# Lesson 18

Equations with Unknowns

## Warm-up: Notice and Wonder: Equations with an Unknown (10 minutes)

### Narrative

The purpose of this warm-up is to introduce equations with a symbol for the unknown value. While students may notice and wonder many things about this equation, how the equation relates to the image is the important discussion point. When students notice that the unknown value represents a specific quantity within the image, they reason abstractly and quantitatively (MP2).

### Launch

• Groups of 2
• Display the image.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time

### Activity

• 1 minute: partner discussion
• Share and record responses.

### Student Facing

What do you notice?
What do you wonder?

$$4 + \boxed{\phantom{\frac{aaai}{aaai}}} = 10$$

### Activity Synthesis

• “How does the equation with the unknown value match the picture?” (There are 4 basketballs in the open bag and there are some more things in the other bag but we don't know how many. There must be 10 altogether.)

## Activity 1: Match Stories and Equations (20 minutes)

### Narrative

The purpose of this activity is for students to match story problems to equations with a symbol for the unknown (MP2). Each equation is written to match the way the numbers are presented in the story problem. Problem G has more than one equation, which prompts students to discuss the relationship between addition and subtraction (MP7). During the synthesis, students discuss how an equation with a symbol for the unknown matches a Take From, Result Unknown story problem.

Representation: Access for Perception. Provide appropriate reading accommodations and supports to ensure student access to story problems.
Supports accessibility for: Language,Memory

### Required Materials

Materials to Copy

• Story Problem Cards Grade 1

### Required Preparation

• Create a set of Story Problem Cards and Equation Cards for each group of 2.

### Launch

• Groups of 2
• Give each group a set of both cards.

### Activity

• “You have two sets of cards. One set of cards has the story problems we used in the last lesson. The other set of cards has equations with unknown values.”
• “Work with your partner to match the story problems to the equations. One story has more than one equation. Be sure you can explain how you know they match.”
• 10 minutes: partner work time

### Activity Synthesis

• “Which equation matches Card C? How do you know?” ($$9 - 6 = \boxed{\phantom{3}}$$. 9 represents how many students were sliding. 6 represents how many students leave so that is $$9 - 6$$. The box represents how many are left, which is the answer to the problem.)
• Repeat for problems F and H.
• Display equation cards 6 and 8.
• "What do you notice about these equations?" (They both have a total of 9 and one part is 4. The other part is the unknown. They both match problem G.)
• “How does each of these equations match the story problem?” (There are 9 students jumping Double Dutch and 4 students jumping on their own. I need to find the difference, so I can subtract $$9 - 4$$ to find the answer or I can say that $$9 = 4 + \boxed{\phantom{5}}$$. 9 equals 4 plus some more students.)

## Activity 2: Which Equation? (15 minutes)

### Narrative

The purpose of this activity is for students to interpret two different equations with a symbol for the unknown in relation to a story problem. Students are presented with a Put Together, Addend Unknown story problem and two equations that match it, which allows students to further explore the relationship between addition and subtraction. Students explain how each equation matches the story problem and make connections between them. When students interpret different equations in terms of a story problem, they model with mathematics (MP4).
Reading: MLR6 Three Reads. Display only the problem, without revealing the question. “We are going to read this story 3 times.” After the 1st Read: “Tell your partner what this story is about.” After the 2nd Read: “What are all the things we can count in this story?” (number of students playing bingo, number of students using blue chips, number using yellow chips, number of other students). Reveal the question. After the 3rd Read: “What are different ways we can solve this problem?”

### Launch

• Groups of 2
• “We are going to look at one more story and two equations that match. This story is about students playing the game called bingo.”

### Activity

• 5 minutes: independent work time
• 4 minutes: partner discussion
• Monitor for students who create a clear drawing and can use it to explain how each equation matches the story.

### Student Facing

9 students are playing bingo.
3 students are using blue chips to cover their boards.
The other students are using yellow chips.
How many students are using yellow chips?

Explain how each equation matches the story problem.
Show your thinking using drawings, numbers, or words.

1. Clare wrote $$3 + \boxed{\phantom{6}} = 9$$

2. Jada wrote $$9 - 3 = \boxed{\phantom{6}}$$

### Activity Synthesis

• Invite previously identified students to share.
• “How do the equations relate to each other?” (The second equation can be used to find the missing number in the first equation. The number that goes in the box is the same.)

## Lesson Synthesis

### Lesson Synthesis

“Today, we saw that for some story problems, there are addition and subtraction equations that can match the problem. Which kind of equation do you prefer to write? Why?"