Polynomial Playground

Teacher notes

Expressions you can pick up and move

Polynomial Playground turns every term of an expression into a tile. Students see that a term travels with its sign, watch a factor being multiplied into parentheses one term at a time, and see like terms light up in the same color before they merge.

Getting an expression on the board

Type an expression, or build it with the buttons for + − × ÷, parentheses, powers (aⁿ), fractions (a/b) and the variables x and y, then press Put it on the board. A number or term written right before parentheses multiplies them, so 3(x + 2) and −2x(x − 4) both work. If something can’t be read, the message above the card says what is missing.

For a quick example, choose how many terms (3 to 8), which variables (none, x, or x and y), whether to use powers up to 4, and whether to include parentheses, then press New expression. Random expressions reuse a few kinds of terms on purpose, so there is always something to combine.

Dragging: the sign belongs to the term

Drag any tile to a new place (or focus it and press the left and right arrow keys). In The term + its sign mode, the operation on a tile’s left moves with it, so 10 − 4 + 3 becomes −4 + 10 + 3 and the value stays 9. Switch to Only the number and the operations stay where they are: moving the 4 to the front gives 4 − 10 + 3, which is −3. The banner reports the value before and after, which makes the point without a word from you.

With numbers only, an = sign and the value sit at the end of the expression and update after every move. As soon as there is an x or a y, the expression has no single value, so the = sign goes away.

Distributing, step by step

Press Distribute, then click the parentheses. The factor lights up and an arrow points to each term inside in turn: first the multiplication is written out, like (−3)·(−5), then its result, +15. When every term has been multiplied, the parentheses fade away, then the factor does too.

• A minus sign in front, as in 5 − 3(x − 2), goes with the factor: the tool distributes −3 and says so.
• Parentheses with nothing in front, like −(x + 1), distribute −1, and +(…) just comes off.
• When the parentheses are part of a product, like 2 × 3(x + 1), the factor is distributed but the parentheses stay, and the banner explains why.

Combining like terms

Combine like terms takes one group at a time: the like terms glow, the banner writes out the sum (3x − 2x), then they merge into one tile. To let students decide, press Choose terms, click the terms, and press Combine selected. If the terms aren’t alike, the banner says why: different powers, a term that is part of a product, or a term still inside parentheses.

With Color like terms on, every set of terms that can be combined shares a color. Turn it off when you want students to find them on their own.

Pacing for the whole class

• Time between steps goes from no delay (instant) up to 10 seconds, so you can talk through each multiplication. Skip finishes the current one at once.
• Hide panel gives the whole screen to the expression when projecting.
• Undo takes back the last move, and Reset returns to the expression you started with.

Frequently asked questions