Latest Contributions by JosephKerski

Teaching Geography for the 21st Century eNetLearning Certified Facilitators Provided for Each Course Video:  Teaching Geography in the 21st Century: Course Overview - YouTube DATES, TIMES, NUMBER OF SESSIONS: Check the course catalog for dates athttp://www.enetlearning.org/course-catalog-and-descriptions/. COURSE CONTENT: Fundamental to geography is the study of issues surrounding land use, natural hazards, population, economics, land use, and political issues, which will be emphasized in this course. However, as geography encompasses all that is in the world, at multiple places, scales, and time periods, it is impossible to cover its breadth in the short time that our course will run. Therefore, this course will touch on these issues but will focus on how to use 21st Century perspectives, themes, and tools to teach these issues. Rural, Urban, Economic, Land Use, and Population Issues: Over the 5 weeks of this course, participants will deepen their understanding of and ability to effectively teach population dynamics (including such concepts as settlement, land use, age, birth rate, growth rate, and human-environment interaction), land use issues (such as zoning, sense of place), urban issues (such as historical and current development of cities, site vs. situation, and challenges facing cities), and economic geography (including industrialization, employment, measures of development). Core Geography Themes: Embedded in studying these issues are core geography themes such as considerations of scale in patterns and processes, interpreting maps and analyzing geospatial data, understanding and explaining the implications of associations, networks, and interconnections among phenomena in places, defining regions and the regionalization process, and understanding the nature of and limitations of geographic data. Spatial Perspectives and Tools: The spatial perspective is critical to understanding geographical content and processes. Being competent and confident in the application of the spatial perspective to geographical understanding enhances and strengthens our ability to communicate and teach about human geography. A number of powerful web mapping and related tools are now available for the geography instructor, and this course builds familiarity and confidence in using these tools through a series of hands-on activities. ... View more

Folks: I have over 2,500 videos on STEM, place, GIS, education, geography on: http://www.youtube.com/geographyuberalles --Joseph Kerski ... View more

I recently mentioned that maps, tools, and applications in ArcGIS Online continue to expand, highlighting the new map showing the distribution of Starbucks as an example. Another example touches on a subject that many students know very little about--agriculture.  We have written about this topic in the past, offering curricular resources such as this one that asks students to analyze the distribution of four crops in the USA  and this one asking students to investigate the distribution of five crops around the world using ArcGIS.  A starting point for such investigations is simple but powerful maps of agricultural data, such as this one showing the acres of total cropland by county in the USA as a percentage of total land in acres.  The data comes from the 2007 Census of Agriculture. Does the pattern of agricultural land as a percentage of total land surprise you?  Do the statistics that are visible when you select a county, indicating how much of the cropland is harvested, surprise you?  What are some of the reasons for the spatial patterns that you see?  If you live in the USA, how does your own county compare to the others in your region and across the country?  What are some factors that explain how much land in a county is dedicated to agriculture?  How would you rank the following factors:  Soil health and type, climate, growing seasons, frequency of hailstorms and floods, landforms, relief, urban areas, and the height of the water table?  Zoom in on some of these counties, change the basemap to satellite image, and examine the type of farms and ranches.  Do the croplands rely on precipitation alone or are the croplands irrigated?  If they are irrigated, are they irrigated from a canal or from wells? Change the style--the colors and classification method.  How do these changes affect the way you understand the cropland patterns?  Based on your answers above to the importance of factors explaining cropland patterns, use "Modify Map" and then the "Add" button to find, add, and investigate these other factors.  For example, add the Crops 2009 map by "hillrc" to examine the type of crops grown in Indiana.  Which crop type(s) exhibit the most intensive agricultural land use?  If you are logged in using an ArcGIS Organizational subscription, search the "Landscape" group under Esri Map Layers for USA Land Cover GAP and soil layers.  Also, change the basemap to topographic or add USGS topographic maps to determine the effect of landforms and steepness of terrain on crops. Sort the table and find the counties with the highest percentage of their land in crops. Then, change the style and choose a different attribute to map, such as average size of farms, cotton or soybeans, orchards, or milk cows.  This single table of data contains many variables that can be mapped, compared, and contrasted. How might you use these maps and resources in your own instruction? Cropland in Use Map of the USA in ArcGIS Online. ... View more

Maps, tools, and applications in ArcGIS Online continue to expand, affording exciting new opportunities for teaching and learning.  One of the new maps highlights the new capability of generating “heat maps” by showing the distribution of Starbucks coffee locations.  The map is quick to load but contains 18,680 Starbucks around the world.  The points are grouped at a small scale, for analyzing regional and continental patterns, and at a large scale, for analyzing patterns within a metropolitan area.  Examine this map via the above link, shown below, guiding students through inquiry using some of the following questions followed by investigations. Does the pattern of Starbucks in Manhattan surprise you?  What are some of the reasons for the spatial pattern?  How do the number and pattern compare to other boroughs of New York City, to your own city, and to other cities around the world?   What are some factors that explain how Starbucks determines where to locate?  How do these factors and the spatial pattern compare to other coffee-oriented businesses, and to other food-related businesses, and to non-food businesses? Make the two heat maps associated with the Starbucks locations at the two different scales visible.  A heat map is another way to visualize data, creating a “density surface” of the points, with brighter oranges and yellows indicating a higher density, and greens and blues indicating a lower density.  What are the differences between the heat maps at the two different scales?  How does the heat map help you understand the clustering of the Starbucks locations?  Starting in March 2015, you can now easily create heatmaps of any point data using ArcGIS online. This map isn’t a fabrication created for educational use:  Indeed, Starbucks uses Esri GIS solutions at many levels and for many reasons, from managing its suppliers to packaging operations to selecting optimal retail outlet sites.  During the unit where you and your students are exploring the map, you could show this video from the Esri User Conference where Starbucks GIS analysts explain why and how they use Esri GIS technology to make their business more efficient and sustainable.   For more detail,  your students could read and reflect upon this article in Forbes written about how big data helps retailers like Starbucks pick store locations. A related mapping application in the “coolmaps” gallery allows you to filter stores by the average income in neighborhoods in San Francisco, California, and to buffer the most effective distance for a mobile “coupon” message to potential customers.  If you are interested in analyzing patterns of other businesses, the locations of thousands of businesses are included in the Esri online products Business Analyst, Business Analyst Online, and Community Analyst. How might you use these maps and resources in your own teaching? Starbucks in New York City - locations and heatmap. ... View more

Those of us in GIS education continually strive to ensure that our teaching methods adhere to respected and innovative learning styles.  Adult learning theorist David Kolb's Experiential Learning Theory (1984) works on two levels:  A four stage cycle of learning and four separate learning styles.  I believe Kolb's cycle and styles can help inform how we can more effectively teach with GIS and about GIS. Kolb's experiential learning style theory includes these "stops" along a cycle:  1.  Concrete Experience, where a new experience of situation is encountered, such as what happens while performing a task, followed by 2. Reflective Observation of the new experience, followed by 3. Abstract Conceptualization, where reflection gives rise to a new idea, or a modification of an existing abstract concept, and, finally 4. Active Experimentation, where the learner applies the experience to the world around them to see what results.  At first glance, pausing at each of these stops seems like something we already do in our GIS-based assignments. However, at times we hear from students who feel that they are "going through the motions" in technical tasks and aren't assimilating and conceptualizing what they are doing.  Therefore, a critical examination from time to time of how we are enabling students to reflect upon their learning and apply it may be challenging, but helpful as we strive to improve the effectiveness of our instruction. Kolb's learning styles attempt to identify an individual's predominant way of learning, and include (1) Diverging--those who watch from different perspectives; they are good brainstormers. (2) Assimilating--those who prefer a concise, logical explanation and approach.  They are good organizers.  (3) Converging--those who can solve problems and will use their learning to find solutions to practical issues. (4) Accommodating--those who prefer "hands-on" learning, often rely on intuition rather than logic, are able to meet challenges, and who like new experiences. Kolb's learning stages and cycle could be used by GIS educators to critically evaluate how they are teaching, and ensure that they design GIS activities to be carried out in ways that offer each learner the chance to engage in the manner that suits them best. Also, the activities should be taught in ways that usually take students through the whole cycle. Kolb believes that the learner must be involved in the planning of the learning experience if experiential learning is to be fully effective.  How can we ensure that the learner has a say in our GIS courses, over and above the standard "GIS project" assignment? Kolb, D. A. (1984). Experiential learning: Experience as the source of learning and development (Vol. 1). Englewood Cliffs, NJ: Prentice-Hall. How might you use Kolb's Learning Cycles when you teach GIS? ... View more

A fascinating and practical book entitled Facilitating Seven Ways of Learning by James R. Davis and Bridget D. Arend is a resource for more purposeful, effective, and enjoyable university teaching.  In addition, I believe that the seven ways presented by the authors provide a useful framework for instruction focused on spatial thinking and geotechnologies.  The seven ways include behavioral learning, cognitive learning, learning through inquiry, learning with mental models, learning through groups and teams, learning through virtual realities, and experiential learning.   Each way of learning is associated with intended learning outcomes, or what students learn, and is accomplished through specific methods.  For example, the intended learning outcomes in learning through inquiry are developing critical, creative, and dialogical thinking, and is accomplished through question-driven inquiries and discussions. As we have discussed numerous times in this blog, teaching and learning with GIS invites students to ask questions, solve real-world problems with real data, and think critically about why and how they are solving that problem.  Every single one of the seven ways of learning identified in this book have been used by educators and students who analyze spatial relationships, patterns, and trends through GIS, as is evident in these and other case studies.  Furthermore,  all of the methods identified in the Seven Ways book, including tasks and procedures, practice exercises, presentations, explanations, inquiries, discussions, problems, case studies, labs, projects, group activities, team projects, role playing, simulations, games, internships, and service learning, are the "bread and butter" of teaching with GIS.  No one single method is used, which illustrates the versatility of GIS in instruction to meet different learning objectives.  We use all of them when we model effective teaching with GIS at our annual T3G instructor institutes. I recently met with one of the authors, Dr. Arend, who is the Director of University Teaching at the Office of Teaching and Learning at the University of Denver, and I believe that the Seven Ways can be used effectively by instructors (1) to make a strong case to their administrators on campus that teaching and learning with GIS meets numerous instructional objectives and learning styles, and (2) as a guideline in their own instruction, to ensure that they take full advantage of the 7 ways, and the result will truly be more purposeful, effective, and enjoyable teaching! How might you be able to use this book and framework in your own instruction? Facilitating 7 Ways of Learning: Book. ... View more

In my last post, I described some simple but powerful activities that you can use with students to engage them in mathematics using ArcGIS Online.   What else can you do with mathematics with ArcGIS Online?  Using another activity I have written, I invite students to investigate global temperature extremes.   The activity begins by asking two questions:  (1)  Can you work effectively with numbers so that they can understand extreme temperatures around the world?  (2) Can you compare and interpret information so that you can understand patterns over space and time? Students conduct seven mathematics investigations in this activity: 1. Analyze temperature extremes data around the world including the temperature reading and the date. 2. Examine the relationship between the location (primarily: Altitude and latitude) of the extreme temperatures and the value of the temperature, and whether that temperature was a high or a low extreme. 3. Order and compare numbers in temperature data tables and on maps. 4. Round numbers in temperature data tables and maps. 5. Visually represent numbers in temperature data tables and maps. 6. Add and subtract whole numbers and decimals. 7. Compare temperature extremes over time by constructing graphs. The activity begins by asking the students to describe the hottest and then the coldest day they have experienced, and what they did to cool down or warm up.  Next, using a map of temperatures plotted as points on a world map in ArcGIS Online, they describe the spatial pattern of global maximum and minimum temperature extremes.  Then, exploring the attribute table in tandem with the map, they answer the following questions:  "What is the range of maximum temperatures shown on this map (between the lowest maximum and the highest maximum)? How many times hotter is the highest maximum temperature than the lowest maximum temperature? Round your final answer to the nearest degree. Show your work." Students then sort the table on latitude and graph the temperatures by latitude, and then create a histogram of temperature extremes by month of the year, using these graphs to make connections between the data, the map, climate, and seasons.   They zoom in to selected extreme temperature locations and examine the effect of local topography and proximity to oceans on extreme temperatures.   They also examine the temporal components of the data to determine the existence and length of heat waves and cold snaps. What else could you do with this data or with other weather related data to connect science, geography, and mathematics using ArcGIS Online? Examining global temperature extremes with ArcGIS Online. ... View more

A new article in ArcNews entitled Four Guidelines for the New GIS Professional not only offers insights for those new to the field of GIS, but also for educators who teach the subject and who use it as a tool to teach history, geography, earth science, and other subjects. The article identifies four strategies that can ensure that a GIS professional remains at the forefront of this profession:  (1)  Build a strong platform; (2)  Extend the platform across the organization; (3) Leverage existing GIS investments; and (4)  Be active in the GIS community.  I believe that educators can use the "building and extending the platform" strategies as an encouragement to spread spatial thinking and GIS beyond their own classroom walls.  If you are at a university or community college, that might mean giving a few presentations each academic year to colleagues across campus, in history, language arts, biology, or another discipline that is maybe a bit outside your comfort zone.  Spatial thinking has a way of bringing diverse disciplines together around the "whys of where", solving problems, and providing career pathways for students.  If you are at a primary or secondary school, it might mean a presentation at a faculty meeting where you discuss why you are using GIS in your instruction, or having your students discuss their work at a school assembly, or conducting a hands-on workshop for educators in another school or the neighboring school district. Leveraging existing GIS investments implies that, like anything worthwhile in education, teaching with GIS requires time and effort. These efforts will be longer lasting and more impactful on students if they are conducted in collaboration with your education colleagues on your campus or in your school district, or with colleagues far away who share similar interests.  And finally, being active in the GIS community is important for geospatial educators, to garner support for your efforts from administrators, to share instructional practices, data, maps, and apps, and to share your stories so that others will be inspired to use these approaches and tools in their own instruction.The article points out four ways that the "GIS technology ecosystem" is rapidly changing, including cloud-based GIS, the widespread use of web mapping, the increasing adoption of open data, and the app revolution.  What do these and other changes mean for the GIS educator? The article reminds us that this is an exciting time in GIS.  New applications and a growing awareness of the power of GIS are accelerating the need for skilled people in this field. Web mapping and visualization have opened the world's eyes to the power of the spatial visualization of information and are transforming how people understand the world.  You, as a GIS educator, are key in making this happen, by enabling students to visualize, question, analyze, and interpret our world. Visualize, question, analyze, and interpret: Four key parts of teaching and learning with GIS. ... View more

One theme that we frequently discuss in teaching and learning with GIS is that maps are representations of reality.  To be sure, they are very useful representations of reality, but they are representations nonetheless, laden with meaning, different possibilities for interpretation, and yes, some distortions and error.  In the fast-paced world that GIS analysis and creating maps has become, it is easy to lose sight of these representation fundamentals when we have maps and imagery at our fingertips, at multiple scales and over multiple themes.In a video, I discuss just one place where care needs to be made in interpreting maps.  In the video, observe my surroundings as I stand near the traditional “line” that divides the deciduous forest to the south from the coniferous forest to the north in North America.  On most maps, this is indeed shown as a line.  However, consider the following:  Is the “line” really a line at all, or is it better described as a gradual change from deciduous to coniferous as one travels north? Is that vector line then better symbolized as a “zone”, or is vegetation better mapped as a raster data set, with each cell representing the percentage of deciduous and coniferous trees in that cell? How many other data sets do we tend to see as having firm boundaries, when the boundaries in reality are far from being "firm"?  How does that affect the decisions we make with them?  Even the boundary between wetlands and open water were originally interpreted based on land cover data or a satellite or aerial image.   In another example, as stated in the GIS and Public Domain Data book, contour lines are not surveyed lines, but rather are interpreted, often from aerial stereo pairs.  And each data set that we can analyze with maps was collected at a specific scale, with certain equipment and software, at a specific date, and within certain margins of error that the organization established. Maps are representations of reality.  They are some of the most useful tools ever invented, but care needs to be taken when using this or any abstracted data.  How might you be able to use these examples and considerations for "teachable moments" in your own instruction to foster critical thinking? Maps as representations of reality: The deciduous-coniferous tree "line". ... View more

The two most important qualities I believe that we seek in job applicants is:  Be Yourself, and Be Curious.  What do I mean? Be Yourself means being honest about your own job and personal strengths and your own weaknesses, or areas that you are seeking to improve.  Don’t pretend in an interview to be anything you’re not.  Be Curious means asking questions.  This means to ask questions at the interview, of course.  But beyond the interview, on the job and while you are still in school, ask lots of questions. Be curious about the world.  Good questions lead to good investigations. Investigate and solve problems.  If you don’t have some of the skills needed to solve those problems, acquire and practice those skills. About 5,000 people work at my company, Esri (Environmental Systems Research Institute).   Our headquarters is in southern California (Redlands), we have 10 regional offices in the USA and some smaller satellite offices, and more than 80 worldwide distributor offices.   We are the largest Geographic Information Systems (GIS) organization in the world and as such receive a lot of applications for every job we post.  If you are serious about making a positive difference on our planet with GIS, I encourage you to gain those skills and consider applying at Esri‌ or another organization that fits your own personal ethos! Esri headquarters building, Redlands, California, USA. ... View more

Building on past field investigations where I studied the spatial accuracy of GPS receivers and smartphone location apps, I recently compared the spatial accuracy of two location apps on a smartphone.   My goals were twofold:  (1) To determine which of two location apps was more spatially accurate in varied terrain and conditions; and (2) To model a field activity that integrates geography, science, and mathematics that students can engage in easily and effectively. On a hike in the chaparral hills of Southern California, I used my smartphone to collect my tracks using two apps--Motion X GPS and RunKeeper--at the same time.  Once the hike was done, I then exported the track lines and points as GPX files and uploaded them into ArcGIS Online.  The results, shown below, indicate that the two tracks were quite similar; within 1 meter of each other.  I was pleased with the spatial accuracy of both, despite the very steep terrain and considering that the phone was in my pocket most of the time rather than held up high to capture a theoretically stronger set of GPS and cell tower signals. It was also evident that in this location, on this day, RunKeeper was a bit more spatially accurate, doing better at maintaining the trail switchbacks as I walked rather than cutting them off.   At one switchback, the two tracks were separated by 4.5 meters.  However, just downhill and to the northeast of the image below, Motion X was more accurate for a specific 10 meter stretch of trail.  It must be remembered, however, that these statements "assume" that the satellite image is the best benchmark of spatial accuracy, but it too contains distortions and error.  Furthermore, on a different day and time, with the GPS constellation in a different array, my results could vary.  Varying the speed walked, the time and date, the location app, the location at which the phone is held, the type of phone, and other factors all make for easy-to-implement field investigations that incorporate science, mathematics, geography, and geotechnologies.  And, while outside, you can have rich discussions on land use, land cover, natural processes, access to open space, animal habitat, climate and weather, and much more, as I do here.  The results are easily examined using ArcGIS Online, and students can also create a presentation or a story map in ArcGIS Online to communicate their results. Give it a try and comment below on the results of your investigations! Comparing the spatial accuracy of two smartphone location apps in the field. ... View more

Teaching about watersheds and river systems has long been a major theme of physical geography, earth science, and environmental science instruction.  ArcGIS Online now provides capabilities for educators and students to create watersheds, trace downstream, and create viewsheds, all of which can serve as an effective means to foster understanding of watersheds and river systems, how they are connected geographically and temporally, and why they are important. Boulder, Colorado, like many mountain-front communities, is prone to periodic devastating floods.  To supplement a lesson that I wrote about floods in Boulder, I used the watershed tool in ArcGIS Online to create the watershed that is drained in Boulder Creek through the mouth of Boulder Canyon.  The area is 130.12 square miles, giving a clear reason why any major rapid snowmelt or any major rain event anywhere in that large area creates flood hazards for the city of Boulder. Watershed upstream from Boulder Colorado. Where does that water flow once it reaches Boulder?  To find out, I used the new Trace Downstream tool with a 15 mile limit.  The result makes it clear that the areas east and northeast of the city also bear the effects of potential floodwaters. Trace 15 miles downstream from the mouth of Boulder Canyon, Colorado. Using the same tool, I ran another Trace Downstream analysis and extended the distance to 3,000 miles.  The result, shown below, fits in well with the lesson but also in any lesson that asks students, "where does a cup of water flowing from my location flow through before it reaches the ocean?" Trace from Boulder Colorado to the Gulf of Mexico. Finally, to get a sense for how the terrain in Boulder is mountainous to the west of the mouth of the canyon but flattens to the Great Plains to the east, I used the new Create Viewsheds tool from a point on top of Green Mountain, above the famous Boulder Flatiron rock formations.  The viewshed, as the name implies, indicates the land viewable from a specific point, and in my case, I specified nine miles for the extent. The result of viewshed analysis can foster understanding of the terrain and how the terrain impacts streamflow and flooding. Nine-mile Viewshed from Green Mountain. These activities require an ArcGIS Online organizational subscription and to generate the analysis layers such as the ones I did above, you need to have publishing rights in that organization.  With your organizational subscription, examine the map I created above, and try these tools yourself for your own area! You'll be amazed at how easy it is, and yet how powerful, because these tools can foster understanding of how streams, watersheds, and terrain are connected spatially and temporally. ... View more

Learning to Learn from Data: GIS Connections. How can GIS encourage and foster critical thinking skills about data? ... View more

We receive many inquiries about how GIS and spatial thinking can be used with primary (elementary) aged students.  In honor of GIS Day and Geography Awareness Week being upon us, I thought it would be the perfect time to highlight a few ideas and resources that you could use to develop and apply spatial thinking skills. We have always advocated (1) that the most appropriate tool be used for the objective at hand; and (2) spatial thinking skills are developed through a variety of means, methods, settings, and media.  These include the appropriate use of ArcGIS Online, for example, to examine world biomes, the locations and growth of cities, land use and demography of their local community, population change by country, the frequency and distribution of earthquakes and other natural hazards, the shape and size of watersheds, and so on.  A selective use of the ArcGIS Online presentation mode, for example, to foster students as "map detectives" can be used effectively, as I have done with this "Name That Place" presentation and with another entitled "Weird Earth." However, fostering spatial thinking at young ages in particular needs to use all five senses, and needs to include outdoor experiences.  Using globes, mapping trees on campus, watching videos about scale coupled with measuring objects around school and the perimeter of the school building are just a few activities that can be effectively used.  I am a firm believer in fostering spatial thinking using tactile-based activities such as this lesson I developed that asks students to create a thematic map on a translucent sheet of paper based on ArcGIS Online imagery, described here and in video form here.   Another tried-and-true lesson is to ask students to draw a map of their classroom, and, depending on the students' age, incorporating map scale.  Another simple but powerful activity I have used during hundreds of school visits over the past 20 years is to ask the students to draw an outline of the school building, as it would look from above, orienting it according to cardinal directions, and labeling the different sections of the building and school grounds.  Then, I ask students to check their maps against the imagery in ArcGIS Online and discuss differences and similarities and the reasons for them. Creating a thematic map from a satellite image. Our colleagues in education and industry continue to create a rich body of resources.  For example, Barbaree Duke created a series of language-arts based activities, some of which can be used in primary school.  The 20 Minute GIS for Young Explorers curriculum from GISetc spans multiple disciplines and though rich in content, each can truly be taught in 20 minutes. Finally, exploring history, geography, art, science, mathematics, and other disciplines can be easily done through studying the gallery of storymaps or ... having the students make their own storymap.  Other ideas exist on the GIS Day website.  I've run out of space.  What are your ideas for fostering spatial thinking at young ages? ... View more

I have created 5 new geography-based lessons and 5 new mathematics-based lessons and placed them in 2 galleries in ArcGIS Online.  All 10 lessons are geared toward Grade 6, but can be modified for primary or for upper secondary school.  All are based on ArcGIS Online and can be used without logging in; they are designed to introduce students to spatial thinking while focusing on core geography and mathematics standards and content. The geography lessons include investigations of volcanoes, rivers, oceans, cities, and agriculture, while the mathematics lessons ask students to study demographics, temperature extremes, earthquakes, the shape of the Earth, and latitude-longitude. Each lesson is grounded in educational content standards, and takes advantage of the ArcGIS Online live web mapping environment to foster critical thinking, problem-based learning, and inquiry. For example, the earthquake activity's introductory questions include, "Can you apply the principles of probability to real-world events and data?  Can you compare and interpret information using maps, databases, and timelines so that you can better understand earthquakes over space and time?"  Mathematics standards embedded in this activity include:  (1)  Describe and order simple events using familiar language, and describe and compare the likelihood of future real-life events using 0, less than ½, ½, more than ½, 1. (2)  Understand, explain, and use the probability of earthquakes at the global, regional, and local scale.  (3) Describe and compare the likelihood of future real-life events (earthquakes) at the global, regional, and local scale.  (4)  Understand, explain, and use the place value of positive numbers of any size.  (5)  Round numbers to the nearest 10, 100, and 1000 and justify rounding in terms of closeness to the number.  (6)  Order and compare whole numbers of any size in ascending and descending order.  (7)  Select and apply an appropriate numeracy strategy to solve addition, subtraction, multiplication, and division problems and justify the choice of strategy.  (8)  Add and subtract decimal numbers with the same and different number of decimal places.  (9) Investigate the units for time and convert between them, and (10)  Draw and interpret timelines to record events. The other activities are similarly grounded in solid content, and foster key skills and the spatial perspective. I encourage you to try the lessons, but also to consider using galleries in ArcGIS Online to serve your own activities.  The gallery presents students with a convenient "one-stop shop" to access content.  Galleries point to a group containing the content that you wish to show, and are easy to set up, as this video explains.  And as you can see from the two galleries I set up here, they can point to more than just web maps. In the case of my galleries, I point to PDFs of the lessons, and in each PDF is a link to the web map that the students are to open to begin their investigations.  Try it! Gallery of Mathematics Lessons in ArcGIS Online. A new Geography gallery exists as well. ... View more