Putting Your Best Foot Forward, Author: Leota Crary, Standards: MST 1,2,3,7, Analysis, Inquiry, and Design: Students will use Mathematical Analysis to pose questions, seek answers, and develop solutions.

LEARNING EXPERIENCE
PUTTING YOUR BEST FOOT FORWARD

By: Leota Crary
Madison Central School

A GRAPHING EXPERIENCE FOR THIRD GRADERS

1. LEARNING CONTEXT

Standard 1: analysis, Inquiry, and Design: Students will use Mathematical Analysis to pose questions, seek answers, and develop solutions.

1.1 Abstraction and symbolic representation are used to communicate mathematically.

1.2 Deductive and inductive reasoning are used to reach mathematical conclusions.

1.3 Critical thinking are used in the solution of mathematical problems.

Standard 3: Mathematics-Students will understand mathematics and become mathematically confident by communication and reasoning mathematically, by applying mathematics in real-world setting, and by problem solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

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

3.1.1 Use models, facts, and relationships to draw conclusions about mathematics and explain their thinking.

3.1.2 Use patterns and relationships to analyze mathematical situations.

3.1.3 Justify their answers and solution processes.

3.1.4 Use logical reasoning to reach simple conclusions.

3.4 Modeling/Multiple Representation-Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communication, and connecting mathematical information and relationships.

3.4.2 Construct tables, charts, and graphs to display and analyze real-world data.

3.4.4 Use variables such as height, weight, and hand size to predict changes over time.

3.5 Measurement-Students use measurement in both metrics 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.

3.5.1 Understand that measurement is approximate, never exact.

3.5.5 Collect and display data.

3.5.6 Use statistical methods such as graphs, table, and charts to interpret data.

3.6 Uncertainty

3.6.6 Make predictions using unbiased random samples.

3.7 pattern and Functions

3.7.6 Interpret graphs

Standard 7: Interdisciplinary Problem Solving

7.2 Solving interdisciplinary problems involves a variety of skills and strategies, including effective work habits; gathering and processing information; generating and analyzing ideas; realizing ideas; making connections among common themes of mathematics, science and technology; and presenting results.

Standard 2: Students will access, generate, process, and transfer information using appropriate technologies.

2.1 Information technology is used to retrieve, process, and communicate information and as a tool to enhance learning.

2.1.1 Students use a variety of equipment and software packages to enter, process, display, and communicate information in different forms.

The NYS Social Studies and Science curriculums include numerous experiences interpreting data. Science requires various measuring skills. The mathematics curriculum supports the development of the measuring skills. this learning experience connects measurement within the content areas. Various reasoning skills are used to reach simple conclusion.

Students will begin to develop an understanding of the following vocabulary words:

Range-the low to high numbers
Median-the number in the middle of the data
Mode-the number that occurs most often in the data

The use of appropriate vocabulary is essential for all students in the development of the mathematical concepts.

Students need to develop the following concepts related to the construction of a graph:

All graphs should have a title.
The graph axis should be labeled.
The graphs should have a scale and be in numerical order.
Data needs to be entered accurately on a graph.
Conclusion can be drawn from the information given on a graph.

At the end of the learning experience the students will be able to construct a rough graph from given data and determine the range, median and mode.

2. PROCEDURE

Day 1-Time-approximately one hour

Pass out rulers.
Measure small items to show closest to nearest inch concept and discuss rounding. (pencil, crayon, paper clip, etc.)
Pose the question: What do you suppose is the typical foot length in our classroom? Lead the discussion on how this problem could be answered. The discussion on how this problem could be answered. The discussion should be answered with a simple-measure all of the students' feet. The actual process on how to measure ones foot should be left open for evaluation as the students begin measuring their feet. This allows the students the opportunity to discover the need for uniform and consistent measuring guidelines. (Discovery approach)
Students measure their foot and write information on an index card. (Guidelines for measuring feet are not given at this point. Discovery approach is used.)
Students compare their foot length to a foot (12 inch) measurement. Data is Charted to Shorter than a Foot Ruler, Equal to a Foot Ruler, or Longer that a Foot Ruler. Students place their post it notes in the correct location on the chart. Discuss the results with the class. (In an average primary classroom, the students foot measures should all be shorter than a foot.)
Discuss scientists' strategy. (Scientists collect data and then sometimes scientists have to redo the data because different people measure things in different ways.) Some students may have measured with their shoe on, some with their shoe off. Some may have measured their right foot while others may have measured the left. Students need to realize that the data collection process has to be as accurate as possible.
Make decisions: as a class the decisions should be made in regards to how the students' feet will be measured. this is to ensure some accuracy. a) Shoe on/off b) Sitting/standing c) Right foot/left foot d) Toe to heel/heel to toe
Students measure their foot again according to class established rules, record on an index card and also on a post it note.
Students place post it notes on the chalkboard in a random fashion. (Be sure students names are on the post it notes.) Discuss with the class what is the best way to organize these foot lengths from the lowest to the highest. (Range) Students should work in pairs to draw a rough draft of a graph showing the distribution of foot lengths. Partners should think about what the graph shows and record a statement about their rough graph. *Before the partners begin work on their rough draft graphs a review discussion of different types of graphs would help students determine what type of graph they should draw.
Whole class discussion of rough drafts should occur. Allow partners to share graphs and statement. Discussion should be flexible but be prepared to discuss misconceptions. The types of graphs should be discussed and the concepts related to the construction of a graph should be discussed: all graphs have a title, the graphs axis should be labeled, the graph should have a scale and be in numerical order, data needs to be entered accurately on a graph, and conclusions can be drawn from the information given on a graph. Students should be encouraged to use the terms of range, mode, and median. If these concepts are not used address these words in the questions the teacher directs to the students as they display their rough drafts. (The introduction of these words should not be a testing situation or a formal lesson on these words, just an easement in of important vocabulary words.)
Make a whole class graph based on the rough drafts. Students can record their shoe size on a foot cutout to use on the class graph.
Discuss middle sized foot (median), range of foot sizes, and mode (most often).
Ask the students: What would happen to the data on our graph if we added our parents' feet? Do you think your parents' feet will be shorter or longer than yours? How much shorter, longer? What do you predict? What data do we need to collect?
Homework: Measure a parents foot? Follow the classes established rules for measuring the foot. Record the data on an index card.

Day 2-approximately 45 minutes. Based on parent's foot measurement.

Following day one: Compare parent's foot measurement to the chart of less than a foot, equal to a foot, more than a foot.
Students should randomly post foot sizes of parents on the chalkboard.
Working with partner, students draw a rough draft graph with the collected data.
The students should write a statement about their graph. They should also record the graphs range, median, and mode.
Group discusses the graphs. Refer to Day 1 #10. Analyze the data. Make a parent foot graph as a group.
Students should record the parent's foot size on a paper cut out of a foot. Suggest using a contrasting coloring from student's foot.
Post the parents' feet on the classroom foot graph. Discuss the range, mode, and median. Also, have students' record statements about the graph.

Day 3-Technology:

Students can now take the collected data of foot measurement of students and parents and enter that information into a graphing computer program to generate a computerized graph of the data. These computer programs can be a commercially purchased graphing program (Money, Time, Measurement-by IBM is an example of a commercially purchased graphing program.) or one used with Microsoft Programs. Microsoft Excel offers graphing capabilities. It allows for the data entered to be shown in a variety of graphs: column, line, bar, etc. This enables the students to see their data graphed in a variety of graphic forms.

The various graphs can be printed and displayed with the class-generated graph.

Day 4-Assessment

Have the students complete the assessment piece to this learning experience. Evaluate the assessment utilizing the rubric.

3. INSTRUCTIONAL/ENVIRONMENTAL MODIFICATIONS

The range of student abilities will be accommodated by having students work with partners for measuring-collecting data, organizing information, sketching graphs, and interpreting the graphs. The classroom setting will include collecting data from home.

4. TIME REQUIRED

Planning: Minimal time to reproduce handouts.

Implementation: Approximately a total of two hours over two or three days of instruction.

Assessment: Twenty minutes of one class period.

5. RESOURCES

Student: inch rulers, blank paper, index cards (2), post it notes, foot cut out for students and parents for graph.

Teacher: overhead/blackboard for recording of measurements, area of the room to display foot graph of students and eventually to include parents' foot measurements.

6. ASSESSMENT PLAN

Students will be aware of their progress by observing the foot graphs development on the board. The progress made by the students will be evident through observation, group discussions, and written interpretations of the graphs.

An assessment question and grading rubric are attached to this document.

7. STUDENT WORK

Attached to this document

8. REFLECTION

This learning experience was used in conjunction with a math unit on reading and creating graphs. Students were learning the different types of graphs: tally-graph, bar graphs, histograms, pictographs, and pie graphs. Students were learning what makes a graph and what all graphs must have. Students had the opportunity to make various graphs, create questions for the class to answer and correct students work.

Standard 3.4 of the MST standards specifically addresses the construction of table, charts, and graphs and analyzing real-world data. In this unit students were able to conduct surveys, construct graphs from the data and share the work with their peers.

This unit was peer reviewed by colleagues at school. They had opportunities to see student work on display and critique the development of this learning experience.

A special thanks is sent to Elaine Main from the V.V.S. School District for her collaboration on the creation of this learning experience.

PART A:

Miss King's Third grade class had their heights measured by the school nurse. Below is a list of their heights. Make a graph of the heights and then answer the questions below.

Heights:

51 in., 51 in., 52 in., 50 in., 51 in., 54 in., 50 in., 52 in., 48 in., 52 in., 53 in., 51 in.,

54 in., 50 in., 52 in., 38 in., 52 in.

Write one sentence about the graph. __________________________________________________________________________________________________________________________________________________________________________________________

PART B:

Look at the graph and answer the following questions:

1. What is the range of the heights of the class? __________

2. What is the mode of the heights of the class? __________

3. What is the median of the heights of the class? __________

RUBRIC

Part A Development of Graph

5 Both axis are correctly labeled.

Correct title.

Axis arranged numerically.

Data organized correctly.