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| Many times it is not
enough to just give an answer. You must
explain your answer.
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| Seldom
is there just one way to explain your answer. In this lesson,
you will look at different ways to represent or explain your
problem: verbally, numerically, algebraically, or graphically. |
| How do I explain it
verbally? |
That one's easy-
just share strategy with a partner! |
| How do I explain it
numerically? |
Make a number model. |
| How do I explain it
algebraically? |
Make a number model
with a variable. |
| How do I explain it
graphically? |
Make a graph!
It could be a line, bar, or circle graph or a pictograph. |
Now,
how do you decide
what representation (explanation) you should use?
Sometimes it might be hard
to choose an explanation, but usually one method is clearly better than
another. Let's take a look at some examples
and investigate what method is the best for that one!
Let's start with the algebraic and
numeric explanations.
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Jane has six
puppies. Each puppy needs at least 2 cups of dry food a
day. What is the total number of cups of food Jane
needs to have for her puppies? |
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A number model
can show how the facts in the problem are related.
6 * 2 = total
6 * 2 = 12 cups of puppy food
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|
Laura has kittens that weigh a total of 15 pounds. She has
5 kittens; what is the average weight of each kitten? |
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An
algebraic number model
can show how the facts in the problem are related. The
unknown is now the average weight of each kitten. Let w = the
weight
5w = 15
5w = 15
5 5
w = 3 lbs
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| Susan and
Linda counted the change in their purses. Susan had 2
quarters, 3 dimes, and 2 nickels. Linda had 5 dimes, 5
nickels, and 5 pennies. Write an inequality
comparing the two girls' amount of money. |
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Susan's change
2Q + 3d + 2 n =
$0.50 + $0.30 + $0.10 =
$0.90
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Linda's change
5d + 5n + 5p =
$0.50 + $0.25 + $0.05=
$0.80 |
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$0.90 > $0.80 |
| Kristen and
Kate were in a ski race. Kristen skied the course in 89
seconds. Kate finished the same course in 1 minute 15
seconds. Write an inequality comparing the two girls'
times. |
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Kristen's time =
89 seconds |
Kate's time (change to seconds)
1 minute 15 seconds = 60 + 15 seconds
= 75 seconds
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89 seconds
> 75 seconds |
Remember:
when asked to represent a problem situation, you have many choices of
representation: algebraically, graphically, numerically - with an
equation or inequality, or verbally.
Ready for Practice?
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