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### The Golden Ratio

6-8

Students learn about ratios, including the “Golden Ratio”, a ratio of length to width that can be found in art, architecture, and nature. Students examine different ratios to determine whether the Golden Ratio can be found in the human body.### What's Your Rate?

6-8

Students learn to write and solve proportions by gathering data and calculating unit rates.### Do You Measure Up?

6-8

Students learn the basics of the metric system. They identify which units of measurement are used to measure specific objects, and they learn to convert between units within the same system.### Discovering Gallon Man

6-8

Students experiment with units of liquid measure used in the customary system of measurement. They practice making volume conversions in the customary system.### In Your Shadow

6-8

Students extend their knowledge of proportions to solving problems dealing with similarity. They measure the heights and shadows of familiar objects and use indirect measurement to find the heights of things that are much bigger in size, such as a flagpole, a school building, or a tree.### Off the Scale

6-8

Students use real-world examples to solve problems involving scale as they examine maps of their home states and calculate distances between cities.### Commutative Rectangle

6-8

Students typically learn about the concepts of identity, inverse,
commutativity, and associativity by exploring the four basic operations
(+, –, ×, and ÷) with integers. In this lesson, students investigate
these concepts using a geometric model. Moves are performed with a
rectangle, and the results of an operation that combines two moves are
analyzed. Students determine if the operation is commutative or
associative; if an identity element exists; or if there are inverses
for any of the moves.### The Plus Sign and Triangle

6-8

Using a scheme similar to the one in the Rectangle
lesson of this unit, students will further explore the concepts of
identity, inverse, and commutative and associative properties. Students
investigate and analyze moves performed with a plus sign, and an online
activity is available to help students with this investigation.### Building A Box

3-5, 6-8

This lesson uses a real-world situation to help develop students' spatial visualization skills and geometric understanding. Emma, a new employee at a box factory, is supposed to make cube‑shaped jewelry boxes. Students help Emma determine how many different nets are possible and then analyze the resulting cubes.### Taking Its Toll

6-8

In this lesson, students will compare the price of a toll to the distance traveled. Students will investigate data numerically and graphically to determine the per-mile charge, and they will predict the cost if a new tollbooth were added along the route.