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In this lesson, students will learn how to identify ratios and use ratios to describe comparisons between two numbers using division. They will write ratios in different ways, including in sentences of the form “There are 2/3 times more…” Students will learn how to distinguish between additive relationships and multiplicative relationships. And, finally, students will learn how scientists use ratios in the form of astronomical units (AU). One AU is equal to the distance from the Sun to the Earth.

Module 1 Video

The video explains that a ratio is a comparison number. This term will be important to emphasize as students gradually learn more about ratios. Although ratios are often shown as having two parts—like a numerator and denominator—a ratio is just a single number that represents a comparison between two values using division. When a ratio is shown using two values, the order of writing those values matters. So, for example, the video shows the ratio 10/5, which compares the number of fish to the number of turtles. The ratio 5/10, which compares turtles to fish, is a different ratio.

Module 2 Video (1 of 2)

This video summarizes the ideas students worked through in the previous 4 problems. Have students watch this video only after working through those 4 interactive items. In the second video in the app, we show additive and multiplicative comparisons applied to a real-world quantity (boxes or cups of cereal). The video then summarizes some differences between additive and multiplicative relationships.

Module 3 Video

In this example, Bode’s Law is introduced—a numerological “law” popularized in the late 1700s which coincidentally approximates the astronomical units (AU) a planet is from the Sun. One AU is equal to the distance of the Earth from the Sun. Bode’s Law is way off for the planet Neptune and other outer bodies of the Solar System. The distances given in the diagram (and in Bode’s Law) are astronomical units. One astronomical unit is equal to the distance of the Earth from the Sun.