> CEBy bjbj 42{{tt <d jf777$j7"777ttu$eee7.tle7ee,eѹee:0jeeeep77e77777e777j7777777777777 :: The boys swim team and the girls swim team held a car wash. They made $210 altogether. There were twice as many girls as boys, so they decided to give the girls team twice as much money as the boys team. How much did each team get?
1. Where can we start? What do we know?
$210 is being divided among the boys and girls. The girls get twice as much as the boys. (Talk the problem through in your own words and write it out.)
2. What do we want to find out?
How much the boys get and how much the girls get.
3. What mathematical relationships are involved?
The amount that the boys get and the amount that the girls get adds up to $210. The girls get two times as much as the boys.
4. Can we draw a picture of this, or make a table of values?
5. How can we write these relationships mathematically? Choose a variable.
Let b stand for the amount that the boys get. Then how much do the girls get?
b = boys amount 2b = girls amount
b + 2b = 210
6. Solve the equation.
b + 2b + 210 3b = 210 b = 70
7. Answer the questions.
Boys get $70, girls get twice that amount, or $140.
8. Ask yourself, does the answer make sense?
Yes! $70 + $140 = $210
Teachers can help in this process by using a think-aloud explain your own thinking as you go through this process. Then use a similar problem and let students work in pairs, using the outline. Provide feedback as needed, clarifying each question, but not answering it for the pairs. Ask one or two pairs to show their work, then repeat the process several times. Finally let students do it on their own, providing feedback as needed.
Processes used: Teacher think-aloud, small-group discussion, drawing a representation (bar model) or making a table of values, asking if the answer makes sense.
Problem:
1. Where can we start? What do we know?
2. What do we want to find out?
3. What mathematical relationships are involved?
4. Can we draw a picture of this?
5. How can we write these relationships mathematically? Choose a variable.
6. Solve the equation.
7. Answer the questions.
8. Ask yourself, does the answer make sense?
A hot-air balloon 70 meters above the ground is falling at a constant rate of 6 meters per second while another hot-air balloon 10 meters above the ground is rising at a constant rate of 15 meters per second. To the nearest tenth of a second, after how many seconds will the 2 balloons be the same height above the ground?
This is a good way to list what we know about the problem:
1. Write every number in the number column.
2. Write the units of that number in the units column.
3. Determine a label for each number that says what the number represents.
numberunitlabel70metersheight of balloon 16meters per secondrate of falling of balloon 110metersheight of balloon 215meters per secondrate of rising of balloon 21/10secondaccuracy of answer2balloonsI knew that already
Then use the steps listed on previous pages.
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