# Measurement and data

Contents

If you think about it, we measure almost everything: time, distance, size, weight, volume, etc. Every THING can be measured. The question is, what unit of measurement is used and how is that unit constructed, compared, and converted? This last part is what we explore in these tutorials.

## Volume intro

Welcome to the 3rd dimension! [cue spooky music] This tutorial explains how to find volume.

7:51

Intro to volume

Sal introduces volume and compares it to length and area. He also introduces cube units.

Exercise

Volume with unit cubes 1

Find volume of 3-dimensional figures by counting unit cubes.

7:22

Measuring volume as area times length

Sal transitions from measuring volume with unit cubes to multiplying area time length.

Exercise

Volume formula intuition

Practice problems that help you see why the volume formula makes sense.

Exercise

Compare volumes with unit cubes

Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

## Finding volume

This tutorial has us calculate the volume of rectangular prisms.

1:59

Volume of a rectangular prism

Sal finds the area of a rectangular prism with labeled side lengths.

Exercise

Volume 1

Find volume of a rectangular prism with labeled side lengths. Find a missing side length on a rectangular prism when given the volume.

3:19

Volume in unit cubes by decomposing shape

Find volume of a rectangular prism with labeled side. Find a missing side length on a rectangular prism when given the volume.

3:49

Volume through decomposition

Sal finds the volume of an irregular 3D figure by breaking the figure into 2 rectangular prisms and finding the volume of each part.

Exercise

Decompose figures to find volume

Find the volume of irregular 3D figures by dividing the figures into rectangular prisms and finding the volume of each part.

4:40

Volume word problem: water tank

Sal using volume of a rectangular prism to solve a word problem.

Exercise

Volume word problems

Find volume of rectangular prisms to solve word problems.

## Unit conversion

Wait, I'm in Europe and my car only tells my distance traveled in kilometers! But I'm used to a units of distance devised by the Romans to measure the average length of 1000 paces of a soldier (the "mile")! How do I operate? This tutorial is about the fundamental skill of unit conversion. Sal's cousin Nadia being a bit confused with this was actually the reason why he started tutoring her (which led to the creation of the Khan Academy). Common Core Standard: 5.MD.A.1

4:54

Converting units: minutes to hours

Sal converts 549 minutes to hours.

4:02

Converting units: metric distance

Sal orders 1 decameter, 13 meters, 15,000 millimeters, and 1900 centimeters from least to greatest.

3:04

Converting units: centimeters to meters

Sal converts 37 centimeters to meters.

Exercise

Convert units (metrics)

Convert between metric measures of distance, volume, and mass.

5:17

Converting units: US volume

Sal converts 3 1/2 gallons to cups.

5:23

Adding units of volume

Sal adds 16 fluid ounces + 3 pints + 4 quarts.

5:48

Same length in different units

Sal shows how we can describe the length 4.5 yards in a variety of different units.

Exercise

Convert units (US customary)

Convert between US customary measures of distance, volume, and mass.

## Unit measurement word problems

Now that you have some experience converting between units, let's apply that skill in some real-world problems (okay, some of them are a bit concocted, but it's all about the learning)! We'll tackle word problems that deal with distance, weight, volume, time, and more! Common Core Standard: 5.MD.A.1

3:38

Time word problem: Susan's break

Sal solves a time word problem and involves converting hours and minutes.

4:05

Measurement word problem: tea party

Sal solves a metric volume word problem involving milliliters and liters.

Exercise

Convert units word problems (metric)

Solve word problems that involve converting between metric measures of distance, volume, and mass, as well as measures of time.

4:14

Measurement word problem: distance home

Sal solves a US customary distance word problem involving yards and feet.

3:29

Measurement word problem: blood drive

Sal solves a US customary volume word problem involving pints and gallons.

7:08

Measurement word problem: elevator

Sal solves a US customary mass (weight) word problem involving pounds and tons.

8:04

Measurement word problem: running laps

Sal solves a US customary distance word problem involving miles, yards, and feet.

Exercise

Convert units word problems (US customary)

Solve word problems that involve converting between US customary measures of distance, volume, and mass.

## Data

Unit conversion and data points on a line plot.

6:08

Line plot distribution: trail mix

Sal uses different bags of trail mix to find the amount of trail mix each bag would contain if the total amount in all the bags were redistributed equally.

Exercise

Interpret dot plots with fraction operations

Interpret fraction data on dot plots to solve word problems.