Lesson 17

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 use grouping strategies to visualize the quantities in the \(10 + n\) structure they come to see that some can be taken from one group and added to the other to make a ten and some more (MP7).

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

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

• “Who can restate the way _____ saw the dots in different words?”

The purpose of this activity is for students to find sums when one addend is nine. Students represent sums on the 10-frame to encourage them to use the structure of a ten. During the launch, the teacher demonstrates playing a round of the game. It is important to let students discover patterns as they play the game. For example, when finding the sum of \(9 + 5\), some students may represent each addend on a separate 10-frame and count to find the sum. Other students may use the associative property and move one counter from the five, and add it to the nine to make a ten.

Students may generalize that when they take one from an addend to make 10, the sum has one less one than that addend. When students build this understanding, they may no longer need to show their thinking on the 10-frame and can just write an equation. By repeatedly making the ten by taking one from an addend, students may see and use the structure of ten to add on (MP7, MP8).

• Each group of 2 needs a set of Number Cards (0-10).

• Groups of 2
• Give each group a set of number cards and access to double 10-frames and connecting cubes or two-color counters.
• “We are going to play the 9 Plus game. In this game, we add different numbers to 9 and record our thinking with equations. Let’s play the first round together.”
• Demonstrate displaying 9 counters on the double 10-frame to start the game.
• “Now we pick a number card. I add that many counters to 9 and figure out the sum.”
• Demonstrate placing each counter on the empty 10-frame.
• “What is the sum? How do you know? What equation can I write to show the total?” (The sum is 13. I counted on from 9. We could move 1 from the 4 to the 9 to make 10 and then there are 3 more. \(9 + 4 = 13\) or \(10 + 3 = 13\))
• 30 seconds: quiet think time
• Share and record responses.

• “Talk with your partner about the patterns you notice as you play the game.”
• 8 minutes: partner work time

• “What patterns did you notice as you played the game?” (I saw that any \(9 + \) expression can be written as a \(10 +\) expression. You can take one from the other addend. The nine goes up by one and the other addend goes down by one.)
• “We can write the equation \(9 + 5 = 10 + 4\) to represent that the expressions are equal.”

The purpose of this activity is for students to solve addition story problems in which one addend is close to 10. Students may use any method or representation that makes sense to them. During the synthesis, the double 10-frame is used to visually show decomposing one addend to make ten with the other (the associative property).

• Groups of 2
• Give students access to double 10-frames and connecting cubes or two-color counters.

• Read the task statement.
• 4 minutes: independent work time
• 3 minutes: partner discussion
• Monitor for students who use these methods:
  • shows 6, shows 8 more, and counts all
  • shows 8, and counts on 6
  • shows 6, adds 4 to make 10, adds 4 more
  • shows 8, adds 2 to make 10, adds 4 more

• Invite previously identified students to share in the sequence above.
• “What did _____ do to represent the problem?”
• Record each method with an equation.
  • 6 + 8 = 14
  • 8 + 6 = 14
  • 6 + 4 = 10, 10 + 4 = 14
  • 8 + 2 = 10, 10 + 4 = 14