How Adding and Subtracting Integers Changes the Game

You can add and subtract integers by using tokens to represent positive and negative numbers, and by making jumps on a number line to show the calculation. In the token model, a positive integer is shown by a '+' token and a negative integer by a '−' token. Zero pairs are formed when a '+' and a '−' token are together, and they cancel each other out, leaving no value. On a number line, adding a positive integer means moving right, while adding a negative integer means moving left. Subtracting an integer is the same as adding its additive inverse (opposite sign). For example, to add (−3) + (+5), you start with 3 '−' tokens and 5 '+' tokens. Pairing up three zero pairs leaves two '+' tokens, so the answer is +2. On the number line, start at 0, move 3 steps left (to −3), then 5 steps right, ending at +2. For subtraction, (+4) − (−2) is the same as (+4) + (+2), which is +6. Many students forget that subtracting a negative is like adding a positive, leading to sign errors.

You can use integer addition and subtraction to solve problems involving changes in temperature, movement in lifts, or money transactions. In such problems, increases are shown by positive integers and decreases by negative integers. For example, if the temperature in Shimla was 5°C in the morning and dropped by 7°C, the new temperature is 5 + (−7) = −2°C. If a lift is on the 3rd floor and moves down 5 floors, it goes to 3 + (−5) = −2, which means 2 floors below the ground level. For money, if you have ₹500 and spend ₹700, your balance is 500 + (−700) = −₹200, showing you owe ₹200. Students often confuse which value should be positive or negative, especially in context problems, so always define what increase and decrease mean in the situation.

To complete integer grids and puzzles, you fill in the missing numbers so that the sum of each row and column matches the given totals. Start by looking for rows or columns with only one missing value, as you can find it by subtracting the sum of the known numbers from the total. For example, if a row has a total of 7 and the known numbers are 3 and −2, the missing number is 7 − (3 + (−2)) = 7 − 1 = 6. After filling in easy spots, check if the new numbers help you solve other rows or columns. Always verify your answers by adding each row and column to see if they match the totals. Sometimes, students forget to check all directions, so double-check both rows and columns before finishing.