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What makes up a whole(one)

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The amount of something for 1. The rate for one unit of a given quantity.

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A multiplicative relationship between (usually two) quantities

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4 quarters make up a dollar. In this case, the four quarters(each 1/4) make up the unit which is the dollar.

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Any amount of something that does not make a whole(one)

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http://www.morewithmusic.org/2011/02/1-2-3-4-quarters-in-1.html

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If eight pineapples are sold for $2, then the unit rate would be a quarter (.25 cents) for each pineapple.

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Eight pineapples are sold for $2. Two pineapples for .50 cents is not a unit rate.

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https://www.tes.com/lessons/xhlXgb_faMjkuw/unit-rate

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Amount of sugar in ounces needed for each batch of cookies ( 3 to 12)

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Kilometers per hour

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https://www.pinterest.com/pin/98164466852630231/

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Describing a change through addition

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y=x+a
A change from 2 to 10 would be adding 8

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y=mx
A change from 4 to 20 would be multiplying by 5.

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http://calmcoachin.blogspot.com/2016/11/additive-and-multiplicative-patterns.html

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Describing a change through multiplication

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A change from 2 to 10 would be multiplying by 5

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A change from 7 to 21 would be adding 14

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http://calmcoachin.blogspot.com/2016/11/additive-and-multiplicative-patterns.html

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Comparing absolute quantities, with no reference to the whole

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Claiming that two different sized cups have the same amount of juice (4 ounces each)

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Claiming that one cup has more juice than the other because of how much space the juice takes up in each cup

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http://slideplayer.com/slide/4409156/

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One part of a whole to another part of the whole

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Girls to boys in a classroom, dogs to cats in a pet store

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The ratio of cats to pets at the store because that is a part-to-whole relationship.

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https://www.onlinemath4all.com/writing-ratios.html

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One part of a whole to the whole

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Fractions, percentages, and probabilities

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3/8 of a mile because it is not a relationship between two quantities.

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http://spmath81412.blogspot.com/2012/10/jessica-da-silvas-proportion-post.html

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Two proportional quantities changing at the same time

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2 boys to 3 girls, then 4 boys to 6 girls. As boys increased, girls increased.

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If you are parked, time increases but distance stays the same. Only one quantity changed.

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http://www.statisticshowto.com/covariance/

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Proportional quantities that change at the same rate

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2 cats to 5 dogs, then 4 cats to 10 dogs. The ratio between them stayed the same, and they both increased by multiplying by 2.

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Two quantities changing by different factors. For example 2:3 changing into 4:12. The first changed by a factor of 2, and the second number changed by a factor of 4.

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https://www.nctm.org/Handlers/AttachmentHandler.ashx?attachmentID=VmUa%2FpVjhZI%3D

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One quantity is directly proportional to another when the ratio of the two quantities is constant.
It must also always go through the origin

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y=kx in which y is the dependent variable, k is the constant, and x is the independent variable

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y=kx+b, in which the variables are the same as in the example, and b is the y-intercept

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When one quantity increases while another quantity decreases, and the product of the quantities remains constant.
The graph is a curve with no x or y intercept

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Y=k/x (or xy=k) in which y is the dependent variable, k is the constant, and x is the independent variable

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y=-kx, in which the graph is a line with a negative 🤬 that passes through the origin