1. Teaching Measurement
Grades 3 to 6
Carlo Magno
De La Salle University, Manila

2. K to 12 Mathematics Content Areas
• Numbers and Number Sense
• Measurement
• Geometry
• Patterns and Algebra
• Probability and Statistics

4. Question:
• Why is measurement important in the math
curriculum?

5. Measurement Outcomes:
• Choosing units
• Measuring
• Estimating
• Time
• Using relationships
Mathematics: A curriculum profile for Australian
Schools (1994)

6. Measurement in K to 12
• Use of numbers and measures to describe,
understand and compare mathematical and
concrete objects.
• Focuses on attributes such as length, mass and
weight, capacity, time, money and temperature.
• Applications involving perimeter, area, surface
area, volume, and angle measure.

7. Grade 4 Competencies
• Describes and illustrates the perimeter of a given
figure.
• Finds the perimeter of triangles, squares,
rectangles, parallelograms and trapezoids.
• Solves word problems involving perimeter of
squares and rectangles, triangles, parallelograms
and trapezoids.
• Estimates the area of an irregular plane figure
made up of squares and rectangles using non-
standard units.

8. Grade 4 Competencies
• Derives inductively the formulas for the area of
squares and rectangles
• Finds the area of a figure made up of squares
and rectangles using cm2 and m2.
• Estimates the area of triangles, parallelograms
and trapezoids using non-standard units.
• Derives inductively the formulas for the area of
triangles, parallelograms and trapezoids.

9. Grade 4 Competencies
• Finds the area of triangles, parallelograms and
trapezoids using cm2 and m2.
• Solves word problems involving the area of a
figure made up of squares and rectangles.
• Solves word problems involving the area of a
triangle, parallelogram and trapezoid.
• Visualizes and builds rectangular prisms using
unit cubes.
• Derives inductively the formula for the volume
of rectangular prisms.

10. Grade 4 Competencies
• Finds the volume of a rectangular prism using
cubic units.
• Solves word problems involving the volume of a
rectangular prism.

11. Grade 5 Competencies
• Represents and describes the circumference of a
circle.
• Uses a model to estimate the circumference of a
circle.
• Derives a formula for finding the circumference
of a circle.
• Finds the circumference of the given circle using
the formula/s derived.
• Solves problems involving circumference.

12. Grade 5 Competencies
• Estimates and uses appropriate units of measure for
area.
• Converts sq cm to sq m and vice versa.
• Names the appropriate unit of measure used for
measuring area for accuracy.
• Estimates and uses appropriate units of measure for
volume.
• Converts one cubic unit of measure to a larger or
smaller unit.
• Names the appropriate unit of measure used for
measuring the volume of a cube and a rectangular
prism for accuracy.

13. Grade 5 Competencies
• Represents and describes the area of a circle.
• Uses a model to find the area of a circle.
• Derives a formula for finding the area of a circle.
• Finds the area of a circle using the formula/s
derived.
• Solves problems involving area of circle using
appropriate formulas and procedures.
• Describes the volume of cube and a rectangular
prism.
• Derives a formula for finding the volume of cube
and a rectangular prism.

14. Grade 5 Competencies
• Solves problems involving volume of a cube and
rectangular prism using appropriate formulas
and procedures.
• Describes and estimates the temperature inside
and outside of the classroom.
• Identifies the parts of a thermometer.
• Reads a thermometer.
• Measures temperature using the degree Celsius.
• Solves problems involving temperature.

15. Grade 6 Competencies
• Finds the area of composite figures formed by any
two or more of the following: triangle, square,
rectangle, circle and semi-circle.
• Solves word problem involving area of composite
figures formed by any two or more of the following:
triangle, square, rectangle, circle and semi-circle.
• Identifies the faces of a geometric solid.
• Visualizes and describes surface area and name the
unit of measure used for measuring the surface area
of solids.

16. Grade 6 Competencies
• Derives a formula for finding the surface area of
cubes, prisms and cylinders.
• Finds the surface area of cubes, prisms and
cylinders.
• Solves word problems involving measurement of
surface area.
• Describes the meaning of the volume of a solid.
• Determines the relationship between the volume of
a rectangular prism and of a pyramid and between a
cylinder and a cone.
• Obtains formulas for finding the volumes of
cylinders, pyramids and cones.

17. Grade 6 Competencies
• Finds the volume of a cylinder, pyramid or a cone.
• Solves problems involving volumes of solids.
• Reads and interprets electric and water meter
readings.
• Solves problems involving electric and water
consumptions.
• Estimates the duration of time in seconds and
minutes.
• Measures time using a 12-hour and a 24-hour clock.

18. Grade 6 Competencies
• Converts measures of time from a 12-hour to a
24-hour clock and vice versa.
• Calculates time in the different world time
zones.
• Calculates speed, distance and time.
• Solves problems involving average rate and
speed.

19. Premise in Measurement
• Measurement activities are based on everyday
life experiences:
▫ More or less
▫ Tall or short
▫ Faster, slower
▫ Softer, lighter

20. Prerequisite skills
• Comparison skills
• Estimation skills
• Development of measurement understanding:
▫ Natural (body): The length of my bed is 10
handspans.
▫ Informal (comparison): My big sister measured
my bed and said its 10 handspans.
▫ Formal (standard units): My bed is 2 meters long.

21. • Regardless whether students use formal or non
formal measurement they should make decision
about:
▫ Which quantities should be measured at hand
▫ Which units to use
▫ The measuring tool appropriate

22. K to 12 Mathematics
• The framework is supported by the following
underlying learning principles and theories:
▫ Experiential and Situated Learning
▫ Reflective Learning
▫ Constructivism
▫ Cooperative Learning
▫ Discovery and Inquiry-based Learning

23. K to 12 Mathematics
• Experiential learning as advocated by David
Kolb is learning that occurs by making sense of
direct everyday experiences.
• Experiential learning theory defines learning as
"the process whereby knowledge is created
through the transformation of experience. “
• Knowledge results from the combination of
grasping and transforming experience" (Kolb,
1984, p. 41).

24. K to 12 Mathematics
• Situated learning, theorized by Lave and
Wenger, is learning in the same context on
which concepts and theories are applied.

25. K to 12 Mathematics
• Reflective learning refers to learning that is
facilitated by reflective thinking.
• It is not enough that learners encounter real-life
situations.
• Deeper learning occurs when learners are able to
think about their experiences and process these
allowing them the opportunity to make sense
and meaning of their experiences.

26. K to 12 Mathematics
• Constructivism is the theory that argues that
knowledge is constructed when the learner is
able to draw ideas from his own experiences
and connects them to new ideas that are
encountered.

27. K to 12 Mathematics
• Cooperative Learning puts premium on
active learning achieved by working with
fellow learners as they all engage in a shared
task.

28. K to 12 Mathematics
• The mathematics curriculum allows for students
to learn by asking relevant questions and
discovering new ideas.
• Discovery and Inquiry-based learning
(Bruner, 1961) support the idea that students
learn when they make use of personal
experiences to discover facts, relationships and
concepts.

29. Experiential and Situated Learning
• Ask students to record the time it takes them to
travel from home to school in minutes for one week.
• Tabulate the results
• Ask students to make interpretation
▫ Which days took the longest time? Why is this so?
▫ Which days took the shortest time? Why is this so?
• Open google maps and see how many kilometers is
the distance from your house to school.
• What is the average time required to get to school?
• How many minutes per kilometer does it take you to
travel?

30. Experiential and Situated Learning
• Watch your favorite cartoons.
• Count all the words being said in the cartoons.
• How long is the cartoon in minutes?
• If the time of the cartoon is doubled, can you predict
the number of words that can be mentioned?
• If you talk in the telephone for a 10 minutes, what is
the estimated number if words you can use?
• If you need to tell your friend an important message
with 50 words, how much time will it require you to
tell him/her?

31. Experiential and Situated Learning
• Measure how much volume can your bathroom
pail contain water.
• Determine the time it takes you to fill the pail.
• If you double the size of your pail, how much
time will you fill it?
• Take the time in consuming the one pail of water
when taking a bath. How many pails do you
consume?
• Given the pails of water you consume, estimate
how long you take a bath.

32. Ask for 2 volunteers
• Participants will provide their own example of
an activity for experiential and situational
learning.

33. Reflective learning
• Use google maps and estimate the kilometers
from your house to where your father is working.
• Ask for the total amount spent when
commuting.
• Ask for the total amount spent when driving
your won car.
• Show your data to your father and recommend
which mode of transportation is better.

34. Reflective learning
• Get the weight of each of your family members.
• Determine their ages and check who is
underweight and overweight.
• Given your data make recommendations on the
following:
▫ Money spent on food
▫ Menu for the week
▫ Exercise activities for the family

35. Reflective thinking
• Keep a journal and take note of all your travels
via plane.
• Jot down in the journal the time you spent in the
plane and the places you went.
• Summarize the following:
▫ What places took the longest plane ride? Why?
▫ What places took the shorted plane ride? Why?
▫ What is the relationship between time and
distance?

36. Reflective thinking
• Get the square meter of your land area.
• How much does your land cost?
• Get the square meter of other land areas.
• How much do they cost?
• Get the square meter of residential lands in the city.
How much do they cost.
• Compare the cost of equal land areas in the city and
in the province?
• Is there a difference? Why is this so?
• What do you need to do if you want to live in the
city?

37. Ask for 2 volunteers
• Participants will provide their own example of
an activity for reflective learning.

38. Constructivism
• Students will identify a problem in their
community in the following areas:
▫ Waste management
▫ Overcrowding
▫ Increased air temperature
• Collect data to serve as evidence to these
problems by:
▫ Measure the weight of garbage produced by each
household each day for 4 weeks
▫ Count the number of people living in each
household and the floor area of their house. Report
the ratio.
▫ Get the temperature each day and tabulate it.
• Provide recommendations given the severity of
the problem (reflective learning)

39. Constructivism
• What type of body pains did you experience as the
most painful? Why did you had such pain?
• List them down.
• For each pain indicate how painful it is using a scale
from 0 (no pain) to 10 (very painful)
• Ask your classmates to rate the list of pain you have.
• Get the average of the rating for each pain.
• Report the standard deviation.
• Given the SD are you all having a similar feeling for
each pain? (reflective learning)

40. Constructivism
• Measure the temperature for the months of April
and May.
• Go to the malls and ask some sales person which
types of clothes are bought and the quantity.
• Tabulate the number of purchases for each type
of clothes for each day and the temperature?
• What does the temperature got to do with the
type of clothes sold?

41. Constructivism
• Which model of cell phone do you have?
• What do you think is the best cell phone model?
• List down different cell phone models and count
the number of people in your community who
has it.
• For each model of cell phone, ask the owners
how long does their battery last. Ask also what is
the total minutes they used to call and text.
• Which characteristic of cell phone do you
recommend that can save more energy?

42. Ask for 2 volunteers
• Participants will provide their own example of
an activity for constructivist learning.

43. Cooperative learning
• Form a group and each one will be assigned to a
place to take the air temperature for 7 days.
• Compare the temperature for each person.
• Why is there variation in the temperature?
• Report the findings.

44. Cooperative learning
• Students form three groups and are assigned to
measure the floor area of the classroom.
• One group will only use a one inch paper clip.
• One group will use an 8 inches pencil.
• One group will use a 15 inches long stick.
• Which group do you think will measure the floor
area the fastest? Why?

45. Cooperative learning
• Students will work together to build an
improvised anemometer and a rain gauge.
• When the rain comes they record the speed of
the wind.
• They measure the amount of water collected in
the rain gauge.
• Students make a report and present to class the
relationship between wind speed and amount of
rainfall.

46. Ask for 2 volunteers
• Participants will provide their own example of
an activity for cooperative learning.

47. Discovery
• Students will ask their parents at home the
different tools they use to measure length of
objects.
• The students will bring this material and
demonstrate to their classmates how the tools
are used.

48. Discovery
• Self-study on the procedure to convert oC to oF.
• Show how it is done in class

49. Ask for 2 volunteers
• Participants will provide their own example of
an activity for cooperative learning.

50. Insights