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The Lumenary
三至五年级Algebra计划中

Expressions, unknowns and rules

Numerical expressions and the order of operations, finding unknown numbers in equations such as 3 × □ = 24, and describing input–output rules.

math.algebra.expressions-and-unknowns

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前置知识

Whole-number arithmetic

4 项必需的前置知识（一直追溯到底）

你将学会

  • Evaluate expressions using brackets and the conventional order of operations.
  • Find the unknown in equations such as 3 × □ = 24 or □ + 17 = 40, explaining the method with inverse operations.
  • Describe input–output rules in words and with expressions such as 2 × n + 1, and complete tables from a rule.

定义

  • An expression is a combination of numbers and operations, possibly with brackets, that names a number.
  • An equation states that two expressions have the same value.
  • An unknown is a number, shown by a box or a letter, whose value we are asked to find.

定理

  • Brackets group operations; without them, multiplication and division are carried out before addition and subtraction.
  • Adding a number is undone by subtracting it, and multiplying by a non-zero number is undone by dividing by it.

常见误解

  • Working strictly left to right, so that 2 + 3 × 4 is taken to be 20.
  • Thinking an equation must have 'the answer' on the right of the equals sign.
  • Believing a letter stands for an object ('a for apples') rather than for a number.

通向

Variables and algebraic expressions

可选发现