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.

## Saturday, September 28, 2013

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

Labels:
children,
children's faces,
faces,
Fractions,
Fractions as part of a whole,
guess who,
kids,
mean,
median,
mode,
patterns,
ratio,
sorting

### 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.

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.

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.

## 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.

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.

Labels:
chemical reactions,
chemistry,
combustion,
elements,
science,
tidal zones

### 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.

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.

Labels:
angles,
circle area,
circles,
geometry,
quadrilaterals,
symmetry,
triangle area,
triangles

### 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?

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?

Labels:
2D objects,
3D objects,
angle measurement,
geometry,
pictures,
protractor

### 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.

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.

Labels:
art,
blind drawing,
monster,
monsters,
tracing

### 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?

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?

Labels:
algebra,
algebra tiles,
factoring,
Fractions,
geometry,
manipulatives,
marbles,
pattern blocks,
playing cards,
probability

## Tuesday, August 6, 2013

### To the Count of Ten - Manipulatives, Base Ten, Counting and Multiplication

Below are a selection of slides that provide some cheerful, basic manipulatives for teaching a range of topics. Counting, addition, subtraction, multiplication and place value are among the topics that can be covered using these slides.

Base Ten Blocks - https://app.box.com/s/09z3ikcg44a3u0o5j5pq

The three slides all provide basic manipulatives of base ten blocks, the first zoomed in closer than the later two. The subsequent slides feature place value columns. The first focuses on ones, tens and hundreds while the second can be used to represent decimals, with ones, tenths and hundredths filling the columns.

Lesson/activity ideas:

1) Demonstrating relationships - How many red squares does it take to cover one yellow rod? How many rods are needed to cover one blue block?

2) Representing numbers - How many ways can you show the number 192? (example: 2 squares, 9 rods, 1 block OR 2 squares, 19 rods). Which blocks must you use? Why?

3) Addition and subtraction/performance evaluation - Create a video showing how you would solve 239 + 473.

Multiplication Arrays - https://app.box.com/s/z9lvlego10p831dy9fts

This activity consists of groups of objects that will help students master the basic multiplication facts. The first ten pages focus on just one multiples of just one number each from 1 through 10. The final two pages contain images of all the possible arrays from 1 through 10

Lesson/activity ideas:

1) Counting/representing numbers - Select three rods of five tea pots. How many tea pots in total did you select?

2) Commutative property - What are two ways of showing 4x6?

3) Factoring - 4x6 is 24. What is another multiplication fact that results in the number 24?

Ten Frames and Counting Flowers - https://app.box.com/s/hxkukzjxgfgn4c2nmaen

Thre sets of counting tools are included, the first being a basic ten frame with the dots free moving. The second slide has ten frames representing the numbers 1 through 10 premade. The final slide is effectively like the second, accept instead of ten frames it uses collections of flowers.

Lesson/activity ideas:

1) Counting - Show me the number 6.

2) Multiple representation/ Addition - What are some ways to show the number 15 using different bunches of flowers? Can you show that in an addition sentence?

Labels:
addition,
base ten,
base ten blocks,
commutative property,
counting,
manipulatives,
multiplication,
multiplication arrays,
subtraction,
ten frames

## Tuesday, June 25, 2013

### 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?

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?

Labels:
area,
blocks,
duck,
fish,
garden,
geometry,
grids,
lily pad,
measurement,
non-standard units,
perimeter,
pond

## Monday, June 24, 2013

### Calculator Games for all! - Order of Operations

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.

Level 1 - https://app.box.com/s/abk4nk4meixwx9y8jj9x

Level 2 - https://app.box.com/s/nobhj24pbwxfroc0ennk

Level 3 - https://app.box.com/s/b6wsvvjr1yhv14qbfoo9

Level 4 - https://app.box.com/s/3budui8du8xpaycjmkdf

Level 5 - https://app.box.com/s/7gqe1q7pmlsdmr3blsga

### Cake or Book? - Fractions

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.

Pie Chart Fractions - https://app.box.com/s/80jpejfc4eg8x0cktzm4

Book Fractions - https://app.box.com/s/fhk7ee0mkbodxoexjakf

Cake Fractions - https://app.box.com/s/48k8sab9eiwmoi1wcaue

Labels:
addition of fractions,
equivalent fractions,
Fractions,
Fractions as part of a whole,
number line

### When snakes go to war - Cartesian grids

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.

Happy hunting to all!

Board 1 - horizontal snakes https://app.box.com/s/7vx0ck7o5586gchhhuir

Board 2 - vertical snakes https://app.box.com/s/3fmmc8cihbs1kruc2vwf

Board 3 - horizontal and vertical snakes, single quadrant https://app.box.com/s/179xrd2xhqxvnj3k14c0

Board 4 - horizontal and vertical snakes, four quadrants https://app.box.com/s/0ie1yqlw03231g10fydq

Board 5 - sloping snakes https://app.box.com/s/lruxzzke80dp5kovsmdl

Board 6 - elaborate snakes https://app.box.com/s/58ehorowf10agkitwo0j

Labels:
battlesnake,
cartesian plane,
graphing,
integers,
line segments

## Thursday, May 9, 2013

### Students and Teachers Creating Learning Objects with Explain Everything

###
**Students and Teachers Creating Learning Objects with**

###
**Explain Everything**

Dr. Tim Pelton

Associate Professor

Department of Curriculum and Instruction

University of Victoria

ISTE – SIGML

Webinar

March 14, 7:00 pm EST

...and again on May 21 - recording here:

http://iste.adobeconnect.com/p7kmxaogyti/

...and again on May 21 - recording here:

http://iste.adobeconnect.com/p7kmxaogyti/

__Introduction__
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__

__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__

__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..

Download the project file: https://www.dropbox.com/s/phc3cdwz17jznev/Canadian_change_table.xpl

Video using the EE coins project

E.g., 2

Fraction Strips:

Students can use images of various fraction strips to explore such concepts as equivalent fractions and comparative size of fractions.

Download project file:

Video using the EE fraction strips project:

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

###
**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**

__Mastering the Tools:__

*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

**Sketch a triangle***Paper 53:*- 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
– with white background*Photos*

Using

*Trim off the background so that it can be manipulated***Background Eraser:**- Load image
- Crop
- Erase background
- Export as PNG file
- Now in
– with transparent background (shows as black)*Photos*

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
- Export project as video
- Save it into
*Photos*

Add finishing touches in

*iMovie*- Add audio track overlay (music – quiet)
- Export to YouTube account

Questions?

## Monday, May 6, 2013

### Please join us...

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

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

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