Names:
Derek Compton
Anna Edge
Sarah Otvos
Carnival
Names:
Derek Compton
Anna Edge
Sarah Otvos
Grade Level: 3-5
Teacher Materials Needed: None
Student Materials Needed:
· Measuring cups
· String
· Yardsticks
· Rulers
· Counting Tiles
· Counting Blocks
· Measuring Tapes
· Beakers
· Measuring Spoons
Mathematical Goals for This Lesson:
· Begin to assess student understanding of measurement (measurable
attributes, appropriate tools, formulas, techniques)
· Review Metric and English Standard Systems (units, processes,
base of 10)
· Begin to make estimated measurements
· Provide a Math activity that will create interest and allow
students to approach measuring comfortably
· Practice using conversions
· Create and establish an awareness of Math in everyday life
· Develop an appreciation of the benefits of group work
Related NC Standard Course of Study Goals/Objectives:
Grade 3:
1.04 Use estimation techniques in determining solutions to problems.
2.06 Estimate and measure length (inches, feet, yards, centimeters,
meters), weight (grams, ounces, pounds), and capacity (cups, pints, quarts,
gallons, liters) using appropriate tools and units. 2.07 Model and
compare units within the same measurement system.
2.13 Solve problems using measurement concepts and procedures.
Explain the solutions.
3.05 Use patterns to make predictions and solve problems.
4.01 Gather and organize data from surveys and classroom experiments,
including data collected over a period of time.
4.02 Display data on charts and graphs: picture, bar and line plots;
describe data using mode.
Grade 4:
1.02 Use estimation techniques in determining solutions to problems.
1.18 Solve multi-step problems; determine if there is sufficient data
given, then select additional strategies including
- Make a chart or graph
- Look for patterns
- Make a simpler problem
- Use logic
- Work backwards
- Break into parts.
· Verify and interpret results with respect to the original
problem; use calculators as appropriate. Discuss alternate methods
for solution.
2.07 Estimate and measure length, capacity and mass using these
additional units: inches, miles, centimeters, and kilometers; milliliters,
cups, and pints; kilograms and tons.
4.03 Collect, organize, and display data from surveys, research,
and classroom experiments, including data collected over time. Include
data from other disciplines such as science, physical education, social
studies, and the media.
4.04 Interpret information orally and in writing from charts,
tables, tallies, and graphs.
4.05 Use range, median, and mode to describe a set of data.
Grade 5:
1.17 Determine if there is sufficient information to solve a problem;
identify missing or extraneous data in problem-solving situations.
2.08 Investigate similar figures using rulers and protractors.
2.09 Use an organized approach, appropriate strategies, and technology
as needed to solve multi-step problems involving geometry, spatial visualization,
and measurement (length, weight, time, capacity, temperature, perimeter,
area, volume.)
2.10 Verify and interpret results with respect to the original problem;
identify alternate strategies for solving a problem. Use calculators and
computers as appropriate.
4.03 Systematically collect, organize, display and interpret data both
orally and in writing using information from a variety of content areas.
4.04 Compare increasingly complex displays of data, including multiple
sets of data on the same graph, computer applications, and Venn diagrams.
Launch:
The famous Canadian Carnival is coming to town soon. We are going
to use math to help us figure out a problem about carnival rides.
At first you will work individually and then we will divide into small
groups to come up with a solution.
The problem is that there are some rides at the carnival that require
you to be at least 1.2192 meters tall to ride. Brainstorm some ideas
of ways to find out if you are tall enough to ride and what you would use
to find out how tall you are. Make sure you write down all of your
ideas and whether you think you are tall enough to ride (1.2192 meters).
Explore:
Have students brainstorm ideas individually. Walk around and
observe students ideas and decide how to group them. Allow students
ample time to think of ideas, and then let them choose a tool and try to
find out how tall they are.
After students have manipulated the tools and made an estimate of their height, put them in pairs. Each partner should help the other find his/her height by using the tool and idea he/she used to measure him/herself.
Once more precise measurements are made pairs should discuss the tool
and method they each used to measure their height. Then they should
decide (by vote if necessary) which of the tools and methods used would
produce the most precise measurement. They should measure each other
using that tool and method to get the most accurate measure of each person’s
height. After exact measurements have been made, the students are
to convert the measurements from the Standard System to the Metric System.
Then determine whether they are tall enough to ride the rides. All
students should reassemble for whole group discussion to finish the activity.
The final part of the problem is to convert the carnival ride height requirement
to the Standard System and discuss their methods of solving the problem.
Summarize:
· When the students have finished, have the groups present their
findings in a creative way (chart, graph, etc.)
· Ask students if they have any questions. Then ask students
to tell a few things that they learned and can apply in everyday life.
Assessment/Evidence of Learning:
While the students are working individually I will look for:
· The types and variety of ideas students have
· Students writing down all potential ideas without eliminating
any possibilities
· Mention of the two measuring systems
· Tools they choose (to measure themselves with)
While students are in pairs and groups I will look for:
· Cooperation with group members
· Individual ideas about why a certain tool/method is more precise
· Supportive arguments in the decision making process in choosing
the most precise tool
· Ideas of how to convert the measurements
· Individual student’s participation in activity
· Knowledge of the metric system
· Relation to other math or life experiences
Closure Activity:
Each student should write down an example of a situation in which having
two different measuring systems creates a problem.
Making Lesson Adaptable
Grade 3:
· Only carry the decimal out the tenths place
Grade 4:
· Convert from Metric system to English system and back again
· Carry decimal out to hundreth’s place
Grade 5:
· Have students make out a conversion chart for themselves
· Carry decimal out to thousandths place and beyond
· Convert decimal to fractions
· Make a chart or diagram to demonstrate the measurements taken
Time Stands Still For No One
Names:
Derek Compton
Anna Edge
Sarah Otvos
Grade Level: K – 2
Teacher Materials Needed:
· Teacher model clock
· “The Grouchy Lady Bug” by Eric Carle (big book if possible)
· Chart paper with a school schedule
Student Materials Needed:
· Clocks
· Television schedules
· Clock worksheet
Mathematical Goals for This Lesson:
· Begin to assess student understanding of the concept of time
(telling time, hours, minutes, standard and digital clocks)
· Integrate math and literature
· Allow students to work together and learn the benefits of
pair/group work
· Create an awareness of math in everyday life
· Introduce the use of schedules and their importance in life
Related NC Standard Course of Study Goals/Objectives:
Kindergarten:
2.03 Compare and order objects using appropriate vocabulary.
2.06 Name the days of the week.
3.03 Identify, copy, continue, and describe patterns.
3.04 Create patterns with actions, words and objects.
4.01 Collect data to create concrete and pictorial graphs and describe
the results as a group activity.
Grade 1:
2.08 Divide regions into two, three, and four equal parts.
2.11 Tell time to nearest hour using digital and analog clocks.
2.12 Solve problems involving non-standard measurement and explain
strategy.
4.01 Gather, organize and display information as a group activity.
4.03 Make predictions based on experiences.
4.04 Create concrete, pictorial, and symbolic graphs using prepared
grids.
Grade 2:
2.10 Sequence months; use the calendar to solve problems.
2.11 Tell time to the nearest half-hour using digital and analog clocks;
record. Solve problems related to time.
3.02 Identify classification and patterning in the environment.
4.01 Collect, sort, organize, and display information in charts, graphs,
and tables with correct labeling.
Launch:
· Have students look at a clock and ask them “What time is it?”
See how many students raise their hands. Call on a child and listen
to their answer. (This will help you assess how much the students
already know about telling time and who feels comfortable with it.)
· Regardless of the answer you receive (correct or incorrect),
explain that in order to tell time, one much know and understand the parts
of a clock. At this time, review the parts of a clock: big hand,
little hand and how each number on the clock represents a multiple of five.
Be sure to use the big teacher clock as a visual.
· Show the students “The Grouchy Lady Bug” and flip through
the book to look at the pictures. Ask the students what they think
the book will be about.
Explore:
· Hand out a clock to each student.
· Read “The Grouchy Lady Bug” aloud to the class. As you
read, have the students move the hands on their clocks to show the times
mentioned in the book. Instruct the students to hold their clocks
in the air when they are finished with each time and as they do this, set
the teacher clock to the correct time. This way, students can check
whether their clock was correct. (Be sure to allow time for the children
to observe the illustrations in the book. They are very vivid and
also show what time it is.)
· Once the book is completed, show the class the class schedule
for that day. The schedule can include the time school starts, reading
time, lunchtime, school dismissal and any other major points of the day.
The teacher will demonstrate what each of the times looks like on the clock
and students can do so as well on their own clocks.
· Once students have had enough practice, split them into pairs
or, if necessary, small groups of three. Each group will receive:
a) a television schedule listing time and names of popular children’s shows
and b) a worksheet showing blank standard and digital clocks.
· The students will work in their groups to come up with a list
of their favorite TV shows and the time they are on television. Each
child will fill in the standard and digital clocks showing what time each
show comes on. (Be sure to make the worksheet look identical to the
class schedule shown earlier. This will make the process easier to
understand and relevant to what they have seen in class.)
Summarize:
· When the students have finished, collect their worksheets.
If they have not finished, they may finish at home.
· Ask students if they have any questions. Then, ask students
to tell a few things that they learned today.
Assessment/Evidence of Learning:
· While reading the book: Look to see which
students are setting their clocks to the correct times and whether they
are beginning to grasp telling time on a standard clock.
· While students are working in groups:
Look to see if both students have input in making the schedule, or if one
student is doing all the work. Check to see if the students are cooperating
in their pairs/groups. Ask questions to probe thinking if the students
seem stuck or confused.
· While looking over the students’ worksheets:
Look to see if students filled in the clocks correctly. If they are
having trouble, assess what the problem may be by observing the mistakes
or talking about it in class the following day.
Closure Activity:
As an extra activity, you could ask the students to make a list, at
home, of all the things they do in the morning before coming to school.
Once this has been done, have them add what time they do each thing.
This can lead into a discussion on periods of time (how long an hour, minute,
second, etc. is).
Making Lesson Adaptable
Kindergarten:
· Only make a chart for a single day’s activities
Grade 1:
· Make a chart for a week’s activities and put it into a month
Grade 2:
· Make a chart for the entire year and include holidays, special
events, etc.
Group Notes
Derek Compton
Anna Edge
Sarah Otvos
NCTM Principles and Standards
(Geometry)
· Math instructional programs should enable students to analyze
characteristics and properties of 2 and 3 dimensional geometric shapes
and develop supportive arguments for geometric relationships
· Students should be able to specify locations and describe
relationships using correct terms and systems (Above, near, under, between)
· Students should apply transformations and symmetry to analyze
situations (Flips, slides, turns “using mirrors, paper, folding, and tracing”)
· Solve problems using reasoning, visualization, and modeling
· Learn about geometric shapes and structures – their characteristics,
how to analyze them, and their relationships to each other and other math
· Perceive objects of different geometric shapes from various
perspectives and work with proofs in high school
· Use and apply Geometry and spatial reasoning in life and various
areas
of math
· Use technology to learn Geometry and Geometry to learn to
reason and see axiomatic structure of math
· Understand abstract attributes and properties of shapes and
use deductive reasoning to solve problems
· Hands-on experiences with geometric objects
· Develop understanding of congruence, similarity, and transformations
· Interpret and create top and side views of objects
(Measurement)
· Understand measurable attributes of objects, units (inches,
cm, ft, etc.), systems and process of measures (length, weight, time, area,
volume, temperature, angle measure, etc.)
· Use tools, techniques, and formulas correctly and proficiently
· Assign numbers to characteristics of a situation
· Recognize and make connections to importance of measurement
in everyday life
· Note the connections of measurement to math areas and non-math
areas
· Hands-on manipulation of concrete materials and making comparisons
· Measurement emphasized more in elementary and middle grades
· Formulas necessary to figure measure (a=l x w x h)
· Measuring angles and understanding angle relationships
· Understand that changing an object’s attributes affects measure
· PreK-2nd begin study of measure using non-standard units a
variety of objects (tiles, paper clips, pencils, cups) and have opportunities
to use standard units as students recognize need for a standard
· Different units can be difficult for young kids to grasp –
need to learn which tools and units and formulas to use for various measures
· Learn metric systems first – simple and consistent; however
both systems should be learned (Metric and Standard[English]) and understand
how to make all conversions
· Units and place value and measures are approximations
· Raise ideas of precision and accuracy
· Measurement techniques – tools/ formulas, counting, estimating
· Elementary and Middle grades have difficulty with area and
perimeter so teach this young cause formulas often used without understanding
measure
· Prek- 2nd focus on estimation using benchmarks
· 3rd – 5th use maps and make scale drawings – help learn proportional
relationships
· High school (more sophisticated aspects of scaling)
Kindergarten – 2nd Grade
(Measurement)
· Measurement is one of the most widely used applications in
math and life
· K-2 should be able to:
- Understand length, volume, weight, time…
- Order and sort items according to these things
- Use tools for measurement
- Learn to apply measuring techniques and formulas
· Children many times learn best when they can get their hands
on what they’re learning
· Seeing and visualizing relationships is important for them
to grasp measurement concepts
· Early years emphasize linear measurements, then moving to
volume and weighing objects ® balances and scales
· Time is also a big concept, and the ways its measured – teachers
should call attention to the time and the clock periodically so kids get
a grasp on how important it is in life
· Hands-on tools are the best way to teach measurement
· Teachers can’t assume that students understand measurement
fully, until they are able to make practical sense of it in the real world
(example: ruler)
· Estimation is another important application in early school
(Geometry)
· K-2 should be able to:
- Know characteristics of shapes
- Spatial relationships
- Use summary and transformations
- Use visualization
- Do all this through exploration, investigation, and discussion, etc.
(drawing, constructions…)
· Geometry offer more than just #’s, a different kind of thinking
· Build on the strengths and students should be more enthusiastic
about math
· Children begin learning about shape way before formal schooling
· Kindergarten begin with basic knowledge and lays the foundation
for more formal Geometry in later grades
· Teachers should provide a variety of shapes in different positions
and contexts
· Spatial relationships – important understanding:
- Direction
- Location
- Distance
- Representation
· You can integrate other subjects…Literature (Read 3 “Billy
Goats Gruff” to demonstrate over, under, near, far)
· Pattern blocks are a great way to teach symmetry
· Use tangible items to emphasize these concepts of Geometry
3rd Grade – 5th Grade
(Spatial Sense, Measurement, and Geometry)
· Students in grades 3-5 measure distance, area, and capacity
in both customary and metric units
· Students tell and write time using digital and analog clocks
· Using clocks and calendars they explore elapsed time problems
· Students explore concepts of perimeter and area of rectangles
and squares and develop the basic formulas for computing these quantities
· Students approximate or measure the areas of irregular figures
by covering them with simpler figures such as squares or triangles
· Students estimate distances and draw and build plane and solid
figures
· Students learn about angle measurement, basic properties of
circles, and classification of polygons and polyhedra
· Students investigate the basic geometric relationships, such
as parallel, perpendicular, congruent, and similar
· Students recognize symmetry and geometric transformations
· Students plot points on a rectangular grid and read graphs
drawn on rectangular grids
Individual Notes
Derek Compton
I interviewed both the teacher (Mr. Russ Hiatt) and the student teacher (Mr. Nick Rogowski) about what mathematical concepts and ideas of this strand – Spatial Sense, Measurement, and Geometry was the most difficult. I found out that both of them said Measurement. I asked them to explain and they replied that Measurement is a very abstract concept that is taught only a few times and is hard to apply outside of the classroom. When asked about the specifics of the applications they responded that it is hard for a student in their class to have a concept of a mile or a yard or a foot to name a few. For instance, they would not be able to estimate how many feet they were tall without a measuring device. Also, they mentioned that measurement should be done more often and integrated into a lot of the lessons throughout the year so that the students can have a lot of practice, practical applications, and experience in doing measurement.
Anna Edge interviewed her teacher and found out that measurement was the hardest concept to understand and this was also evident in Sarah’s interview. The particulars of their interviews were a little different as Anna’s principle part of measurement that came under fire was one of conversions. Sarah’s concept of time was the hardest for them to come up with.
Taking these interviews into consideration, we developed two lesson
plans to tackle these problems with a practical application. Lesson
Plan #1 deals with the use of time and calendars. Lesson Plan #2
deals with conversions from the Metric System to the English System and
back again. Not only can these lesson plans be useful in Math but
can be further applied to several other curricula areas. These concepts
of measurement can also be extrapolated to deal with the issues of practice
and practical applications.