Background |
| Anchor Video |
| Concept Map |
| Project Calendar |
| Lesson Plans |
Letter to Parents |
| Assessments |
| Resources |
Modifications |
| Grant |
Abstract, Description, Rationale, Calendar, Budget, Potential Impact, Evaluation
The project "The Size of Things" is a project that aims to give students a better understanding of the world around them. By using different types of algebra, students are able to connect with the world around them. Over the course of six weeks, students will be asked to keep a journal, in which they will write down observations they make about the size of things around them. Then, over the course of the semester, students will be introduced to new ideas in mathematics they can use in trying to discover the size of things. By keeping the journal, the students will be able to see how their perspective of the world has changed, and then can use these problem-solving skills in their final project.
This project accomplishes a variety of important mathematic goals. First off, it brings math to the "real world". Students often complain that the math has no practical use. This project will hopefully help students see how math can be used in everyday life. Also, it helps develop skills that many people don't have. Many people are unaware of the size of things and cannot accurately estimate sizes. Most importantly, this project will help students understand measurements and develop problem-solving skills, abilities that are important according to the National Council of Teachers of Mathematics.
This project will be a great fit for our school, A.N. McCallum High School. McCallum is called the Fine Arts Academy, yet so often math does not mix with the arts. Much of this project is based around understanding perspective, and in art that can be very important. When making a drawing or creating a sculpture, students have to be aware of perspective. For example, many statues made by Leonardo De Vinci appear disproportionate when looked at straight on. But, when looking at the statue from bellow, which is what De Vinci intended, they appear to be perfectly proportioned. Bringing in the Art teacher will connect math with other disciplines. By linking the two disciplines, students will see how important understanding perspective is in creating art and in all areas of our lives.
Many people have a hard time truly understanding the world around them. They don't understand how tall or how large things are unless they see it for themselves, and then people have a hard time talking about it afterward. A project on "The Size of Things" is relevant to students because it would help them in three main ways: give them a better understanding of the world, integrate math with real life around them, and teach students problem solving skills.
This project addresses a variety of the standards and expectations held by the National Council of Teachers of Mathematics. Some of the standards this project meet include the ability to:
- Make decisions about units and scales that are appropriate for problem situations involving measurement.
- Analyze precision, accuracy, and approximate error in measurement situations.
- Build new mathematical knowledge through problem solving
- Solve problems that arise in mathematics and in other contexts
- Apply and adapt a variety of appropriate strategies to solve problems
- Monitor and reflect on the process of mathematical problem solving
These are a few of the standards that students will develop by participating in this project.
I recently interviewed several random people, asking them about the size of things. Some people were able to come fairly close to the answer, but several were way off. For example, one woman when asked the circumference of the earth said 250,000 miles. The actual circumference is just less than 25,000 miles. How did this college-educated woman have such a skewed perception of the earth that she gave an answer 10 times the actual size? She had no way to begin to try and understand the question or how to find an answer. Had she considered that the United States is about 3000 miles wide, she probably would have given a smaller number, unless she truly thought the world is 83 times the length of the United States. By giving students a background in these types of ideas, they will have a better understand of the world.
Also, by having students looking at things around them, it is easier to relate it to the real world. Students are able to conduct observations in their own back yard to get an idea of things. How tall is their school? How many miles do they drive to get to school? How much water does the pool hold and what does that mean? These are all things that students could look at that would relate with their own life and things around them. They don't have to go to the moon to think about size.
Finally, this project requires all different types of math skills that have to be used in all different types of problem solving activities. If they were to measure a shadow to find the height of a building they would be using geometry. If they try and compare milk jug with the amount of water coming out a fire hose they might use Algebra. It forces students to take math and apply it, instead of being told. Through the process they'll learn when it is appropriate to use different forms of math, so in the long run the math will stick with them since they will have to understand the math o understand their world.
This project is an opportunity to bring math to students and make them interested in learning about the world. As they begin to ask bigger questions, they will have to learn more complex math, and the world will come alive for them.
The Size of Things Project examines the mathematics behind estimation skills. Students will be asked to become involved in the Wonders of the World project. By incorporating research and analysis of the Wonders of the World into the math classroom, our students will be more connected to the mathematical concepts behind such constructs. It is likely that they would uncover these ideas themselves rather than be introduced to them through the traditional lecture format. This project will allow students to form their own understanding of advanced mathematical concepts such as estimation, ratio and proportion, probability, and trigonometry.
This project uses historical monuments to gain student interest and show students that math can be found everywhere. During the first of the six-week course students are exposed to different natural and man-made wonders. They would be encouraged to pick one to explore mathematically. A review of units of measure and scales through number bases will be explored. In the second week, students will learn about estimation thorough algebraic thinking and rates and proportion. During week three students will work with land surveyors' equipment and use smart draw software to explore map-making processes. Here we investigate spatial reasoning through area, volume and speed. Later students would examine probability and odds as well as sequencing that appear in patterns in real life. Students will also look into estimation through geometric and trigonometric ratios.
Once the groundwork is laid through these lessons, students are now equipped with the tools necessary to examine specific constructs of world wonders. Success of their final project relies on the mathematical knowledge accumulated via lessons and their own constructs of mathematical ideas. Throughout the weeks, students are asked to relate new knowledge they gained to the various mathematical principles present in their everyday lives. They would need to think about how best to represent their scaled 3-D model of the wonder of the world of their choice. Students record their reflections in a running journal.
The best way to evaluate the students' understanding of the presence of these mathematical ideas in their everyday life is to have the students identify them for themselves. Extending what they learn through this course to what they see around them will help develop the student's ability to draw connections, notice patterns and relate new things to what they already know.
This project would provide students the opportunity to explore math outside the traditional sense and form their own mathematical understanding by using estimation to describe and create works of art. This project takes advantage of the interest generated by World Wonders that have captivated the imagination of millions. Many students who are turned off by the traditional format of school mathematics would be inspired by this avenue for exploring important mathematical concepts.
Many students finish high school not knowing the size of things. From there some even graduate and work at their job not being able to estimate their surroundings. Through this project, students will learn skills that will provide skills that they can use for the rest of their lives.
Initially the project will consist of three teachers teaching five algebra classes which consists of about thirty students. This totals to about four hundred and fifty students. From there, this can impact their lives as they are able to predict and estimate better. Studies done by Jo Boaler in Experiencing School Mathematics show that students struggle to solve problems outside the box in a typical learning environment. This is because students want a exact answer and not an estimated answer. Estimating is a real life skill. When students in school do not want to use estimation, the students may struggle indefinitely in real life.
Teachers will aim at a goal different from most typical classrooms. They will not base the class around passing a standard test rather, they will teach students to understand and use skill that will be used in their future. Students will always be asked to think rather than to recite techniques. Students will learn knowledge that is useful outside their class. Most of all, students will excel through thinking rather than memorizing
| Monday | Tuesday | Wednesday | Thursday | Friday | |
| Week 1 | Anchor Video The Size of Things Brainstorm in groups: Where do you see math? Introduce journal writing |
Engaging investigative activity on Units of Measure and conversion tables Memory matrix |
Review memory matrix Explore application of Powers of Ten and other number bases Assign Homework |
Investigative lesson on Estimation and Reasonableness Introduce Project "Wonders of the World in My Hands" Start Journal reflection |
Short quiz over units of measure, conversion and estimation Brainstorm Project ideas Problem of the week Discuss Journal entries |
| Week 2 | Introduce Patterns, Relations, and Algebraic Thinking Check Homework Assignment |
Benchmark lesson inequality signs and the idea of positive and negative numbers, and the idea of a variable. | .Investigative lesson and activity on Age Estimates Assign Homework |
Fun and engaging activity on rates and proportion | Small assessment over rates and proportion Due Content outline of Final Project Discuss Journal entries |
| Week 3 | Investigative Lesson Proportional Reasoning in Measurement area perimeter circle and circumference Check Homework Assignment |
Explore the Spatial reasoning volume of solids inscribed polygons |
Apply indirect measurement to solve problems Revisit Pythagorean Theorem ……….. Assign Homework |
Rates of Proportional changes in maps. Investigate how changes in dimensions affect linear, area, and volume measures Journal reflection |
Small assessment over proportional scaling and maps Discuss Journal reflections ………... Problem of the week Check progress on Final Project |
| Week 4 | Sequence activity Recognizing patterns activity Check Homework Assignment |
Investigate Percent of Change …. Sequences, patterns, and probability Journal reflections on Real world sequence |
Re-evaluate driving question Discuss modeling Assign Homework |
Investigate Probability and Odds -Recreate world monuments Assign personal graph |
Small assessment over probalility and odds, Sequences Discuss Journal reflections ………... Problem of the week Check progress on Final Project |
| Week 5 | Investigating Geometry - Similar Triangles Check Homework Assignment |
Benchmark Lesson on Trigonometry Journal reflections on Real world Trigonometric application |
Lesson Trigonometric Ratios Real world personal graph due Assign Homework -Present and discuss graphs |
Lesson and activity on Estimation using trigonometry | Small assessment over geometry and Trigonomtric Ratios Discuss Journal reflections ………... Problem of the week Check progress on Final Project |
| Week 6 | Review Unit Test using Problem Recognition Task Check Homework Assignment |
Presentation of best Journal entries | Unit Test | Introduce final modeling poster …. Work in class on final project | Presentation of Final Project and Scaled model Peer Review using Minute Paper |
| Assessment |
Percentage of Total Grade |
| Homework |
15 % |
| Weekly Quizzes |
15% |
| Word Journals |
10% |
| Journal Presentation |
5% |
| Final Project |
15 % |
| Project Presentation |
10 % |
| Formative Assessment CAT |
15 % |
| Final Assessment |
15 % |
Formative Assessments
Summative Assessments
Memory Matrix: For assessing prior knowledge, recall and understanding,
Since our project deals with applications of Units of Measure, it is important that students get an overview of the relations between the different scales of measurements; metric, imperial, Richter, how to convert from one to the other and when best to choose certain scales. In planning for a quick skim over this, we had decided to set up stations featuring objects/ scaled drawings of various lengths, weights, areas, volumes and rates. Students would be asked to measure, make observations and arrive at their own conversion charts, which would be handy for other lessons further into our unit project. The graphic quality of this method of assessment makes it an efficient tool and facilitates for easy retrieval of facts. This is useful as the students can provide feedback that can be quickly scanned and easily analyzed. We can see not only whether the students have knowledge of the basic information but also how well they have organized the information and processed the inter-relationships between the key facts.
Content, Form, and Function Outlines: to evaluate students' skills in analyzing and critical thinking.
We would require students to write brief notes answering the "what, how and why" in an outline form that can be quickly assessed. In eliciting the information, I can check how well they separate and analyze information. This exercise encourages students to analyze information methodically and critically. It also promotes thinking about patterns and common structures to represent real world situations mathematically. We would implement this CAT frequently during my lessons of functions; linear, polynomial, logarithmic, and exponential growths and decay. In reading about real world phenomenon; different rates and speeds, population growths, roller coaster rides students would need to build a table of data to best interpret and organize information provided. They would also find it useful to display the data in graphical forms. We hope to impress students on how important it is to choose scale and appropriate unit of measures in functional representation of subject matter of very similar content. Being able to verbalize, discuss and negotiate the best representation of a given set of data is a useful skill to develop.
Problem Recognition Tasks: To evaluate students' skills in problem solving
Once students have attained mastery of the necessary knowledge and skills, we would put forth more challenging word problems to hone in their skills to prepare for exams. Good problem solvers recognize the types of problems they are dealing with and are able to decide on the principles and techniques need to solve them. To assess how well the students are able to distinguish between different types of functions for example, they will receive a short one page assignment adapted from the final exam. Students work in small groups to benefit for the collaborative learning process. This is especially useful where there is a wide variation in metacognitive skill levels among students. The students need to indicate or predict which kind of graphical representation would best model the set of data given. If students were found to be having problems with say, exponential functions, the calendar could be revised to spend more time on this area. I need to be aware of course that even though students may be able to recognize a problem type, they would not necessarily know how to solve it.
Word journal: To evaluate students' skills in synthesis and creative thinking.
I would require students to make two a week. The first would record at least one new concept learnt. The second would be a little more involved as students would be asked to explain how they applied e.g. rates and proportion to their everyday life. This way we get to examine how well students synthesize prior knowledge and course content. Additionally we can assess their ability to interweave the familiar with the new in unexpected and stimulating ways. We are considering giving extra credit if they show evidence of having discussed their ideas with others. This is to encourage students to make personal connections, and take responsibility for their ideas. In promoting active learning to help learners construct their own knowledge structures, students should have the chance to articulate and make explicit their implicit ideas.
The project budget is made with the assumption that an overhead projector, graphing calculators for each student, at least 4 computers with Internet access and Microsoft Office installed and access to Computer lab and art workshop is available to the class by the school districts.
| Item |
Quantity |
Unit Price |
Total Price |
| Design Workshop Classic Software |
1 |
$80.00 |
$80.00 |
| Smart Draw Software |
1 |
$141.95 |
$141.95 |
| Geometer's Sketchpad Software |
1 |
$50.00 |
$50.00 |
| Wonders of the World CD |
1 |
$32.35 |
$32.35 |
| Wonders of the World Posters |
2 |
$10.00 |
$20.00 |
| |
2 |
$15.00 |
$30.00 |
| Land Survey Equipments |
1 set |
$276.40 |
$276.40 |
| World Regional Maps |
2 |
$15.00 |
$30.00 |
| Blank overhead Transparencies |
2 box |
$14.00 |
$15.00 |
| Transparency markers |
6 sets |
$3.30 |
$19.80 |
| Tape measures |
20 |
$5.00 |
$100.00 |
| Meter sticks |
20 |
$4.00 |
$80.00 |
| Yard sticks |
20 |
$4.00 |
$80.00 |
| Protractors |
20 |
$1.75 |
$35.00 |
| 12 inch Rulers |
20 |
$0.75 |
$15.00 |
| 30 cm Rulers |
20 |
$0.75 |
$15.00 |
| Graph paper |
200 sheets |
$8.30 |
$8.30 |
| 3-D plastic geometric shapes |
3 sets of 14 shapes |
$20.00 |
$60.00 |
| Poster Board |
1 |
$6.00 |
$6.00 |
| Journals |
150 |
$0.80 |
$120.00 |
| 3 " thick Balsa wood (32 by 36" sheets) |
20 |
$1.65 |
$33.00 |
| 3/16 " thick Foam board (40 by 32 sheet) |
4 boxes |
$90.00 |
$360.00 |
| Cardboard (38 by 26 " sheet) |
7 packs |
$32.00 |
$224.00 |
| Styrofoam packing blocks |
4 sets |
$2.50 |
$10.00 |
| Wood Blocks |
3 sets |
$5.50 |
$17.50 |
| Spongy foam |
6 blocks |
$3.00 |
$18.00 |
| Scissors |
20 |
$1.25 |
$25.00 |
| Tempera paint |
18 32oz bottles |
$4.70 |
$84.60 |
| Paint Brush Sets |
6 sets |
$12.00 |
$96.00 |
| Large Sponges |
4 sets |
$2.00 |
$8.00 |
| Exacta knives |
10 |
$3.00 |
$30.00 |
| Popsicle sticks |
1 box |
$2.50 |
$2.50 |
| Toothpicks |
1 box |
$3.00 |
$3.00 |
| All purpose glue |
6 bottles |
$1.85 |
$11.10 |
| Wood glue |
15 4 oz. bottles |
$1.90 |
$28.50 |
| Glue gun |
4 |
$10.00 |
$40.00 |
| Glue gun sticks |
30 packs |
$8.50 |
$255.00 |
| Scotch tape |
20 rolls |
$1.50 |
$30.00 |
| TOTAL |
$2,491.00 |