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G'day, I'm Dr Peter Price of Classroom Professor. In this week in the Free Math Worksheet Series,
we're looking at the topic of "1% and 0.5%". So this topic is for older students who've
learned about common fractions and about decimal fractions and they're ready for learning about
"Percentages". And almost certainly they'll have learned the larger percentages; we're
getting into the really pointy end of the topic as it were, looking at one percent and
half a percent. So the first thing for students to consider in this question is, "What does
1% mean?" and the worksheets give a short explanation and say that "1% is equal to 1/100".
So it's important that students have a conceptual understanding of what that means, not just
a rote learning and other rote understanding basically accepts what you say, but they can
understand what that is referring to. We'll talk about the meaning of the word "Percent"
meaning "Per-Hundred or out of a Hundred" and of course we have words starting with
"Cent", the word "Cent" itself in the currencies of many countries instead, including Australia
that is 1/100 of a dollar, and we have century, and centurion, and centimetre, you know, quite
a lot of words that refer to the value the prefix "Cent", meaning a "Hundredth". So percent
meaning 1/100, we're going to start there and move forward, so in the worksheets, there
are couple of examples like this, so we start with a number like "300", and say "What will
1/100 of 300 be?" will be just plain "3". And I would want to help students to understand
that by asking them questions like, "If we divide that by 100, if we take 1/100 part
of that, what will it be?" Don't, in my view you shouldn't talk about just moving the digits,
so we're not talking about just moving the digits, they'll see that pattern, but we want
them to understand "Why" first. And have some idea of, you know, how the numbers are changing
as they are, in this case divided by 1/100. So we can make a more advance number, say
"2300, what number will that become?" it will become just plain "23". Let's make this a
little bit more challenging and so we'll say, "This is the ones column and I'll just label
these, so this will be the decimal point, so this will be tenths, and this will be hundredths."
So now we'll start with the number "50" as a whole number and we're going to call it,
"$50" so it's got some monetary value and say, "What would 1% of $50?" Now I should
say the reason for calling it dollars is that we often apply percentages to monetary amounts,
and so it's, you know, it's part of a context for a lot of, you know, introductory learning
about percentages. So "What's going to happen to the $50 is we take 1% of 50?" "What's going
to happen to it?" If we've done the previous exercises and we've seen how the numbers are
moving two places to the right, if we do the same thing here, and I'm using these magnetic
numbers again, "Numerals" I should say, and we put the 50 there, we're going to need a
decimal point, we can put our dollar sign here, but we'll a 0 in the dollars place.
The students should be able to see that we convert $50 to 50 cents, thru following a
pattern of how we apply this question to other larger whole numbers. Now, taking 0.5% of
course is an extension of 1%, so we would approach it from that perspective, so once
the students have seen that 1% is 1/100, half a percent must be half of that. I wouldn't
immediately jump in and say, so there it's for 1/200, which it is, but I think it's easier
for students learning this, knowledge and developing the skill to think of a, taking
1% first and then finding half of it and later on we can other processes to it, and so, I
don't need to put this up in the numbers, but the students will be able to see that,
that if you take 1% which is just a matter of moving the digits two places to the right
and then halve the result, you'll get half a percent. Of course more advance students
will be able to do this mentally, so for example, our example of "34" and converting that, or
rather multiplying it by half a percent. A good student will see that "half of 34 is
17", and one percent, one percent of 34 is "34 cents" and half of it is "17 cents", and
so that's the result. So this really is quite a challenging topic, but I don't think the
students will find it too difficult once they get used to the pattern; we need to reinforce
their learning of course with asking good questions to prompt the conceptual development
as well. So that's it for this video, I hope your students enjoy the worksheets, and I'll
talk to you next time.