In this series we are counting by . When counting by ,  is between  and . 

In this series we are counting by . When counting by ,  is between  and . 

This is an addition problem because we want to know how many total bears the carnival has altogether. We can add the numbers in any order,  

To solve this problem, we first have to find our unknowns. Our unknowns are the number of beads she will have by the end of the summer and the number of beads each of her friends will receive. We can set up equations for these unknowns by letting  represent the beads that she has at the end of the summer and  represent the number of beads each of her friends will receive. 

  because she gets  more beads by the end of the summer.

 because she is splitting up her total amount of beads between  friends. When you split something up evenly you divide.  

To solve this problem, we first have to find our unknowns. Our unknowns are the number of beads she will have by the end of the summer and the number of beads each of her friends will receive. We can set up equations for these unknowns by letting  represent the beads that she has at the end of the summer and  represent the number of beads each of her friends will receive. 

  because she gets  more beads by the end of the summer.

 because she is splitting up her total amount of beads between  friends. When you split something up evenly you divide.  

To solve this problem, we first have to find our unknowns. Our unknowns are the number of miles he runs during the week and the total miles that he runs. We can set up equations for these unknowns by letting  represent the miles that he runs during the weekdays and  represent the total miles that he runs in  week. 

  because he is running  miles  times.

 because to find the total we need to add the miles he runs during the week and on the weekend.

To solve this problem, we first have to find our unknowns. Our unknowns are the number of miles he runs during the week and the total miles that he runs. We can set up equations for these unknowns by letting  represent the miles that he runs during the weekdays and  represent the total miles that he runs in  week. 

  because he is running  miles  times.

 because to find the total we need to add the miles he runs during the week and on the weekend.

To solve this problem, we first have to find our unknowns. Our unknowns are the number strawberries and raspberries she puts in the fruit salad. We can set up equations for these unknowns by letting  represent strawberries and  represent raspberries. 

  because she has  times as many strawberries than watermelon. 

  because when we half something we always divide by 

Now we need to add the watermelon, strawberries, and raspberries together to find our total. 

To solve this problem, we first have to find our unknowns. Our unknowns are the number strawberries and raspberries she puts in the fruit salad. We can set up equations for these unknowns by letting  represent strawberries and  represent raspberries. 

  because she has  times as many strawberries than watermelon. 

  because when we half something we always divide by 

Now we need to add the watermelon, strawberries, and raspberries together to find our total. 

 is added to each X value to get the Y value. 

To find the rule, you may have to do some trial and error. The most important thing to remember is, once you think you have the rule, make sure to test the rule with all of the X values.