Expressions & Equations Vocabulary

Activities to try

1. 1

   Build an equation from an expression (card-sort workspace)

   Why it works: The equals sign turns an inert value (expression) into a statement that can be true or false (equation) and therefore tested; an inequality is also a testable statement, and here (2a + 3 < 11) it is true across a whole range of values (a < 4) rather than at a single answer.

   1. Start with 2a + 3 sitting on its own and say aloud whether there is anything to 'test' or 'solve' — establish that it just names a value.
   2. Drag an '=' and the number 11 alongside it to form 2a + 3 = 11, and say what has now changed.
   3. Sort a set of six cards into Expression / Equation / Inequality bins (e.g. 2a + 3, 2a + 3 = 11, 2a + 3 < 11), pointing each time to the =, <, >, ≤ or ≥ as the deciding feature, or saying that no such sign is present for an expression.
   4. Substitute candidate values of a into 2a + 3 = 11 to test whether the statement is true or false; confirm it is true only at a = 4.
   5. Also do an Always / Sometimes / Never true card sort, TESTING each statement by substitution rather than trying to 'solve' it, and recognising that one counterexample rules out 'always' (and one true case rules out 'never'), but checking a few values alone cannot prove 'always' or 'never' — give a reason for those.
2. 2

   Read '=' as balance and sameness

   Why it works: The equals sign asserts that both sides have the same value; it is not an instruction to 'produce the answer on the right', so reversed and two-sided equalities are perfectly valid.

   1. Using a balance scale (physical or depicted), show that both sides of an equation name the same amount.
   2. Judge and discuss statements written in unfamiliar orders, e.g. 7 = 3 + 4 and 3 + 4 = ___ + 2, deciding whether each is legitimate and what goes in the blank.
   3. Explain to a partner why 3 + 4 = 7 and 7 = 3 + 4 are NOT different statements despite one looking 'backwards'.
3. 3

   Name terms, coefficients and factors — keeping the signs

   Why it works: Terms are the parts separated by + and − (each carrying its own sign); a coefficient is the number multiplying a letter, signs included; factors are what is multiplied together — and a letter stands for a number, not a labelled object, so unlike terms cannot be merged.

   1. On 5x − 2y + 7, box each term WITH its sign and count the boxes (three terms).
   2. State the coefficient of x (5) and of y (−2), being explicit that the minus sign belongs to the coefficient, and name 7 as the constant.
   3. Contrast 3a + 2b (two terms, cannot be combined) with 3a + 2a (like terms that can) to resist conjoining and the '5ab' error.
   4. On 2(a + 3), identify it as an expression whose factors are 2 and (a + 3), and state what would turn it into an equation.