# Lesson 1

Expressing Mathematics

These materials, when encountered before Algebra 1, Unit 2, Lesson 1 support success in that lesson.

## 1.1: Notice and Wonder: Party Planning (5 minutes)

### Warm-up

The purpose of this warm-up is to elicit the idea that there can be several quantities in a given situation. This will be useful when, in a later activity, students practice representing quantities and the relationships that exist between them. While students may notice and wonder many things about the situation, known and unknown quantities are the important discussion points.

### Launch

Display the situation for all to see. Give students 1 minute of quiet think time and ask them to be prepared to share at least one thing they notice and one thing they wonder. Give students another minute to discuss their observations and questions.

### Student Facing

What do you notice? What do you wonder?

“Kiran is helping his aunt and uncle plan a cookout. His family has a lot of experience planning parties."

“Kiran’s uncle is in charge of the food. He tells Kiran that he plans to use $$\frac14$$ pounds of ground beef per person and 2 ears of corn per person."

“Kiran’s aunt is getting plates and paper towels. She plans on buying one plate per person, plus 10 extra plates just in case, and she’s going to buy one roll of paper towels for every 10 people.”

### Activity Synthesis

Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the situation. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information, etc. If representing the quantities with numbers and variables do not come up during the conversation, ask students to discuss this idea.

## 1.2: Feeding Operation (20 minutes)

### Activity

The goal of this activity is for students to continue to notice quantities and relationships in written situations, and connect them to operations on variables. Students can use the notice and wonder strategy to help them connect to the context. During the synthesis, you will draw out how students connected each situation to the operation that made sense to perform, so encourage students to think about this. They can write in words how they calculate the number of mice for each snake. This might also help them see patterns in calculations and generalize it to an expression.

Monitor for students who develop incorrect expressions, especially expressions using the wrong operation, e.g., $$2x$$ for the number of mice needed. Ask students to put their information in a table, but write out each calculation like this:

number of snakes number of mice
10 10 + 2
6 6 + 2

### Launch

Continue to display the information about Kiran’s party for all to see. Ask students, “If I told you Kiran’s aunt and uncle were expecting 100 people to attend the party, what else could you tell me?” (They need 25 pounds of ground beef. They need 200 ears of corn. They need 110 paper plates. They need 10 rolls of paper towels.)

Follow up by asking what calculations they did to answer the question. Record their calculations and results, e.g., $$2 \boldcdot 100 = 200$$ or $$100 \boldcdot \frac14 = 25$$. Ask students, “How did you decide it made sense to use that operation? What does the 100 represent here? What does the 2 (or $$\frac14$$) represent here?”

Ask students, “Did anyone use different operations but get the same answer?” (I divided the number of people by 4 instead of multiplying by $$\frac{1}{4}$$.)

Ask students, “If I told you Kiran’s aunt and uncle were expecting 40 people, what else could you tell me?” (They need 80 ears of corn. They need 10 pounds of ground beef. They need 50 plates. They need 4 rolls of paper towels.)

Record students’ operations for 40 guests below what you recorded for 100 guests. The operations should look exactly the same, just with a 40 in place of the 100.

Ask students, “What is different between the calculations that involved 40 guests and the ones that involved 100? What is the same?” (Only the number of guests changes. It’s always 2 times the number of guests for ears of corn, for example.)

Ask: “What if we wanted a way to compute the pounds of ground beef for any number of guests? Like, for $$x$$ guests? What could we write?”

Record students’ operations for $$x$$ guests below what you recorded for 100 guests and 40 guests. The operations should look exactly the same, just with an $$x$$ in place of the 100 or 40.

Tell students that they are going to study another situation and write expressions based on that situation.

### Student Facing

A zookeeper is preparing to care for snakes in an exhibit. For each question, write an expression representing the supplies needed.

1. She needs one mouse for each snake, plus two extra mice. How many mice are needed if the number of the snakes is:
1. 10
2. 6
3. $$x$$
2. She needs 4.5 ounces of crickets for each snake. How many ounces of crickets are needed if the number of snakes is:
1. 10
2. 6
3. $$x$$
3. For every 2 snakes, she needs 1 bowl of water. How many bowls of water are needed if the number of snakes is:
1. 10
2. 6
3. $$x$$
4. There is one male snake, and the rest are female. She needs one vitamin pill for every female snake. How many vitamin pills does she need if the number of snakes is:
1. 10
2. 6
3. $$x$$

### Activity Synthesis

Invite students to share the expressions they came up with. For each expression, ask students:

• What does the $$+2$$ (or $$\boldcdot 4.5$$, or $$\div 2$$, or $$-1$$) represent in this expression? What does the $$x$$ represent in the expression?
• Did anyone come up with different expressions? ($$1x+2$$, $$x \boldcdot \frac12$$, $$1x-1$$) Do these expressions make sense also?

Display the expression for all to see: $$2x$$. Tell students someone in another class came up with this expression for the amount of mice needed in the first question. Ask students to turn to a partner to discuss why this expression doesn’t make sense.You may also wish to replace the incorrect example given in the activity synthesis with (anonymous) incorrect answers used by multiple students.

Here are more questions for discussion:

• How many mice are needed for the exhibit with 10 snakes?
• How does that help us see $$x + 2$$ is a better expression?
• What situation might this expression represent?

Tell students the strategy of checking a number in the story to see if it works in your expression is one that mathematicians use all the time, and one that they can practice today.

## 1.3: Important Quantities (15 minutes)

### Activity

The purpose of this activity is for students to practice identifying the different quantities involved in a situation, both known and unknown. In the associated Algebra 1 lesson, students will create expressions to represent situations. This lesson prepares students for the associated Algebra 1 lesson and allows students to reason abstractly and quantitatively when they think through a situation and describe the quantities so that they will know what to represent in their expressions (MP2).

### Launch

Allow students to complete the task statement individually.

Monitor for students who create expressions or equations to represent the situations. Students will create equations in the associated Algebra 1 lesson, so if time permits, allow students to explain their reasoning for the expressions or equations they create.

### Student Facing

To understand the situation, what is some information you would like to know? What information is already given?

1. Clare is in charge of getting snacks for a road trip with her two friends and her dog. She has \$35 to go to the store to get some supplies.
2. Andre wants to surprise his neighbor with a picnic basket of fruit and vegetables from his garden. The basket can hold up to 12 food items.
3. Tyler is packing his bags for vacation.
4. Mai's teacher orders tickets to the local carnival for herself, the entire class, and 2 more chaperones.
5. Jada wants to prepare the fabric for the bridesmaids dresses she is creating for a wedding party.