Commutative and associative properties

As you have seen in our math classes, we've been studying the properties of numbers. So, let's take a look at them:

• The Commutative Property of Addition and Multiplication

3 + 2 = 2 + 3

(5 = 5)

3 x 6 = 6 x 3

(18 = 18)

If you change the order of the numbers, the results won't change.

Remember: You can only use the Commutative Property with Addition or Multiplication. Don't use it with Subtraction or Division.

• The Associative Property of Addition and Multiplication

(2 + 3) + 7 = 2 + (3 + 7)

(5) + 7 = 2 + (10)

12 = 12

(2 x 3) x 4 = 2 x (3 x 4)

(6) x 4 = 2 x (12)

24 = 24

Moving the parentheses will not affect the results.

Let's Practice

Use the commutative property to solve the equations:

a) 2 x 3 x 2 = 2 x 2 x 3

b) 3 + 4 + 12 = 3 + 12 + 4

c) 32 x 2 = 2 x 32

d) 44 + 3 + 15 = 44 + 15 + 3

 

 

Now use the associative property to solve:

a) (123 + 3) + 23 = 123 + (3 + 23)

b) (9 x 8) x 2 = 9 x (8 x 2)

Order of Operations

Welcome back for our new term!!! Hope you had a great holiday.
 

This week we've begun studying the Order of Operations. Why is it important? Because if we don't follow the order we may not come to the right solution.

 

There are two ways to help you remember, choose the one you prefer:

 

Please excuse my dear Aunt Sally

   or

                                                PEMDAS

 

 

P - parentheses

E - exponents

M - multiplication

D - division

A - addition

S- subtraction

 

 

Let's give it a try. Solve:

 

 

2 - 2 x 2 + 2 = ?

 

1st: 2 x 2 = 4

 

2nd: 2 - 4 + 2 = 0

 

The answer is 0.

 

 

Here are some more. Post your answers!!!

 

a) 9 - (2 x 3) + 15 : 3 = __________

 

b) 8 x (4 + 3) - 46 = __________

 

c) 12 : 3 - 3 + 2 x 6 = __________

Perimeter, Area, and Volume

What are the three dimensions when you watch a 3-D movie? Have you ever thought about it? We say a movie is 3-D when it seems to have length, width, and depth. It is almost as if you could touch the scenes.
In class, we've read the book Perimeter, Area, and Volume - A Monster Book of Dimensions by David A. Adler and discussed some dimensions.

Each one of us has three dimensions, we are not flat.

We also discussed the use of measurement units when we talk about perimeter and area. We saw that when we measure the perimeter, we use metric or US standard units like: cm, m, km, in, ft, yd... And, when we measure area we use square units of measurement like: cm², ft², m², in²...

Hope you've enjoyed our measurement classes. We'll start a new topic soon.

See you ;) Ms. Sarah Giansante

Metric vs US customary measurement units

   For the past few weeks we've been studying the US customary measure units. Now it's time to compare these units to the Metric System we use in Brazil.

      The Metric System, also known as International System, is based on a decimal system of measurement using multiples of ten.

Units of length

Here's a chart comparing the metric units and the US customary units:

 

 

Units of liquid volume

 

 

     Now, compare the metric units and the US customary units:

 

 

Units of weight

 

       And what about the units to measure weight?





 

 

 

US customary units: weight

     How much does an elephant weigh? 

In the US customary measurement system we use units like onces (oz), pounds (lb), and tons (T) to measure weight. So, in your opinion which unit would be more appropriate to weigh an elephant?

     As we've seen in our classroom we can convert these units (ounces to pounds, pounds to tons...) using some standards:

     So remember these and you'll be fine:

1 ton = 2,000 pounds

1 pound = 16 ounces

Homework

Activity adapted from http://www.superteacherworksheets.com/

Send your answers until Tuesday - May 28th.

Way to go guys!

US Customary units: Liquid Volume

When we want to measure water, juice, milk, soda, and other liquid we can use units such as: gallons, quarts, pints and cups.

Today in the classroom, Grade 6 made Mr and Mrs Gallon to illustrate the relationship among these units. Here are the results:

So we learned that:

1 pint (pt) = 2 cups (c)

1 quart (qt) = 2 pints (pt)

1 gallon (gal) = 4 quarts (qt) = 8 pints (pt) = 16 cups (c)

Homework

Use the GallonBot illustration to help you answer the questions.

a. Which is greater: a quart or a pint? ________________

b. Which is less: a cup or a pint? ____________________

c. How many pints are in 2 quarts? __________________

d. How many cups are in 3 pints? ___________________

e. Which is greater: 8 cups or 1 quart? ________________

f. Which is less: 4 quarts or one gallon? _______________

Activity adapted from 

http://www.superteacherworksheets.com

Post your answers until Tuesday - May 21st

Good job Hedra, Daniel, Danielly, Julia C., Guilherme, Julia B. and Nathan!!

US Customary units : Length

Customary units or US Standard Units are the units of measurement that are used in the United States; different from the metric units used here in Brazil.

The first Customary units that we'll learn are the ones we use to measure length. These measures can answer questions such as: How tall are you? How big is your table? How wide is the classroom board?

We'll talk about inches (in.), feet (ft.), yards (yd.) and miles (mi.).

• inches are small units of length. The last joint of your finger or thumb is about 1 inch (depending on how big your fingers are!). Lots of things are measured in inches from rainfall to paper length.

       If you have 12 inches of something, you have a foot.

       

                       12 inches = 1 foot

• A long time ago, people had to use their own feet to measure things.  However, since everyone has different sized feet, it did not let everyone understand the size or distance in the same way. 

Using 12 inches put together to make feet allows for everyone to have a more accurate picture of what exactly a "foot" of length is.

• If you have 3 feet together, you have a yard.

3 feet = 1 yard

• When you put together 1,760 yards, you have a mile. 

1,760 yards = 1 mile

Miles are long distances and are mostly used to measure the distance between places which are far away from each other.  Most people refer to miles when they are driving, biking or jogging.

Remember:

1 foot = 12 inches

1 yard = 3 feet = 36 inches

1 mile = 1,760 yards = 5,280 feet = 63,360 inches

Here's a video that talks about Customary units:

http://www.youtube.com/watch?v=cqSHf4dfa4s