Lesson 4

The purpose of this How Many Do You See is to allow students to use subitizing or grouping strategies to describe the images they see. 

• 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.

• “What equations could we write to represent the last image?” (\(10 + 7 = 17\), \(8 + 2 + 7 = 17\), \(10 + 5 + 2 = 17\))

The purpose of this activity is for students to make sense of and solve Add To and Take From, Change Unknown story problems in a way that makes sense to them. Students represent the method they used and different methods are discussed during the synthesis. When students connect the quantities and action in each story problem to an equation and then solve the problem, they reason abstractly and quantitatively (MP2).

The teacher may want to incorporate movement into this activity by writing each problem on a piece of chart paper and placing each one in a different location around the classroom. Students can solve the problem at one location, discuss the problem with their partner, then move on to a new problem at a new location.

• Groups of 2
• Give each group access to connecting cubes in towers of 10 and singles. 
• “Have you ever been to an aquarium? What do you see when you visit an aquarium?” (fish, sharks, dolphins, stingrays, birds, snakes) 
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.

• “We are going to solve some story problems about what Clare saw on her field trip to the aquarium.”
• 8 minutes: independent work time
• 4 minutes: partner discussion
• Monitor for students who represent and solve the problem about the penguins in different ways, such as:
  • Represent the problem as ​\(17 -  \boxed{\phantom{3}} = 5\)
  • Represent the problem as ​\(5 +  \boxed{\phantom{3}} = 17\)
  • Count back from 17 to 5
  • Add or count on from 5 to 17
  • Subtract \(17 - 5\)

• Invite previously identified students to share.
• “How does \(17 - 5\) help us find the number of penguins that went back into the water?” (If you start with all the penguins and take away the 5 that are still sitting on the rock, you will find out how many went back into the water.)

The purpose of this activity is for students to consider different ways to solve for the unknown in a Take From, Change Unknown problem. Students are presented with an equation that represents the order of the actions in the story. However, students often find that this equation is less intuitive to find the unknown value than an addition equation with an unknown addend. Students may also share the ways they use known sums and differences and how they think of making a 10 to find the unknown number.

In this activity, students show their understanding of the relationship between the quantities in the problem and their understanding of the relationship between addition and subtraction to share ways to solve the problem (MP2, MP7).

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

• Read the task statement.
• 5 minutes: independent work time
• 3 minutes: partner discussion
• Monitor for students who:
  • use the relationship between addition and subtraction to add.
  • make 10 when adding on from 9 (\(9 + 1 + 6 = 16\)).
  • use the relationship between the numbers of frogs to explain why they can use \(16 - 9 =7\) to find the unknown number.

• Invite previously identified students to share.
• “How do you decide if you are going to add or subtract to find the unknown number in an equation?” (I usually subtract because I know what number to subtract, but I don't know what numbers to add. I always add because I like it better. I saw there was a 9, so I just thought about adding because I know I can make a ten and add some more.)