Problem Solving
How can you use what you’ve learned to solve a real-world problem?
Goal:
Goal:
Practice!
Goal: Apply what you've learned in this lesson to solve a real-world problem.
Madelyn and her cousin are training for a bike race. Click through the slides to see how they plan their training schedules.
Bikes racing each other, each of the riders is trying really
hard to win the race.
Shapes for Training
Madelyn and her cousin decide on how they will track their training.
Madelyn is going to ride her bike for 8 days to train for the race. Her cousin is going to ride her bike for 10 days. The girls want a way to visually track their progress, so they decide to partition shapes and color in a part each day that they train. They each decide to use a rectangle for their shape.
A rectangle
Partitioning the Shapes.
Madelyn and her cousin partition their shapes into equal parts.
Madelyn uses a ruler to draw her rectangle. Then, she measures out 8 equal parts. She draws vertical lines to separate the equal parts. Here is what her drawing looks like:
A rectangle partitioned into 8 equal parts.
Madelyn’s cousin also uses a ruler to draw her rectangle. She draws 1 horizontal line across the middle and 4 vertical lines to make a total of 10 parts. Here is what her drawing looks like:
A rectangle partitioned into 10 equal parts.
Comparing the Drawings
Madelyn and her cousin compare their drawings.
When Madelyn and her cousin put their drawings side by side, they notice that their rectangles are the same size, but their parts are different sizes. Madelyn has 8 equal sized pieces while her cousin has 10 equal sized pieces.
A rectangle partitioned into 8 equal parts, each
partition is numbered 1,2,3,4,5,6,7,8. A second
rectangle partitioned into 10 parts. each part is
numbered 1,2,3,4,5,6,7,8,9,10
Fraction Representation
Madelyn and her cousin figure out how far they will train each time they ride their bikes.
Madelyn says that each day she rides her bike, she will complete \(\Large\frac{1}{8}\) of her training because each equal part of her rectangle represents \(\Large\frac{1}{8}\) of the whole rectangle.
A rectangle partitioned into 8 equal parts, the first
part in the rectangle is labelled
\(\Large\frac{1}{8}\)
Madelyn’s cousin says that each day she rides her bike, she will complete \(\Large\frac{1}{10}\) of her training because each of her equal parts represents \(\Large\frac{1}{10}\) of the whole rectangle.
A rectangle partitioned into 8 equal parts, the first
part in the rectangle is labelled
\(\Large\frac{1}{10}\)
All Set
The girls are ready to train.
Now that the girls have their drawings all done, they are ready to start their training!
Bikes racing each other, each of the riders is trying
really hard to win the race.
Question
Madelyn decides that she wants to train for 16 days. On her picture she draws a horizontal line through the middle. What fraction of the whole rectangle does each box represent now?
\(\Large\frac{1}{16}\) because there are now 16 total pieces