1. Measuring Metric Length
MEASURING SMALL ITEMS
Small objects are measured in cm or mm.
How many mm are in 1 cm?
1 cm = _______ mm
When measuring small objects, measure to the nearest mm.

2. USING A METRIC RULER Start from 0! Read first to the nearest cm.
The numbers are cm
Read next to the nearest mm
The small, numberless lines are mm.
This red tape is 2.3 cm long

3. READING A METRIC RULER

4. LET’S PRACTICE!
Did you say 5.1 cm?

5. LET’S PRACTICE!
Did you say 7.1 cm?

6. Volume

7. Volume
The amount of space an object takes up

8. CALCULATING VOLUME OF RECTANGULAR SHAPED SOLIDS
Calculate the volume using the formula:
Volume=L x W x H
(length x width x height)
Width = depth
Make sure you also multiply the UNITS (cm x cm x cm = cm3 )

9. UNIT FOR VOLUME OF SOLIDS
objects with small volumes use cm3 (cubic centimeter)
1 cm3 is equal to the volume of a cube that measures 1cm on each side.
Objects with large volumes use m3 (cubic meters)
1 m3 is equal to the volume of a cube that measures 1m on each side.

11. HOW DO WE FIND THE VOLUME OF THIS?
Treat it like 2 rectangles.
Find the L, W and H for BOTH rectangles.
Calculate volume for both rectangles using L x W x H.
ADD them together.

12. Rectangle 1:
L = 80 mm, W = 10 mm,, H = 20 mm
80 x 10 x 20 = mm3
Rectangle 2:
L = 20 mm, W = 10 mm, H = 40 mm
20 x 10 x 40 = mm3
Total Volume
mm mm3 = mm3

13. VIDEO INSTRUCTION
Optional Video – Calculating Volume

14. SIGNIFICANT FIGURES
When calculating volume, your FINAL answer can have no more decimals than your LEAST accurate measurement.
So, YOU MUST ROUND!
If you are measuring to the nearest millimeter, your answer should have ONLY 1 decimal point.
Example: 1.5 cm x 1.5 cm x 1.5 cm = cm3
This answer is not possible.
If we can only measure with a ruler to the mm place, the answer CANNOT be beyond the mm place.
Therefore, the correct answer would be 3.4 cm3

15. Volume
Volume of Liquids

16. UNIT USED TO MEASURE LIQUID
base unit for liquid is Liter (L)
Small volumes are measured in milliliters (mL)
1000 mL = 1 L
(which you should know from practicing unit conversions!)

17. MEASURING VOLUME OF A LIQUID
Tool used to find liquid volume is Graduated cylinder.
Rules for Reading a Graduated Cylinders
Place on flat surface.
Read from the bottom of the meniscus.
Get to eye level with the level of the liquid.

18. Meniscus
The curve in the top surface of liquid in the graduated cylinder

19. CALCULATING VALUE OF LINES ON GRADUATED CYLINDER
Find the difference between the labeled sections.
Divide by number of sections between them.

20. READING A MENISCUS - PRACTICE
Read the milliliter marking at the bottom of the curve
What is the value of each line on this cylinder?
What is the volume of liquid in this cylinder?

21. MORE PRACTICE! Difference between the marked lines 25-10 = 10 ml
Number of sections between 10
10 / 10 = 1
Value is 1 mL

22. HOW TO READ A GRADUATED CYLINDER - VIDEO
What is the value of each line on these cylinders?
What is the volume of these cylinders?

23. TICKET OUT Liquid Volume
What is the name of the tool used the measure liquid volume?
What is the metric base unit for liquid volume?
What is the base unit for smaller amounts of liquid?
What is the volume of the liquid in the cylinders below? B C A

24. Volume of Irregular Solids

25. FINDING THE VOLUME OF AN IRREGULAR SOLID OBJECT
Use the water displacement method
Steps
Pour water to an even value in a graduated cylinder.
Record amount as V1.
Carefully slide the object into the water. Record the volume as V2.
V2 - V1 = Volume of Object
FINDING THE VOLUME OF AN IRREGULAR SOLID OBJECT

26. How does the water displacement method work?
Video on Displacement

27. UNIT FOR IRREGULAR OBJECT ?
Use cm3 for small irregular shaped objects.
How can something solid be measured in mL?
1 cm3 = 1 mL
UNIT FOR IRREGULAR OBJECT ?

28. LET’S PRACTICE
Find V1
Find V2
V2-V1= ?

29. MASS
Mass is a measure of the amount of matter an object contains.

30. UNITS OF MASS
The basic unit of mass in the SI system is the kilogram (kg).
Best for measuring the mass of people, cars, or bicycles.
For smaller units use grams (g)
Best for measuring mass of small objects like paperclips and cell phones

31. MEASURING MASS
To find the mass of an object use a triple beam balance.
It compares the mass of the object you are measuring to a known mass.

32. THE DIFFERENT PARTS OF THE TRIPLE-BEAM BALANCE.
Beams
Pan
Riders
Pointer

33. USING A TRIPLE BEAM BALANCE
Set balance to 0.
Place the object on the pan
Shift the riders on the beams until they balance the mass of the object
Start with the large rider (increments of 100)
Next, the medium sized rider (increments of 10)
Lastly, the small rider (increments of 0.1)

34. MASS VS. WEIGHT
Weight is a measure of the force of gravity acting on an object.
Mass measures the amount of matter an object contains, it remains constant.
W = mass x gravity
Weight can CHANGE.

35. Density

36. Density
The measure of how much mass is contained in a given volume

37. WHAT EXACTLY IS DENSITY?
Think about it as how heavy something is for it’s size.
Compare a basketball and a bowling ball. They are the same size but the bowling ball has more mass.
So which has more density?

38. CALCULATING DENSITY
Density = Mass / Volume ( D = m/v )

39. UNIT FOR DENSITY
Because density is actually made up of two other measurements (mass and volume) an objects density is expressed as a combination of two units
Density of Solids
g/cm³ (you say it as grams per centimeter cubed)
Density of Liquids
g/mL (you say it as grams per milliliter)

40. DENSITY TRIANGLE
If you know two of the three measurements in the density triangle, you can solve for the third.
Cover the measurement you want to solve for and you are given the formula necessary for solving the problem.
Example: Cover the D and you are left with m/v.
Cover the M and you are left with D x V. To solve for mass use the formula M = D x V
Cover the V and you are left with M/D. To solve for volume use the formula V = M/D

41. DENSITY TRIANGLE PRACTICE SOLVE for Volume D = 10 g/mL M = 100 g
Solve for Mass
V = 25 mL
D = 100 g/mL
Solve for Density
V = 10 cm3
M = 150 g

42. DENSITY “RULES” Density is a characteristic property of a substance.
All samples of a specific substance will have the same density. It doesn’t matter how big or small the sample is.
Density can be used to identify what a substance is. It is very useful!
Example (find the density):
1 cm3 of gold has a mass of 19.3 g.
2 cm3 piece of gold has a mass of 38.6 g.
Density of common substances
Ice- 0.9 g/cm3
Water- 1.0 g/mL
Aluminum- 2.7 g/cm3
Gold g/cm3

43. Densities of Some Common Substances
Figure 6: Applying Concepts: How could you use density to determine whether a bar of metal is pure gold?
Densities of Some Common Substances
Substance
Density
(g/cm³)
Air
0.001
Ice
0.9
Water
1.0
Aluminum
2.7
Gold
19.3
If the bar of gold has a density that is greater than or less than 19.3 g/cm³, then the sample is not pure gold.

44. FACTORS THAT AFFECT DENSITY
Add “something” to a liquid or gas to increase it’s density.
Ex. Adding sugar or salt to water
Temperature – increase the temperature and the density will decrease.
“warm air rises”
Changing the pressure.

45. FLOATING AND SINKING
An object will float if it is less dense than a surrounding liquid.
An object will sink if it is more dense than a surrounding liquid.
The density of water is 1 g/mL.
If an object has a density of greater than 1 g/mL it will sink in water.
If an object has a density less than 1 g/mL it will float in water.