Marie Curie Math & Science Center
Marjan Perry, Liberty, 7B

Grade 4, "Am I A Square?" Measurement Animal Adaptation, Introduction to Ratio.

Commencement content standard

  • Standard 3: Mathematics- Students will understand mathematics and become mathematically confident by communicating and reasoning mathematical, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
  • Standard 4: Science- Students will understand and apply scientific concepts, principles, and theories pertaining to the physical setting and living environment and recognize the historical development of ideas in science.
  • Standard 5: Technology- Students will apply technological knowledge and skills to design, construct use, and evaluate products and systems to satisfy human and environmental needs.
  • Standard 6- Interconnect Common Themes- Students will understand the relationships and common themes that connect mathematics, science, and technology and apply the themes to these and other areas of learning.
  • Standard 7: Interdisciplinary Problem Solving- Students will apply the knowledge and thinking skills of mathematics, science and technology to address real life problems and make informed decisions.

Benchmark standards
Content standards

  • Standard 3- Mathematics

Mathematical Reasoning-Students will use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.

Number and Numeration- Students will use number sense and numeration to develop and understanding of multiple uses of numbers in the real world, use of numbers to communicate mathematically, and use of numbers in the development of mathematical ideas.

Measurement-Students will use measurement in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data.

  • Standard 4- Science

The Living Environment
Number 1-Students will understand that living things are both similar to and different from each other and nonliving things.

Number 2- Students will understand that organisms inherit genetic information in a variety of ways that result in the continuity of structure and function between parents and offspring.

Number 3- Students will understand that individual organisms and species change over time.

  • Standard 5- Technology

Engineering Design- Engineering design is an iterative process involving modeling and optimization used to develop technological solutions to problems within given constraints.

Tools, Resources & Technological Processes- Technological tools, materials, and other resources should be selected on the basis of safety, cost, availability, appropriateness, and environmental impact; technological processes change energy, information, and material resources into more useful forms.

Standard 6- Interconnectedness: common themes

Magnitude and Scale-The grouping of magnitudes of size, time, frequency, and pressures or other units of measurement into a series of relative order provides a useful way to deal with the immense range and the changes m scale that affect the behavior and design of systems.

Patterns of Change- Identify patterns of change is necessary for making predictions about future behavior and conditions.

Standard 7- Interdisciplinary Problem solving

Strategies- Strategies and technology are used together to make informed decisions and solve problems, especially those relating to issues of science/technology/society, consumer decision making, design, and inquiry into phenomena.

Performance standards

  • Students will use models, facts, and relationships to draw conclusions about mathematics and explain their thinking
  • Students will use patterns and relationships to analyze mathematical situations.
  • Students will justify their answers and solution processes.
  • Students will use logical reasoning to reach simple conclusions.
  • Students will understand and apply ratio, proportions, and percent through a wide variety of hands-on explorations.
  • Students will understand the attributes of area, length, capacity, weight and volume, time, temperature, and angle.
  • Students will estimate and find measures such as length, perimeter, area, and volume using both nonstandard and standard units.
  • Students will collect and display data.
  • Students will use statistical methods such as graphs, tables, and charts to interpret data.
  • Students will describe the characteristics of and variation between living and nonliving things.
  • Students will recognize that traits of living things both inherited and acquired or learned.
  • Students will describe how the structures of plants and animals complement the environment of the plant or animal.
  • Students will plan and build, under supervision, a model of the solution using familiar materials, processes, and hand tools.
  • Students will use appropriate graphic and electronic tools and techniques to process information.
  • Students will provide examples of natural and manufactured things that belong to the same category yet have different sizes, weights, ages, speeds, and other measurements.
  • Students will identify the biggest and the smallest values as well as the average value of a system when given information about its characteristics and behavior.
  • Students will use instruments to measure such quantities as distance, size, and weight and look for patterns in the data.
  • Students will analyze data by tables and graphs and looking for patterns of change.
  • Students will participate in projects that require them to work efficiently, gather and process information, generate and analyze ideas, observe common themes, realize ideas, and present results.

Content standards

  • Students will measure their height in both metric and standard units.
  • Students will measure their arm span in both metric and standard measures.
  • Students will use a tape measure.
  • Students will tally the class data on a chart.
  • Students will enter the class data onto a spreadsheet.
  • Students will transfer the data to a variety of chart forms (bar graph, pictograph, etc)
  • Students will calculate the range of heights and arm spans in the class.
  • Students will calculate the average height and arm span in the class.
  • Students will present and interpret graphs.
  • Students will research animal species.
  • Students will compare and contrast the height: arm span ratio of humans to that of another species.
  • Students will explain how height and arm span make each species unique.
  • Students will describe how the body designs determines movement, eating habits, protection, and adaptation to the environment for all species.
  • Students will combine all of the information from research into a well written report.
  • Students will design a perfectly "square" student.
  • Students will plan draw, and cut out a model of a "square" student.

Performance measures

  • All measurements will be made correctly.
  • The "square" student will have its height = arm span.
  • The essay will be graded on a rubric;

4) Very well organized detail4 and descriptive.
Highly interesting.

Very well edited, no errors.

3) Well organized, detailed, and descriptive.
Very interesting.

Well edited few to no errors.

2) Fairly organized, detailed, and descriptive.
Fairly interesting.

Well edited, few errors.

1) Poorly organized. Lacks detail and descriptions.
Uninteresting. Several errors in editing.

Enabling Activities
Grouping- Pairs

Time - 2 weeks



Computer Lab


Props /Material-Tape measures, large roll of paper, scissors, markers, calculators, Programs (ClarisWorks, Encarta, Student Writing Center).

Days 1,2,3- Data Collection

Discussion- We will discuss the fact that they have just bought back to school clothing and will soon be buying Halloween costumes. I will ask them what their most common problem is that they have with new clothing. Most will say that the legs or arms are too long or short. We will list the various problems with finding a size that fits all of their dimensions.

Measurements- Working in pairs the students will predict their height in both inches and in centimeters. I will model this to give them a reasonable number range to choose from. They will use a tape measure. Each partner will check the other's measurements. they will record their answers, and write about the differences between their prediction and the actual measurement(see attachment #I).

Ratios/Comparisons-They will be asked to compare their height to their arm span to see if they are equal or if one is larger than the other. Are you a square or a rectangle? I will model the process of drawing my body on a piece of paper and drawing lines around the shape that will either create a square or a rectangle. (see attachment #1a)

Visualize- I will have them draw themselves inside of the appropriate shape (see attachment #2) depending on the measurements. This will help the students who have a hard time visualizing themselves as a shape.

Journal Writing- The students will hypothesize what life would be like if humans had legs that were only half as long as they are , or twice as long as they are. What could they do or not so? What if humans had arm span that were only half as long as they are, or were twice as long as they are?

Human Abilities- They will research and list the things that humans can do based on their height and arm span (use tools, tumble, wash things, reach, etc.). We will discuss what makes us uniquely human.

Days 4,5,6- Data Processing

 Tally- As a class we will discuss the findings of our data collection. We will tally our body types on a chart.

Height > Arm Span

Height = Arm span

Height < Arm Span


Spreadsheet- We will go to the computer lab and enter the data onto a ClarisWorks spreadsheet. The program will find the average height and arm span for us. We will also find them in class using calculators.

There will be columns for Name, Height (US), Height (Metric), Arm span (US), Arm span (Metric).

Range- They will determine the smallest and the biggest height and arm span. The students will record these as the class range in their science notebooks.

Graphs- The students will use ClarisWorks to translate the spreadsheet data into bar graphs and pictographs.

Interpretation- We will discuss which heights and arm spans are the most and least common. We will also discuss the wide variety of sizes we found in a class of students who are roughly the same age.

Days 7,8,9 - Research

Comparing- Each student will choose an animal to compare to humans. It must be something with arms/wings and legs (i.e. chimps, bats, penguins).

They will use Encarta and the Internet to gather information on that animal. They will fill in the compare and contrast chart (see attachment #3). They will be looking to compare the animal's height arm span, and general
abilities. They should see the relationship between body design and abilities.

Report- Each students will write an organized essay with at least 5 paragraphs;

1. The significance of the height : arm span ratio in animals.
2. What humans can do.

3. What their animal can do.

4. The similarities between the two.

5. Conclusions.

Day 10 - Designing and Sharing

Sharing- The students will share their reports and answer questions.

Designing- The students will work in groups of three to create a perfectly "square" student. The will have a tape measure, large paper, markers, scissors.etc. Each team will produce a life size paper student whose height

is equal to its arm span. These will be cut out and displayed around the room.


Name_____________________ Partner________________________

Predict your height and arm span first, then find the actual measurements with your partner. Use the tape measure which has inches and centimeters.

HEIGHT ______________inches _______________inches
  ______________cm _______________cm
Arm Span ______________inches _______________inches
  ______________cm ______________cm

How close were your predictions?

What surprised you?


Are you a square or a rectangle ?

Find out by comparing your height to your arm

If Height = Arm span =Square
If Height < or > Arm span = Rectangle

Try to figure out what this means and explain it using the space below.





St. Thomas Aquinas College, 125 Route 340, Sparkill NY 10976-1050