Lines, Angles & Shapes_Measuring Our World

In this lesson, you will make observations and learn how to

make precise calculations and measurements.

Lines, Angles & Shapes:

Measuring Our World

The yellow area is larger.

The white area is larger.

They are equal.

​

​Is there more yellow or more white?

​No fancy math is needed.

We need to look at the shapes differently.

The small squares are half white and half yellow.

The shape on the left

The shape on the right

The fractions are the same.

​

Sometimes shifting perspective on the size of a figure can be very helpful.

​Which checkerboard has a bigger fraction of its area made of white squares?

Sometimes in life, precise measurements are required.

But we also do a lot of estimating in measurement,

often without numbers at all.

For example, you can’t build a strong foundation of a building without being able to make a proper square.

Imagine this: you are driving a car.

Your brain is constantly measuring the distance between your car and the car in front of you.

Open Ended

Write three examples of a measurement that is the distance between two points.

Multiple Choice

What do we use a meter stick to measure?

• volume

• distance/length

• mass

• weight

Multiple Choice

William measured the distance from the door knob to the floor and got 1 meter.  What tool did he use?

• meter stick

• thermometer

• graduated cylinder

• electronic scale

Multiple Choice

John measured the width of a quarter.  What unit did he use?

• meter

• kilometer

• millimeter

• centimeter

Multiple Choice

What would you call a number that is not exact, but a careful guess?

• Estimate

• Dimensions

• Width

• Height

Multiple Choice

What do we call the length of a path between two points?

• Width

• Height

• Depth

• Distance

Multiple Choice

What is the size or length of something established by measuring?

• Measurement

• Measure

• Estimate

• Yard

Multiple Choice

What are measurements in length, width, height and depth?

• Distance

• Inches

• Dimensions

• Graduations

Multiple Choice

What is the measurement of from base to top?

• Heigth

• Depth

• Width

• Length

Multiple Choice

What is the measurement of something from side to side?

• Height

• Width

• Depth

• Length

Multiple Choice

What is the measurement of something from front to back?

• Heigth

• Width

• Depth

• Length

Multiple Choice

Which of these would best be called the distance between two points?

• Height

• Length

• Depth

• Width

You can think of the number of people coming and how much space they’ll need to dance. And you can move the furniture to clear a dance floor without a ruler or tape measure in your hand.

​

​Imagine this: Imagine you are having a party in your apartment and you expect there to be dancing.

Open Ended

Write three examples of a measurement that is the size of a surface.

Multiple Choice

Which measurement would you use to measure the following?
the length of the science room

• meters

• liters

• grams

• kilometers

Multiple Choice

What does area mean?

• the distance around a shape

• half the distance around a shape

• the amount of space outside a shape

• the amount of space inside a shape

Multiple Choice

The __________ is the space occupied by a shape.

• area

• perimeter

Multiple Choice

What is the formula for the area of a triangle?

• A=bh

• A=lw

• A=s²

• A=1/2(bh)

Multiple Choice

What is the formula for the area of a parallelogram?

• A=bh

• A=lw

• A=s²

• A=1/2(bh)

Multiple Choice

The space inside an 2-D object is called its ____________________.

• area

• perimeter

• volume

• circumference

Multiple Choice

Find the area of the square.

• 49 mi²

• 28 mi²

• 14 mi²

• 21 mi²

Multiple Choice

What is the area of a square with a side length of 4 cm?

• 1 cm2

• 16 cm2

• 8 cm2

• 2 cm2

After dinner, when you look through your tupperware to choose the right size container for your leftovers, how do you know which one to choose?

​

​Imagine this:

Open Ended

Write three measurement examples that talk about the space inside an object.

Match

Match the following

• $$A=\pi r^2$$

• $$V=\pi r^2h$$

• $$A=base\times width$$

• $$V=base\times width\times height$$

Area of a circle

Volume of a circle

Area of a rectangle

Volume of a rectangle

• Area of a circle

• Volume of a circle

• Area of a rectangle

• Volume of a rectangle

Multiple Choice

What is the volume of this cube?

• 10

• 1,000

• 1,500

• 75

Multiple Choice

What is the volume of a cube with the following dimensions: L=10ft, W=10ft, W=10ft

• 100 ft^3

• 1000 ft³

• 1000 ft²

Multiple Choice

These stacks of pennies both have the same amount of coins in each stack. Do the stacks have the same volume? Why?

• No

• Yes because they have the same height

• Yes because they have the same cross-sectional area at every plane parallel to the base

length is one dimension

measured in units

the area is two dimensional

measured in square units or units²

volume is three dimensional

measured in cubic units or units³

​The situations describe three categories of measurement (length, area, and volume)

​

Match

Imagine the following situations and decide whether each is a

the measure of length, area, or volume.

• The distance from the floor to the ceiling

• The number of tiles needed to cover a bathroom floor

• The distance between my car and the car in front of you on the highway

• Your height

• The size of a coffee mug - how much liquid it will hold

length

area

length

length

volume

• length

• area

• length

• length

• volume

Match

Which would you use to measure length, area, or volume?

• volume

• area

• volume

• length

• area

The space inside a Tupperware container

The amount of skin on your body

The size of a tupperware container needed to store leftovers

The distance between The Empire State Building and Niagara Falls

The number of tiles needed to cover a bathroom floor

• The space inside a Tupperware container

• The amount of skin on your body

• The size of a tupperware container needed to store leftovers

• The distance between The Empire State Building and Niagara Falls

• The number of tiles needed to cover a bathroom floor

Match

Which would you use to measure length, area, or volume?

• The total land in New York state

• The size of a room

• The amount of water a bathtub can hold

• The size of a room

area

length

area

volume

length

area

volume

• area

• length

  area

• volume

• length

  area

  volume