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Math Snacks: Over-Ruled

 

Curator: William Stremple

 

Brief Description of Tech Tool: This resource features a six minute video centered on two kingdoms (one ruled by a King and one ruled by a Queen) attempting to build a bridge. It is agreed upon that half of the bridge will be built by each kingdom. During the construction, the bridge does not meet in the middle of the water due to the fact that each kingdom measures a foot by the king's/queen's foot size. This causes a discrepancy in the height of the bridge. The video then provides the ratio of kings feet: queens feet and uses a table and a graph to demonstrate how each unit can be converted to one another so that both kingdoms will be able to use their unit of measure to build the bridge. After the video there is a supplemental resource for students. The worksheet provides students with a different ratio and encourages students to correct an error in a table which models the relationship between the two units of measure. Students are also required to graph the situation using the table. Finally, a third situation is presented and students are required to create two tables and graphs - one for each kingdom. This also requires labeling of the axis and identification of the dependent and independent variables.

 

Link to Tech Tool or Tool homepage: http://mathsnacks.com/overruled.html

 

Evaluation

Description of Learning Activity

 

I would use this tool as a way to explore a new mathematical idea. The lesson would begin by playing the video of the King and Queen who fell in love. After watching the video, a discussion of the big ideas or key points in the animation should occur. The included worksheet provides an extension activity of converting different units of measurement. There are also bonus activities listed in the teacher's guide.

 

1. Learning Activity Types

 

  • Presentation of new content/ideas – Use as a way to interest students in the content

  • Exploring/investigating mathematical ideas – Explore mathematical ideas in a practical way

  • Applying mathematics to problems and situations – How mathematics can be used to solve practical problems.

 

2. What mathematics is being learned?

 

NCTM Standards

  • NCTM-N&0-understand numbers- understand numbers, ways of representing numbers, relationships among numbers, and number systems;

  • NCTM-Alg-patterns- understand patterns, relations, and functions;

  • NCTM-Alg-models- use mathematical models to represent and understand quantitative relationships;

  • NCTM-Alg-change - analyze change in various contexts.

 

VA SOL Strands

  • 8.3 a - The student will solve practical problems involving rational numbers, percents, ratios, and proportions

  • 8.14 - The student will make connections between any two representations of a given relationship

 

Proficiency Strands

  • conceptual understanding - Understand proportional reasoning, unit conversion, and functional representations

  • procedural fluency - Collaborative environment can be used to increase mathematical skills and accuracy

  • strategic competence - Solving the problem of how many King's feet are equal to Queen's feet and representing this as a function

  • adaptive reasoning - Provides inquiry on a realistic situation and opportunities for reflection, explanation, and justification of possible solutions to the problem

  • productive disposition - Students are given a realistic situation where these mathematical concepts can be implemented

 

3. How is the mathematics represented?

 

The representations used in this tech tool are: graphical and numerical. Students are asked to provide the numerical representation of unit conversion as well as a graph to represent appropriate values at any interval. The representations capture the diversity of mathematical concepts. This tech tool provides learners with connections between different mathematical skills and ideas. The technology describes the dynamic representations of proportions, unit conversion, and functions. It serves to highlight rate of change between two units of measurement.

 

4. What role does technology play?

 

Representing Ideas & Thinking - The proportions involved in the animation are represented numerically and graphically in relation to the situation.

Communicating & Collaborating - The animation ignites discourse between students about the mathematical concepts. ‍Students can also work on the available assignments in groups or pairs.‍

 

What advantages and/or disadvantages does the technology offer for facilitating learning?

 

Advantages

Motivates and engages students.Provides opportunities for discourse.Promotes active learning and/or collaboration in classroom.Develops problem solving skills.Combines several concepts into one lesson.Opportunities for higher-level bonus activities.

 

Disadvantages

Depending on the skill levels of students, this could be a quick lesson (30 minutes or less).The technology is lacking in diverse approaches to problem solving. The animation discusses proportions in terms of graphing, but does not address ‍alternate methods‍.

 

5.  How could this resource supplement/facilitate PBL?

This resource can be used to supplement PBL by getting students interested in a topic followed up by a problem to solve.

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