L3 · Writing equations with one or two operations

Learning goal

“I can translate a sentence or a real situation into an equation with one or two operations - using coefficient form (4n) and fraction form (n/5) - with an equals sign that states the two sides have the same value.”

Equation — a statement with an equals sign saying two expressions have the same value, like n + 6 = 15.

Unknown value — the value the variable stands for in a situation; the equation is written to find it.

Operation — one of add, subtract, multiply, divide; an equation in this unit uses one or two of them on the variable's side.

Represent — to show a situation in symbols: the equation represents the story.

Worked example

Sentence: "A number plus 6 is 15." Step 1: The unknown is "a number" - call it n. Step 2: "Plus 6" attaches to the number: n + 6. Step 3: "Is" is the equals sign, and 15 is the other side: n + 6 = 15. More forms, quickly: "A number divided by 3 is 7" -> n/3 = 7 (fraction notation from L1 - the variable is divided by the number). "Nine less than a number is 20" -> n - 9 = 20 (the number loses 9; it is not 9 - n). Balance view, in words: the left pan holds the expression built from the unknown; the right pan holds the stated total. The equation claims the pans balance.

Check yourself — explain it

In "nine less than a number," why is the equation n - 9 and not 9 - n?

Paired problem — example still visible

Write the equation: "A number multiplied by 5 is 30" -> 5n = 30

Faded completion — last step is yours

"'A number minus 8 is 14' -> ___ = 14" -> n - 8

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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