# Lesson 4

Change Unknown Story Problems

## Warm-up: How Many Do You See: Numbers to 20 (10 minutes)

### Narrative

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.

### Launch

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

### Activity

• Display the image.
• 1 minute: partner discussion
• Record responses.
• Repeat for each image.

### Student Facing

How many do you see?
How do you see them?

### Activity Synthesis

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

## Activity 1: Field Trip to the Aquarium (20 minutes)

### Narrative

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.

Representation: Access for Perception. Provide appropriate reading accommodations and supports to ensure student access to word problems and other text-based content.
Supports accessibility for: Language, Visual-Spatial Processing, Attention

### Launch

• 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.

### Activity

• “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 $$17 - 5$$

### Student Facing

Solve each problem.
Show your thinking using drawings, numbers, or words.

1. Clare saw 8 sea turtles swimming together in the tank.

Some more turtles joined them.
Now there are 15 turtles in the tank.
How many turtles joined the group?

2. There were 17 penguins sitting on the rocks.
Some of the penguins went back into the water.
Now there are 5 penguins sitting on the rocks.
How many penguins went back into the water?

3. The seal trainer brought out a bucket of 20 fish to feed to the seals.
The seals ate some of the fish.
Now there are 3 fish left in the bucket.
How many fish did the seals eat?

4. In the touch pools, Tyler felt 6 stingrays.
Then he felt some sea stars.
Tyler felt 14 animals all together.
How many sea stars did Tyler feel?

### Activity Synthesis

• 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.)

## Activity 2: Find the Unknown Number (15 minutes)

### Narrative

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).

MLR8 Discussion Supports. Synthesis: Provide students with the opportunity to rehearse what they will say with a partner before they share with the whole class.

### Launch

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

### Activity

• 5 minutes: independent work time
• 3 minutes: partner discussion
• Monitor for students who:
• 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.

### Student Facing

Clare watched 16 bullfrogs at the aquarium.
Then some of them swam away.
Now Clare can only see 9 bullfrogs.
How many bullfrogs swam away?

Andre wrote $$16 - \boxed{\phantom{3}} = 9$$, but he doesn’t know how to find the unknown number.

Show Andre how you would find the unknown number.
Show your thinking using drawings, numbers, or words.

### Activity Synthesis

• 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.)

## Lesson Synthesis

### Lesson Synthesis

Display one of the story problems from the lesson.

“Today we solved story problems where we knew how many of something there was at the beginning and at the end, but we didn't know how much it changed in the middle of the story. We looked at addition and subtraction methods that can be used to make sense of and solve these problems. Explain to your partner why it works to use addition or subtraction to solve these problems.” (You can use addition to add on to one number until you get to the total. The number you added on is the unknown number. You can use subtraction to start with the total and take away the other number you know. The number you have left is the unknown number.)