The Other Side of Zero

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

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)

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?

Solve these: 8 − 13, (−8) − (13), (−13) − (−8), (−13) + (−8) 8 + (−13), (−8) − (−13), (13) − 8, 13 − (−8)

The sum of two positive integers is always positive but a (positive integer) – (positive integer) can be positive or negative. What about a. (positive) – (negative) b. (positive) + (negative) c. (negative) + (negative) d. (negative) – (negative) e. (negative) – (positive) f. (negative) + (positive)

Give your own examples of each rule.

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.

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

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

Make a border integer square puzzle and challenge your classmates.

Is 2 > −3? Why? Is −2 < 3? Why?

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

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?

What is the lowest point with respect to sea level on land or on the ocean floor? What is its height? (This height should be negative).

Do you know that there are some places in India where temperatures can go below 0°C? Find out the places in India where temperatures sometimes go below 0°C. What is common among these places? Why does it become colder there and not in other places?

Which other grids can be filled in multiple ways? What could be the reason?

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

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) = _____

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