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Measuring with Standard and Non-Standard
Units
Objectives:
§
Students will listen and respond to a
literary selection related to non-standard units of measurement.
§
Students will measure and compare the
lengths and widths of various objects using both standard and non-standard
units.
§
Students will develop questions in
reference to the data on the class-generated graph and be able to answer
questions created by other students by interpreting data on the graph.
§
Students will use concrete objects to
determine area and perimeter.
§
Students will gather, organize, and
display data using charts and bar graphs.
§
Students will create a rectangular “quilt” based on given non-standard measurements.
Download as Microsoft Word
Document:
Mathematics Governor’s Institute 2005
Names of group
members:
Heidi
Becker, Barbara Krause, and Catherine Schmitt
Topic/Theme:
“A
Foot is a Foot. Or is it?”
(Measuring
with standard and non-standard units)
Level:
Grade
3
Time Element:
5
one hour class periods
NCTM Standards Addressed:
Use mathematical models to represent and understand quantitative
relationships
• model
problem situations with objects and use representations such as graphs, tables,
and equations to draw conclusions.
Analyze characteristics and properties of two- and
three-dimensional geometric shapes and develop mathematical arguments about
geometric relationships
• identify, compare, and
analyze attributes of two- and three-dimensional shapes and develop vocabulary
to describe the attributes
Understand measurable attributes of objects and the units,
systems, and processes of measurement
• understand such
attributes as length, area, weight, volume, and size of angle and select the
appropriate type of unit for measuring each attribute
• understand the need for
measuring with standard units and become familiar with standard units in the
customary and metric systems
Apply appropriate techniques, tools, and formulas to determine
measurements
• select and apply appropriate
standard units and tools to measure length, area, volume, weight, time,
temperature, and the size of angles
• develop, understand, and
use formulas to find the area of rectangles and related triangles and
parallelograms
Formulate questions that can be addressed with data and collect,
organize, and display relevant data to answer them
• collect data using
observations, surveys, and experiments
• represent data using
tables and graphs such as line plots, bar graphs, and line graphs
PA Math Standards
Addressed:
2.1.3L
Demonstrate knowledge of basic facts in four basic operations.
2.2.3B Solve single- and double-digit
addition and subtraction problems with regrouping in vertical form.
2.2.3.A
Compare measurable characteristics of different objects on the same dimensions
(e.g., time, temperature, area, length, weight, capacity, perimeter).
2.2.3.E
Determine the appropriate unit of measure.
2.3.3.B
Determine the measurement of objects with non-standard and standard units
(e.g., US customary and metric).
2.3.3.F Use
concrete objects to determine area and perimeter.
2.9.3.A Name
and label geometric shapes in two and three dimensions (e.g. rectangle/prism).
2.8.3D Create a story to match a given
combination of symbols and numbers.
2.6.3.B
Formulate and answer questions based on data shown on graphs.
2.7.3.D Analyze data using the concepts
of largest, smallest, most often, least often and middle.
2.11.3.B
Identify least and greatest values represented in bar graphs and pictographs.
2.6.3A Gather, organize and display
data using pictures, tallies, charts, bar graphs and pictographs.
Math Assessment Anchors
Addressed:
M3A.3.1 Solve problems using addition, subtraction and multiplication (straight
computation and word problems).
Reference: 2.1.3.L, 2.2.3.B
A.3.1
M3.B.1.2 Use the attributes of length, area, volume
and weight of objects.
Reference: 2.3.3.A, 2.3.3.E
M3.B.2.1 Determine the measurement of objects with
non-standard and standard
units. Reference:
2.3.3.B, 2.3.3.F
M3.B.2.1.1 Use a ruler (provided) to measure to
the nearest 1/2 inch or centimeter.
M3.B.2.1.2 Find the perimeter of a figure drawn and
labeled (with the same units throughout).
M3.B.2.1.3 Find the area of a figure drawn on a grid (only full grid
blocks inside the figure).
M3.C.1.1 Identify and/or describe two- and three dimensional objects.
Reference: 2.9.3.A
M3.C.1.1.1 Name/identify/describe geometric shapes
in two dimensions (circle, square,
rectangle, triangle, pentagon, hexagon,
octagon).
M3.D.2.1 Create/model expressions, equations and inequalities
to match a problem
situation. Reference: 2.8.3.D
M3.D.2.1.2 Choose the number sentence that matches a given story (one operation, + or – only).
M3.E.1.1 Answer questions based on data shown on
tables, charts,
bar graphs or pictographs.
Reference: 2.6.3.B, 2.7.3.D, 2.11.3.B
M3.E.1.1.1 Analyze data shown on tables, charts,
bar graphs or pictographs using the
concepts of largest, smallest, most
often, least often and middle.
M3.E.1.1.2 Describe, interpret and/or answer questions based on data shown in tables, charts, bar graphs and pictographs.
M3.E.1.2 Organize or display data using tables,
charts, bar graphs
or pictographs. Reference: 2.6.3.A, 2.7.3.C
M3.E.1.2.1 Graph data or complete a graph given
the data (bar graph or pictograph – grid
is provided).
M3.E.1.2.2 Translate information from one type of display to another (e.g., convert tally
chart to bar graph). Limit to tally charts, bar graphs, tables and
pictographs.
|
R4.A.1.1 Identify
the meaning of vocabulary. |
R4.A.1.1.1
Identify meaning of a multiple meaning words used in text. R4.A.1.1.2
Identify a synonym or antonym of a word used in text.
|
|
R4.A.1.3 Make inferences and draw conclusions based on
text. |
R4.A.1.3.1
Make inferences and draw conclusions based on information from text. |
Objectives:
Students
will listen and respond to a literary selection related to non-standard units
of measurement.
Students
will measure and compare the lengths and widths of various objects using both
standard and non-standard units.
Students
will develop questions in reference to the data on the class-generated graph
and be able to answer questions created by other students by interpreting data
on the graph.
Students
will use concrete objects to determine area and perimeter.
Students
will gather, organize, and display data using charts and bar graphs.
Students
will create a rectangular “quilt” based on given non-standard measurements.
Instructional Strategies
and Plan (include strategies used to help different types of learners, i.e.
auditory, visual, etc):
Day
One
1. Read How Big
is a Foot? by Rolf Myller
without revealing the ending. (auditory & visual)
2. Tell the students that they are going
to design special quilts to go along with the bed for the queen.
3. Have each child trace his or her foot on construction paper decorate it, and cut it out.
(visual & kinesthetic)
Day Two
1. Start by arranging the cutout feet in
order from shortest to
longest. (kinesthetic & visual)
2. Divide the children into groups of
four. Have the children place their cut out feet in a bag and randomly select a
foot for each group. (cooperative learning)
3. Discuss the dimensions of length and
width of rectangles. Then instruct the students to design a rectangular quilt
that is 6 “feet” by 3 “feet” using their group’s cut out foot. Distribute the
materials to each group.
4. After measuring, the students will cut
out their quilts. Groups that finish early will be encouraged to decorate their
quilts using various geometric shapes and patterns.
Day Three
1. Then, hang the groups’ quilts to
compare the sizes. Discuss why they are not the same when they were all given
the same dimensions. (visual)
2. Teacher
think
aloud, “I wonder if that is why the queen’s bed was too small?” Finish reading
the book and discuss standard units. (auditory)
3. Show the students a quilt that is
actually 6 feet by 3 feet and place the groups’ quilts on top of it to compare.
(visual)
4. Teacher demonstrates and reviews
measuring with a ruler. Then the students measure their cut out feet in inches.
The students will record their measurements on the cut out feet. (visual &
kinesthetic)
Day Four
1. Each group will measure the length and
width of their quilt and record their measurements on a chart.
2. Review the concept of perimeter by
using the measurements of all four sides of the teacher made quilt. (visual)
3. Have each group determine the perimeter
of their quilt.
4. Once each group has determined the
perimeter, have the students use the data on the chart to calculate the
perimeter of each quilt and record in their math journals.
5. After checking for accuracy, record the
perimeters on the class chart.
Day Five
1. Students will use Excel to create a
chart displaying the perimeter of the quilts recorded on the class chart.
2. Using the data in their charts,
students will create bar graphs.
3. After printing their graphs, the
students will use them to create questions which may be answered by using the
information displayed on the graphs.
Materials/Resources:
How Big is a
Foot?
by Rolf Myller
Construction paper for each student
Scissors
Craft paper
Markers
Rulers/Yardstick
Computers with Microsoft Excel
Chart paper
Interdisciplinary
Connections:
Students
will listen to and discuss How Big is a
Foot? by Rolf Myller. After reading the book, homonyms will be
discussed in a word study mini-lesson. (For example, the multiple meanings of
foot, ruler, bed, …etc.)
Technology
Students
will use basic computer software by using Microsoft Excel.
PA
Standard 3.7.4.D
·
Apply
operating system skills to perform basic computer tasks.
·
Identify
and use simple graphic and presentation graphic materials generated by the computer.
Assessment Strategies:
Formative Evaluation
(checking student understanding during the lesson):
1. Check for accuracy when students
measure their cut out feet.
2. Check journal entries for accurate
perimeter calculations.
Summative Evaluation (How will it be
determined that the objectives were achieved?):
1. Check completed quilts for accurate
measurements.
2. The student-generated questions will be
checked to see if they can be answered by interpreting the data displayed on
the graphs.
Correctives/Remediation:
Small
group teacher directed instruction on measuring in inches and calculating
perimeter.
Learning
centers:
-Perimeter
Patterns using straws
-Perimeter
on a geoboard
-Using
blocks to determine perimeter
Extensions/Enrichment:
-Investigate
how to find the area of the quilts.
-Find
different perimeters for the same area
Special Accommodations
(special needs students)
Description of the Special Needs student
selected:
Michael Angelo appears to be a
disinterested learner. He loves to draw, but it is difficult to motivate him to
do other tasks. His father says, “Well just let him draw if that is what makes
him happy.”
Accommodations to use with this student:
1. Preferential
seating near teacher.
2. Instructions
given orally and written. Have student repeat directions.
3. Have
the student assist with data recording on class chart.
4. Reward
positive attention to task by allowing the student to format the Excel graph by
changing colors or types of graphs.
5. Positive
reinforcement will be continuous throughout the lesson by encouraging artistic
abilities.
6.
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