Lesson 1

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.

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.

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.

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

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.

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.

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). 

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. 

The goal is to practice thinking through a situation and identifying quantities that are involved. Allow students to share the quantities they described for each situation. Invite students to share their responses. Here are some questions for discussion:

• "How did you identify the important quantities in each situation?" (I thought about the type of problem I can solve with the information I was given. Then, I thought about what missing information I still need to solve a problem.)

• "Did anyone identify a quantity for [a particular situation] that has not been shared yet?"

• "Why is [a particular quantity] important or what types of problems can we solve with this quantity?"

If time permits, allow students to explain their reasoning for any expressions or equations they created.