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 teaspoon equals four quarters of a teaspoon. 1tsp. = 4 X

14

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 = l x w

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

Students will work with fractions by measuring objects in unit fractions (12 , 14 ,18 ) and recording the

data 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

The connection of angles and circular measurement. An angle that turns through 1360 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

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

reflex angle between 180 degrees and 360 degrees

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