3rd Grade Measurement

Third Grade Standards for Measurement• 4.M.1      Demonstrate an understanding of such attributes as length, area,

weight, and volume, and select the appropriate type of unit for measuring each attribute.

• 4.M.2      Carry out simple unit conversions within a system of measurement, e.g., hours to minutes, cents to dollars, yards to feet or inches, etc.

• 4.M.3      Identify time to the minute on analog and digital clocks using a.m. and p.m. Compute elapsed time using a clock (e.g., hours and minutes since…) and using a calendar (e.g., days since…).

• 4.M.4      Estimate and find area and perimeter of a rectangle, triangle, or irregular shape using diagrams, models, and grids or by measuring.

• 4.M.5      Identify and use appropriate metric and English units and tools (e.g., ruler, angle ruler, graduated cylinder, thermometer) to estimate, measure, and solve problems involving length, area, volume, weight, time, angle size, and temperature.

Why Do We Measure?

Measuring things helps us answer the questions:

• How big?

• How long?

• How much?

What Do We Measure?

We measure

• Time

• Length & perimeter

• Area

• Capacity & volume

• Weight

Every Measurement Has Units

A measurement always has units. For example, we measure time in millennia, centuries, decades, years, days, weeks, and hours. Without the unit, we don’t know how much time has passed. The units that go with our measurements tell us what we are measuring and how much we have.

Measuring Time

We measure time using clocks and calendars.

The big, dark hand tells us the minute. The small, dark hand tells us the hour, and the long, gold hand tells us the second.

Sunday Monday Tuesday Wednesday Thursday Friday Saturday1 2 3

4 5 6 7 8 9 1011 12 13 14 15 16 1718 19 20 21 22 23 2425 26 27 28

Febuary 2007

Calendars tell us what day each date is on and can help us keep track of how many days have gone by.

Time UnitsSeconds The smallest unit of time on a clock

Minutes There are 60 seconds in one minute.

Hours There are 60 minutes in one hour.

Days There are 24 hours in one day.

Weeks There are 7 days in one week.

Months The number of days and weeks in a month is different for each month.

Years There are 365 ¼ days in one year.

Decades There are 10 years in one decade.

Centuries There are 100 years or 10 decades in one century.

Millennia There are 1000 years, 100 decades, or 10 centuries in one millenium.

Measuring Length

We measure length with a ruler. Each ruler is divided into units. When using a ruler, line up the edge of the ruler with the start of the line or side you are measuring and read the line where the side or object ends.

Length is the size of a straight line, distance, or straight edge on an object.

So this rectangle is 4 6/10 of a cm long or 4.6 cm long.

Units for Length

There are two major units for measurements:

Metric units are used all over the world.

The base unit is the meter. All other units are meters multiplied or divided by a power of 10.

1 centimeter (cm)=10 millimeters (mm)1 meter (m)=100 cm=1000 mm

1 kilometer=1000 m=100,000 cm=1,000,000 mm

Customary Units for Length

U.S. customary units are only used in the U.S.

The smallest unit is the inch, but on a ruler, an inch can be divided up into smaller pieces—halves, quarters, eighths, sixteenths, even thirty-seconds!

1 foot (ft.)=12 inches (in.)

3 ft.=1 yard (yd.)

1760 yds.=1 mile (mi.)

5,280 ft.=1 mi.

Moving Between Units Sometimes you start out with one kind of unit, but you need another unit. For example, you might have 6 feet but want to know how many yards you have. Take one of the equations from before—in this case,

3 ft.=1 yd.Since you are starting with feet, you divide the number of feet by 3 to find out how many yards there are. If you had started out with the number of yards, you would have multiplied that number by 3 to get the number of feet.

Moving Between Units

In general, if you are moving from the unit with the larger number (the smaller unit) to the unit with the smaller number in the equation (the larger unit), you will divide by the larger number to get to the next unit. If you are moving from larger unit to the smaller unit, you will multiply by the larger number to get the new unit.

Moving Between Metric and Customary Units

You can also change units from metric units to customary units and from customary units to metric units using the same methods and these equations.

1 in.=2.54 cm1 ft.=0.305 m1 yd.=0.914 m1 mi.=1.61 km

Measuring PerimeterPerimeter is the distance around the sides of an object or space.

To find the perimeter of a shape, add the lengths of each of the shape’s sides together. This sum is the perimeter of the shape.

Because you are adding up units of length, the unit of a perimeter will be the same as the units used to measure the length.

Measuring AreaArea tells us how many squares you can lay out on a flat surface like a

shape.

To find the area of a• Rectangle: multiply the length of the object by its width• Triangle: Multiply the length of the triangle’s base by its height• Different Shape: Cut the shape into rectangles and triangles. Add the

areas of these shapes to get the total area of the shape.

Units: You are measuring area in squares, so your units must also be squares—square inches (sq. in.), square meters (m2), etc. Basically take the units that the length was measured in and let us know that they are now squares.

Capacity & Volume

Capacity is how much you can fill a space with. We usually talk about capacity with empty containers.

Volume is how much space an object takes up. We talk about volume with both solid objects (no empty spaces) and with empty containers.

Measuring Capacity and Volume

One way to measure the capacity or volume of an object is by using the lengths of the height and the sides of the base to find the volume of the solid. You will learn about this in later grades.

Another way to measure volume is to find out how many cubes of the same size you can fit into the object.

The other way you can measure the capacity or volume of an object is to find out how much liquid you can fill it with.

Units for Measuring Volume with Cubes

Your units in volume with always be cubic units. If you know the length of the sides of your cube, you use that unit and show that it is a cube.

For example, if each side of your cube is 1 cm long, your unit will be cubic centimeters (cm3).

If each side of your cube is 1 in. long, your unit will be cubic inches (cu. in.).

Measuring LiquidsWe use measuring cups to measure liquids. When using a measuring cup, make sure you hold the level of the water in your line of sight or crouch down until the water line is in your line of sight and read the line that that water goes up to.

Customary Units for Measuring Liquids

1 cup (c.)=8 fluid ounces (fl. oz.)

2 c.=1 pint (pt.)

2 pts.=1 quart (qt.)

4 qts.=1 gallon (gal.)

Like with metric units for length, all units are the base unit (in this case the liter) multiplied or divided by a power of 10.

The main units you will use in measuring liquids will be milliliters and liters.

1,000 milliliter (mL)= 1 liter (L)

A little connection with volume of solids:

1mL=1 cubic centimeter (cc)

Metric Units for Measuring Liquids

Moving Between Customary and Metric Units for Measuring

Liquids

1 fl. oz.=29.57 mL

1 gal.=3.785 L

1 mL=0.034 fl. oz.

1 L=0.264 gal.

Measuring Weight

When most people talk about weight, they are really talking about mass—or how much matter or “stuff” is in something. Measuring an object’s weight tells us how much matter is in it.

We measure weight on scales and balances.

Using Scales and BalancesWhen using a scale like this one, make sure the scale is always set to 0 before you weigh anything. Once you put the object on the scale, the scale will show you how much it weighs.

There are two kinds of balances. With this kind of balance, you put the object in one dish and put weights in the other dish. When the two dishes are balanced, you add the weights in the other dish to find the weight of the first object.

With this kind of scale, you put the object onto the dish and move the sliders along the three rulers. When the line at the end of the arm lines up with the line on the right side of the balance dish, you add up the values on the rulers to find the weight of the object.

Customary Units for Weight

The smallest unit is the ounce, although it can also be broken into smaller pieces or fractions of an ounce.

16 ounces (oz.)=1 pound (lb.)

2000 lbs=1 ton (T.)

Metric Units for Weight

The base unit is the gram, and all other units of weight in the metric system are grams multiplied or divided by powers of 10.

1000 milligrams (mg)= 1 gram (g)

1000 g=1 kilogram (kg)

Moving Between Customary and Metric Units for Weight

1 oz=28.35 g

1 lb=0.454 kg

1 g=0.035 oz.

1 kg=2.202 lbs.