Multiplication and Division, Part 1

1. Skip-count by twos, fives, and tens. 
2. Solve multiplication problems involving twos, fives, and tens by skip-counting, i.e.:
   • Keeping track on their papers or on their fingers of how many twos, fives, or tens have been counted,
   • Stopping the skip-counting sequence when they reach the number of twos, fives, or tens they intend to count, and
   • Knowing that the last number said in the skip-counting sequence is the solution. 

• There are three main levels of ways students can represent and solve multiplication and division problems, two of which are the focus of this unit:
  • Level 1: Making and counting all of the quantities involved in a multiplication or division, and 
  • Level 2: Skip-counting, or repeated counting on a given number.

To achieve fluency, the goal is to help students move along this progression, eventually to the point of "just knowing" products and quotients.

• Students should be proficient in counting by 2s, 5s, and 10s in Grade 2 (2.OA.3, 2.NBT.2). If they haven’t, however, you can help students develop facility with skip-counting with the following process. Instead of having students say all the numbers in the count sequence, have them hum, clap, or make some sort of noise in place of the number names that aren’t part of the count sequence, just thinking about what those numbers are instead. For example, for the skip-count sequence for twos, students would do: <clap> "two!" <clap> "four!" <clap> "six!" <clap> "eight!" etc. Then, they can remove the interspersed sounds and just say the skip-counting sequence. This provides a nice scaffold for students to use a placeholder for those numbers not in the count sequence before removing them entirely.
• Skip-counting to solve a multiplication problem can be more challenging than skip-counting to solve a division problem. As the OA Progression notes, “for $$8\times 3$$, you know the number of 3s and count by 3 until you reach 8 of them. For $$24\div 3$$, you count by 3 until you hear 24, then look at your tracking method to see how many threes you have. Because listening for 24 is easier than monitoring the tracking method for 8 threes to stop at 8, dividing can be easier than multiplying” (OA Progression, p. 25). Thus, giving students ample time to practice will be greatly beneficial, and practice can be even more targeted in Lesson 7 when students apply the commutative property to solve even more multiplication problems.
• Students will only see multiplication problems where 2, 5, and/or 10 is the second factor, i.e., the size of the group. Students will explore the commutative property in Lesson 7, allowing them to solve multiplication problems where 2, 5, and 10 are the first factor, i.e., the number of groups
• As a supplement to the Problem Set, we recommend 2 additional games you can play with students.
  • "Double Up" from Building Conceptual Understanding and Fluency Through Games by the North Carolina Department of Public Instruction to review twos facts. (You'll need to modify it so that students are focusing on their twos facts within $$10\times 2$$, and you could modify the game so that it instead focuses on fives facts or tens facts.)
  • "Charlotte Speedway Race" from Building Conceptual Understanding and Fluency Through Games by the North Carolina Department of Public Instruction to review twos and fives. (The directions can be changed to have students give a multiplication fact using 2, 5, or 10 (instead of just 2 or 5).

• Problem Set