Math+Snacks+Overruled


 * Math Snacks: Overruled**

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.


 * Grade Level:** 6-9 (Depending on math placement)
 * PSSM Content Standard:** Algebra
 * Math Content:** Ratio, Proportions, Multiplication, Graphing Linear Equations

Evaluation & Annotations

 * What is being learned? What mathematics is the focus of the activity/technology? Is relational or instrumental understanding emphasized?**

This resource is dedicated to an understanding of ratios and equivalent fractions. The conversion between King's feet and Queen's feet demonstrates to students that ratios can be found by analyzing real world situations and through multiplication. While graphing is not the cornerstone of this resource, students are required to create tables and transfer information from a table into a linear equation. This enables students to see that conversions between units form lines when graphed. This resource definitely emphasizes relational understanding. Rather than simply showing students how to cross multiply proportions to gain equivalent fractions, students are led through an application where the manipulation of a conversion allows for the creation of a table and a line, which will ultimately enable students to have a deeper understanding of ratios and proportions.


 * How does learning take place? What are the underlying assumptions (explicit or implicit) about the nature of learning?**

Learning takes place through a number of different mediums with this resource. Initially, learning about conversions and ratios is presented in a situational manner, through the videos' direct instruction**.** The video connects the mathematical concepts of conversions (ratios), tables, and graphs to demonstrate that by creating a line comparing two quantities, endless conversions can be found using points on the line. The worksheet furthers student thinking by requiring them to apply this understanding of ratios and conversions to two new situations. Students are required to create tables and graphs based on new situational information. There are several underlying assumptions presented through this resource. First, it is apparent that the creators value the engagement that comes along with technology. Second, it is apparent that the assumption is made that students' ability to connect mathematics to real world situations is essential. Finally, another underlying assumption about this activity is that it is crucial for students to see connections between various mathematical concepts (ratios, tables, lines).


 * What role does technology play? What advantages or disadvantages does the technology hold for this role? What unique contribution does the technology make in facilitating learning?**

Technology is not "essential" in the use of this resource. The story of the two kingdoms and the bridge could be accomplished without the use of the video. However, its use does add a great deal to the activity. The video will certainly engage students, given that there are jokes throughout the lesson. The video also adds to the situational aspect of the lesson and will undoubtedly keep students invested in the activity. Additionally, technology allows for the table and graph to be explained quickly and clearly with detailed explanation. A teacher would not be able create the graph and table, while explaining in such a clear manner. The only disadvantage of the technology is that the video moves rather rapidly. If students were to be expected to take notes the video, it would have to either be stopped constantly or played several times.


 * How does it fit within existing school curriculum? (e.g., is it intended to supplement or supplant existing curriculum? Is it intended to enhance the learning of something already central to the curriculum or some new set of understandings or competencies?)**

This resource would work best as a supplement to existing curriculum. Many students are taught about ratios and proportions in an instrumental manner. This resource would enable students to view ratios relationally, as part of a real world situation. Furthermore, this resource would enable students to view connections between ratios, tables, and graphs. I would insert this activity prior to discussing ratios directly. This would allow students to gain an understanding of equivalent fractions and would contextualize proportions before diving into a lesson on cross multiplication. The implementation of this activity would enhance student understanding of ratios and equivalent fractions by connecting them to existing prior knowledge, such as tables and graphs.


 * How does the technology fit or interact with the social context of learning? (e.g., Are computers used by individuals or groups? Does the technology/activity support collaboration or individual work? What sorts of interaction does the technology facilitate or hinder?)**

This activity could be used individually or in groups. The worksheet calls for students to analyze a created table, create a new table, create a graph, and answer a higher level thinking question about the accuracy of tables. This could be accomplished individually or in pairs. I would recommend having students complete this individually and then compare their answers with another classmate. This would allow each student to test their individual understanding of ratios, tables and graphs. It would also allow for students to form arguments about their answers and would encourage peer to peer learning.


 * How are important differences among learners taken into account?**

This video certainly meets the needs of diverse learners. Ratios are represented numerically (through tables) and visually (through graphs). These multiple representations allow for students with multiple intelligences to grasp the concept of ratios. The story behind the lesson and the explanation in the video provide an adequate means for auditory learners to create a relational understanding of fraction and ratios. The activity itself does not provide different levels of difficulty for learners at different levels. While the video must remain the same for all learners, the teacher could provide struggling students with page one of the worksheet and provide advanced learners with both pages.


 * What do teachers and learners need to know? What demands are placed on teachers and other "users"? What knowledge is needed? What knowledge supports does the innovation provide (e.g., skills in using particular kinds of technology)?**

Learners do not need to have any specific technology understanding to participate in this activity. The video is simple to operate and the adjoining worksheet can be easily distributed to students. However, in order to fully understand the video students need to have a basic understanding of graphing linear equations through the use of tables. If students do not understand how to construct axes and plot points they will be unable to understand much of the lesson. The resource itself does not provide students with any technological understanding. More importantly, the resource enhances students' ability to transition between tables and graphs, and the resource builds a relational understanding of conversions and ratios through use of a real world situation.