Up and Down
Part of the Numbers & Operations section of Coddy's Pre-Algebra journey. Lesson 50 of 57.
Heights are measured from sea level, which plays the part of zero. A cliff top 30 metres above the sea is at 30; a reef 7 metres under the water is at -7. Moving up adds and moving down subtracts, whichever side of the surface you are on.
A seal rests on a rock 4 metres above the water. It dives 10 metres down, then swims 3 metres up. Use h for height: . Left to right, 4 - 10 is -6, so the next line is , and then . The seal is 3 metres below the surface.
The signs do the bookkeeping for you. You never need a separate rule for crossing the surface: the seal passes zero on its way down, and the arithmetic handles it. The sign of the result tells you which side you ended on.
Challenge
A diver is 12 metres below the surface, at -12 metres. She rises 5 metres, then dives 9 metres. Find her depth d as a signed number. Write d equal to the story's calculation, then work it down to one number.
Start the lesson to read it in the interactive player and track your progress.
All lessons in Numbers & Operations
1Order of Operations
Your First AnswerLeft to RightParentheses FirstBrackets Inside BracketsThe Fraction Bar GroupsRecap: Order of Operations4Adding Integers
Adding Two NegativesDifferent SignsZero PairsAdding Several IntegersRecap: Adding Integers5Subtracting Integers
Add the OppositeSubtracting a NegativePlus and Minus in a RowDistance Between NumbersRecap: Subtracting Integers