<p>Students will apply their knowledge of conversions and distance in this unit. In particular, students will:<br>- apply their knowledge of length, capacity, and weight conversions to real-world problems.<br>&nbsp;</p>

<p>- In what contexts does distance arise in mathematics?&nbsp;<br>- How does distance connect to other concepts in mathematics?&nbsp;<br>- What applications are there in the actual world for distance, distance conversion, and other measurements?&nbsp;<br>&nbsp;</p>

<p>- Application: The act of putting to use a rule, principle, or algorithm in order to accomplish a task, such as solve a problem.&nbsp;<br>- Capacity: The amount of space that may be contained within a fixed location; capacity is commonly expressed in units such as fluid ounces, pints, quarts, gallons, milliliters, or liters.&nbsp;<br>- Conversion: The process of changing one unit to another unit.&nbsp;<br>- Distance: The length of a segment or perimeter of an object.&nbsp;<br>- Estimation: The act of making a judgment about the magnitude or value of a quantity; estimates are generally performed by examining but not measuring the objects in question.&nbsp;<br>- Length: The distance between the endpoints of a line.&nbsp;<br>- Weight: The mass of an object that represents the gravitational pull of the object, commonly expressed in tons, pounds, ounces, grams, or kilograms.</p>

<p>- Art materials for optional Extension</p>

<p>- Consider the suggestions that students have for scenarios and difficulties during each activity, and assess their merits. Prioritize uniqueness above all else, then consider pragmatic issues like measurement.&nbsp;<br>- Assess students' ability to both listen and critically analyze other people's perspectives during class conversations. As they consider each concept, ask them to identify its similarities and contrasts.&nbsp;<br>&nbsp;</p>

<p>Modeling&nbsp;<br>W: There is a lot of room for creativity in this lesson. In reality, the activities set the lesson's direction. With their independent work, students are at the forefront of their learning.&nbsp;<br>H: Each activity's exploratory and engaging design creates a "hook" and "hold" mechanism.&nbsp;<br>E: The nature of all activities is abstract. Both the lesson's beginning and conclusion are abstract.&nbsp;<br>R: Students are encouraged to rewrite, reread, reconsider, and reflect because each task has demanding and sophisticated cognitive needs.&nbsp;<br>E: Students analyze themselves as they reason, argue with themselves, and engage in group discussions.&nbsp;<br>T: Students who require extra help can receive customized application problems and one-on-one instruction from teachers. All students can benefit from group collaboration as well.&nbsp;<br>O: During the class, students must draw connections and unearth the most crucial information regarding conversions and duration.&nbsp;</p>

<p>Tell students: <strong>"Distance can be examined and explored through the use of a variety of mathematical topics. Such a mathematical goal can be expressed as a cumulative problem. A cumulative problem simply takes an in-depth view of a topic and includes multiple ideas in a very clear and related manner. Here's an example of a cumulative problem:"</strong><br><br><strong>Activity 1</strong><br><br>Read aloud the following situation:<br><br>Robert is in charge of installing a sun roof or awning. The width must be 9 feet. The roof should cover an area of 108 ft². Approximately 20% of the roof should have a window or windows. Robert can decide on the shape of the window or windows. He must decide the following:<br><br>the required length of the sun roof.<br>the number and shape of the windows, as well as the&nbsp;dimensions for the given area percentage.<br>(The answers may vary since the windows can be configured in a variety of ways; 20% of 108 square feet is approximately 22 square feet. That could range from one square window about 4.7 feet wide to 22 windows, each 1 foot wide.)<br><br><strong>Activity 2</strong><br><br>Tell students <strong>"Create a cumulative problem in which data will be gathered for the distance examination. You must include percent and unit rate in the problem. Write an article appropriate for an academic journal outlining your approach to the specific distance topic&nbsp;you are discussing."</strong><br><br><strong>"The plotting of distances on grids and maps is extremely prevalent. Examples could include a primitive video game, an archeology dig site grid, cubicle layout in a large office workstation, and local storms on a county-sized weather map."</strong><br><br><strong>"Consider possible requirements for plotting distances on a coordinate grid." Look into various&nbsp;professional industry sectors.</strong><br><br><strong>1. Create a list of these requirements and associated illustrations, placed on a section of a coordinate grid.</strong><br><br><strong>2. Determine at least one distance for each need and explain how it relates to the context of the scenario.</strong><br><br><strong>3. Discuss any challenges you encountered while mapping the distances you envisioned. For example, if you wanted to plot and study distances using latitude and longitude coordinates, what areas would you be concerned about?</strong> (<i>horizontal and vertical distances and how to measure them</i>) <strong>Does the distance between coordinate points accurately represent distances between locations? Why, or why not?</strong> (<i>The actual distance is related to the coordinate points by the scale of the drawing.</i>)<br><br>The components of this&nbsp;activity should be given in both visual and audio modes. You will narrate and show your findings utilizing the animation and recording tools of PowerPoint, Jing, or Camtasia, depending on the resources available to you."<br><br>Students will work in groups of three to four to apply their understanding of distance and measurement conversions to create self-awareness of the reasonableness and appropriateness of using estimation in measurement. In other words, students work together to critically examine and debate whether accurate and estimated measures are more suitable, reasonable, and even desirable. Create a list of at least 10 examples. Classify each example&nbsp;as either <i>Estimation Preference </i>or<i> Exact Measurement Preference</i>. Students group examples together based on whatever categories they may perceive. Students also submit illustrations for at least three of the examples, as well as a&nbsp;justification&nbsp;for each. A table can be generated with either Word or Excel. Each group will present&nbsp;its table and provide a brief 5-minute presentation on the topic.<br><br>Consider the idea that humans make&nbsp;preferences every day based on specific criteria. For example, a person may have preferences when purchasing a computer. For those looking for a processor with Internet access, a Notebook™ or iPad™ are ideal options. However, if the person needs a CPU with plenty of memory and the ability to read and write DVDs, he or she will most likely choose for a laptop.<br><br><strong>Note:</strong> An example of an <i>Estimation Preference</i> is the desire to estimate how many light years a star is from Earth or another star. An example of an Exact Measurement Preference is the distance between an artery and a surgery site.<br><br>Convert the distance between the Earth and the nearest star, Proxima Centauri, to millimeters using the information available at <a href="http://heasarc.gsfc.nasa.gov/docs/cosmic/nearest_star_info.html">http://heasarc.gsfc.nasa.gov/docs/cosmic/nearest_star_info.html</a>. Demonstrate your process and solution; share any difficulties.<br><br><strong>Activity 3</strong><br><br>Discuss the importance/need for the metric system against the customary system. (Students should prepare a debate similar to the well-known e vs. pi debate.) In other words, a student must select between the metric or customary system. The student must provide thorough and detailed reasons to support the choice. It is agreed that understanding of both systems is extremely advantageous. This activity involves examining the applicability of each system in our environment. Where can we see similar measurements? What are some of the most common conversions? and so on. Students should present at least three conversion examples in their debate. Students must prepare a 5-minute presentation to debate their views with their classmates.<br><br>Provide an open forum&nbsp;for students to share ideas, questions, and challenges with the activities&nbsp;as a means of reviewing the lesson.<br><br><strong>Extension:</strong><br><br>Ask students to develop a graphic to complement Activity 1. The visual will have a labeled drawing with the proper units. The drawing should also be scaled appropriately to show relative sizes.</p>