Copy the rows of equations below and write what you predict will be the next five rows in the sequence.

          $1·9+2=11$
          $12·9+3=111$
          $123·9+4=1111$ 
          $1234·9+5=11111$

1. What patterns do you see? Write your answer in complete sentences.

   Step 1 (a):

   Look at the equations in separate parts, then compare each row.

   Step 2 (a):

   In complete sentences, write about the patterns that you see from one row to the next.

   Answer (a):

   The added number increases by $1$. The first factor in the multiplication adds another digit, the next consecutive number. The answers add a digit of one as they increase.

   $12345·9+6=111111$
   $123456·9+7=1111111$
   $1234567·9+8=11111111$
   $12345678·9+9=111111111$
   $123456789·9+10=1111111111$

2. Use a calculator to discover whether your predictions were correct. If they were not correct, look at the pattern again and figure out how it is changing.