Students use their understanding of place value to generate expressions that have the greatest product. They take turns selecting number cards 0–9 and placing them strategically to make the greatest product of a two-digit number and a three-digit number. Students will need to think about how the different place values influence the value of the product and choose where to put their digits accordingly. There is also a large element of chance, since they do not know in advance which numbers they will select.

• Display a blank image from the gameboard.
• “If this is your gameboard and you pick an 8, where would you write the 8? Why?” (I would either put it in the hundreds place of the top number or the tens place of the bottom number because it’s a big number and those are the biggest place values.)
• Write the 8 in the hundreds place of the top number.
• “What if you next select a 1? Where would you write the 1? Why?” (I would put it in the ones place of one of the numbers because I want to put a bigger number in the tens place.)
• “What did you find challenging about the game?” (Since I didn’t know what numbers I was going to get on later picks, I sometimes wasn’t sure where to put a number because I didn’t know if I would get a bigger number on a later pick.)

The purpose of this activity is for students to make products of a two-digit number and a three-digit number, using five given digits, with a goal of getting as close as they can to a given target number. This builds on their work from the previous activity and lesson, in which they tried to make the greatest possible product. It is not important that students select the best possible products, and the Activity Synthesis focuses on the strategies that they use. Fundamental to these strategies will be understanding place value and making estimates of the products of a two-digit number and a three-digit number (MP7).

• Invite selected students to share how they changed their reasoning about where to put each digit.
• “When your target number was 50,000, what did you choose for the hundreds place?” (I chose a 9 because I thought I could use the 5 or the 6 in the tens of the other factor and get pretty close to 50,000.)
• “When your target number was 20,000, what did you choose for the hundreds place?” (I used the 6 because I thought with the 3 in the tens of the other factor, that would give me 18,000, which is pretty close.)