Comparing Mixtures


Mixtures GraphicFor problems 1 through 5, use the "Mixing Orange Juice" applet to check your answers to the problems in the "Orange Juice Mixture" problem. (You need to decide whether one mixture will taste more "orangey" than the other or whether they will taste the same.)

1. Mixture 1 Mixture 2
3 Orange 3 Water
3 Orange 2 Water
 
2. Mixture 1 Mixture 2
 
3 Orange 2 Water
4 Orange 3 Water
 
3. Mixture 1 Mixture 2
 
3 Orange 2 Water
2 Orange 1 Water
 
4. Mixture 1 Mixture 2
 
3 Orange 2 Water
6 Orange 4 Water
 
5. Mixture 1 Mixture 2
 
1 Orange 1 Water 1 Orange 2 Water
2 Orange 1 Water 1 Orange 3 Water

In problems 6 through 8, use the applet to compare the two mixtures. Come up with a way to reliably determine which mixture is more "orangey" than the other or whether they are the same amount of "orangeyness."

6. Mixture 1 Mixture 2
1 Orange 1 Water 1 Orange 2 Water 1 Orange 1 Water
1 Water 2 Orange 2 Water 1 Orange
 
7. Mixture 1 Mixture 2
 
1 Water 2 Orange 1 Water 1 Orange 1 Water 1 Orange
1 Water 2 Orange 2 Water 1 Orange 1 Water 2 Orange
 
8. Mixture 1 Mixture 2
 
1 Water 1 Orange 1 Water 1 Orange 1 Water 1 Orange 3 Water
1 Water 1 Orange 3 Water 1 Orange
 

9. Come up with a new pair of mixtures in which the second mixture is more "orangey" than the first mixture.

10. Come up with a new pair of mixtures in which the two mixtures have the same amount of "orangeyness."
Why these problems?
These problems:
blue check Address the misconception that proportionality is based on additive relationships;
blue check Highlight the difference between part-to-part ratios and part-to-whole ratios;
blue check Provide a visual model for thinking about ratios;
blue check Require the learner to synthesize his or her learning about comparing proportions to create new examples.

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