Posts by GrreatTeacher

Not all problems on multiple choice tests are designed to be solved. Some are there to test concepts that, if you had the knowledge, you could eliminate all the other answers.

Let's try an example using calculating a tip.

Find the dollar amount of a 10% tip on a $28 bill.

a. $5.40

b. $5.60

c. $2.80

d. $0.28

The knowledgeable student knows he only needs to move the decimal place one place to the left. So the actual numerals are not changing. This means that a and b are obviously incorrect. Now consider c and b. The numerals are the same as the $28 amount. But in c the decima point was moved 1 place to the left while in d it was moved 2 places to the left.What is the rule when multiplying by factors of 10? Only move the decimal one place to the left.

So, the teacher is likely only giving you the time to really think about two answers since the first two are so obviously wrong.

How do teachers choose the other wrong options on test? I chose b because it represented 20% If we had been working with lots of 20% tips in class a lazy reader or rigid thinker might automatically go for choice b. I just learned something about that student. I chose a because it represents a math error on the 20% tip. This means all of the above, plus their calculation skills are poor.

How about this problem?

Which represents 80% of 200?

A 16000

B 280

C 1000

D 160

You should be able to look at that and immediately know the answer is D because it's the only answer that is less than the original number 200. When you multiply a whole number by a fraction, the answer is always smaller. As a teacher, I dont want you to solve that problem, I just want to know that you understand that concept.

Maybe you can figure out the errors in the wrong options and then the concepts that I would then have to reteach.

1

Merry 4th, gimme a fifth!

by zed is dead in

jw
friends

he's going to end up, on the dirty boulevard.

get to end up, on the dirty boulevard.

i want to fly away.

GrreatTeacher

Happy 4th of July, everyone. Stay safe around those fireworks.

76

Do You Like or Dislike Algebra? Why and Why not?

by Scott77 in

july 28, 2012is algebra necessary?by andrew hacker .

a typical american school day finds some six million high school students and two million college freshmen struggling with algebra.

in both high school and college, all too many students are expected to fail.

GrreatTeacher

Mathematics is the umbrella term and arithmetic is just one type of math. Algebra, geometry and statistics are others.

Arithmetic is addition, subtraction, multiplication and division and is typically covered in elementary school. However, fractions and percentages are also arithmetic and these stump plenty of adults. Hmm, how much should I tip on this $25 check at 20%? If you know the algorithm, you can figure it out on the back of the check. So called "kill and drill" worksheets will get that result. However, mental math is quicker and it comes from understanding the concepts. Most easily, we could move the decimal in $25 to the left a space and know that $2.50 would be 10%. So, we can then double it to get $5 as your 20% tip. Or, you could know that 20%represents the fraction 1/5 and to find 1/5 of $25 you can just divide by 5. You still get $5. You can fugure these things out quickly if you have a good conceptual understanding and you are not a rigid thinker.

Rigid thinkers know the algorithms and they will set up and solve the problem 25 x .2 and get the answer 5 after correctly placing the decimal in the answer. Worksheets and drills promote this type of learning. If this is the way that our students are able to do math, then we need to teach them that way. However, the goal is to get flexible thinkers who can understand and relate concepts from one math discipline to another. To teach to these students, a problem solving approach works best. Teachers need to help them make connections, but then they need to work to solve these problems.

Instead of setting up a lesson in which we find a percentage of a number, I want to set up a problem in which we need to discover the amount of a tip for a restaurant bill. Would a tip be larger or smaller than the bill? They will say smaller. With a bill of $43 what do we know about a percent, say 20%? A percent is a part of a whole. Then, what is the whole? 43. Good, now when I say I want to know 20% of 43, take note of the word of because of means to multiply. So what are we multiplyi g? 43 x .20. Yes! A percent is a decimal. We only have to move the decimal point to the left two places. Now, usually we get a larger number as a product when we multiply. Do you think that will happen this time? No, when you multiply by a fraction or decimal we are only finding a part of the original number, which was 43 in this instance. So go ahead and multiply 43 x .20. You got 86? Don't forget to place your decimal point in the right place because we are looking for a smaller number and 86 is bigger. Yes, move the decimal point to the left and you get 8.6. Yes, now you remember that rule? So, what is our 20% tip on $43? Yes, $8.60. Can you think of another way to do that? What do you notice about the numbers 43 and 86? They're doubled. Good. Why might they be doubled? Because we multiplied by 2 in 20%. Good. What if we multipled by 10? Yes, we could just move the decimal to the left and get 4.30. Easy! That's 10 percent, so we can just double that to get $8.60

Can you see the different ways of teaching. We want to teach like the latter example.This makes sure that kids get a good conceptual understanding. But, not all kids will and then we have to move to direct instruction of the algorithms and use worksheets to reinforce the raw memorization necessary for this approach. Often special ed students need this approach. And that's howcwe give students a passing understanding of math even though we really want to teach to deep conceptual understanding, but it doesn't always happen with every student. The difficulty is having both types of students in the same classes in heterogeneous grouping. Teachers complain about this problem a lot because it really is an inefficiency that would be easily solved by homogenous grouping.

89

US Supreme Court: Hobby Lobby wins we lose

by designs in

the old guys sided with hobby lobby today in denying birth control coverage to its female employees based on the owners religious views.

intact- is viagra for the guys.

funny how the far right evangelical owners of hobby lobby didn't want to touch that one.... read judge ginburg's scathing counter argument and opinion.. www.supremecourt.gov/opinions/13pdf/13-354_olp1.pdf.

GrreatTeacher

Maybe Workmen's Comp is what you're thinking of?

89

US Supreme Court: Hobby Lobby wins we lose

by designs in

the old guys sided with hobby lobby today in denying birth control coverage to its female employees based on the owners religious views.

intact- is viagra for the guys.

funny how the far right evangelical owners of hobby lobby didn't want to touch that one.... read judge ginburg's scathing counter argument and opinion.. www.supremecourt.gov/opinions/13pdf/13-354_olp1.pdf.

GrreatTeacher

"45% of the people in this country are on some kind of welfare" -UN informed

Would you like to back up this claim?

I certainly hope you are not talking about the elderly on Social Security and Medicare, since they obviously paid into these systems?

76

Do You Like or Dislike Algebra? Why and Why not?

by Scott77 in

july 28, 2012is algebra necessary?by andrew hacker .

a typical american school day finds some six million high school students and two million college freshmen struggling with algebra.

in both high school and college, all too many students are expected to fail.

GrreatTeacher

Math is about patterns, and to some people they are beautiful when they see them. But more importantly, math is about problem solving. And, I think, problem solving is pretty darn important in the real world.

When I teach an elementary school math lesson, it is always introduced as a real world problem. We make connections to the real world, connections to mathematical properties and we reach for the Big Ideas, for example, equivalence, or the fact that fractions and percentages are two different ways of representing the same thing, that is parts of wholes.

If students don't understand these things then no amount of formulas and calculations will ever make sense. They will simply exist as algorithms that can get you the right answer, but true mathematical reasoning will not be taking place.

I have taught functions in first grade and the distributive property in third grade. Functions can be taught with a problem solving "What's my rule?" method. The distributive property can be taught with manipulatives built into an array of 28, 7 long and 4 wide. Then, cut the array in two parts along the side with 7, say into 5 by 4 and 2 by 4. Then you have two groups which are the same size as the original group.

Ask the student if these two groups are equal to the original one. They will say yes. Ask them how many was in the first array. It was a 7 by 4 array of 28. Ask how many was in each of the smaller groups. A 5 by 4 array of 20 and a 2 by 4 array of 8. So, do you think you could add the two smaller arrays which were 20 and 8 and you would get 28? Well, count and see! When they agree you can show them that 20 + 8 =28. Then you can go back to the names of the arrays and show them that (7 × 4) = (5 × 4) + (2 × 4). And, they can learn it! They can also use this for calculation in multiplication for difficult facts like the sevens. We just did that . We broke that 7 down into a 5 and a 2. 5×4 and 2×4 are much eadier to compute mentally than 7×4. Why? For the fives, you skip count by fives and for the twos you skip count by twos.

I could go on, but suffice it to say, if these concepts are taught early enough and developmentally appropriately, then young students can really learn what otherwise might seem to be difficult concepts.

89

US Supreme Court: Hobby Lobby wins we lose

by designs in

the old guys sided with hobby lobby today in denying birth control coverage to its female employees based on the owners religious views.

intact- is viagra for the guys.

funny how the far right evangelical owners of hobby lobby didn't want to touch that one.... read judge ginburg's scathing counter argument and opinion.. www.supremecourt.gov/opinions/13pdf/13-354_olp1.pdf.

GrreatTeacher

Yes, bring on single payer. However, until that is politically feasible, the conservative creation of "Obamacare" will have to do for now.

Romney created it, Obama embraced it, and now the Right hates it. Go figure.

18

ex elder sentenced to 14 years.

by ThomasCovenant in

http://www.walesonline.co.uk/news/wales-news/im-relieved-everybody-now-knows-7357125.

.

http://www.bbc.co.uk/news/uk-wales-south-east-wales-28127683.

GrreatTeacher

I don't know how pedophiles are regarded by the other inmates in the UK, but if it's anything like the US, he's in for a rough 14 years.