Multiplication and Division, Part 2

1. Skip-count by sixes. 
2. Use mental strategies, such as making ten, to find unknown terms in the count-by sequence for six.
3. Determine the unknown whole number in a multiplication or division equation relating three whole numbers, one of which is six, including equations where the unknown is represented with a letter. 

Similar to Unit 2, it is recommended to give students frequent practice with skip-counting to build toward fluency with up to 1-digit by 1-digit multiplication. Here are some possible routines you can use with students: (Source for these routines: Jessica Shumway, Number Sense Routines: Building Numerical Literacy Every Day in Grades K–3, pp. 55–67, 2011)

• Choral Counting: Choral counting is simply skip-counting out loud as a whole class. It’s a good routine to use when learning new skip-counting sequences or when you notice a large number of students struggling with a particular skip-counting sequence. You could use a visual to help students with their counting, especially in the beginning, such as a hundreds chart or number line. This also helps students notice patterns in the count sequence. You can involve movement, as well, by having students count on their fingers, do jumping jacks with every count, etc. It might be difficult to catch incorrect counts from students, which could reinforce incorrect counts, so it’s recommended not to rely just on this routine. You can ask some basic questions about the count sequence, but because this routine really just helps introduce students to new sequences or ones that they struggle with, more rigorous questions can be saved for the other routines (which are in bullets below).
• Count around the Circle: Have one child start with the first number in the skip-counting sequence, and go around the circle having each child say one number. You could decide to write the numbers on the board as students say them, either as a scaffold for them or to encourage a discussion of patterns afterward. Some questions you can ask before/during/after this routine to encourage sense-making include:
  • If we count by twos around the circle starting with Student A, what number do you think Student Z will say? If you didn’t count to figure that out, how did you solve? 
  • If we count around the circle by fives and we go around twice, what will Student X say?
  • Why did you choose ____ as an estimate?
  • Why didn’t anyone choose ____ as an estimate?
  • How did you know what comes next?
  • (After a child gets stuck but figures it out:) What did you do to figure it out? 
  • (If you’ve written the numbers on the board as students counted:) What do you notice? What do you wonder?

• Problem Set