Measurement in Math and Science

Presented byFrank H. Osborne, Ph. D.

© 2015

EMSE 3123Math and Science in Education

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Nature of Science

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• Science is concerned with describing and learning about the natural world.

• Scientists learn by counting things, making observations and measuring things.

• Accurate, precise measurements are a must when seeking knowledge in a scientific way.

• Children need to be taught how scientists do their work so that they can learn these techniques the right way.

Measurement in Math and Science

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• Measuring length

• Measuring volume of liquid

• Measuring mass

• Measuring area and perimeter

• Measuring angles

• Measuring geometric volume

• Measuring temperature

Attributes of Objects

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• Objects have properties or attributes. These can be qualitative or quantitative.

• A qualitative property is an attribute that permits sorting into categories but cannot be measured. Example: male or female.

• A quantitative attribute can be measured. These include length, mass and volume.

Attributes of Objects

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• In Grade K, children are encouraged to describe measurable aspects of objects such as length or weight.

• Also, describe several measureable attributes of a single object.

• For example, they could be presented with a collection of wood blocks of varying length (and also mass as well). They see which is longest or shortest. They learn that a wood block has a length and a weight.

Attributes of Objects

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A Collection of Wood Blocks

Measuring Length

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• As children transition into first grade, they can devise their own ways of measuring.• They might use paper clips.• A line of paper clips could be used as a

measuring scale.

• Children guess the lengths of different objects then see how they measure on their measuring scale.

Measuring Length

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• Children estimate relative lengths of objects using their measuring scale.

Measuring Length

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• The objective is that the children express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end.

• They understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.

• Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.

Measuring Length

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When they learn that a paper clip is about one inch long they can begin to use the ruler.

Measuring Length

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• Grade 2 brings on measurement using the English and the Metric systems.

• The students will be able to measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

Measuring Length

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• They should also be able to measure the length of an object twice, using length units of different lengths for the two measurements, and describe how the two measurements relate to the size of the unit chosen. Remember that English and metric units are different in size.

Measuring Length

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• Estimate lengths using units of inches, feet, centimeters, and meters

• Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

• Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

Number Line

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• Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.

Measurement

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• Third grade brings the requirement to solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

• The student will be able to tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

Measurement of Liquid Volume

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• In laboratories, liquids are contained and stored in bottles.

• When working with liquids, several types of glassware are involved. They come in various sizes and capacities.

Measurement of Liquid Volume

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• The only accurate container used for measurement of liquid volume is the graduated cylinder. Beakers and flasks may have markings on them but they are not certified by the manufacturer to be accurate.

• Graduated cylinders are sized from 10 ml up to 1000 ml. They always give you the volume of the liquid in ml (milliliters). • There are 1000 ml in one liter (l).• One ml is exactly the same as one cc (cm3)

Measurement of Liquid Volume

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• When reading a graduated cylinder you need to pay particular attention to the meniscus.

• An interesting property of water is that it prefers to stick to other objects than itself. So it begins to run up the insides of the cylinder and make a curved bottom surface, the meniscus.

Measurement of Liquid Volume

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• To read the graduated cylinder, hold the meniscus at eye level and sight across the bottom.

Measurement of Liquid Volume

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• Children need to be taught starting early on that measurement of any kind, be it volume, length or mass has to be done slowly and deliberately.• If we can instill good, slow, accurate technique

in the children when they start learning these things, it will make their later work more successful.

• Speed and sloppy habits go together and should be avoided. Measurement is not done at video game speed.

Measurement of Mass

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Difference Between Mass and Weight•Mass is the amount of matter in an object.

•In the figure, the largest mass is 250 g. It also weights 250 g because we are on Earth. On the Moon it would still be 250 g of mass but it would weigh less because the Moon’s mass is less.

Measurement of Mass

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We measure mass using a balance.There are various types of balances.

Measurement of Mass

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Measuring the mass of an object•To measure the mass of an object:

– Place the object on the pan. The balance arm will raise up.

– Slide the large 100 g weight until the arm drops. When the arm drops to the bottom, it is too heavy, so back up one unit. Repeat for the 10 g weight, then for the 1 g weight until the arm balances.

Measurement of Mass

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How to weigh out chemicals•To weigh out amounts of chemicals:

– Use a plastic weighing dish or a beaker.– Slide the weights until it balances. This is called

the tare weight.– Scoop out small amounts of material from its

container using a spatula.– Never pour powders or salts.– It makes a mess and you will undoubtedly dump

too much into the container.– Never, never scoop materials back into the

container once they have been taken out.

Measurement of Mass

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Making a 5% solution of sodium chloride•Example: We wish to make a 5% solution of sodium chloride (table salt). •Here are the materials we will need.

Measurement of Mass

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Making a 5% solution of sodium chlorideProcedure: 1.Balance the 250-ml beaker to tare it. Rule is to contain a volume of liquid solution, use a container at least twice the final volume.2.Slide the 1-g slide over 5 grams so that the beaker side is 5 g too heavy.3.Using the spatula, carefully add sodium chloride crystals, little by little, until the balance arm returns to the balanced position.

Measurement of Mass

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Making a 5% solution of sodium chlorideProcedure: 4.Remove the beaker from the balance.5.After placing the beaker on the work bench, carefully pour in the 100 ml of water and stir it with the stirring rod until the sodium chloride dissolves. Never stir with a thermometer.6.Result: 100 ml of a 5% sodium chloride solution.

Measurement of Area

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Area is measured in square units•We begin with the concept of a unit square. •A square with a side length of 1 unit is called a unit square and it has one square unit of area.•We measure area by finding out the number of unit squares it would take to fill the space.

Measurement of Area

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Area is measured in square units•A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.•In the figure, the larger figure is completely covered (tiled) by 12 unit squares.

Measurement of Area

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Area is measured in square units•The units of area depends on the length of the side of the unit square.

•Use the size that is most convenient for the area you are measuring.

English System Metric SystemLength Unit Square Unit Length Unit Square Unit

Inch (in) Square Inch (in2) Millimeter (mm) Square Millimeter (mm2)

Foot (ft) Square Foot (ft2) Centimeter (cm) Square Centimeter (cm2)

Yard (yd) Square Yard (yd2) Meter Square Meter (m2)

Mile (mi) Square Mile (mi2) Kilometer Square Kilometers (km2)

Measurement of Area

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Perimeter is an Attribute of Plane Figures•Among the attributes of plane figures is shape as we have learned. •We have just studied that plane figures have area.•Another is perimeter. We obtain the perimeter of a figure by adding the lengths of all of its sides.•Perimeter is reported using linear units, not square units.

Measurement of Angles

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• An angle is a geometric shape that is formed by two rays when they share a common end point.

• They form an angle that can be measured with a protractor.

• This one is 60ْ.

Measurement of Geometric Volume

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• Geometric volume is measured in cubic units in the same way that area is measured in square units.

• The starting point is the unit cube. We used it when we studied density. In this example, the units are cm.

Measurement of Geometric Volume

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• We also used Dienes Blocks which can also represent volume.

Measurement of Temperature

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• Temperature is measured using a thermometer.

• School children will need to be able to use both the Celsius and Fahrenheit Scales.

Measurement of Temperature

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Using a Laboratory Thermometer•Some children may be acquainted with the household medicinal (clinical) thermometer.

•It has a constriction so that the mercury does not retract into the bulb after it is removed from the patient.•It has to be shaken down before use.

Measurement of Temperature

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• A laboratory thermometer will measure the temperature to which the bulb is exposed.

• It does not have a constriction so it is never shaken to return the liquid to the bulb.

• Room temperature is about 22ْC.• Let us say that you are to measure chilled water

at a temperature of 9ْC. You have to leave the thermometer in the container of water and bend down to read it.

Measurement of Temperature

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• When measuring the temperature of the 9ْC water with a laboratory thermometer, taking it out to bring it to eye level will cause the bulb now to be in 22ْC air and it will give a false reading because it will warm up.

• Clinical thermometers have a scale reading a from a few degrees below to a few degrees above human body temperature. They can be in either Fahrenheit or Celsius degrees.

Measurement of Temperature

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• Laboratory thermometers are always in Celsius degrees and are range from about -20ْC to about 110ْC.

• Always remember that the bulb needs to be in constant contact with the substance whose temperature is being measured.

The End

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