Most students fear the dreaded word problems. Because of this, most standardized tests feature these problems. Using mathematics in every day life, requires we understand the situations when it is applicable.
There are some standard phrases that students will need to understand prior to conquering the word problem dilemma and that's what this page is all about.
Is - Usually means equals. As in the phrase 5 + 3 is 8.
Of - usually means multiply. As in the phrase 1/2 of 8 = 4. Note, when multiplying by a fraction less than 1, the total is less than the original amount.
A very valid question. There seems to be a lot of variance in the way Algebra is presented. This is my website, so - I'm presenting things my way. Before we really get into Algebra, it's important that students understand word problems. Most standardized tests are geared around word problems.
It's an unfortunate fact of life that the standardized tests are becoming more and more important for a variety of reasons. Sure, most studies have shown that they are not very accurate at predicting success in mathematics. According to the one report in Politifact (a Virginia publication) quoted some congressmen saying that the United States ranked 25th out of 25 countries in mathematics in 2006).
Gosh - we must be a nation of idiots, right? Well, not really. The article goes on to say that the Congressmen exaggerated the true findings (Congressmen - exaggerated? - we are all shocked!) But, according to these statistics, the United States is definitely not #1 in mathematics (obviously, our representatives in congress aren't too bright, maybe they represent the general population in more ways than we're giving them credit for).
These scores are all about standardized test results. It's the only measure we have, and we're not going to abandon it just because it's fairly useless. We send our kids to school 9 months out of the year (other countries send their kids for 12 months). We do 9 months because we need our kids to harvest the crops in the summer, or at least that was the case when we started this practice. We send our kids to class when they don't have pictures, or sports practice, or band trips, or anything else to do. Going to class ranks fairly low on the priority scale for most schools. The parents that complain about this pull their kids 2 or 3 days early for vacations because they have tickets to wherever. For some reason, most kids don't think school is that important. (Wonder where they got that idea from?)
Anyway, scholarships, admittance, national results, and many other things are based on standardized tests. So, it's important that our kids are prepared for them.
You can print from this sheet - or go to 1,2 Word, for a cleaner version.
1.2 - Pre-Word Problems Worksheet
Part 1 - Convert each to it's algebraic equivalent.
1) The difference of 7 and 5 2) x decreased by 17
3) The quotient of 12 and 6 4) Half of 16
5) x increased by 5 6) The product of x and 3
7) 3 squared 8) The sum of x and 7
9) Twice y 10) Six plus seven is x
11) The quotient of 12 and x 12) a cubed
Part 2 Solve each expression
13) One third of 27 14) 4 squared
15) 18 is reduced by 6 16) 7 doubled
17) The quotient of 8 and 2 18) The product of 5 and 3
19) 12 divided by 3 20) 20 increased by 3
21) 10 decreased by 7 22) 5 tripled
23) 6 less than 10 24) 2 times 4