracting, multiplying and dividing. We also want students to be able to reasonably estimate time and distances. About how long does it take for us to get from Point A to Point B? Approximately what time will it be when you finish all of your homework? About how many miles is a walk from The Guggenheim Museum to the Sony Technology Lab if 20 blocks is about a mile. Time estimation skills are an important part of executive functioning, and we want students to develop a sense of estimating reasonable time for both short and long range planning. 

When teaching computational estimation to elementary and middle school students, there are at least five different strategies to consider depending on the context. It’s important to teach all five so that students develop a repertoire of strategies for various situations. But most importantly, we want students to understand why estimating is valuable before getting caught up in the minutiae of the skill, and we certainly want students to understand that estimation does not replace the need to come up with accurate answers. What we’re really talking about is teaching students to be critical thinkers and to understand what’s being asked of them. 

Rounding whole numbers 
Estimating a sum 
Front end estimation 
Compatible numbers 
Cluster estimation 
http://mylearningspringboard.com/why-teaching-both-estimation... 


Here recently I was asked a question about estimation methods: 

My daughter's homework was to estimate the number of 953 divided by 18, using front-end estimation, using rounding to estimate, and using compatible numbers to estimate. What are the differences between these three methods? Do we get the same result? Thanks! 


You definitely don't get the same results as these three methods are quite different! 


Front-end estimation means you keep the "front" or first digit of each number, and make the other digits to be zeros. 

So, 953 ÷ 18 is estimated to 900 ÷ 10 = 90. 

Another example: 56 × 295 would be estimated as 50 × 200 = 10,000. 


Rounding means you round the numbers, usually to their biggest place values, but sometimes you can round "creatively". In any case, the numbers you round to should be easy to work with mentally. 

So, in 953 divided by 18 we round 953 to nearest hundred, and 18 to nearest ten. 953 ÷ 18 becomes 1,000 ÷ 20 = 50. 

Another example: 56 × 295 would become 60 × 300 = 18,000. 

An example of rounding "creatively": with 24 × 32 you can round 24 to 25 (to the "middle five"), and 32 to 30. The estimated result is 25 × 30 = 750. The exact result in this case would be 768 so the estimation was fairly close. 

Another principle to keep in mind with when using rounding to estimate is that if you have an addition or multiplication problem, it's best to round one number down, the other up, in order to minimize the rounding error. If you have a division or subtraction, it's best to round both numbers "the same direction", either up or down. 


Compatible numbers means finding numbers that are close to the numbers in the problems but such as are easily to work with mentally. 

So, 953 ÷ 18 could be estimated as either 960 ÷ 20 or 1000 ÷ 20, depending on your mental division skills. 

960 ÷ 20 = 96 ÷ 2 = 48. 

Another example: estimating 56 × 295 depends, again, on your mental multiplication skills. You could try to leave 56 as it is, and make 295 to be 300, to get 56 × 300 = 16,800. Or, you might make the numbers to be 60 and 300 (the same as in the rounding method) and get 18,000. 

To compare all three methods, we check the exact result of our problem, which is 953 ÷ 18 = 52.944444444... From this we can see that the rounding method was most accurate in this case (it gave us 50), and front-end estimation did really bad (it gave us 90). 

In the other example, the exact result is 56 × 295 = 16,520. Again, rounding (18,000) or compatible numbers (16,800 or 18,000) method did best, and front-end estimation the worst (10,000). 
http://homeschoolmath.blogspot.com/2010/09/estimation-methods...