NVACS: Measurement and Data
Measurement, Word Problems, Area and Perimeter, Data, Angles
Concept Overview for 4th Graders
4.MD.1.2.3
Solve problems involving measurement and conversion of measurements from a larger unit to a
smaller unit.
4.MD.4
Represent and Interpret Data
4.MD.5.6.7
Geometric measurement: understand concepts of angle and measure angles.
Development of Benchmarks and Mental Images of Measurement
Students need to have experiences using both metric and customary measurement systems in
real world applications so they can develop an understanding of benchmark measurement and
mental images.
Comparison of measurement within one system
1
1 teaspoon equals four quarters of a teaspoon. 1tsp. = 4 X 4
Centimeter and meter equivalences shown in a conversion table
cm
m
100
1
200
2
300
3
500
1000
Some references adapted from North Carolina and Arizona K-5 instructional documents
RPDP.net
Page 1
NVACS: Measurement and Data
Measurement, Word Problems, Area and Perimeter, Data, Angles
Concept Overview for 4th Graders
Foundational understandings to help students understand and apply the concept of measurement.
Iteration
The same unit can be repeated to determine the measure.
Partition
Larger units can be subdivided into equivalent units.
Compensatory principal
Understand the relationship between the size of a unit and the number of units needed.
Multi-Step Word Problems using all 4 operations to solve measurement problems.
The multi-step word problems should involve situations that include the following systems of
measurement:
intervals of time
liquid volumes
masses of objects
money
The multi-step word problems should require students to express measurements given in a
larger unit in terms of a smaller unit.
Example: 1 quart = 2 pints= 4 cups=32 ounces
Models should be used by students to show a representation of the process of solving and the
solution.
Example: A number line diagram or picture featuring a measurement scale.
Some references adapted from North Carolina and Arizona K-5 instructional documents
RPDP.net
Page 2
NVACS: Measurement and Data
Measurement, Word Problems, Area and Perimeter, Data, Angles
Concept Overview for 4th Graders
Area and Perimeter
In third grade students develop a conceptual understanding of perimeter and area of rectangles.
Fourth graders construct arrays and connect the area to multiplication and construct the understanding
to the abstract formula for area listed below.
A=lxw
P = 2l + 2w
The formula is a generalization of the understanding, that, given a unit of length, a rectangle whose
sides have length w units and l units, can be partitioned into w rows of unit squares with l squares in
each row. The product l x w gives the number of unit squares in the partition. When students
understand this concept they then apply it to help construct the formula for area.
As students build their understanding from concrete to pictorial and then to abstract they need to
verbalize their understandings by explaining the formula they construct with words.
Multi- step word problems involving area and perimeter.
Example: A rectangular garden has an area of 60 square meters and a perimeter of 32 meters.
What are the length and width of the room?
Line Plot
1 1 1
Students will work with fractions by measuring objects in unit fractions ( , , ) and recording the data
2 4 8
on a line plot.
X
X
X
X
X
X
X
X
X
X
Some references adapted from North Carolina and Arizona K-5 instructional documents
RPDP.net
Page 3
NVACS: Measurement and Data
Measurement, Word Problems, Area and Perimeter, Data, Angles
Concept Overview for 4th Graders
Concept of Angles
Angles
1
The connection of angles and circular measurement. An angle that turns through 360 of a circle is called
a 1 degree angle.
Classification of Angles
Name
Measurement
right angle
90 degrees
straight angle
180 degrees
acute angle
between 0 and 90 degrees
obtuse angle
between 90 degrees and 180 degrees
reflex angle
between 180 degrees and 360 degrees
Some references adapted from North Carolina and Arizona K-5 instructional documents
RPDP.net
Page 4
NVACS: Measurement and Data
Measurement, Word Problems, Area and Perimeter, Data, Angles
Concept Overview for 4th Graders
Measurement of Angles
Angle measure is additive.
Students will solve for the unknown.
Example Word Problem for computation with angles:
If the water sprinkler rotates a total of 25 degrees then pauses. How many degree cycles will it
go through for the rotation to reach at least 90 degrees?
Benchmark Angles
30 degrees, 45 degrees, 60 degrees, 90 degrees
Students should use their understanding of benchmark angles to develop mental images where they can
check their computation by understanding reasonableness of their answers.
Protractor
Before students begin using the protractor as a tool in 4th grade, they need to have experiences with
benchmark angles. They transfer their understanding that a 360 degrees rotation about a point makes a
complete circle to recognize and sketch angles that measure approximately 90 degrees and 180 degrees.
They extend this understanding and recognize and sketch angles that measure approximately 90
degrees and 180 degrees. They extend this understanding and recognize and sketch angles that
measure approximately 45 degrees and 30 degrees. They use appropriate terminology (acute, right,
and obtuse) to describe angles and rays (perpendicular)
Some references adapted from North Carolina and Arizona K-5 instructional documents
RPDP.net
Page 5