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Unit 2, Lesson 1

Expressing Mathematics

Extra Support Materials for Algebra 1

1.1

Warm-up

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

Notice and Wonder

Materials

None

Activity Narrative

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

This Warm-up prompts students to make sense of a problem before solving it, by familiarizing themselves with a context and the mathematics that might be involved (MP1).

Launch

Arrange students in groups of 2. Display the situation for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time and then 1 minute to discuss with their partner the things they notice and wonder.

Activity

None

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

Kiran’s uncle is in charge of the furniture. He tells Kiran that he plans to have 1 table for every 4 people and 1 chair 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.

What do you notice? What do you wonder?

Student Response

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Activity Synthesis

Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the situation. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and to respectfully ask for clarification, point out contradicting information, or voice any disagreement.

If representing the quantities with numbers and variables does not come up during the conversation, ask students to discuss this idea.

1.2

Activity

Instructional Routines

MLR2: Collect and Display

Materials

None

Activity Narrative

The goal of this activity is for students to continue to notice quantities and relationships in written situations and to connect those quantities and relationships to operations on variables. Students can use the notice and wonder strategy to help them understand the context. They can write in words how they calculate the number of mice for each snake. This might also help students see patterns in calculations and generalize them to an expression. As students use patterns to generalize expressions, they are looking for and expressing regularity in repeated reasoning (MP8).

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

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

This activity uses the Collect and Display math language routine to advance conversing and reading as students clarify, build on, or make connections to mathematical language.

1.3

Activity

Instructional Routines

Aspects of Mathematical Modeling

Materials

None

Activity Narrative

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 by asking them to determine what information is important and what quantities would be helpful (MP4) when given information about a situation in written form.

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.

Activity

None

Launch

Continue to display the information about Kiran’s party from the earlier activity. Ask students, “If I told you that Kiran’s aunt and uncle were expecting 100 people to attend the party, what else could you tell me?” (They need 25 tables. They need 100 chairs. 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, for example or . Ask students, “How did you decide it made sense to use that operation? What does the 100 represent here? What does the 1 (or ) 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 .)

Ask students, “If I told you that Kiran’s aunt and uncle were expecting 40 people, what else could you tell me?” (They need 40 chairs. They need 10 tables. 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 and the other numbers adjusted accordingly.

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 10 more than the number of guests for the plates needed, for example.)

Ask: “What if we wanted a way to compute the number of tables for any number of guests? Like, for guests? What could we write?”

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

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

As students work, direct them to focus on how they know what operation to use.

Use Collect and Display to create a shared reference that captures students’ developing mathematical language. Collect the language that students use to write expressions and equations. Display words and phrases, such as “expression,” “unknown,” “variable,” “equals,” “model,” and “constraint.”

Activity

None

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

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
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
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
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

Student Response

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Audience

Assessment Access

Lesson 1

Expressing Mathematics

Warm-up

Standards Alignment

Building On

Addressing

Building Toward

HSA-CED.A.1

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Activity Synthesis

Activity

Instructional Routines

Materials

Activity Narrative

Activity

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Building on Student Thinking

Launch

Activity

Student Response

Building on Student Thinking

Activity Synthesis

Student Response

Building on Student Thinking

Activity Synthesis

Standards Alignment

Building On

Addressing

6.EE.A.2.a

Building Toward

HSA-CED.A.1

Standards Alignment

Building On

Addressing

Building Toward

HSA-CED.A

HSA-SSE.A.1