Number and algebra discs
Drag a disc onto the pad, or tap it to add it. Tap discs to choose them, then use the tools under the pad. A disc and its opposite (1 and −1, x and −x) make a zero pair — together they are worth 0.
How to use the discs
- Add: drag a disc from the row above the pad, or tap it to put it in the first free space.
- Choose: tap a disc; Shift-tap adds more; or drag across empty paper to box several. Drag chosen discs to move them — dragging a disc off the pad takes it away.
- Flip turns a disc over (1 ↔ −1, x ↔ −x); double-tap does the same. Zero pairs shows every zero pair — press it again to remove them.
- Group puts a box round the chosen discs (tap its caption to rename it); Negative adds the red − wedge that makes it the negative of the group — then Flip turns every disc inside over.
- Add a zero pair puts a 1 and a −1 on the pad; Combine joins number discs into one (5 and 3 make 8).
- With a keyboard: Tab to the pad. N / P step through the discs, the arrow keys move the chosen one, F flips, G groups, Z shows zero pairs, Delete takes away, Ctrl+Z undoes and Esc lets go. The discs above the pad and the tools are buttons.
Balance
Type a linear equation and it goes on the balance, one pan for each side. Do the same thing to both pans to keep it level, until the unknown is on its own — every step is written in the table below, in pictures and in algebra.
Try:
How to use the balance
- Take away: tap the discs you want on one pan (a ring shows they are chosen), then press Take away … from both pans. The same discs are crossed out on the other pan too.
- Add: tap a disc above the balance, choose how many (×), then press Add … to both pans. A disc added next to its opposite makes a zero pair.
- Simplify both sides clears the crossed-out discs and the zero pairs. Divide both sides by splits each pan into equal groups — simplify again to keep one group.
- Dragging a disc onto one pan, or off one pan, changes one side only — watch the balance tilt. Undo takes back the last step; Hint suggests the next one.
- With a keyboard: Tab to the balance and use the arrow keys to move between the discs on the pans; Space chooses one, T takes the chosen discs away from both pans, S simplifies, U undoes. To add, Tab to a disc above the balance, press Enter, type how many, then press Add … to both pans.
Your steps
Number line
Choose the numbers the line runs between. Put points on it and drag them, add jumps to see a sum step by step, or switch to an inequality.
Drag a point along the line (or Tab to it and use the arrow keys). To add a jump, type its size under the line and press Add jump — it starts where the last jump landed, else at the first point, else at 0 — or drag from just above a point to where the jump should land.
A circle ○ means x cannot be that number; a dot ● means it can. Drag the circle (or Tab to it and use the arrow keys); tap it, or press Space, to swap circle and dot.
Bar model
Each row is a bar made of boxes. Tap a box to change what it says (a letter such as x, or a number), use + and − for more or fewer boxes, and name the rows below. For a total, tap the names of the rows, type the total and press Brace the selected rows.
Multiplication frame
Type two factors. One goes down the left of the frame and the other along the top; each space in the frame is the product of the disc (or term) at the start of its row and the one at the top of its column.
Try: