Objective: To organize the facts of a problem in a chart.
Using a chart to organize the facts of a problem can be a helpful problem solving strategy.
Organize the given information in a chart
A swimming pool 25 m long is 13 m narrower than a pool 50 m long
There are two different charts you could create:
In the first chart we started with
Let w = the width of the 2nd pool; so to write the 1st pool in terms of the second we would place w-13 in place of the ?
In the 2nd chart we started with
Lt w = the width of the 1st pool; so we write the 2nd pool in terms of the first, so we would place w + 13 in place of that ?
We then solved the following:
Find the number of calories in an apple & a pear…
1) the pear contains 30 calories more than the apple.
2) Ten apples have as many calories as 7 pears.
Let a = the number of calories in an apple
Then a + 30 = the number of calories in a pear.
We glued in the “orange- colored” chart here and completed it to look like:
This time we reread the given facts and with the second fact, we realize that we can set
The last column expressions equal to each other
10a = 7(a + 30)
solving this equation, we find that a = 70
Therefore, an apple has 70 calories and a pear has 100 calories
Next we used the following two given facts to set up a chart and create an equation
1) An egg scrambled with butter & milk has 1 more gram of protein than an egg fried in butter.
2) Ten scrambled eggs have as much protein as a dozen fried eggs.
Let x = the number of protein in a fried egg.
Then x + 1 = the number of protein in a scrambled egg.
We glued in the “orange- colored” chart here and completed it to look like:
Our equation would be 10(x + 1) = 12x
We then turned to our textbook to Page 122-123 and completed problems 1 and 3 in our spiral notebook as follows:
Solve each problem using the two given facts. Complete a chart to help you solve each problem
1. Find the number of full 8 hour shifts that Maria worked last month
1) She worked twice as many 6 hour shifts as 8 hour shifts
2) She worked a total of 280 hours.
We also found that some problems, such as # 16 on page 124 could be easily worked out without a chart. However, the goal of this section was to attempt to use charts NOW so that in the future, using charts would help organize the information given in more complext word problems.
the Eiffe; Tower is 497 Ft taller than the Washington Monument. If each were 58 ft shorter, the Eiffel Tower would be twice as tall. How tall is each?
Let w = the height of the Washington Monument.
then Let w + 497= the height of the Eiffel Tower.
Taking the phrase " if each were 58 feet shorter" write
w -58 for the Washington Monument and (w + 497) - 58 for the Eiffel tower.
Now it states that the Riffel tower whould be twice as tall as the Washington Monument... so you would need two Washington Monuments to equal the Eiffel Tower... write an equation from that as follows
2(w - 58) = (w+497) -58
2w - 116= w + 439
w = 555
So the Washington Monument would be 555 ft tall
and the Eiffel Tower would be 1052 ft tall
