The purpose of this activity is for students to represent a two-digit number in multiple ways. Students may choose to use connecting cubes as they work and then show their thinking with drawings, numbers, or words. If students use expressions to represent 94 as tens and ones (for example, 90 + 4, 80 + 14, 70 + 24), ask them to explain how each addend represents the value of tens and ones. During the Activity Synthesis, students discuss whether all of the different ways to represent 94 have been found and how they know. When students explain that when the number of tens decreases by 1, the number of ones increases by 10 because a ten is the same as 10 ones, they are using the base-ten structure of the numbers to express regularity in repeated reasoning (MP7, MP8).

• Invite previously identified students to share.
• “Do you think we found all the ways? Why or why not?”
• If needed, ask: “What do all of these have in common? What patterns do you notice?” (Every time I break apart a ten into ones, the number of ones increases by 10.)
• “Which representation of 94 would you like to work with the most? Which would you like to work with the least? Why?” (I would like to work with 9 tens and 4 ones because it is the easiest. You can easily count 9 tens and you can just see there are 4 ones. I would like to work with 94 ones the least. It is really hard to know how many you have when there are so many.)

The purpose of this activity is for students to identify two-digit numbers or a part of a number represented in different ways, with different amounts of tens and ones. Students determine how many connecting cubes are in each bag, given clues about how many tens and ones are in the bag. Students also determine how many tens or ones are in a bag, given the total number of cubes and either the number of tens or ones. Students may use connecting cubes to make sense of the problems, and show their thinking using drawings, numbers, or words. 

• “How can you act out this problem?”
• “How can you use towers of 10 connecting cubes to solve the problem?”

• Invite previously identified students to share.
• “How are these ways for finding the mystery number of tens alike? How are they different?” (They both used tens and ones. One student started with 29 ones and added the tens, the other student started with 4 tens 9 ones and broke apart tens until there were 29 ones.)