The Other Side of Zero

You start from Floor +2 and press −3 in the lift. Where will you reach? Write an expression for this movement.

Evaluate these expressions (you may think of them as Starting Floor + Movement by referring to the Building of Fun). a. (+1) + (+4) = _____ b. (+4) + (+1) = _____ c. (+4) + (−3) = _____ d. (−1) + (+2) = _____ e. (−1) + (+1) = _____ f. 0 + (+2) = _____ g. 0 + (−2) = _____

Starting from different floors, find the movements required to reach Floor −5. For example, if I start at Floor +2, I must press −7 to reach Floor −5. The expression is (+2) + (−7) = −5. Find more such starting positions and the movements needed to reach Floor −5 and write the expressions.

Evaluate these expressions by thinking of them as the resulting movement of combining button presses: a. (+1) + (+4) = _____ b. (+4) + (+1) = _____ c. (+4) + (−3) + (−2) = _____ d. (−1) + (+2) + (−3) = _____

Compare the following numbers using the Building of Fun and fill in the boxes with < or >. a. −2 _____ +5 b. −5 _____ +4 c. −5 _____ −3 d. +6 _____ −6 e. 0 _____ −4 f. 0 _____ +4

Imagine the Building of Fun with more floors. Compare the numbers and fill in the boxes with < or >: a. −10 _____ −12 b. +17 _____ −10 c. 0 _____ −20 d. +9 _____ −9 e. −25 _____ −7 f. +15 _____ −17

Complete these expressions. You may think of them as finding the movement needed to reach the Target Floor from the Starting Floor. a. (+1) − (+4) = _____ b. (0) − (+2) = _____ c. (+4) − (+1) = _____ d. (0) − (−2) = _____ e. (+4) − (−3) = _____ f. (−4) − (−3) = _____ g. (−1) − (+2) = _____ h. (−2) − (−2) = _____ i. (−1) − (+1) = _____ j. (+3) − (−3) = _____

Complete these expressions. a. (+40) + ____ = +200 b. (+40) + ____ = −200 c. (−50) + ____ = +200 d. (−50) + ____ = −200 e. (−200) − (−40) = ____ f. (+200) − (+40) = ____ g. (−200) − (+40) = ____

Is 2 > −3? Why? Is −2 < 3? Why?

What are (i) −5 + 0 (ii) 7 + (−7) (iii) −10 + 20 (iv) 10 − 20 (v) 7 − (−7) (vi) −8 − (−10)?

Use unmarked number lines to evaluate these expressions: a. −125 + (−30) = _____ b. +105 − (−55) = _____ c. +80 − (−150) = _____ d. −99 − (−200) = _____

Complete the additions using tokens. a. (+6) + (+4) b. (−3) + (−2) c. (+5) + (−7) d. (−2) + (+6)

Evaluate the following differences using tokens. Check that you get the same result as with other methods you now know: a. (+10) − (+7) b. (−8) − (−4) c. (−9) − (−4) d. (+9) − (+12) e. (−5) − (−7) f. (−2) − (−6)

Complete the subtractions: a. (−5) − (−7) b. (+10) − (+13) c. (−7) − (−9) d. (+3) − (+8) e. (−2) − (−7) f. (+3) − (+15)

Try to subtract: −3 − (+5). How many zero pairs will you have to put in? What is the result?

Evaluate the following using tokens. a. (−3) − (+10) b. (+8) − (−7) c. (−5) − (+9) d. (−9) − (+10) e. (+6) − (−4) f. (−2) − (+7)

Suppose you start with 0 rupees in your bank account, and then you have credits of ₹30, ₹40, and ₹50, and debits of ₹40, ₹50, and ₹60. What is your bank account balance now?

Suppose you start with 0 rupees in your bank account, and then you have debits of ₹1, 2, 4, 8, 16, 32, 64, and 128, and then a single credit of ₹256. What is your bank account balance now?

Why is it generally better to try and maintain a positive balance in your bank account? What are circumstances under which it may be worthwhile to temporarily have a negative balance?

What is the highest point above sea level on Earth? What is its height?