**Translating, evaluating, and simplifying expressions**

**Essential Questions for students (objectives): **How can mathematics help us model real-world problems so that we can make informed decisions?

**Supplies: **You-tube video on essential question: http://www.youtube.com/watch?v=nXBL79tlBg4 (see below), Post-its, Factor Question poster, Essential Question poster, Journal Prompt Page, Follow up video if needed: http://www.youtube.com/watch?v=Iew9nppByKs

**Common Core Math Standards:** 6. EE.1-4, 7.EE.1, 7.EE.2, 7.EE.4

**Time needed:** 20 minutes

**Instructional Format: **Video, teacher–lead instruction, cooperative groups

**Prior Knowledge/ Possible Warm-up Activities: **Order of Operations, Integer Operations

**Description of lesson:**

1) Show essential question expressions video to students. (This is a you-tube video that takes approximately 3 minutes)

2) Pause the video at the slide titled, “Discussion: What factors…” Ask students to either work in groups or partners to brainstorm ideas on what possible factors could be involved in creating such a time discrepancy. Have them write their ideas on post-its and attach them to the “factors poster.” Discuss as a class.

3) Restart video and play to the finish. Did your students come up with similar ideas? Did they have additional reasonable ideas? Have them record their responses on the journal page.

4) Post the Essential Questions Poster – How can mathematics help us model real-world problems so that we can make informed decisions?

5) Ask students to start generating ideas on how they could model this problem and come up with some reasonable ways to test their models. Students can write their ideas as exit tickets that get attached to the Essential Questions poster.

6) Many students have difficulty understanding what math modeling means. As they are discussing a model –note if many students try to build or draw a physical map/model of a small city. If so, there is a follow up video explaining modeling: http://www.youtube.com/watch?v=Iew9nppByKs

7) Following this introduction lesson are multiple lessons on recognizing variables and constants, translating expressions, evaluating expressions, and simplifying expressions on my you-tube channel – making mathematicians (http://www.youtube.com/channel/UCZA3T7BgGokfW82sKqT7Kmw.)

Visit this over-arching essential question regularly to see if students can tie new information to the question. For instance, what are the variables and constants in our “15 minutes to arrive at volunteering” window? This exercise is at the bottom of the journal page.

**Cautionary notes/ misconceptions/additional connections: **This introductory lesson is a great time to mention the CCSS Mathematical Practice #4 – Mathematical Modeling. If you want to see lessons or information on the 8 Mathematical Practices click here.