Add and subtract integers: input/output tables

Learning Objectives Define integers, positive integers, and negative integers. Accurately add and subtract integers using various strategies. Identify the 'input' and 'output' values in a mathematical table. Apply a given rule to complete an input/output table involving integer addition or subtraction. Determine the mathematical rule (addition or subtraction of an integer) that connects input and output values in a given table. Explain their reasoning for determining rules and completing tables involving integer operations. Ever wonder how meteorologists predict temperature changes, especially when it goes below zero? 🌡️ Or how a submarine's depth changes? These are all about adding and subtracting integers! In this lesson, you'll dive into the...

TermDefinitionExample IntegerA whole number (not a fraction or decimal) that can be positive, negative, or zero. Examples: -3, 0, 5.The numbers ..., -2, -1, 0, 1, 2, ... are all integers. Positive IntegerAn integer greater than zero. It can be written with a '+' sign or no sign at all.5, 12, +7 are all positive integers. Negative IntegerAn integer less than zero. It is always written with a '-' sign.-3, -10, -1 are all negative integers. InputThe starting value in an input/output table, which is fed into a rule or operation.In a table where the rule is 'add 3', if the input is 2, then 2 is the input value. OutputThe result or ending value after applying a rule or operation to the input.If the input is 2 and the rule is 'add 3', the output is 5. So,...

Adding Integers with the Same Sign $$a + b = \text{sign}(a) \times (|a| + |b|)$$ If two integers have the same sign (both positive or both negative), add their absolute values and keep the original sign. For example, $3 + 5 = 8$ and $(-3) + (-5) = -8$. Adding Integers with Different Signs $$a + b = \text{sign of larger absolute value} \times (||a| - |b||)$$ If two integers have different signs (one positive, one negative), subtract their absolute values. The sum will have the sign of the integer with the larger absolute value. For example, $5 + (-3) = 2$ and $(-5) + 3 = -2$. Subtracting Integers (Add the Opposite) $$a - b = a + (-b)$$ To subtract an integer, change the subtraction sign to an addition sign and change the sign of the second integer to its opposite. The...