Equal Shares Widget

Equal Shares is a circle, square or rectangle that students cut into parts by joining two dots on its outline. They can also shade parts by tapping them. Berdee works out every part exactly, so it knows how many parts there are, whether they are the same size, and how much is shaded.

Use it for Grade 1 and Grade 2 sharing work: "Split the circle into fourths and shade one", "Is this cut into halves?", or a sort of cards that show equal and unequal shares. A student who cuts the square into 4 pieces and gets one big piece and three small ones sees that 4 pieces are not always fourths, and Berdee can tell them so.

Select the widget on the canvas and click the floating ⚙ Configure button to set it up. The settings read in the order you decide them: what students do, the shape, the cut, what to shade, then what students see and hear. Press Try it as a student to use it exactly as a student will.

Set it up

What students do

Each choice says what students do, and is tagged Graded or Not graded.

• Show (Not graded): a picture of a whole that is already cut, and maybe shaded. Students can't change it. Use it for questions about the picture, or put 8 or 16 of them on a scene as cards to sort. A Show card scores 0 of 0 and never holds a scene back.
• Split (Graded): students cut the whole into the number of equal parts you ask for.
• Shade (Graded): the whole is already cut. Students shade the amount you ask for, like "Shade a half of the circle."
• Split and shade (Graded): students cut first, then shade. "Split the circle into 4 equal parts. Then shade 1 part." A switch under the prompt moves between the Cut and Shade tools.
• Equal or not? (Graded): the whole is already cut. Students tap Yes or No to say whether the parts are the same size. They get one answer, right or wrong, and then the widget is finished.

The Graded modes turn Scoring on for you. Show has nothing to score, so the Scoring section says Not graded and why, instead of showing points.

The shape

• Pick a circle, a square or a rectangle.
• A rectangle also has Proportions: how many wide and how many tall, from 1 to 12 each. "3 wide, 2 tall" is a rectangle one and a half times as wide as it is tall. Berdee draws it as large as fits the widget, so making the widget bigger never changes the rectangle's shape.
• Parts (in Split and Split and shade) is 2 or 4. This version doesn't do 3, 6 or 8.

The cut

In Show, Shade and Equal or not?, you make the cut that students see. Tap one dot, then another, on the live board. Each pair of dots makes a cut. Undo takes away the last cut and Clear starts over.

Under the board, a line only you see says what you made, such as "4 parts, not equal" or "4 equal parts". It is information for you, not a warning. If you'd like a starting point, press Show me one and choose "2 equal parts" or "4 equal parts". It replaces your cut, and you can undo it. If the dots you've turned on can't make that many equal parts, the button is off and says why.

Shading

• Show: switch the board under The cut to Shade, then tap parts to shade them. Tap again to take the shading off.
• Shade and Split and shade ask under What to shade for a target. Choose a number of equal parts ("Shade 3 parts") or an amount of the whole: a half, a fourth, two fourths, three fourths or the whole. Amounts that the cut can't make aren't offered. A target of "a half" accepts any two fourths when students have cut fourths, because the amount shaded is what's checked, not which parts.

What students see and hear

• Prompt: what students read above the shape and hear from the speaker button. Leave it empty and Berdee writes one from your choices, like "Split the square into 2 equal parts." or "Shade a fourth of the circle." Type your own to change the words. Your words don't change what counts as right.
• Letter (Show): a letter from A to Z beside the figure, and the card's name for screen readers ("Card K"). Use it for sorting cards, so students can say "A and C are the same."

How it's checked

Equal means decides what counts as equal. There are two choices.

• Same size: every part covers the same amount of the whole. The parts can be different shapes.
• Same size and same shape: every part is also the same shape.

Most Grade 1 work needs Same size. The standard says equal shares don't have to be the same shape. The difference shows when you cut a rectangle corner to corner both ways. You get 4 triangles that are the same size, so they are 4 fourths. But two of the triangles are tall and thin and two are short and wide, so they are not all the same shape. With Same size, that cut is right. With Same size and same shape, it isn't.

In Equal or not?, the panel works out the right answer from your cut and tells you: "Students should tap No: the parts aren't the same size."

Scoring

The Scoring section stays where it is in the Configure dialog. Set the points there. Done, Yes and No each count as one attempt, so a perfect run is one attempt. Cutting, shading, undoing and clearing never count.

More options

• Which dots: all of them, or Choose dots. A rectangle or square has 16 dots (the corners, the middle of each side and the quarter points). A circle has 9: the points around the rim at the clock positions 12, 1:30, 3, and so on, plus the middle. Fewer dots make the task easier. If you take away the middle dots, halves become harder to make, and the dialog tells you when the dots you left can't make the parts you asked for.
• Shading look: whether the pattern over the shading is stripes or dots. The pattern is always drawn, so color is never the only cue. The shading color itself is under Style & Layout in the sidebar. If a theme's accent color is too close to the unshaded color to see, Berdee uses a default blue for the shading and says so in the dialog.
• Outline width: how thick the shape's edge is. Its color is under Style & Layout.
• Example cut (Split and Split and shade): draw a cut for Show the next cut to reveal one line at a time. It is drawn dashed and is never the student's answer. Leave it empty and Berdee picks one.
• Reveal the cut one line at a time (Show): the card starts uncut, and each Show the next cut draws the next line. This is for "fold it in half, then in half again."

If the dots would be too close together for a young child's finger, the dialog says so. Make the widget bigger.

Try it as a student

Press Try it as a student to cut, shade and tap Done on the real widget in the Configure dialog and see what Berdee accepts.

How a student uses it

1. Tap a dot, then tap another dot. A line appears between them. Or drag from one dot to another. If the finger lets go away from every dot, nothing is cut.
2. In Split and shade, use the Cut and Shade buttons to choose a tool. In Shade, tap a part to color it in. Tap it again to take the shading off.
3. Undo takes away the last cut. Clear starts over.
4. Done checks the answer. After a right answer the shape is finished: the dots go away and the buttons hide. After a wrong one the cuts stay so the student can fix them, and a short question helps: "Count your parts. You need 4." or "Are all the parts the same size? Look again."
5. In Equal or not?, the student taps Yes or No, and that is their one answer.
6. The speaker button beside the prompt says it again.

In Split and shade, changing a cut after shading clears the shading, and a line says so: "Changing a cut takes away the shading." Undo brings it back.

Example: split the circle into fourths and shade one

1. Add an Equal Shares from the toolbox and click ⚙ Configure.
2. Under What students do, choose Split and shade.
3. Under The shape, choose Circle and set Parts to 4.
4. Under What to shade, choose A number of equal parts and set it to 1. The prompt becomes "Split the circle into 4 equal parts. Then shade 1 part."
5. Press Try it as a student. Join the top dot to the bottom dot, then the left dot to the right dot. The circle is in 4 parts. Switch to Shade, tap one part and tap Done: it's right. Try an off-center cross: 4 parts, but Done says "Are all the parts the same size? Look again."
6. Click Save.

To ask for "a half" after students cut fourths, change the target to an amount. Any two of the fourths are right.

Step-by-step, with a pizza to cut and a sandwich to judge: Cut a pizza into equal shares.

Example: Equal or not?

Under What students do, choose Equal or not?. Make a cut on the board: join the top middle dot and the bottom middle dot of a square, and the square is cut into two equal parts. The panel says "Students should tap Yes." Make a second widget with a cut that leaves one side bigger than the other, and it says "Students should tap No."

A set of 4 of these, with different shapes and cuts, is a quick check for the idea that 4 pieces aren't always fourths. Keep the cuts in a mix, so that students have to look at the size of each part and not just count the parts.

Example: a card sort

Put 8 Show widgets on a scene and give each a letter tag from A to H. Make some cut equally and some not. Then ask a question with narration or a text widget: "Which cards show halves?" Students answer by tapping, dragging or writing the letters, depending on the other widgets you add. A Show card never says whether its parts are equal.

Grading and what you see

Berdee checks every answer again on the server, using the lesson as it was published. On each student's attempt page you see one line:

• Split the circle into 4 equal parts · shaded 1 of 4 parts ✓
• Split the square into 4 parts, not equal (largest 3 times the smallest) ✗
• Shaded 1 of 4 equal parts · asked for a half ✗
• Equal or not? · said yes to 4 unequal parts ✗

Berdee also notes the mistakes behind wrong answers when it can: the right number of parts but not equal, a Yes for a cut that isn't equal (counting pieces instead of comparing them), or one part shaded when a half of fourths was asked for.

Use it in logic

Equal Shares has three events:

• On Cut: when the parts change: a learner adds a cut, or undoes or clears one.
• On Shade: when a learner shades or unshades a part.
• On Done: when a learner taps Done, or taps Yes or No in Equal or not?.

It reports Parts, Parts are equal, Shaded parts and Shaded amount (a number: 0.5 for a half), alongside Is correct and Is answered. It has four methods: Start over, Clear, Show the next cut and Shade the example parts. See Widget properties and methods and Events, actions and conditions.

Add a behavior on On Shade with the condition Shaded amount is 0.5 that shows "That's a half!" Call Show the next cut from a Show me button on a Show card with Reveal the cut one line at a time on, to fold a card in half, then in half again.

Accessibility

• Keyboard: Tab reaches the shape. The arrow keys move a ringed cursor from dot to dot around the outline. On a circle, Home jumps to the middle dot. Enter or Space starts a cut and ends it at the next dot. Escape lets go of a first dot and Backspace undoes the last cut. In Shade, Tab moves from part to part and Enter or Space shades or unshades it. Tab then moves on to the tool buttons, Undo, Clear and Done.
• Screen readers hear each dot by its place ("top side, middle"; "the 3 o'clock point"; "centre") and each change ("Cut from the top side, middle to the bottom side, middle. 2 parts."). In Split and Equal or not? the descriptions never say whether parts are equal, and describe each part by where it is and what it looks like ("top-right part, a piece with one curved side"). A Show card is described by its cuts and shading with no size words, so the description doesn't answer the card's question.
• Color is never the only cue. Shaded parts always have a stripe or dot pattern, cuts are thick lines, and the dot a student picked is bigger and ringed.
• Big targets. A cut takes two taps, and never needs a steady drag. A press has to start on a dot, so brushing the screen draws nothing.
• When a device asks for reduced motion, cuts appear without animating.

What's not in this version

• Splitting into 3, 6 or 8 parts.
• More than one whole in a widget (comparing "a half of this circle" with "a half of that one").
• Cuts that don't join two of the given dots.
• Removing one cut from the middle: use Undo or Clear.

Related

• Dot paper: draw a shape dot to dot.
• Shape: a plain shape for pictures and backgrounds.
• Pattern blocks: build with the six classic blocks.
• Choose the right widget