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y=m/x
When graphed the lines never reach zero. One quantity increases while the other quantity decreases.

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Teacher resources and professional development across the curriculum

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y=mx
This relationship shows that as x intercept increases so does y. This is considered a linear function.  The ratio is a direct proportion.For example, time and money.

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Teacher resources and professional development across the curriculum

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Looking at the relationships. Focusing on the ratio. Comparing quantities. Multiplicative comparison.

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Video on Demand - Learning Math: Number and Operations - Absolute and Relative Reasoning

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Finding what makes up a unit. Example Red Trapezoid was worth 1 unit. Or the example in the video, the unit was different dependent upon the interpretation. All have to agree to what makes up one unit.

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Video on Demand - Learning Math: Number and Operations - Units and Unitizing

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When two quantities are changing by the same factor they are invariant. A=k/B where K is the constant or factor. Relationship remains unchanged.

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Two quantities vary together. Example 5 Mangos for 2.00 but if you get 10 Mangos the cost also goes up.

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Looking at the just the numbers. Additive relationship.

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Video on Demand - Learning Math: Number and Operations - Absolute and Relative Reasoning

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-Fractions
-Percentages
-Probabilities

9/16 girls to boys
or 56% girls are in the class

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- the two parts that make up the whole

2 apples to 3 oranges
3 oranges to 2 apples (refer to video)

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Deals with absolute thinking where you are only looking at the numbers. Langrall & Swafford would consider this Level 0 of proportional reasoning.

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Looking at relationships and ratios. This lines up with relative thinking.

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-number that relates to two quantities
-multiplicative relationship
-part to whole
-part to part
-ratios as quotients
-ratios as rates

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Two rates corresponding to a given pair of quantities. Refer to Van De Walle and Cramer post.