Body proportions investigation

Overview

An investigation for learners to measure different parts of their bodies and look for patterns, relationships, and develop the idea of proportionality and practice rounding.

Focus Questions

What is proportion?
Are body parts proportional?
What are my dimensions?
Is there a mathematical relationship between heights of different body parts?
How do people chart values when the numbers are larger than the number of squares on a piece of paper?
What is a rounded number and how do mathematicians decide how to round numbers?
How can math be used to find relationships of bodies?

Dimensions and Concepts

Measuring, rounding, graphing, scaling, categorical data,

Practice of mathematics: Problem solving, communication, connections, reasoning and proof, and representation

Data can be quantified to find real world relationships among variables.
Organizing data in a chart or graph helps to visualize information and can be a useful strategy to help in solving problems.
Values and relationships can be represented and communicated in charts and graphs.
Procedures can be supported with proof.

Number values, geometry and measurement, algebra, and data analysis

Number value

Number value of similar increments are proportional (e.g. the number of increments a person puts between 2 and 3 can be put between 4 and 5 …)
Five is mid way between 0 and 10.
Proportion is a relationship between two values

Algebra

Relationships can be expressed mathematically.
Relationships of two quantities may be described in terms of ratios, rates, percents, or proportional relationships.
Sometimes proportions are defined as relationships between values with the same attributes. While rates are defined as relationships between values with different attributes.

Measurement

Measurement uses a known unit to iterating across an unknown value.
Standard units of linear measurement include: inches, feet, millimeter, meter...
Measurement is used to communicate information more accurately.
When using a ruler or number line you count the spaces.
All measurement is an estimate.
Information that is scaled maintains its value and proportions.

Data analysis

Information can be grouped into categories. Numbers can be rounded to group values by range categories.
Numbers are rounded according to the precision needed to analyze the properties that are being quantified.

Background

Students will measure different points on their body from the floor

Point on right ankle,
Top of right patella,
Top of right hip on the side,
Top of shoulder blade,
Top of head.)

And chart the data.

Points on the body are picked to create at least two problems:

First a small number (ankle) that hopefully some will see the need to be rounded to zero and
Second a large number that would require that the values be scaled to fit on the chart (shoulder, head).

Activity Sequence

Measure student body parts
Record them on a class table.
Chart them on a jumbo class table (one to one not scaled).
Discuss what to do with values that don't fit.
Scale by tens.
Round numbers.
Chart on chart scaled to ten.
Review what learned.

Activity Descriptions

General description. Need to add specific mention of how the dimensions will be discused with the students.

Ask. What is the average height of a fourth grader is?
Ask. Do you think that the distances from the floor to different people's ankles, knees, hips, shoulders are different?
As. Do you they think that there might be a pattern between the heights?
Have everyone find the same points on their own ankle, knee, hip, shoulder, and head.
Show them a metric ruler and ask them if they know how to use it.
Have them demonstrate how to measure the height from the floor to the bottom of the chalkboard. Have another critique the procedure used.
Pair learners, have them measure each other, and record the distances, in cm, on a chart provided.

	Person's name	Person's name
Ankle bone height
Top of patella
Top of hip
Top of shoulder
Height - top of head

Create a chart with numbers 0,1,2,3,4,5,6,7,8,9… for as far as the chart goes. However, make sure that the chart will NOT be large enough to include all of their shoulder measurements.
Provide them with five different colored dots.
Have each put their green dot on the chart in the proper location.
Chart with numbers 0,1,2,3.. up the left side (y axis) and each student's name across the bottom (x axis). Write a title across the top (Fourth grade student's body parts heights)
Continue until all ankle heights are placed, then pick another colored dot and have them chart the patella and so on until they run out of room or a student claims they will run out of room.
Ask students what they should do? Students may want to just stick them on the wall above the chart. If so allow them to do so and finish the charting.
Lead or introduce them to the idea of scaling the numbers. Suggest that there is another way the mathematicians could have solved the problem.
Bring out a new chart that looks the same only the numbers in the y axis are 0, 10, 20…
Ask them if they were going to put their measured number into one of the following boxes (0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110…), which one would it be and their reason why.

Person's name	Measured height	Ten box	Reason why
Ankle bone height
Top of patella
Top of hip
Top of shoulder
Height - top of head

Have them report their decisions and their reason why.
Ask them if they can see a pattern to how they organized them. If not, then ask them how they could rearrange them so that there was a rule and all would know what box to put them in.
Have them refer to a hundreds chart, number line, or metric ruler to give reasons to support their answers.
When they agree on what rules give consistent solutions, have them use it to put their dots onto the chart with the multiples of ten.
Have students compare the second chart with the first.
*** Depending on learners interest the following could be interchanged.***
Review the rules that they created. Have them use it on different numbers (3, 15, 26, 34, 65, and others desired) and illustrate it on the hundreds chart and that
Have the students look at the chart and see if they can find any patterns between students and between the measurements of different body part heights. One relationship would be that all increase in value. If students place their dots in order height, do the distances between each person's body parts and another person's body parts increase proportionally?
Ask them how else they can use what they learned. When would they want to round numbers? When could they make a graph to solve a problem? When would they need to scale their data. Does scaling their data change the results? Why or why not?

Explore more body proportions: Learners measure body parts and compare their ratios to height and the use of ratio in Egyptian art , Greek sculpture and more. Learners can explore proportion of body parts and a person's height with diagrams, scatter plots, graphs, and regression lines.

Rubric or scoring guides with outcome levels...

Add scoring guides with levels for proportional reasoning, measurement, and data analysis.

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