Paired Number Tables

The students are learning how to find patterns within paired number tables also known as input/output tables. The students were taught skills and strategies for solving tables at the beginning of the week. They were ready to practice applying the skill and they did so in an unconventional way. Rather than giving them a practice to complete independently at their desks, I posted cards around the room to be solved. The students had a recording sheet to keep track of their answers. The students were in charge of finding missing numbers on some of the tables. For these types of problems, the students were given the rule (basically the key to unlocking the pattern) and they had to find the missing input or output. 

The card above is missing the output, so the students would apply the rule of +3 to solve. 7+3=missing output. 

Some of the cards were also missing the input which was more challenging for the students. 

The rule is -7, so in order to find the missing input the students had to use the opposite operation. Missing input-7=10. Many students wanted to say the answer is 3, but when they checked their answer it didn't work. 3-7 does not equal 10. They had to do 10+7 to find the missing input. 

Below is an example of the missing rule. They had to decide if it was addition or subtraction and by how much. The rule will be the same all the way down the table so they had to test each row. 

The students had to remember you always work title to title, or input to output, rather than down the table. We refer to working down the table as slime on our number machine which we don't want. They did very well! Now, we will raise the bar and incorporate these into word problems and have the students solve numbers not shown on the table. They will also solve tables with multiplication and division once they are taught these operations more thoroughly. This is a skill we will practice all year.