Saturday, September 28, 2013

Ratios and mean, median and mode - learning with the children

These two projects employ a wide range of children's faces in order to teach about various different qualities of proportion. Mean, median, mode, ratios, fractions and percent excersizes can all be constructed using the images of the children. Simply change the text in the excersize and a new challenge can quickly be constructed, either by a teacher or a student.

Ratio Kids - https://app.box.com/s/su71biz5qbgdnqaaqmnz
Designed to help students explore the relationships between fractions, ratios and percentages, a few slides have already been created featuring problems that can be solved, or adjusted as seen fit. In total, there are 24 different faces available, but whoever is designing a new excersize can easily simplify the excersize to fewer students. Or possibly replicate a few faces and insist there are identical twins in the sample. The final few slides provide an image of simply the faces, one with names and one without. These can be copied between new Explain Everything projects as can images in any of the other projects. This can be useful for creating new projects without needing to start from scratch all over again. The slide with names can also be used like a "guess who" game, where students secretly select one of the children's faces and then try to guess, based on a series of yes/no questions which face their opponent has selected,

Averages - https://app.box.com/s/aridrd7yqzxcrclmmo8o
This project involves a few different excersizes in determining mean, median and mode. The first is based on hair length, the second test scores and the last bouquets of flowers. The flower slide in particular can be changed so that the numbers of bouquets varies and new excersizes can be constructed.

Telling Time

This post has just one project on it, but within it are a few different slides for helping students learn how to tell time, both on analog and digital clocks!

Clock Timeline - https://app.box.com/s/vtqjv3hgxz66fx2o1gm1
The basic principle with all the slides is that students are challenged to arrange a series of clocks from "earliest" to "latest." In the first slide, accompanying images are given in order to help the student deduce what time of day the clocks are depicting. Later slides simply have pictures of either analog clock faces or digital clocks. These can lead to discussions about what is meant by "earliest" and "latest." Possible questions of discussion include:
How do you know which clocks are showing earlier or later times?
Why is knowing if the time is a.m. or p.m. important?
What happens when it changes to a new day? How many possible right answers might there be then?
Finally, the last slide includes copies of the digits used for the digital clocks so that teachers may easily construct additional excersizes. Simply add the digits by triple tapping them to the clock to get them to stay in place, then shrink the clock to the appropriate size.

Sorting and Patterns

The next couple of projects involve sorting objects and creating patterns.

Object Sorting Game - https://app.box.com/s/3cj8q3ueylrfuh1gbrkg
A mish-mash of objects in the style of "I Spy" and search n' find books. Students can be asked to sort things based on a variety of qualities - colour, whether something is edible, whether it's a plant - so forth and so on. A good exploratory excersize, where the objects can be moved into categories determined either by the student or the instructor.

Candy Patterns - https://app.box.com/s/bnvgoj6rdi7ooy9plo9b
A game for pattern completion, the slides range from fairly easy to fairly complex. Items can vary by colour, type of candy and - in later slides - whether or not they are spotted. Extra slides are included so that it is easy for instructors to make additional excersizes. Below is just a short clip of when four year-old Hayden was building the rest of the patterns for the first excersize. This one was quite the favourite of his.
video

Friday, September 27, 2013

Science gets a turn - Tidal Zones and Chemistry

Another deviation from Math, this time we're venturing into Science, it's close cousin! These projects really just scratch the surface of the number of possible science related projects that could be made with Explain Everything. Right now, they tackle chemistry and biology and make for good challenges for students.

Tidal Zone Creator - https://app.box.com/s/huv9sa7eqqpplo0ls37s
On the first slide of this project is an assortment of sea creatures and plants typically found within the tidal regions of the BC coast. But where do each of these critters typically make it's home? In the relatively dry splash zone, or down near the subtidal fringer, where predators like starfish are always on the move? This project allows students to copy and paste the images between the slides. It may require some research for students to find where all the different plants and animals go. Or, conversely, teachers could simply require students only to place a few of the images. The second slide, where students would be copying their work onto, includes three moveable rock shelves that students can bring forward or send backward, depending on how they want to make their tidal scene. The image above is a complete version of the tidal zones, with everything placed where you would find it in the ocean (though some organisms will travel between various zones) and can be copied by students who feel less confident with creating the excersize from scratch.

Chemical Reaction Balancer - https://app.box.com/s/gpg7f2asq7tk98r2xut0
As promised, here is one of our chemistry excersizes! Designed to help students see that they often need varied numbers of molecules in order for chemical reactions to come out balanced at the end. Currently, the molecules are joined together, but by triple tapping on the individual elements, the atoms will come apart and allow students to reassemble them into new molecules. Joined molecules can also be duplicated so that students can get enough components in order to finish chemical reactions.

Combustion Balancer - https://app.box.com/s/joidcmgc7trulaihmr35
Similar to the project above, but focusing exclusively on hydrocarbons and combustion. Students can see how the number of oxygen molecules changes in combustion equations based on what type of hydrocarbon is being burned.

From Circles to Symmetry - More Geometry projects!

Another collection of geometry projects, these run the gamut of excersizes for symmetry, to circles, triangles and quadrilaterals.
Symmetry - https://app.box.com/s/ygce0jmdjiiotuohuyys
The long black line can be moved around, as can the images! Using the black line, students can divide the images in half and try to get a better sense of if the image is truly semmetrical or not. One or two of them are tricky to see! And make sure you assure the students that yes, one of the images has NO lines of symmetry. (It's a sneaky one)

Circle Area - https://app.box.com/s/vz06ht16gxjbokehy3zv
With three squares layered on top of a circle with bases the length of the radius, students can begin to visualize why it is that the area of a circle is equal to the radius multiplied by pi. Once the bits of the squares that don't fit into the circle are moved around to the empty quadrant, it becomes clear that there's actually enough room for three radius lengthed squares, plus a bit extra. The second slide is already assembled to show the relationship, in case students become frustrated with dragging all the little bits around.

Quadrilaterals - https://app.box.com/s/pve2cgt17ezfc90nv25x
A few problems where students can explore the relationship between various different types of quadrilaterals. By dragging the appropriate shapes into place, students can demonstrate that a square is a rectangle, which is a parellelogram, which is itself a regular old quadrilateral.

Triangle Area Slider - https://app.box.com/s/ssj0gpwjspg81526w44l
Like the circle area problem, here students can begin to see how just because a triangles dimensions might change, if it's base and height are the same, the area will be too. The Triangle in the centre comes apart into several peices, which can be moved over top of other triangle outlines. While it might not be exact, it does give a good impression of the way that area doesn't always  change even when the angles in a triangle do.

Triangle Sorter - https://app.box.com/s/ubjddfhzbb8pdkmr5bkv
A good activity for sorting and learning the difference between acute, right, and obtuse triangles. Using a right angle, students are challenged to sort the triangle sinto the correct bins.

Who are the shapes in your neighbourhood?

Plenty of the projects we've created for Explaining Understanding deal with spacial skills and geometry. In this particular set of excersizes, students are encouraged to use real life images to make comparisons. After all, it's important to see geometric shapes for what they are - things that exist in the real world!

Angle Measurement on Pictures - https://app.box.com/s/9ut78776ajfppthxxicf
A series of photos of different things made up of multiple angles. The protractor image is provided and students can then zoom in on the images they are measuring as much as they like. Aside from simply "measuring" things, possible discussion points include:
Do you see certain angles more frequently than others? (right, acute, obtuse?) Why do you think this is?
Which pictures are easiest to measure? Which ones are hardest? Why does perspective matter in photographs? What's the difference between measuring angles on a two-dimensional versus a three-dimensional object?

2D objects - https://app.box.com/s/b3v0ow18tv0cp9b04dy4
Here students can slide images of two dimensional shapes on top of the various slides and vind them in the images. Some are easy to recognize, like squares and circles, while others are more difficult, such as the trapezoid. Any shapes that are not age appropriate can be eliminated from the excersize before handing it to children.

3D objects - https://app.box.com/s/8dtyybdvozp5rg6ntcs3
Similar to the above excersize, except this time students are challenged to find three dimensional shapes in the images. Some are much more common than others. Possible points of discussion include things like:
What makes something a cube and not a rectangular prism?
Squares are relatively common 2D objects but not very common 3D objects. Why do you suppose that is?


Monsterful Art!!!

After putting together numerous Mathematics projects, we decided to branch out and add a few based around other subjects. Here are the first couple that were assembled with art classes in mind.

Monster Shapes - https://app.box.com/s/a32980zje9x6oraic26u
A sort of meeting place between math, art and monsters, this project is filled with images of noses, mouths, eyes, ears, horns and fangs that can be used to build wild, crazy looking monsters. Math teachers can discuss which shapes are geometric objects (I happen to know some of the mouths are rather trapezoidal). Not all the teeth are pointy either, and not all the eyes are round. The above photo gives one idea of how the images can be combined, but it's certainly not the only way!

Art Tracer - https://app.box.com/s/hdaixly0ob1abmkx3j02
While the draw function on Explain Everything isn't perfect, it can do some interesting things that are difficult to find elsewhere. For regular drawing, I greatly prefer Paper 53. But Explain everything allows you to do something rather strange - to draw in white on a white background, unable to see what you're doing. How could this be helpful? Well, I remember in Grade 7 our teachers trying to help us learn to draw by sight, rather than relying on constantly checking what our hands were doing. It was nearly impossible to stop us from staring down occasionally as we drew. But in Explain Everything, a student can try to copy one of the images pictured in the project, entirely invisible and in white. Once they're done, they can simply select the drag tool and pull the white outline over top of the original image they were copying, so that they can see just how close they got.

More and More Manipulatives!

One of the things we wanted to do with Explain Everything was create some basic classroom manipulatives. Digitally, it's much harder to loose peices to your tangram and pattern block sets than when you're using physical blocks! Below are links to a score of different manipulatives we've put together. Now that scale and position can be locked invidually, students will be able to do a great deal with the various manipulatives.

Pattern Blocks - https://app.box.com/s/ki2t3jy4flwapg6rmmq5
This project contains two slides - one simple set that only has a few peices and then a second with a wider range of peices. Students can lock the relative size of the peices, duplicate them and then go crazy making patters! Possible applications include:
Comparing sizes of angles/side lengths
Measuring the area of various shapes using smaller shapes.

Playing Cards - https://app.box.com/s/mlu05b1ndp7us4jkkkno
While these can't be randomized like regular playing cards, this single slide project contains images of a complete deck. Teachers can use it to create videos to explain an excersize to students or two discuss ways cards can be sorted into groups, (ex; by suit, by colour, by face value) and discuss relationships of probability.

Algebra Tiles - https://app.box.com/s/4k658o7psvwhzr30zz5e
Like traditional algebra tiles, these images can be used to model all sorts of algebra related problems. Containing ones, X tiles and X squared tiles, teachers and students can model addition, subtraction and multiplication tiles.
Ex: Show me how you would solve 2x + 4 = x + 6

Factor/Probability Trees - https://app.box.com/s/4ll8qf3k6ufly8xo8d6z
These branching images can be used to show how numbers grow exponentially larger as they are multiplied further. They can also be used to model probability of multiple independent events.
Ex: Model the following proglem - Bob can choose between three kinds of ice cream and four kinds of toppings for his sundae. How many possible sundaes can he create?

Big Bag of Marbles - https://app.box.com/s/86x2pkprbytdxg9u79hi
While not a perfect representation of randomization (due to the layering affect of Explain Everything's program) this manipulative still provides a fun simulation of real probability. Inside the bag, there are equal numbers of green, red, yellow and blue marbles, but they're all mixed up inside! What are the chances of drawing each colour out of the bag?