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6-GM-3-2

Page history last edited by Brenda Butz 6 years, 2 months ago

6.GM.3.2 Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.

In a Nutshell

Weights, capacities, geometric measurements, and time can be converted within the same measurement system by using ratios and reasoning about multiplication and division. Ratios used to convert measurements are formed from common knowledge about unit equivalencies, and the ratios that are formed are equivalent to one. For example, the ratios and are formed from the knowledge that 12 inches = 1 foot. Students must understand the relationship between the size of the unit of measurement and the number of units that will be needed. As the size of the unit of measurement increases, the number of units needed will decrease, and vice versa. This understanding is crucial when choosing to either multiply or divide to solve conversion problems. For example, when converting between feet and inches, an inch is a smaller unit. Therefore, more units would be needed, so students must multiply by the ratio .

Student Actions	Teacher Actions
Develop mathematical reasoning by selecting the appropriate size and type of unit for a given real-world and mathematical problem. Develop a conceptual understanding of how to use ratios and reasoning strategies to multiply or divide in order to solve real-world and mathematical problems. Develop strategies for problem solving by using multiple representations to identify equivalent ratios within a measurement system (Ex: Use ratio tables to show equivalent ratios.) Communicate through writing and discussion with others about different strategies that can be used to convert units of measures within the same measurement system.	Implement tasks that promote reasoning and problem solving that will encourage students to consider different strategies to either multiply or divide to solve measurement problems. (Ex: Make connections to place value when converting between the metric system and students may use the acronym KHDUDCM to move within units.) Use and connect representations that will engage students in making connections among equivalent ratios by modeling multiple approaches to converting units within a measurement system. (Ex: Create ratio tables so students can see the equivalent ratios.)
Key Understandings	Misconceptions
That the size of the unit and the number of units needed to measure an object are inversely related. (Ex: An inch is the smaller unit when compared to a foot. Therefore, you would need more inches than feet to measure the length of a given object.) That ratios equivalent to one such as and reasoning about multiplication and division are used to convert units of measure within a measurement system.	Incorrectly multiply when converting to larger units and divide when converting to smaller units. Not know the prefixes used in the metric system or their meanings. Not be able to form mental pictures of measurement units, especially metric units, making it difficult for them to choose appropriate units.