Estimating Area

Here's one way to estimate area.

You will probably be given a problem similar to this on the STAAR.  The reason why things like this are useful is for arts and crafts projects where part of an object has something done to it, like part of it is painted and the rest is not, or part of it has glitter on it, etc.

The estimated area tells us something about how much of a cover we need to get, so how many bottles of glittter or buckets of paint would be needed.  This way we don't have to make extra trips to the store either to buy more or to return what we had that was too much.

This is not the only example of the use of this concept, but is one of the most clear.  Other examples include washing windows on a building that isn't completely covered with them, figuring out how much floor wax to use when buffing a wood or tile floor, figuring out how much grass a sprinkler head would cover.  I bet you can think of some others.

Teaching Creativity

A TED talk about teaching creativity through beating back fear of failure with small successes.

Dave Kelley's TED

Estimation or Using the Test Against Itself

Hello everyone.  I'd like to discuss using estimation as a test taking strategy.  This is one of my favorites, but one some students that I encountered did not willingly embrace.  Some of the complaints were that it was extra work, or that they were not careful enough with the estimation.  I believe they may have had bad experiences in the past with estimation and rounding, as it has a few arbitrary rules that they may have been caught up in.

Estimation is a vital skill that we use every day whether we know it or not.  When we're out shopping, we estimate prices all the time.  19.95 becomes 20 very quickly.  This in turn, helps us calculate and budget how much should be spent on each item.  It also helps us compare prices, especially when the stores don't want to give out cost per unit.  3.99 for 10 apples for example versus 0.67 for 1 apple.

Where students seem to be falling down is that they don't understand when to estimate, or what information the estimate gives us, thus why it's useful.  Estimation is especially useful on problems that involve measurement, as they nearly all include multiplication, sometimes multiple step multiplication.  Thus, having an easier set of multiplication to do can eliminate answers, perhaps even enough answers that the correct one is left alone.

Estimation gives us minimums and maximums.  In my example above, the maximum it will be is $20.  Then estimating tax of 10% gives us tax of $2, so we should have $22 ready to spend at the register for our item that costs $21.64 exactly.  Thus, we got a maximum price, exceeded it so that we would get change back instead of having to leave without the item.

Likewise with measurement.  We should estimate close to the measurements given but make sure we always round down to get our minimum, then always round up to get our maximum.  This strategy can help students who are not careful with decimals when they multiply.  Students who know their multiplication facts will also find that estimation is much faster than multiplying the decimals out.  Other things to point out would be when a number is very close to an easy multiplication fact, like 2, 5, or 10.

The problem with this strategy, when the test is really mean, is that it is possible that it will not eliminate enough answers and a guess or the long multiplication is still required.  In that case, remind students that their exact answer will fall between their minimums and maximums.  Looking at the entire question including the answers would be the best idea to determine if they should estimate or not.  If the numbers vary greater than 3-4, estimation will eliminate 1-2 answer choices and possibly all 3 of the wrong ones.

Product Review: Kuta Software: Infinite Pre-Algebra

Mr. V. here.  I purchased a product called Kuta Software's Infinite Pre-Algebra to help me generate content during summer school.  After using it all through the past few weeks, I thought I would give it a review for their information if they ever stumble over my blog, and for any fellow teachers out there.

The options on Kuta's website are Pre-Algebra, Algebra, Geometry, Algebra 2, and Calculus.  All of these options would load in the same program if ordered together.  As a teacher of middle school math, I limited my purchase to Pre-Algebra.  Any Elementary teachers should do the same, as the content will quickly become more and more limited to the specific subject, and Pre-Algebra had the broadest set of concepts.

Kuta is strong at reinforcing the mechanics of calculation, as you have near complete control over difficulty of problems through slider bars and can "regenerate" them as needed (the software will swap out one problem for another).  You could also use it to try to build teaching worksheets, that move from easier problems and concepts to more difficult ones or ones that use the previous information.  I found this style to be a bit more successful, as it reminded students of what they needed to keep track of when they were doing more complicated questions.

Where I found Kuta falling down a bit, and this may be just the package that I bought, was in measurement of shapes and solids.  It seemed like the program's idea of difficulty was to include decimals in measurement.  Basically this challenges students who's foundation of multiplying decimals is weak, and that's it.  There were no Integers only check boxes for measurement, and the number slider did not seem to adjust the shapes in the same way it did other problems like fractions and order of operations.

Another area that I wasn't quite pleased with was Kuta's attempt at creating word problems.  While some seemed interesting to the students, they seemed to lack that STAAR craziness quality that the students hate.  It was usually very clear what the student was supposed to do.  This is a strange complaint, I know, but one of my goals is STAAR readiness, and these word problems do not come as close as I'd like.  While there is a way to write custom questions, this somewhat defeats the purpose of buying this software as an aid.

Overall, I would give Kuta's Pre-Algebra package an 8 of 10 and would recommend it to late elementary school teachers onward.