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?

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?

Round and Round the Garden - Area and Perimeter

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?