We have created this website to share our experiences with flipping and fortifying using videos and interactive projects created with an app called Explain Everything. This is just one example of a new type of app that can be used to support students and educators in creating exploration activities and videos/animations to explain concepts to themselves and others.
Gardening is of course just one of several ways a sound understanding of area and perimeter can be put to good use. And of course, what's mathematics without some horticulture thrown in for good measure? Below you will find several different projects for teaching area and perimeter, including additional slides to help teachers and students create more excersizes for their own classrooms. We have more in mind to come, but here are the first four. There's just so many ways to teach area!
Unit by unit area measurement - https://app.box.com/s/381op67m5zanmgsdbs4a
Students use single square units to fill in the area of images on different slides, counting them individually. The first slide focuses on simple rectangles while the second introduces some shapes with twists and turns.
Filling a Garden - https://app.box.com/s/i50i3y6xi1rthm73dm4k
Two types of problems are presented here. The first is another unit by unit fill in excersize. Afterwards, students are challenged to create gardens using images of tomato, eggplant, caggabe and broccoli plants. And don't worry - all four plants require roughly 1 square foot of space to grow so students can stack them along side each other as equal units.
Non-standard Triangle unit measurement - https://app.box.com/s/rnudthm3tti8h9axfek7
Instead of squares, this excersize challenges students to measure a variety of shapes using equilateral triangles. This excersize can also help facilitate a discussion about the relationships between triangles and parellelograms or hexagons
Grid block measuring - https://app.box.com/s/9fi0vgchzcsicmwotuee
Instead of measuring unit by unit, students are encouraged to measure irregular shaped objects by using colour coded grids of single unit blocks to isolate sections. The extra slides at the end of the project enable students and teachers to make additional problems.
Area Pond - https://app.box.com/s/a1hirv57u5c6057x7j4e
Here students can look at the relationship between area and volume by filling a pond with fish, lily pads and ducks! By locking the scale of each item, they can compare how many fish, lily pads or ducks are needed to fill the pond. Possible questions include:
Which unit of measure do you think makes the best indication of pond size? Why?
If you knew the depth of the pond, how would you calculate the ponds volume?
Calculator games! Creating these problems is easy, but its incredible what a headscratcher a well placed multiplication sign can result in.
These games force students to make choices about where in a multi-step problem they will place a limited number of digits. Once the free moving calculator buttons run out, so too do their options. However, some problems can still be solved multiple ways, resulting in discussions about the relationships various numbers share.
Teachers can choose to either make digits for incorrect answers available or use the handy trash can icon on the side, allowing students to obtain needed clues. The games come in various levels, with each increase in level adding an additional step to the problem. Finally, Level 5 flips the whole excersize on its side (literally) and asks students to balance equations. Each level comes with a blank slide at the end that will help teachers - or students - to make additional challenges.
There are truly endless ways to represent a fraction and knowing that, isn't it far more fun to have a cheerful way of thinking of fractions? Below are several projects designed to help teach students about equivalent fractions as well as a few ideas for how problems can be constructed using these colourful manipulatives.
The first is a rather simple piece that provides a few pie chart manipulatives for helping students measure equivalent fractions. The pies are divided into fourths, fifths, eigths and tenths.
Next is the bookcase. Using the transparent books, students can compare the lengths of different sizes of various fractions as they fill the shelves. A single dictionary fills 1/2 the shelf, but what about the entire case? Then it only fills 1/6. How many copies of "Treasure Island" would be needed to fill the case? The books can also be compared on a number line ranging from 0 through 1. On the final slide, students can practice adding fractions by combining the first two shelves into a single string of books at the bottom.
Finally, everything is better with cakes, and of course that includes fractions! Students stack layers of cake to create giant, teetering monstrosities of birthday merriment. A few "finish the cake" problems are included and the vertical alignment gives another concrete way of thinking about how fractions can be presented in day to day life.
Over the past several weeks, we've been working hard to put together some more fun projects that will help bring mathematics to life in your classrooms. Now we have some ready to share and are very excited to be doing so!
First off, we have Battlesnake - a search and destroy style game for teaching kids about graphing lines on a Cartesian plane. Students can use one of the two boards to position their own snakes (either green or blue) and then use the other grid to keep track of their opponent as they hunt down the opposing colour. Simply name a coordinate point and - if your friend is hiding a snake there - SPLAT! Move one of the hit markers over that spot on the page. Keep track of how many snakes you've hit and the first to kill all of the opposing team's snakes wins!
The first few boards simply use positive integer coordinates and horizontal or vertical snakes. Later boards allow students to try to hunt down snakes in all four quadrants and along sloping lines. They may discover relationships between the points the snakes cover. Board 6 has even more varied shapes, including a parabola snake and a Fibonacci spiral.
Our abstract from our SITE 2013 Paper (with Leslee Francis Pelton) entitled:
Using an iPad to Explain Everything by Creating Interactive Activities and Vignettes
Explain Everything is a fantastic app that has huge potential to support students and educators in the learning process. The Explain Everything App (and others like it) allows teachers and students to create projects such as interactive activities that can be used by others to explore concepts and processes. As well, through its recording functions, it also allows teachers and students to generate and publish vignettes or video expositions of their understandings, and demonstrate proficiency in applying such knowledge to real situations. Besides introducing the potential of Explain Everything, this paper presents an outline of a workshop to support others in exploring this tool in their schools and districts.
Note: I am one of the creators of the free MathTapper apps (www.mathtappers.com) - for iOS devices (yes free - no ads or up-sells either). I have no affiliation with any of the apps presented below. They are just useful tools.
I teach Mathematics Education to Pre-service teachers so most of my examples will be mathematical – but hopefully it will illuminate the potential for an app like Explain Everything to generate learning objects in any area.
Outline for Webinar:
Big Picture
Reviewing the Potential
Mastering the Tools
Big Picture
How can iPads (and Tablets generally) support education?
access to content (textbooks, websites, blogs, wikis, etc.);
exploration of interactive content/activities – to discover relationships, to master concepts, etc.;
consolidation of processes within some context – to build mastery and fluency;
demonstration of mastery and skills - by capturing a performance;
creation of interactive activities to share understandings; and
creation of conceptual vignettes to support the learning of others.
What are Learning Objects?
a digital object that can be used to support learning
interactive spaces or linear presentations
stand-alone activities, demonstrations, observations, etc. – or collections of such
purpose created or collected and repurposed
easy to share
created by educators to support learning or by learners to demonstrate mastery
may be augmented with supporting content and search terms
e.g., learning objectives, teacher guides, assessments and other information
Who is going to create them and why?
instructional designers – to illuminate concepts and processes
educators – to support their classroom learning process
students – to demonstrate understanding
students – to educate younger students
parents – to share their understanding
scientists, authors, etc. – to share their discoveries/creations/ideas
Reviewing the Potential of Explain Everything
Interactive objects to support exploration and consolidation
Project files can be created, retrieved, exported, imported, shared by email and by websites. They end in ".xpl"
E.g., 1
Canadian coins: This EE project presents Primary and Intermediate level learners with an activity where they can manipulate images of coins (high fidelity) and record the process as they demonstrate proficiency in recognition, counting change, making change, explaining relationships, etc..
E.g., 3 Multiplying Fractions: By creating a collection of fraction regions (1/2. 1/3, ¼. 1/5) and then generating a set of the possible fractions that might be represented – in horizontal and vertical orientations - we can manipulate these to examine the potential meaning of fraction multiplication, and use that model to support the development of an understanding of the nature of the traditional process. Download the project file: https://www.dropbox.com/s/147x7pnld2er51z/rect-mult-fractions.xpl>
Video using the fraction multiplication project
Grant underway to encourage the development of more Explain Everything Learning Projects - both Teacher and Student generated
Animations/vignettes to support student understanding through demonstration
How tall is a tree?
Sum of fractions
Trip to Grandma’s house
Volume/capacity of a box
Mastering the Tools: Quick overview of some useful apps
Paper 53 (free +)
Nice interface – e.g., Sketchbooks
Tools: eraser, pen, watercolor and others + rewind (bi-directional)
Free for fountain pen, some additional cost for additional features
Export by screen capture
No zoom
www.fiftythree.com/
Background Eraser for iPad Mini ($0.99)
iPhone app also works – and scales up well.
Easy to use
1.Import images
2.Crop
3.Erase background (adjust threshold and feathering)
4.Export (PNG or jpg) - note that the background looks black on ‘Photos’ app
iMovie ($4.99)
Nice interface – Easy to use
Everything on your iPad – no need for external devices
Can take audio from external mic
Import movies and improve audio, add background, etc.
www.apple.com/ca/apps/imovie/
Photos (free)
photo managing app for iOS
Explain everything ($2.99)
Create slideshows
Screen casting with animation
Effective set of tools
Each slide can be recorded independently
Newest version supports editing within a slide
External (mac based) compressor available for $15
www.explaineverything.com
Guided practice
Choose a simple example that supports the exploration of all of the tools and share it with the participants. E.g., Angles in a triangle
Use the problem solving process to complete
Understand the problem:
What needs to happen for this learning object to be effective?
Clear voice and diagrams
Accurate information
Short (very important!)
Visually appealing
Make a plan:
E.g., create a storyboard with Paper 53.
Carry out the plan
Using Paper 53:Sketch a triangle
Moderately careful sketch
Angles are distinct (recognize that they will have to be inverted)
Color in, and trim with eraser
Screen capture (hold down power button – then tap on home button)
Now in Photos – with white background
UsingBackground Eraser: Trim off the background so that it can be manipulated
Load image
Crop
Erase background
Export as PNG file
Now in Photos – with transparent background(shows as black)
Using Explain Everything:
Make first slide – title page
Choose template (color of background and text)
Text “The sum of the angles in a triangle is 180°”
Audio overlay after ‘The sum of the angles in a triangle is 180°’
Make second slide – One triangle turns into three copies
Import image from photos – three copies of the triangle – stacked
Audio overlay ‘to demonstrate this … 3 copies’
Simultaneously move the 3 copies apart
Duplicate slide
Make third slide – with the two outside copies rotated and brought together
Rotate the two outside triangles 180° (without recording animation)
Audio overlay ‘rotate two of the triangles… bring them adjacent…”
Simultaneously move triangles adjacent to the middle triangle
Then draw a arc showing 180°
Duplicate slide
Make Fourth slide
Zoom in on central triangle
Audio overlay ‘To sum up…’
Simultaneously use laser pointer tool to highlight angles
We are creating this blog to share projects and videos that we have created to support learning in our classroom.
More specifically we are focusing on interactive projects and videos that have been created using Explain Everything - an iPad app that lets you create resources and share understandings.
If you are interested in contributing, please send me an email at tpelton(at)uvic.ca
