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6-8

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Auditory, Visual

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In this video adapted from Maryland Public Television, learn about an immersive digital game that develops the mathematical thinking skills used in pre-algebra. Created for middle school students, *Lure of the Labyrinth* presents players with a monster-inhabited world in which they must explore and solve mathematical puzzles to succeed. Find out how this serious game builds student understanding of fractions, proportions, variables and equations, and number and operations.

To learn more about this cybertool and to play the game, visit *Lure of the Labyrinth* on Thinkport.

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*Lure of the Labyrinth* is an immersive digital game in which players use mathematical thinking skills to progress through a graphic-novel story. The sections of the game correspond to typical pre-algebra curricula: fractions, proportions, ratios, variables and equations, and number and operations. Within each section, there are puzzles at multiple levels that the students must solve as they move forward in the game. *Lure of the Labyrinth* can be played as a game, or the puzzles can be used as standalone activities.

Students become engaged in *Lure of the Labyrinth*, developing mathematical proficiencies as they play. As a cyberlearning tool, this serious game allows students to think creatively and learn at their own pace. Along the way, they practice skills that allow them to become efficient problem solvers by making mistakes, learning from them, and persevering. In addition, they have opportunities to interact with other students to discuss strategies, while also practicing communication skills.

*Lure of the Labyrinth* was developed to integrate seamlessly into the classroom. The game works best when it can become a basic part of math instruction. Rather than treating it as a special resource or reward, *Lure of the Labyrinth* should be used as another effective learning tool that can help students build pre-algebra skills. It should be woven throughout the school year, using puzzle play to support particular math concepts.

The game can be used to add a new dimension to teaching. For example, when students are playing a puzzle in the game, the educator no longer instructs in a traditional manner but instead becomes the "guide on the side." In this guiding role, rather than presenting problem-solving techniques directly, the teacher asks students questions that help direct efforts and encourage collaboration, in order to build knowledge and strategies. The teacher can then help students understand how the processes used to play the puzzle are related to particular math concepts.

- How would access to this cybertool change the way that you organize how time is spent in your math classroom?
- What would you need to do to prepare your students to use this cybertool?
- Would you need to convince your department head that using this cybertool is a valid approach to teaching? If so, how would you approach that?

10J ( Grades: K-2 ): Harnessing Power

10J/H3 ( Grades: 9-12 ): Today, changes in technology continue to affect patterns of work and bring with them economic and social consequences.

11B/H1b ( Grades: 9-12 ): A mathematical model may give insight about how something really works or may fit observations very well without any intuitive meaning.

11B/H2 ( Grades: 9-12 ): Computers have greatly improved the power and use of mathematical models by performing computations that are very long, very complicated, or repetitive. Therefore, computers can reveal the consequences of applying complex rules or of changing the rules. The graphic capabilities of computers make them useful in the design and simulated testing of devices and structures and in the simulation of complicated processes.

11B/M2 ( Grades: 6-8 ): Mathematical models can be displayed on a computer and then modified to see what happens.

12A/H2 ( Grades: 9-12 ): View science and technology thoughtfully, being neither categorically antagonistic nor uncritically positive.

12C/M2 ( Grades: 6-8 ): Use computer databases to store and retrieve information.

1C/H3a ( Grades: 9-12 ): Progress in science and invention depends heavily on what else is happening in society.

1C/H3b ( Grades: 9-12 ): History often involves scientific and technological developments.

1C/H4 ( Grades: 9-12 ): Science disciplines differ from one another in what is studied, techniques used, and outcomes sought, but they share a common purpose and philosophy, and all are part of the same scientific enterprise. Although each discipline provides a conceptual structure for organizing and pursuing knowledge, many problems are studied by scientists using information and skills from many disciplines. Disciplines do not have fixed boundaries, and it happens that new scientific disciplines are being formed where existing ones meet and that some subdisciplines spin off to become new disciplines in their own right.

1C/P1 ( Grades: K-2 ): Everybody can do science and invent things and ideas.

2B/H1 ( Grades: 9-12 ): Mathematical modeling aids in technological design by simulating how a proposed system might behave.

2C/H2 ( Grades: 9-12 ): Much of the work of mathematicians involves a modeling cycle, consisting of three steps: (1) using abstractions to represent things or ideas, (2) manipulating the abstractions according to some logical rules, and (3) checking how well the results match the original things or ideas. The actual thinking need not follow this order.

3A/E4 ( Grades: 3-5 ): Technology extends the ability of people to change the world: to cut, shape, or put together materials; to move things from one place to another; and to reach farther with their hands, voices, senses, and minds. The changes may be for survival needs such as food, shelter, and defense; for communication and transportation; or to gain knowledge and express ideas.

3A/H1 ( Grades: 9-12 ): Technological problems and advances often create a demand for new scientific knowledge, and new technologies make it possible for scientists to extend their research in new ways or to undertake entirely new lines of research. The very availability of new technology itself often sparks scientific advances.

3A/H4 ( Grades: 9-12 ): Engineers use knowledge of science and technology, together with strategies of design, to solve practical problems. Scientific knowledge provides a means of estimating what the behavior of things will be even before they are made. Moreover, science often suggests new kinds of behavior that had not even been imagined before, and so leads to new technologies.

3C/E2 ( Grades: 3-5 ): Any invention is likely to lead to other inventions. Once an invention exists, people are likely to think up ways of using it that were never imagined at first.

3C/E3 ( Grades: 3-5 ): Transportation, communications, nutrition, sanitation, health care, entertainment, and other technologies give large numbers of people today the goods and services that once were luxuries enjoyed only by the wealthy. These benefits are not equally available to everyone.

3C/H1 ( Grades: 9-12 ): Social and economic forces strongly influence which technologies will be developed and used. Which will prevail is affected by many factors, such as personal values, consumer acceptance, patent laws, the availability of risk capital, the federal budget, local and national regulations, media attention, economic competition, and tax incentives.

3C/H3 ( Grades: 9-12 ): In deciding on proposals to introduce new technologies or curtail existing ones, some key questions arise concerning possible alternatives, who benefits and who suffers, financial and social costs, possible risks, resources used (human, material, or energy), and waste disposal.

3C/H5 ( Grades: 9-12 ): Human inventiveness has brought new risks as well as improvements to human existence.

3C/H6 ( Grades: 9-12 ): The human ability to influence the course of history comes from its capacity for generating knowledge and developing new technologies—and for communicating ideas to others.

3C/M1 ( Grades: 6-8 ): The human ability to shape the future comes from a capacity for generating knowledge and developing new technologies—and for communicating ideas to others.

3C/M4 ( Grades: 6-8 ): Technology is largely responsible for the great revolutions in agriculture, manufacturing, sanitation and medicine, warfare, transportation, information processing, and communications that have radically changed how people live and work.

3C/M5 ( Grades: 6-8 ): New technologies increase some risks and decrease others. Some of the same technologies that have improved the length and quality of life for many people have also brought new risks.

3C/M7 ( Grades: 6-8 ): Societies influence what aspects of technology are developed and how these are used. People control technology (as well as science) and are responsible for its effects.

3C/M8 ( Grades: 6-8 ): Scientific laws, engineering principles, properties of materials, and construction techniques must be taken into account in designing engineering solutions to problems.

4E/M2 ( Grades: 6-8 ): Energy can be transferred from one system to another (or from a system to its environment) in different ways: 1) thermally, when a warmer object is in contact with a cooler one; 2) mechanically, when two objects push or pull on each other over a distance; 3) electrically, when an electrical source such as a battery or generator is connected in a complete circuit to an electrical device; or 4) by electromagnetic waves.

6B/H4 ( Grades: 9-12 ): The development and use of technologies to sustain, prolong, or terminate life raise social, moral, ethical, and legal issues.

7G/H5 ( Grades: 9-12 ): Communication and transportation technologies, coupled with political and economic policies, now allow people to interact with people in different countries almost as easily as they interact with people in their own country. This has allowed for the spread of political, economic, and cultural influences across the planet much more rapidly than had been the case in the past. Like any social change, there are trade-offs in the globalization of the planet, and it benefits some people more than others.

8B/H4 ( Grades: 9-12 ): Increased knowledge of the properties of particular molecular structures helps in the design and synthesis of new materials for special purposes.

8B/M4 ( Grades: 6-8 ): Automation, including the use of robots, has changed the nature of work in most fields, including manufacturing. As a result, the demand for workers with some knowledge and skills has decreased while the demand for workers with other knowledge and skills has increased. Furthermore, as the pace of innovation has increased, workers have needed to learn new skills throughout their careers.

8D/E2 ( Grades: 3-5 ): Communication involves coding and decoding information. In any language, both the sender and receiver have to know the same code, which means that secret codes can be used to keep communication private.

8D/E3 ( Grades: 3-5 ): People have invented devices such as paper and ink, engraved plastic disks, and magnetic tapes for recording information. These devices enable great amounts of information to be stored, retrieved, and sent to other people or places.

8D/H1 ( Grades: 9-12 ): Almost any information can be transformed into electrical signals. A weak electrical signal can be used to shape a stronger one, which can control other signals of light, sound, mechanical devices, or radio waves.

8D/H2c ( Grades: 9-12 ): Digital coding of information (using only 1's and 0's) makes possible more reliable transmission, storing, and processing of information.

8D/H3 ( Grades: 9-12 ): As technologies that provide privacy in communication improve, so do those for invading privacy.

8D/M2 ( Grades: 6-8 ): Information can be carried by many media, including sound, light, and objects. In the 1900s, the ability to code information as electric currents in wires, electromagnetic waves in space, and light in glass fibers has made communication millions of times faster than mail or sound.

8E/E1 ( Grades: 3-5 ): Computers are controlled partly by how they are wired and partly by instructions called programs which are entered in a computer's memory. Some instructions stay permanently in the machine, but most are coded on disks and are transferred into and out of the computer to suit the user.

8E/M1 ( Grades: 6-8 ): Most computers use digital codes containing only two symbols, 0 and 1, to perform all operations. Continuously variable signals (analog) must be transformed into digital codes before they can be processed by a computer.

8E/M4 ( Grades: 6-8 ): An increasing number of people work at jobs that involve processing or distributing information. Because computers can do these tasks faster and more reliably, they have become standard tools both in the workplace and at home.

9D/H1 ( Grades: 9-12 ): Even when there are plentiful data, it may not be obvious what mathematical model to use, or there may be insufficient computing power to use some models.

2.2 ( Grades: K-12 ): Models are tentative schemes or structures that correspond to real objects, events, or classes of events, and that have explanatory power. Models help scientists and engineers understand how things work. Models take many forms, including physical objects, plans, mental constructs, mathematical equations, and computer simulations.

B.5.1 ( Grades: 9-12 ): The total energy of the universe is constant. Energy can be transferred by collisions in chemical and nuclear reactions, by light waves and other radiations, and in many other ways. However, it can never be destroyed. As these transfers occur, the matter involved becomes steadily less ordered.

E.1.2.a ( Grades: 9-12 ): Students should demonstrate thoughtful planning for a piece of technology or technique. Students should be introduced to the roles of models and simulations in these processes.

E.1.5.a ( Grades: 5-8 ): Students should review and describe any completed piece of work and identify the stages of problem identification, solution design, implementation, and evaluation.

E.2.4 ( Grades: 5-8 ): Perfectly designed solutions do not exist. All technological solutions have trade-offs, such as safety, cost, efficiency, and appearance. Engineers often build in back-up systems to provide safety. Risk is part of living in a highly technological world. Reducing risk often results in new technology.

F.5.4 ( Grades: 5-8 ): Science and technology have advanced through contributions of many different people, in different cultures, at different times in history. Science and technology have contributed enormously to economic growth and productivity among societies and groups within societies.

G.1.1 ( Grades: K-4 ): Science and technology have been practiced by people for a long time.

G.3.3 ( Grades: 5-8 ): Tracing the history of science can show how difficult it was for scientific innovators to break through the accepted ideas of their time to reach the conclusions that we currently take for granted.

CCSS.Math.Cont.3.NF.A.1 ( Grade 3 ): Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts of size 1/𝘣.

CCSS.Math.Cont.3.NF.A.2a ( Grade 3 ): Represent a fraction 1/𝘣 on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into 𝘣 equal parts. Recognize that each part has size 1/𝘣 and that the endpoint of the part based at 0 locates the number 1/𝘣 on the number line.

CCSS.Math.Cont.3.NF.A.2b ( Grade 3 ): Represent a fraction 𝘢/𝘣 on a number line diagram by marking off a lengths 1/𝘣 from 0. Recognize that the resulting interval has size 𝘢/𝘣 and that its endpoint locates the number 𝘢/𝘣 on the number line.

CCSS.Math.Cont.3.NF.A.3 ( Grade 3 ): Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

CCSS.Math.Cont.3.NF.A.3a ( Grade 3 ): Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

CCSS.Math.Cont.3.NF.A.3b ( Grade 3 ): Recognize and generate simple equivalent fractions, (e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

CCSS.Math.Cont.3.NF.A.3c ( Grade 3 ): Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

CCSS.Math.Cont.3.NF.A.3d ( Grade 3 ): Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

CCSS.Math.Cont.4.NF.A.1 ( Grade 4 ): Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

CCSS.Math.Cont.4.NF.A.2 ( Grade 4 ): Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

CCSS.Math.Cont.4.NF.B.3b ( Grade 4 ): Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.

CCSS.Math.Cont.6.RP.A.1 ( Grade 6 ): Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

CCSS.Math.Cont.6.RP.A.2 ( Grade 6 ): Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship.

CCSS.Math.Cont.6.RP.A.3a ( Grade 6 ): Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

CCSS.Math.Cont.6.RP.A.3b ( Grade 6 ): Solve unit rate problems including those involving unit pricing and constant speed.

CCSS.Math.Cont.6.RP.A.3c ( Grade 6 ): Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

CCSS.Math.Cont.6.RP.A.3d ( Grade 6 ): Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

CCSS.Math.Cont.7.RP.A.1 ( Grade 7 ): Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

CCSS.Math.Cont.7.RP.A.2c ( Grade 7 ): Represent proportional relationships by equations.

CCSS.Math.Cont.7.RP.A.3 ( Grade 7 ): Use proportional relationships to solve multistep ratio and percent problems.

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Cyberlearning is a collaboration of WGBH Educational Foundation, Office of STEM Education Partnerships at Northwestern University, and KQED.

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