| Glossary | P-CCS Curriculum |
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Multiplication: Everyday Mathematics stops at 2-digit multiplication. Anything bigger should be estimated, and then solved with a calculator. As a stretch exercise, a student may be asked to multiply a 3-digit number by a 2-digit number. Let's look at: 75x12=? Traditional: A simple, compact method, with few chances for errors. How does Everyday Mathematics treat the same problem? Everyday Mathematics encourages children to 'discover' their own algorithms. They believe 'discovery' is the only way children can learn and retain information. Teachers 'facilitate' this discovery in early grades, then show two methods; Lattice and Partial Products. Children are then supposed to choose the method they like best (including their own) and use it from then on. Many children choose the lattice method because it is 'fun'. They adopt it and use it exclusively. They can fill out the lattice in any order. Try it, it is a fun party trick. Ask your child which method she uses. Also ask "Why?" Everyday Mathematics does introduce the short method in 6th grade (the standard algorithm). By that time, the lattice method may be so ingrained into your child that she will not adopt it. Fortunately P-CCS deviates and introduces the standard algorithm at the same time as the Lattice and Partial Products. No shortcomings of the Lattice or Partial Products are shown. Also, we are fortunate that we don't use Everyday Mathematics in 6th grade. They force students to learn the "Egyptian Method". This is a 3-step binary process that was last used thousands of years ago. It has absolutely no use in the modern world. So, what is wrong with the Lattice and Partial Product methods? Let's look at them with a few examples. Lattice: Let's look at the same problem: 75x12=? The lattice set up is:
5x1=5 Enter it as 0 / 5 in the top right box. Continue to fill the boxes. Once they are full, it's time to add along the diagonal lines (right to left) and put the answer on the outside of the box. Carries get put in the next column to the left. The answer is read left to right, starting at the left. 0900. Still no big problem, right? The answer is the same. It seems efficient. The major benefit is that the multiplication and addition are done separately. The lattice can be filled out in any sequence. If the subject is treated properly, it does make sure all the partial products are computed. But wait; when did Everyday Mathematics teach adding right to left with carries? It does, but it prefers Partial Sums. To use Partial sums, you would have to rewrite the lattice into columns first. The standard method as the only way to make the lattice work. Everyday Mathematics calls this the "Fast Method", but does not emphasize it as being more important than the other methods. Can someone please explain to me how the lattice teaches place value? Tilt your head to the right and squint a little bit. Ask any student or teacher to show you the place values. Everyday Mathematics is all about the big concepts, right? Lattice multipication doesn't reveal the deep concepts of multiplication more than the standard method. Still, if it works and kids like it, what's the problem? Let's expand the task a little bit to 975x12=? Set up the lattice: Fill it out: Now I'm getting worried. I have to add 4 numbers and a carry along the diagonal in my head. Let's take it up another notch with a bigger number and throw decimals into the lattice. Try 329.75x1.23=? Here's the lattice. To locate
the decimal, find where the two decimals intersect. Then follow the
diagonal down to the left to place it in the answer? That was a mess! Try asking
your child to do the same multiplication. It will take at least half
a page. Most likely, the answer will be wrong. Of course, the right
answer isn't always important anymore. Think about the problem above. If I own a business and need to charge 23% above my cost to stay in business, one way to figure my list price is to multiply my cost times 1.23. So: "If my cost is $329.75 for a DVD player, what should I charge if I have a 23% markup?" $405.59 or round up to $405.60. Of course, the Everyday Mathematics answer to the question begins with, "Reach for a calculator…" Later on, in middle school, Connected Math will begin with, "Create a spreadsheet…"
Place value is clearly the priority here. This would actually be a very good supplement for those students who don't understand the standard method at first. Or show this first as an introduction to the standard algorithm. Here is a quote from the
Everyday Mathematics Handbook about Partial Products. Let's check the $329.75 x 1.23 using the standard method; Yeah, right! Fifteen rows to add. Not likely to get a correct answer. I set this up nicely in a spreadsheet so I could make sure I didn't miss any products. -------------------------------------------------------------------------------------- Unfortunately, the State of Michigan is following this trend also. Check here for the reduced emphasis on correct answers in the MEAP. Meanwhile, our children must be taught the standard methods for addition, subtraction, multiplication and division. These standard algorithms must be the only acceptable methods used for daily computation. Alternate algorithms are a good tool to use for those students who need help learning the standard methods. Forcing our children to 'discover' 2,000 years of mathematics on their own is wrong. Forcing non-standard algorithms on our children is wrong. Preparing our children for success is right. Teach Our Kids!
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