Determine the Unit standards and the ways in which your students can demonstrate those standards to you.
Unit 3
Develop the preliminary summative assessment criteria that you will use to assess learning of the standards.
Unit 4
Develop higher order thinking and engaging questions that you can use to get students thinking about the content you want them to learn.
Unit 5
Develop a project that students can work on throughout the unit to gain experience and practice using the content you want them to learn.
Unit 6
Incorporate multimedia resources that enhance your instructional activities and provide students will other ways to learn content.
Unit 7
Incorporate the use of Web 2.0 tools or resources that extend learning by providing opportunities for learning through collaboration.
Section 1: General Informatio
Name
Tony Yiannakos
Title
Teacher
SAU
38
Grade Level
9-12
District
Hinsdale School District
Content Area
Math
School
Hinsdale High School
Content Domain
Algebra, Geometry
Backward Design Unit Planning
Unit 2: Standards and Learning Goals
Online or Hybrid Unit
Chapter 8-9 Area and Volume of 2 and 3 dimensional figures
Source of Standards
NH Curriculum Frameworks Grade 7-12 (1999)
What are the standards you want to teach with this unit?
Brainstorm ideas for how students can demonstrate this standard to you.
1 Standard 4.4a.Students will name, describe, model, classify, and compare geometric shapes and their properties with an emphasis on their wide applicability in human activity
use formulas to find surface area, perimeter, volume and area
Use Geometers sketchpad to show how formulas are derived
Write an essay about the practical uses of knowing each of the properties
Solve a problem where certain problems must be solved by using the properties of different types of figures.
2 Standard 4.4a.2 Investigate the properties of two and three dimensional shapes
Use geometers sketchpad to measure angles or sides of various shapes Write a report.
3 Standard 1.1a.5 Apply problem solving strategies to solve problems in the natural and social sciences and in pure mathematics.
Build a scale model of different shaped rooms using construction paper. Experiment in the model how furniture could be arranged in the room.
4 Standard 4.4a.3 Deduce properties of and relationships among figures from given assumptions
Provide a two column, paragraph or flowchart proof of one of the formulas
5 Standard 1.1b Students will use mathematical reasoning.
Given a multi step problem, indicate in written form a strategy that you might use to solve the problem.
Set up a mathematical model for some set of data.
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Unit 3: Assessment Criteria and Measurement
Design a draft of the assessment you will use to determine students have achieved the standards.
List your Criteria for Assessment based on the demonstrations you expect students to know or be able to do if they achieve the standard.
What are the levels of quality or understanding of content you might expect? Design the measurement scale for the rubric.
1Student needs to be able to find area, perimeter, volume and surface area, relate them to common concepts relating to purchasing and laying out a space. Student needs to demonstrate a knowledge of scale, ratio and proportion, and demonstrate that by being to make accurate drawings of spaces, or scale models of the same.
Homework Problems in each section of the unit. Completion of all problems shows involvement of student.
Homework should be 65 % accurate for 10% of unit grade
2 Student needs to show familiarity with software that is used in design and in geometric drawing
.Geometers Sketchpad Exercises. Drawing a box in Two Point perspective, Exercises on perimeter and Area.Writing assignments on each exercise to indicate what was done, and what was discovered. 20% of unit grade.
Log of sites visited from selection by teacher, and brief summary on line of each site visited. Completion of required "remedial" work, or passing grade in initial quizzes is 20% of grade for unit
3. Student needs to be able to show ability to apply skills learned to problems, and to analyze and critically evaluate existing building plans.
Project. presented with a situation, solve it. Situation solution relates to comprehending material in chapter.20% of unit grade. Skills questions should be aimed at showing skills used and in explanation of problem solving approach. 20% of grade for unit. Also, analysis of different house plans on websites to indicate how improvements could be made
4 The student needs to be able to apply the concepts of area, perimeter and volume to explain how to design a space for a specific purpose, to improve that design in light of certain criteria such as cost, fire safety, different use, etc.
Solution should have show evidence that chapter material was used, a path to solution followed, record of activity kept, and written discussion with other students and teacher. A variety of presentations is permitted - Paper, diagram, presentation, etc. 30% of unit grade.
Inset more rows if necessary.
Unit 4: Instructional Design: Discussion Questions
Design a discussion starter question, or set of questions that require students use higher order thinking skills to develop a deeper understanding of the concept. Connect this discussion question to your unit standards and assessment criteria.
On what cognitive level of Bloom’s Taxonomy would you place this discussion starter question? If the discussion starter frame consists of more than one, identify all of them.
To what assessment criteria does this discussion question connect? Tie the learning students will get through this discussion to the assessment criteria/standard you want them to achieve.
I would consider this on the level of Analyzing and Evaluating, Level 4 and 5.
This question is associated with all five standards I have indicated in Unit 2.It involves relations between congruent figures, develops math reasoning, investigates properties of two dimensional figures, has an application component, and uses mathematical reasoning
Write the Discussion Starter question or set of questions below. Include all framing language necessary.
In this chapter, we are investigating the properties of 2 and 3 dimensional figures. The concept of Perimeter and Area in two dimensional figures closely corresponds to the concepts of Surface area and Volume in Three dimensional figures. Explore the similarities and differences between the two, compare the formulas which apply to each and examine some of the parallel applications each one has. Discuss some of these ideas with your peers and make some conclusions about the differences and similarities.
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Unit 5: Instructional Design: Projects
Design a short online project or activity that would provide students with an opportunity to gain experience and practice with the content of your unit. Connect this project to your unit standards and assessment criteria.
Describe a project or activity that you could use with your students to help them meet the assessment criteria for learning the standards on which your unit is based. How does the project provide evidence of learning?
To what assessment criteria do this does this project or activity connect? Tie the learning students will get by doing this project to the assessment criteria/standard you want them to achieve.
One project would be to develop a proposal for the Fire Chief of the Town of Hinsdale, to evaluate the Industrial and Commercial Buildings in the Town as to the design difficulties within them that create difficulties for fire fighters attempting to fight fires in their buildings. What building flaws, poor layout, structural problems might be involved and how might they be remediated? The student groups ( a group project) would be in the role of a company that was trying to win a contract from the Town for such a survey. Students would have to learn about building design, open spaces, and how this relates to construction. Evidence of learning would be a logbook, a list of problems that would be searched for and a proposal to remediate them.
This project relates directly to the first three standards I have listed above. The students will learn the properties of two and three dimensional geometric shapes, learn about congruent and similar figures, and use mathematical reasoning to solve real world problems ( e.g. if a crawlspace measures x by y x z, can a fire fighter with pack get into it to fight a fire?)
Inset more rows if you have additional projects you want to include.
Unit 6: Instructional Design: Multimedia Resources
Find multimedia resources online that would provide students with an opportunity to gain a deeper understanding of the content of your unit. Connect the content of the multimedia resource to your unit standards and assessment criteria.
From Thinkfinity: Describe the multimedia resource could you use with your students to help them meet the assessment criteria for learning the standards on which your unit is based.
To what assessment criteria do this does resource connect? Tie the learning students will get by doing this project to the assessment criteria/standard you want them to achieve.
Area Contractor allows students to put themselves into the place of a contractor. this is very effective in "placing" the students, and looking at the concepts or area, volume, etc in a way that follows the project.
Purple Prisms helps students interactively see the connections between perimeter, volume area and surface.
1.Standard 4.4a.Standard 4.4a.Students will name, describe, model, classify, and compare geometric shapes and their properties with an emphasis on their wide applicability in human activity
2 Standard 4.4a.2 Investigate the properties of two and three dimensional shapes
From You Tube: Describe the multimedia resource could you use with your students to help them meet the assessment criteria for learning the standards on which your unit is based.
To what assessment criteria do this does resource connect? Tie the learning students will get by doing this project to the assessment criteria/standard you want them to achieve.
Area, Perimeter and Volume is a You Tube Video from Teachertube. Unlike most videos which consist of a lecture caught on tape, this one has an aspect that relates formulas to an actual house volume.
The second video, Surface Area and Volume, with Mrs Jenkins, covers surface area and volume in a simple way, and allows and encourages students to interact with the video by stopping and starting in in order to continue activities. this encourages student attention and feeling of participation. It asks reasoning questions
and explains how the answers are worked out.
1 Standard 1.1a.5 Apply problem solving strategies to solve problems in the natural and social sciences and in pure mathematics.
2. Standard 1.1b Students will use mathematical reasoning.
The links relate to the project which is planned for the unit, by having students apply their knowledge to a situation which models the project on a small scale. it shows strategies for dealing with more complex situations like they are facing in their project.
Inset more rows if you would like to include more resources in your project.
Unit 7: Instructional Design: Using Web 2.0 Tools
Find an online Web 2.0 tool that could use with your students to help them collaborate with each other in order to gain a deeper understanding of the content they are trying to learn. Connect the content of the multimedia resource to your unit standards and assessment criteria.
Describe the tool you would have them use for collaboration. I would like to have them connect with each other at a site like edmodo, so they could communicate and form project groups
Provide the link to the online multimedia resource www.edmodo.com
How would your students use this tool for collaboration? What would you have them do to learn the content of your unit? I am hoping (and I can't check this out because edmodo is blocked by our server), that edmodo could establish a group similar to ours, a discussion/communication group, monitored by myself to exchange ideas on the Fire Remediation Project I mentioned earlier. AS students learn more about the aspects of building design to provide maximum fire protection, they can help each other design a proposal for the fire chief. I will monitor the site to see how the discussion is progressing, to add comments that relate to the geometry involved, etc.
How would using this tool as you described connect to the assessment criteria or standards for the unit? Tie the learning students will get by using this tool in a collaborative way to the assessment criteria/standard you want them to achieve. In addition to the completed project, there are subunits along the way. Congruence
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Also there are programs on line such as floor planner ( www.floorplanner.com) which enable students to put floor plans such as they find for the buildings in their project on line and manipulate them, add furniture or obstacles, rotate and adjust dimensions. This is a great interactive tool to illustrate volume, area and the like, and would be used directly by the students. It also enables other students to interact, comment, etc as it has an enclosed blog space. it illustrates scale, dimension and is highly interactive, as well as collaborative.
Tony Yiannakos
Use Geometers sketchpad to show how formulas are derived
Write an essay about the practical uses of knowing each of the properties
Solve a problem where certain problems must be solved by using the properties of different types of figures.
Set up a mathematical model for some set of data.
Homework should be 65 % accurate for 10% of unit grade
Purple Prisms helps students interactively see the connections between perimeter, volume area and surface.
2 Standard 4.4a.2 Investigate the properties of two and three dimensional shapes
http://illuminations.nctm.org/LessonDetail.aspx?ID=L762.
http://illuminations.nctm.org/LessonDetail.aspx?ID=L262
The second video, Surface Area and Volume, with Mrs Jenkins, covers surface area and volume in a simple way, and allows and encourages students to interact with the video by stopping and starting in in order to continue activities. this encourages student attention and feeling of participation. It asks reasoning questions
and explains how the answers are worked out.
2. Standard 1.1b Students will use mathematical reasoning.
The links relate to the project which is planned for the unit, by having students apply their knowledge to a situation which models the project on a small scale. it shows strategies for dealing with more complex situations like they are facing in their project.
http://www.youtube.com/watch?v=hgj--7-afDM
I am hoping (and I can't check this out because edmodo is blocked by our server), that edmodo could establish a group similar to ours, a discussion/communication group, monitored by myself to exchange ideas on the Fire Remediation Project I mentioned earlier. AS students learn more about the aspects of building design to provide maximum fire protection, they can help each other design a proposal for the fire chief. I will monitor the site to see how the discussion is progressing, to add comments that relate to the geometry involved, etc.
In addition to the completed project, there are subunits along the way. Congruence