Fifth Grade

 

Measurement

 

Standard 5-5:  The student will demonstrate through the mathematical

                         processes an understanding of the units and systems of

                         measurement and the application of tools and formulas

                         to determine measurements.

 

The indicators for this standard are grouped by the following major concepts:

 

The indicators that support each of those major concepts and an explanation of the essential learning for each major concept follows.

 

Length

 

Indicator

5-5.1     Use appropriate tools and units to measure objects to the

precision of one-eighth inch.

 

In previous years, students have used appropriate tools and units to measure objects to the quarter inch. By fifth grade students have worked with simple rulers and tapes. They should extend their knowledge by making rulers with subunits or fractional units. Fifth grade students have had a variety of experiences with measurement. Therefore, the emphasis should now be on precision and appropriate units. For example, if the length of an object falls between say  and  then the student must understand that if the length is more than half way between  and  the length would be describe as . In essence, students are measuring to the nearest  of an inch because that is the half way point between  and . Simply giving students measuring tools and requiring that they measure in sixteenths is not sufficient to meet the expectation of this Indicator. It is knowing that if one needs to measure to the precision of one-eighth inch, using a measuring tool marked in sixteenths would be a better choice and why that is so.

A lesson that might be used as an introduction to the concept of precision might require that some students use rulers marked in fourths while other students use rulers marked in eighths. After measuring a variety of objects to the nearest eighth of an inch and recording the responses, the class might engage in a discussion as to which group had the more precise measurements and why. (The class should come to the conclusion that the smaller the measurement, the more precise.)

 

 

Connections To:

 

Other Fifth Grade Indicators

5-2.4               Compare whole numbers, decimals, and fractions using the symbols <, >, and =.

 

Since the connection to this indicator is self explanatory, no further explanation will be provided. For details regarding the essential learning for 5-2.4 see the Number and Operations standard.

 

 

Time

 

Indicator

5-5.6     Apply procedures to determine the amount of elapsed time in hours,

minutes, and seconds within a 24-hour period.

 

Fourth grade was the first time students were introduced to the concept of elapsed time. In fourth grade students applied strategies and procedures to determine the amount of elapsed time in hours and minutes within a 12-hour period, either a.m. or p.m.  Fourth grade students did not “cross” between a.m. or p.m. but rather worked within those 12-hour intervals to determine elapsed time. In fifth grade students should not only move between a.m. and p.m. (24-hour interval) but also must consider elapsed time down to seconds. 

A teaching strategy that could be used is to convert the circular measurement to a more linear measurement (similar to a ruler) since the students have experience measuring with rulers. To do so, take two strips of paper and mark them from 12:00 to 12:00. Each strip will be a different color, one representing a.m. and one representing p.m. Between each hour mark, make three smaller marks - each representing 15 minutes. Then demonstrate the use of the analog clock (hands need to be geared together so that the movement of the minute hand also show the movement of the hour hand) to show how much time has passed. Then connect the clock to the number-time line. This lesson can be extended to address smaller units of time.

 

Teacher Notes:  Even though students have had experience in previous grades with both the upper and lower case of A.M. and P.M. it is sound practice to continue to expose students to both forms.

 

Temperature

 

Indicator

5.5.7     Understand the relationship between the Celsius and Fahrenheit

temperature scales.

 

In previous grades students have read thermometers using Celsius and Fahrenheit Temperature scales. By the end of fifth grade students should know how to read both Celsius and Fahrenheit liquid and digital thermometers. Students need to know that the boiling point of water is 212˚ F and 100˚C and the freezing point is 32˚F and 0˚C. These two facts allow students to estimate and interpolate common temperatures such as hot days (above 95˚F or 35˚C), cold days (below 32˚F or below 0˚C), and comfortable days (80˚F or 25˚C). They should also become aware that the temperature considered hot, cold, or comfortable varies from place to place and depends on other weather conditions such as wind and moisture and on personal preference. The goal for this Indicator is not for students to memorize or convert between scales but to understand how the Celsius and Fahrenheit temperature scales relate to each other.

 

 

Angles

Indicator

5.5.2     Use a protractor to measure angles from 0 to 180 degrees. 

 

In third grade geometry students classified angles as either  right, acute, or obtuse. In fourth grade students compared angle measure with referent angles of 45 degrees, 90 degrees, and 180 degrees to estimate measures. Fifth grade is the first time students are introduced to the measurement tool protractor. A connection should be made between the fourth grade referent angles knowledge and the actual measuring which will enable students to avoid the common mistake and reading a protractor from the wrong direction when measuring angles.

 

 

Perimeter, Area, and Volume

 

Indicators

5-5.4    Apply formulas to determine the perimeters and areas of triangles,

rectangles, and parallelograms.

5-5.5   Apply strategies and formulas to determine the volume of

rectangular prisms.

 

In fourth grade students analyzed perimeters of polygons and generated strategies to determine the area of rectangles and triangles. In other words, students have had a variety of concrete experiences with perimeter and area of triangles, rectangles, and parallelograms. As a result, fifth grade students are ready to apply formulas to determine area and perimeters of triangles, rectangles, and parallelograms.

Fifth grade is the first time students are introduced to the concept of volume. However, the expectation is that students will progress from concrete to abstract problem solving situations that involve volume of rectangular prisms. Another important mathematical issue to consider is using the appropriate unit to describe volume versus perimeter or area. For example, when measuring area the unit should be expressed in square units and when measuring volume, cubic units should be used. It is extremely important that students understand when to use the appropriate unit and why that is so.

 

Equivalencies

 

Indicator

5-5.3     Recall equivalencies associated with length, liquid volume, and mass:

10 millimeters = 1 centimeter, 100 centimeters = 1 meter, 1,000 meters = 1 kilometer; 10 milliliters = 1 centiliter, 100 centiliters = 1 liter, 1,000 liters = 1 kiloliter; and 10 milligrams = 1 centigram, 100 centigrams = 1 gram, 1,000 grams = 1 kilogram.

 

In previous grades, students recalled U.S. Customary equivalencies associated with time, length, liquid volume, and weight. Fifth graders should recall metric equivalencies related to length, liquid volume, and mass. These metric equivalencies will be used when fifth grade students make conversions within the metric system.

 

Conversions

 

Indicator

5-5.3     Use equivalencies to convert units of measure within the metric

system: converting length in millimeters, centimeters, meters, and kilometers; converting liquid volume in milliliters, centiliters, liters, and kiloliters; and converting mass in milligrams, centigrams, grams, and kilograms.

 

In fourth grade students used equivalencies to convert units of measure within the U.S. Customary System. Fifth grade students will make conversions within the metric system. Fifth graders should have the understanding that when you change from one unit of measure to another, you need to know the relationship between the two units of measure.

Changing units in the metric system is like changing units in the customary system. But in the metric system, we use decimals instead of fractions and we don’t use mixed measures. Students should have experiences with the metric equivalencies cited in Indicator 5-5.3.