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A ratio is a number that relates two quantities or measures within a given situation in a multiplicative relationship.

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A ratio can relate one part of a whole (9 pink fish) to another part of the same whole (7 blue fish). This is represented as 9/7. This isn't the same as nine-sevenths as it would be in a fraction.

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This is a good starter book that younger kids can relate too.

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This can help with proportional reasoning. There is also factual data on which the proportions are based. Students can figure out how strong or tall they would be if they were one of the featured animals.

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This book provides a good opportunity for students to talk about ratios and can lead into other good conversations as well.

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Ratios can express comparisons of a part to a whole. The number of girls in a class (9) to the number of students in the class (16) this can be written as 9/16, or can be thought of as nine-sixteenths of the class. Percentages and probabilities are examples of part-whole ratios.

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Ratios can be thought of as quotients. Fr example, if you can buy 4 kiwis for $1.00, the ratio of money for kiwis is $1.00 to 4 kiwis, or 1/4, and is a quotient. Diving the values results in $0.25 for one kiwi, the unit rate.

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Rates involve two different units an how they relate to each other (ex. miles per gallon, square yards of wall coverage per gallon of paint). Relationships between two units of measure are also rates (ex. inches per foot, centimeters per inch). A rate represents a infinite set of equivalent ratios.

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(Use tape diagrams.) For every 3 bass that are put in a pond, Edwin puts 8 blue gill in the pond. If (or Assume) Edwin puts 24 blue gill in the pond, how many bass does he need to put in the pond.
Ask questions such as:
What fractional part is the bass compared to the blue gill? (3/8)
What fractional part is the blue gill compared to the bass? (8/3)

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NCTM's Figure This! Math Index: Ratios and Proportions.

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NCTM's Figure This! Math Index: Ratios and Proportions.

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Figure This: The Environmental Protection Agency estimates for gas mileage on 1999 cars vary widely. Which of these cars should go the farthest on one tank of gas? (Hint: suppose you only drive in the city? On the freeway?)

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1. Specific and clear teacher models
2. Examples that are sequenced in level of difficulty
3. Scaffolding
4. Consistent feedback
5. Frequent opportunity for cumulative review

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R-- Remember the problem correctly
I-- Identify the relevant information
D-- Determine the operations and unit for expressing the answer
E-- Enter the correct numbers, calculate and check the answer

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Ratios and Proportions - with Two-Color Counters

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Explain to students that we will be icing cupcakes and selling them at school. The instructions say that to ice 1 batch of cupcakes with aqua-colored icing, we will need 2 drops of green food coloring and 5 drops of blue food coloring. How many drops will we need for 1 batch, 2 batches, 5 batches, etc. (Record in a table.)

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https://drive.google.com/file/d/1MI-6A185BQlfxYpSAFiffD6MWKNcGLNs/view?usp=sharing

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a part, share, or number considered in comparative relation to a whole

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thinking about relationships and making comparisons of quantities or values

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Learning about ratios and proportional relationships begins in elementary school with work in measurement and in multiplication and division. For examples, kids often times like to use half when relating to birthdays or height.

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Students are solving multiplication problems involving multiplicative comparison.

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Students are identifying relationships between two varying quantities.

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A critical area focuses on connecting ratio and rate to multiplication and division. Students are solving problems involving ratios and rates.

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Students are focused on proportionality and solving multistep problems. In this grade, students write proportions as equations and graph them, as well as solve problems involving interest, tax, gratuities, and so on.