Lesson 1

The purpose of this How Many Do You See is for students to subitize or use grouping strategies to describe the images they see. When students look for ways to see and describe numbers as groups of tens and ones and connect this to two-digit numbers, they look for and make use of the base-ten structure (MP7).

• Groups of 2
• “How many do you see? How do you see them?”
• Flash image.
• 30 seconds: quiet think time

• Display image.
• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.
• Repeat for each image.

• “How did we describe the second image using tens and ones? How many tens do you see? How many ones?” (Some people said they saw it as 3 tens and 5 ones.)
• “How could we describe the last image using tens and ones?” (3 tens and 9 ones)
• “How could we write equations to go with the last image?” (\(35 + 4 = 39\) or \(30 + 9 = 39\))

The purpose of this activity is for students to apply their place value understanding to add an amount of tens or ones to a two-digit number. Students also use place value reasoning to determine whether a number of tens or ones was added to a two-digit number. Throughout the activity, students explain how they add and how they determined the unknown addend with an emphasis on place value vocabulary (MP3, MP6).

• Groups of 2
• Give each group a set of number cards and a paper clip. Give students access to connecting cubes in towers of 10 and singles.
• “Remove the 0, 6, 7, 8, 9 and 10 from the number cards.”
• “We are going to play a game where you must figure out the number your partner added. Let’s play a round together. All of you are partner A and I am partner B.”
• Invite a student to spin.
• “You spun (43). I will draw a number card and decide whether to add that many ones or that many tens. I will say the sum aloud.”
• “The sum is (93). What number did I add? Talk with your partner. Be ready to explain how you know.” (You added 50. In order to get from 43 to 93 you add 5 tens. 53, 63, 73, 83, 93.)
• 1 minute: partner discussion
• Share responses.

• “Now you will play with your partner. For each round, decide whether you will add tens or ones and see if your partner can guess what you added.”
• 15 minutes: partner work time
• As students work, consider asking:
  • “How did you choose to add tens or ones?”
  • “How did you determine the number your partner added?”

• “Priya’s partner landed on 34 on the spinner. Priya picked a 5. If she wants to add 5 ones, how could she find the sum?“ (She could count on. 35, 36, 37, 38, 39. She could add 5 more ones to the 4 ones in 34. 4 + 5 = 9 so its 39.)
• “How can she find the sum if she wants to add 5 tens?“ (She could count on by tens. 44, 54, 64, 74, 84. She could add 3 tens and 5 tens and get 8 tens.)

In this activity, students add a one-digit number or a multiple of 10 and a two-digit number, without composing a ten. The order of the problems encourages students to analyze the difference between adding ones or tens (adding 5 or adding 50), which builds on the previous activity. Students rely on methods that they have learned such as counting on or using known facts to add. In the synthesis, students may say they notice that only the digit in the ones place of a two-digit number changes when they add a one-digit number to it. While this statement is true about the numbers in these problems, it will not be true when students add in future work. It may be helpful to record this conjecture on chart paper and revisit it again in future lessons to allow students an opportunity to explain whether or not it is always true. 

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.

• Read the task statement.
• 7 minutes: independent work time
• 3 minutes: partner discussion

If students fill in both equations with the same number, consider asking:

• “How did you find the number that makes each equation true?”
• “How would each expression look with connecting cubes? Would there be the same number of cubes?”

• Display the first three problems.
• “What did you notice about the equations and the sums?” (It was like adding the same number, just to a different place. When I add \(43 + 5\), I only added the numbers in the ones place. When I add \(43 + 50\), I added 5 tens and 0 ones to 43. The number in the ones place stayed the same.)