The purpose of this activity is for students to practice using the standard algorithm and to explain how the placement of the digits in factors impacts the value of the product when multiplying a two-digit number by a one-digit number. Students multiply different factors which use the same 3 digits and determine which combination yields the greatest product. While the problems were intentionally structured to encourage students to use an efficient strategy, such as the algorithm, students should use whatever strategy makes sense to them when solving these problems.

Students critically analyze a claim about the largest product that can be made with 3 digits and discuss their reasoning with several partners (MP3). 

• Display:

• “Why is greater than ?” (Both have the same first partial product of 350 from multiplying ones by tens. But has a greater second partial product from multiplying ones by ones:  is greater than )
• “What did you learn about placement of digits when multiplying a two-digit number by a one-digit number?”

• “Which multiplication expression will have the greatest product?”
• Poll the class.
• Record responses for all to see.
• Display or write these problems for all to see:

  

  

• “Why does switching the placement of the 5 and the 7 increase the value of the product?” (Both products have 35 hundreds, but when 7 is the second factor, the product has 7  groups of 32 instead of 5 groups.)
• Display or write these problems for all to see:

  

  

• “Why does switching the placement of the digits 2 and 3 increase the value of the product?” (Both problems have partial products  and , but the total of the other two partial products is greater in than in .)