Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will be able to:
- apply concepts of density to model situations based on both area (2-dimensional) and volume (3-dimensional)
- apply concepts of density to model situations presented in graphic, numerical, analytical, and written form
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should know how to:
- solve first degree equations as stated in MAFS.6.EE.2.7
- calculate area and volume as stated in MAFS.6.G.1.1
- use and convert among units of measure as stated in MAFS.5.MD.1.1
- understand and use the concept of a ratio as stated in MAFS.6.RP.1.1
Guiding Questions: What are the guiding questions for this lesson?
- What is density? (A ratio that compares the measure of how much of a certain item is packed into a defined area or volume)
- What do you know about calculating density? (It is the amount per unit size)
- What are the units of measure in this situation? (Answers will vary - examples include: grams per cubic centimeter, people per square mile)
- What are the known and unknown variables in this situation? (Answers will vary - but should relate to density (D), mass (m), and area or volume)
- Have you thought about it as a ratio and what do the numerator and denominator represent? (Answers will vary - the denominator probably will represent either area or volume)
- Should you multiply or divide, and why? (Answers will vary - students should be encouraged to think about inverse operations and the process of isolating a variable)
- Is this a reasonable answer, and why? (Answers will vary - students should be encouraged to use number sense and consider units of measure)
Teaching Phase: How will the teacher present the concept or skill to students?
Optional Introductory Activity - Sardines: See attached file Propensity for Density - Packed in Like Sardines for outline, photograph, and answers. Teacher may want to have a can of sardines as a prop.
Teacher asks the class:
- Have you ever heard the figure of speech "packed in like sardines"? If so, where?
- Have you ever felt "packed in like a sardine"? If so when, and why?
- Can someone tell us what this phrase (simile) means?
- Can someone give an example of its use?
- Can someone explain how this phrase relates to the concept of density?
- Note: If students are not familiar with the phrase, teacher may want to provide an explanation
Optional Introductory Activity - Classroom Density:
Teacher asks the class, "How much space is there per person in this room?" and guides students to formulate a plan to model the situation and determine a solution. Conversation should include: if floor area or room volume should be used, what units of measure are appropriate, will dimensions be measured or estimated, and how will the final answer be expressed. Teacher may wish to carry out the process at this time or use the question to pique student interest and leave investigation/execution for later. Measuring tapes and yard/meter sticks may be necessary.
Optional Introductory Activity - Patty Paper: Teacher will distribute two pieces of patty paper (a semi-transparent wax coated square piece of paper used in the food service industry) to each student and tell students to fold and crease the patty paper such that they have a piece of patty paper with a high density of folds and a piece of patty paper with a low density of folds. Dimensions of the patty paper should be determined (usually 5.5" x 5.5" or 6" x 6"), area should be calculated, and folds (creases) should be counted or approximated such that a concluding comparative statement can be written. See attached Propensity for Density - Patty Paper file for an example.
Teacher distributes Propensity for Density - Note Taking Guide and Propensity for Density - Activity 1. Students will be directed to follow along as the class collectively views the PowerPoint, and completes and discusses the situations represented both in the PowerPoint and on the worksheet. Teacher should provide explanation, solicit questions, and ensure discussion and understanding occur. Students should be required to take notes and encouraged to organize thoughts for future reference.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Teacher will distribute Propensity for Density - Activity 2. This has three pages and is organized into four parts (Part I contains traditional science-based 3-dimensional density problems with metric units to compare mass to volume; Part II has a traditional two-dimensional problem - population density - with both metric and US/Imperial units; Part III focuses on real-world three-dimensional problems with non-metric units of measure; and Part IV real-world two-dimensional problems). Teacher may choose to lead the entire class through all or parts of this activity. Alternately, students can be directed to complete this either with a partner, in triads, or via small (teacher formed) cooperative learning groups - method is at teacher's discretion.
Teacher will call on students and/or circulate around the room and provide guidance, clarification, assistance, feedback, and praise as appropriate. Teacher should have guiding questions (see Guiding Questions section for suggestions) in mind and pose them as needed. Discussion, debriefing, and consensus should occur. Misconceptions such as flawed area or volume formula choice and use, improper equation set-up, ignoring units of measure, failing to reduce ratios, or mixing-up the operations of multiplication and division should be clarified.
Teacher should emphasize the process of:
- read the problem
- decide what is know and what is unknown
- choose an appropriate geometric formula for area or volume
- substitute know information and use order of operations to simplify
- use algebra and inverse operations to solve for the unknown variable
- address units of measure
- determine reasonableness of solution
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Teacher will distribute Propensity for Density - Activity 3. This has two pages and the teacher may choose to use just the first page (stanza analysis) or just the second page (four real-world situations), or both pages (photocopied front and back) - depending upon available time, and students' needs and/or interests. Teacher should be sure to print with "landscape" orientation. Students will be directed to complete this either individually or with a partner - method is at teacher's discretion.
Teacher will circulate around the room and provide guidance, clarification, assistance, feedback, and praise as appropriate. Students should be encouraged to look at their notes and previous work. Discussion, debriefing, and consensus should occur.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Teacher will distribute Propensity for Density - Summative Assessment. Students will individually complete the four exercises and submit their justified solutions.
Teacher will have a mental or written checklist to reference as the lesson unfolds. Items of concern include:
- correctly set-up a density equation
- solve for a variable
- attend to and convert among units of measure
- apply the concept of density to situations presented in:
- pictorial/graphic form
- tabular/numerical form
- scientific/analytical form
- descriptive/written form
As the lesson is taught, the teacher should actively monitor student progress, provide guidance and remediation, and praise students for correct responses.
Feedback to Students
Students will receive feedback via internal reflection, oral discussion, written responses, and verbal praise throughout the lesson from themselves, the teacher, and classmates. The lesson is structured such that active participation in and mastery of Activity 1, establishes a strong basis for success with Activity 2, followed by Activity 3. Student understanding should be checked (individually and collectively) via informal means such as questioning, dialogue, and discussion prior to engagement in subsequent activities.