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premium Sign in nowJoin nowIn-Out Boxes #1 (Basic) FREE In-out boxes with basic addition and subtraction; Only the out boxes need to be filled in2nd through 4th GradesIn-Out Boxes #2 (Basic) FREE More in-out boxes with basic addition and subtraction; Students must complete boxes on both sides of the table2nd through 4th GradesSign in nowJoin now The browser you are using is out of date and not officially supported. You may encounter problems while using the site, please upgrade for a better experience. An inputoutput table gives pairs of numbers that follow a certain pattern or rule. In this inputoutput table, the rule is that 2 has been added to each input. To determine the rule for a table, simply look at one pair of inputoutput numbers and figure out what number has been added, subtracted, multiplied, or divided by it. Then, make sure that pattern matches the rest of the numbers. Once you know the rule for a table, you can finish filling in the rest of it. Look at the input and apply the rule. For example, if the rule is Subtract 5 and the input is 9 then you subtract 5 from 9 to get 4, and 4 is the output. Lets take a look at some examples: Example 1 What is the rule for this table? Looking at the first pair (5 and 15), we can tell that either 10 was added to 5 or 5 was multiplied by 3. Lets see which pattern works for the rest of the table. For the second pair (4 and 12) we can see that 10 was NOT added (only 8 was added.) But, 4 times 3 is 12, So, it appears the rule is multiply by 3. Lets make sure this rule works for the rest of the table. 2 x 3 = 6 and 7 x 3 = 21, so yes, the rule is multiply by 3. If you needed to write this rule using a variable, you would say 3 times x which can be written as 3x. Remember that a number next to a variable means multiplication. Thats because x stands for the input. So the output is always 3 times the input (x). Example 2 Find the rule for the table and finish filling it in. First we must figure out the rule. Whats happened with the first pair of numbers (10 and 6)? It looks like 4 has been subtracted by 6. Lets see if this rule works for the rest of the table. 8 - 4 = 4, 11 - 4 = 7, and 4 - 4 = 0. So, yes, the rule is subtract 4. So, yes, the rule is subtract 4. What would this rule be written with a variable? It would be x - 4. (because you start with x - the input - then subtract 4.) Now we can fill in the rest of the table. The next input is 5, and the rule is to subtract 4. So what is 5 - 4? 1, of course. This goes in the output spot. Now our table looks like this: The last input is 20, and the rule is still to subtract 4. 20 - 4 = 16, so that goes in the output spot. The final answer is that the rule is subtract 4 and the filled-in table is Example 3 Complete this table. The rule is divide by 2 then add 1 (or, written as a variable: x ÷ 2 + 1) In this case, we are told the rule and have to fill in the table. Notice that the rule has two steps: divide by 2 and then add 1. Lets start with the first input (20). We have to first divide by 2 then add 1. 20 ÷ 2 = 10 and then 10 + 1 = 11. So 11 goes in the output spot. Now the table looks like this: For the next input (6), we follow the same rule (divide by 2 then add 1). 6 ÷ 2 = 3 and then 3 + 1 = 4. 4 is the output for 6. For the next input (10), 10 ÷ 2 = 5 and then 5 + 1 = 6. 6 is the next output. 10 ÷ 2 = 5 and then 5 + 1 = 6. 6 is the next output. For the last input (18), 18 ÷ 2 = 9 and then 9 + 1 = 10. 10 is the last output. 18 ÷ 2 = 9 and then 9 + 1 = 10. 10 is the last output. Example 4 Which rule was made to create this table? y = 3x + 4, y = 6x + 2, y = 2x + 5 Notice that the input is x and the output is y. To see which rule was used to create the table, we must test the pairs of inputoutputs (xys) in the different equations. Lets test the first pair: x = 1 and y = 7. Substitute this into the first equation y = 3x + 4 7 = 3(1) + 4 7 = 3 + 4 7 = 7 This works, so this could be the right equation. But were not sure yet. Lets try the second pair in this equation: x = 2 and y = 9 y = 3x + 4 9 = 3(2) + 4 9 = 6 + 4 9 = 10 Wait, this isnt right. So, this was not the rule used to create the table. Lets go back and try the first pair in the second equation: y = 6x + 2 7 = 6(1) + 2 7 = 6 + 2 7 = 8 This doesnt work, so this cannot be the right rule. This cannot be the right rule. It seems as if the table must made from the last rule, but we want to make sure. So lets try the first pair (x = 1 and y = 7) in the last equation: y = 2x + 5 y = 2x + 5 y = 2x + 5 y = 2x + 5 y = 2x + 5 7 = 2(1) + 5 7 = 2 + 5 7 = 7 This works. Lets try another pair. Lets try x = 2 and y = 9 y = 2x + 5 9 = 2(2) + 5 9 = 4 + 5 9 = 9 This works again, so it appears this is the rule. To be positive, lets check the last two pairs. Test x = 3 and y = 11 y = 2x + 5: 11 = 2(3) + 5 11 = 6 + 5 11 = 11 True! Test x = 4 and y = 13 13 = 2(4) + 5 13 = 8 + 5 13 = 13 True! The rule used to create the table was y = 2x + 5
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