Benchmark Lessons
A benchmark lesson is a lesson that is necessary either for introducing a concept to students or clarifying concept or abstract material (Wilhelm, 2014). Benchmark lessons are used as scaffolding tools, but are not in the form of a direct lecture. They are used to bring in outside knowledge that will help students take their knowledge and projects to a higher level (Wilhelm, 2014). Students should work cooperatively and view these lessons as an opportunity to ask questions and raise concerns. Teachers should view these lessons as an opportunity to clear up alternative conceptions and gauge student thinking (Wilhelm, 2014).
Benchmark Lesson 1
Overview
Students will be introduced to the idea of exothermic reactions. The students will have a simple “minilab” to do at their desks with a partner. They will have a cup of water and put a heat pack/hand warmer in the water to produce an exothermic reaction. The students will take the temperature of the water at certain points and plot a temperature vs. time graph. The students will take the mass of the hand warmer before the reaction and then have a class discussion about the meaning of their findings. The class will talk about the graphs they produced and bring in the ideas of exothermic reactions being reactions that release heat and calories. The heat capacity equation will be introduced after the activity in the form of a PowerPoint and calculations will be done based on the data the students collected.
Students will be introduced to the idea of exothermic reactions. The students will have a simple “minilab” to do at their desks with a partner. They will have a cup of water and put a heat pack/hand warmer in the water to produce an exothermic reaction. The students will take the temperature of the water at certain points and plot a temperature vs. time graph. The students will take the mass of the hand warmer before the reaction and then have a class discussion about the meaning of their findings. The class will talk about the graphs they produced and bring in the ideas of exothermic reactions being reactions that release heat and calories. The heat capacity equation will be introduced after the activity in the form of a PowerPoint and calculations will be done based on the data the students collected.
Objectives
Students will be able to:
Students will be able to:
 Understand the concept of heat exchange and how this relates to the movement of molecules.
 Understand that chemical reactions can either be endothermic and exothermic and how this relates to food and the amount of calories in different foods.
TEKS Addressed
 Chemistry 8D: use the law of conservation of mass to write and balance chemical equations
 Chemistry 11B: understand the law of conservation of energy and the processes of heat transfer
 Chemistry 11C: use thermochemical equations to calculate energy changes that occur in chemical reactions and classify reactions as exothermic or endothermic
 Chemistry 11D: perform calculations involving heat, mass, temperature change, and specific heat



Benchmark Lesson 2
Overview
Students will be introduced to a system of inequalities. The students will be given a nutritional facts label for a energy bar that already exists. The students will participate in a PEOE (predict explain observe explain) classroom demonstration where they will be analyzing the ingredients, amount of calories, total fat, sugars, and protein in the energy bar. Students will use system(s) of inequalities to see how these nutritional facts are related.
Objectives
Students will be able to:
TEKS Addressed
Students will be introduced to a system of inequalities. The students will be given a nutritional facts label for a energy bar that already exists. The students will participate in a PEOE (predict explain observe explain) classroom demonstration where they will be analyzing the ingredients, amount of calories, total fat, sugars, and protein in the energy bar. Students will use system(s) of inequalities to see how these nutritional facts are related.
Objectives
Students will be able to:
 Use algebraic methods to solve systems of equations or inequalities.
 Model with mathematics.
TEKS Addressed
 Algebra II 3A: The student is expected to analyze situations and formulate systems of equations in two or more unknowns or inequalities in two unknowns to solve problems.
 Algebra II 3B: The student is expected to use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities
 Algebra II 3C: The student is expected to interpret and determine the reasonableness of solutions to systems of equations or inequalities for given contexts.
benchmark_lesson_2.pdf  
File Size:  277 kb 
File Type: 
Benchmark Lesson 3
Overview
Students will review systems of equations/inequalities by constructing a concept map that answers the question: What are inequalities? The students will also continue to prepare for their final artifact by constructing a concept map that answers the question: How can we classify the ingredients in our energy bar?
Objectives
Students will be able to:
TEKS Addressed
Algebra II (a): (1) Foundation concepts for high school mathematics. As presented in Grades K8, the basic understandings of number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry; measurement; and probability and statistics are essential foundations for all work in high school mathematics. Students continue to build on this foundation as they expand their understanding through other mathematical experiences.
(3) Functions, equations, and their relationship. The study of functions, equations, and their relationship is central to all of mathematics. Students perceive functions and equations as means for analyzing and understanding a broad variety of relationships and as a useful tool for expressing generalizations.
Students will review systems of equations/inequalities by constructing a concept map that answers the question: What are inequalities? The students will also continue to prepare for their final artifact by constructing a concept map that answers the question: How can we classify the ingredients in our energy bar?
Objectives
Students will be able to:
 Organize the concepts of inequalities for better understanding of the topic.
 Model with mathematics.
TEKS Addressed
Algebra II (a): (1) Foundation concepts for high school mathematics. As presented in Grades K8, the basic understandings of number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry; measurement; and probability and statistics are essential foundations for all work in high school mathematics. Students continue to build on this foundation as they expand their understanding through other mathematical experiences.
(3) Functions, equations, and their relationship. The study of functions, equations, and their relationship is central to all of mathematics. Students perceive functions and equations as means for analyzing and understanding a broad variety of relationships and as a useful tool for expressing generalizations.
benchmark_lesson_3.pdf  
File Size:  148 kb 
File Type: 
Benchmark Lesson 4
Overview
Students will be introduced to surface area and volume of threedimensional figures. The teacher will have a few model threedimensional figure that unfolds so that the net surface area of these figures can be seen. This will be a PEOE (predict explain observe explain) lesson. Students will predict what the net of a threedimensional figure will look like and explain why they made this prediction. The students will also predict how to calculate the net surface area and volume of figures and threedimensional structures. The students will then investigate if there is a relationship between volume and surface area and if this relationship is useful to their final artifact. Students will leave the lesson knowing how to develop a plan to construct a threedimensional model under certain metric constraints.
Objectives
Students will be able to:
TEKS Addressed
Students will be introduced to surface area and volume of threedimensional figures. The teacher will have a few model threedimensional figure that unfolds so that the net surface area of these figures can be seen. This will be a PEOE (predict explain observe explain) lesson. Students will predict what the net of a threedimensional figure will look like and explain why they made this prediction. The students will also predict how to calculate the net surface area and volume of figures and threedimensional structures. The students will then investigate if there is a relationship between volume and surface area and if this relationship is useful to their final artifact. Students will leave the lesson knowing how to develop a plan to construct a threedimensional model under certain metric constraints.
Objectives
Students will be able to:
 Produce the net of a threedimensional figure.
 Determine a threedimensional figure when given a net.
 Develop a strategy for finding surface area in a realworld problem.
TEKS Addressed
 Geometry 6B: Use nets to represent and construct threedimensional geometric figures.
 Geometry 6C: Use orthographic and isometric views of threedimensional geometric figures to represent and construct threedimensional geometric figures and solve problems.
benchmark_4.pdf  
File Size:  1121 kb 
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Formative Assessments
Students should be given the exit slip following the third day of Investigation 1. Make sure they have enough time to complete it with their group so they are able to hand it in to the teacher at the end of class.
investigation_exitslip_1.docx  
File Size:  34 kb 
File Type:  docx 
These practice problems can be used either on the first or second day of Investigation 1. The teacher should use this resource whenever it is necessary to check in for understanding from students for exothermic/endothermic reactions and the heat capacity equation. Each student should receive his/her own wipe board and make sure to emphasize that they should show their work and explain why for each question. A quick class discussion should be had after each problem.
wipeboards.docx  
File Size:  72 kb 
File Type:  docx 
This short worksheet should be given out either near the beginning or before of Investigation 3 where the student can quickly demonstrate their knowledge of inequalities.
formative_quiz.docx  
File Size:  89 kb 
File Type:  docx 
Students should be given this exit slip following the third day of Investigation 3. This will allow students to show accountability of their work for the day.
surfaceareaexitslip.docx  
File Size:  62 kb 
File Type:  docx 
Students should be given this performance assessment at the end of the investigations. This will help the teacher in determining if students are fully prepared to create their final artifact.
performanceassessment.docx  
File Size:  235 kb 
File Type:  docx 
Summative Assessment
The rubric for the final artifact is below. The students will present their design for their energy bar and will be given this rubric on the first day during the introduction of the project. The students will evaluate the other groups based on the rubric and will participate in a class discussion after the presentations to determine what they would have changed about their project after listening to all of the presentations and getting feedback from their peers.
finalartifactrubric.docx  
File Size:  90 kb 
File Type:  docx 