Grade 6 › U09 Patterns & Functions

Grade 6 › U09 Patterns & Functions › L5
NUMBER · GRADE 6 · ALBERTAOUTCOME AB-MAT6-P1

L5 · Solving with functions: both directions and problem solving

Learning goal

“I can solve with a function in both directions: use the equation to find an output, and work backwards with inverse operations to find the input - including a two-operation equation with a starting number, undoing the steps in reverse order.”

Solve — to find the unknown value in an equation: the input when you know the output, or the output when you know the input.
Inverse operation — the operation that undoes another: division undoes multiplication, and subtraction undoes addition.
Two-operation function — a function whose equation uses two operations, like C = 3k + 4: multiply first, then add the starting number.
Check by substituting — after solving, put your answer back into the equation and make sure both sides match.
Worked example

A van travels 16 km each hour: d = 16t. Question: how long does a 96 km trip take? Step 1: You know the dependent value (d = 96) and want the independent value (t). Step 2: Forward, the equation multiplies t by 16. To undo multiplication, use the inverse operation: divide. t = 96 / 16 = 6 hours. Step 3: Check by substituting: 16 x 6 = 96. The table agrees: the row with output 96 has input 6, and the point (6, 96) sits on the graph.

Check yourself — explain it

To solve 16t = 96 we divide by 16 because...

Paired problem — example still visible

C = 7n (cost of n tickets at $7). If C = 63, find n. -> n = 63 / 7 = 9 tickets

Faded completion — last step is yours

"m = 9b and m = 45. b = 45 / 9 = ___." -> 5

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

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