Is this a term?

What this sequence teaches

One thing: a term is a single piece, and pieces are separated by plus and minus signs. Everything inside a piece — numbers, letters, powers, multiplying, dividing, a minus at the front — is irrelevant to the question.

The sequence assumes students have met expression (the previous resource in this family). It does not touch equations or inequalities: a candidate here is always an expression. Brackets are not used.

Walking through the examples

Example 1 — 3xy² + 2. Opens on the failure students find easiest to see: a plus, and two pieces that look nothing like each other. Deliberately not a small opener; the first piece being fat is what makes “two pieces” visible at a glance.

Example 2 — 3xy². The tail is stripped away, and that single change is the whole lesson: what made it two terms has gone. The first positive is a hard one on purpose — three letters, a power, a number at the front — so nobody leaves thinking a term looks like 3x.

Example 3 — 2. A term with nothing in it but a number. The animation routes back through Example 1 on the way: the tail bolts back on, the sequence pauses on the two-term expression, then the other piece and the plus fade and the remaining 2 moves to the middle. Students see where this 2 came from — it was one of the two pieces a moment ago.

Example 4 — −5x. A minus sign inside a positive example. It attacks “a minus means two things”, and it is needed before the last example, otherwise students take away the over-broad rule “a minus is never allowed”.

Example 5 — −5x − 2. The hardest contrast in the sequence and the one students should leave with. A minus is on screen in both this example and the one before it, and the verdict flips — so the minus itself cannot be what decided it. What decides it is whether the sign is joining two pieces. Both pieces here have already been seen as terms in their own right, which is what “two terms, not one” means.

The rule and the script

The rule, exactly as the Show rule button displays it: For the following examples: if there is no plus or minus sign joining pieces, then the whole thing is one term — whatever is inside it.

The spoken justification for each example:

• 3xy² + 2 — “This is not a term. How do I know? Because a plus sign joins two pieces — so this is two terms, not one.”
• 3xy² — “This is a term. How do I know? Because there is no plus or minus sign joining pieces — so the whole thing is one term.”
• 2 — the same words.
• −5x — “… there is no plus or minus sign joining pieces — the minus is not joining anything, there is nothing before it — so the whole thing is one term.”
• −5x − 2 — “This is not a term. How do I know? Because a minus sign joins two pieces — so this is two terms, not one.”

Whether students see any of this is your call. With some classes the words sharpen what the examples are showing; with others they get in the way and the examples should do the talking. The page never decides for you: the rule stays hidden until you press Show rule, and each justification stays hidden until someone presses Why?.

What the Why? pointer highlights. On a positive, one underline under the whole candidate — it is all one piece, and on −5x the underline visibly includes the minus. On a negative, an underline under each piece with the joining sign coloured. On the last example both minus signs are on screen and the underlines do the explaining: the first sits inside a piece, the second sits between two.

Vocabulary. The page says “letter” and “piece” throughout. Once the idea is fluent, two technical words are worth handing over: the letters are variables (or unknowns, depending on your scheme), and the number at the front of a term is its coefficient.

Running the sequence

• Each example arrives with the verdict hidden. The pause is the point: ask for a prediction before revealing.
• Replay is available on Examples 2, 3 and 5, where something moved.
• Worth asking at Example 3: “where did that 2 come from?” And at Example 5: “there are two minus signs — what is the difference between them?”

What is not covered here

Fractional terms and terms with decimal or unusual coefficients are in the testing card: there were three positive slots and four intuitions worth attacking. Terms with negative powers, division by a letter, and the boundary with equations are on the expansion card.

Deviations from the house pattern, and why

• Two non-examples, one critical feature. The two closing forms are not two features; they are the two ways one feature fails — split by a plus, split by a minus. The minus form is placed last because it is the one students get wrong.
• The middle transit through a non-example. Routing Example 2 → 3 through Example 1 uses the precursor-anchored transit pattern, but with a negative anchor. The pause is not the usual “we are back on safe ground”; it is provenance — this is the expression that piece came from. The paused frame carries no verdict marker, as during any animation.

Where this atom sits

Assumes: Is this an expression? Every candidate here is an expression, and that feature is never varied. Leads to: Is this an equation?, which picks up the relational symbols this atom holds constant — the expansion card’s last two items are the handover. Are these like terms? assumes this atom: a student cannot compare terms before they can see one.

About this card

Ten items in random order, so the same class can run it twice. There is no Show rule button here — the point is to apply the rule without it on screen. Items are static: the strip-and-bolt animation in the teaching sequence is a way of showing a change, not the meaning of the word term, so it is not needed to read an item.

Every item is decidable by the rule exactly as stated. None needs brackets, equations, or expanding.

What each item is diagnosing

Items where the answer is yes and students often say no:

• the long one with three letters, powers and a minus in front — “long means expression”
• the fraction with a single letter on top — “a fraction is a top and a bottom, so it is two things”
• the lone letter — “a term needs a number in front”
• the negative whole number on its own — “a term must have a letter”, and the minus again
• the decimal number in front of a letter — “the number in front has to be a whole number”

Items where the answer is no and students often say yes:

• the short one joined by a plus — the straightforward check
• the one joined by a minus with a number after it — “only a plus splits it”
• the one that begins with a minus and also contains a plus — two signs, one joining, one not
• the one where both pieces are built from the same letter, one squared — it reads as a single algebraic object, and this is the shape students meet constantly when collecting like terms
• the one with three pieces — checks that students count pieces rather than stopping at two

Common confusions

• “It is two terms” as a reflex. Watch for students answering no to everything with a sign in it, including the items where the sign is in front and joining nothing. The three-piece item and the begins-with-a-minus item separate reflex from reading.
• Same letter, so one term. The item with a squared piece and a plain piece of the same letter is the one most likely to be missed by a confident class. Two pieces made of the same letter are still two pieces.
• Fractions. Some students count the top and the bottom as two things. The fraction line divides; it does not join.

Discussion prompts

• “Say the rule, then use it on this item.”
• “Which sign in this item is joining two pieces, and which is not?”
• “How many pieces does this one have? Read them out.”
• “Find an item on the summary grid where the answer was yes even though there is a minus sign in it. What is the minus doing there?”

Reading the summary

Each cell carries two separate signals. The ✓ or ✗ in the corner is what the item is. The green or red tint is whether the student got it right. A green tick with a red tint is a positive item answered wrongly — usually one of the false-negative intuitions above, and the most useful cell on the grid.

About this card

Six items that sit just outside what the teaching sequence covered. Its job is transfer: how far does the understanding stretch? This is where the phrase “for the following examples” in the rule earns its keep — the rule was always scoped, and this is its edge.

Run it after the testing card, and with a class that got most of the testing card right. There is no rule toggle.

The two kinds of item

The rule still works, on an unfamiliar surface (four items). A minus inside a power; a times sign written out; a letter underneath a fraction line; a minus in front of a fraction. None of these appeared in teaching or testing, and in every case applying the rule carefully gives the right answer. What is being tested is whether an unfamiliar surface unsettles a rule the student can otherwise use.

The rule stops working (two items). An equation and an inequality. Both pass the rule — there is genuinely no plus or minus joining anything — and both are wrong. These are the diagnostic items, because the only route to the right answer is meaning: a term is a piece of an expression, and neither of these is an expression. A student who answers yes has a working rule and no concept behind it, which is exactly worth knowing before the next resource in this family.

The justifications

The four unfamiliar-surface items use the teaching template with a clause naming what is new — the minus is inside the power; a times sign does not join pieces; the fraction line divides, it does not join.

The last two extend it: “There is no plus or minus sign joining pieces, so the rule says term — but the rule only works on expressions. An equals sign makes this an equation, and an equation is not a term.”

The pointer works as it does everywhere else: each piece is underlined and any sign between pieces is coloured. On the last two items that sign is the equals or less-than sign, which is the thing the rule does not know about.

Discussion prompts

• “Say the rule, then use it on this item. Did it give the right answer?”
• “This one has a minus sign in it. Is it joining two pieces?”
• “The rule says this is a term, but it is not. What does the rule not know about?”
• “Which of these items would you show to somebody who thinks every minus sign splits an expression?”

Reading the summary

Same two channels as the testing card. A class that scores well on the first four and badly on the last two has learned the rule and not the idea — the follow-up is the next resource in this family, not more practice on this one.