Factors, Highest Common Factors & Least Common Multiples

Factors
A factor is a number that can be divided into another number without leaving a remainder.  For example, 5 is a factor of 10 because it goes in to 10 exactly.  8 has 4 factors (1,2,4 and 8).  Whilst prime numbers like 7 or 11 always have 2 factors (1 and the number)


Task:
Write down the numbers from 1 to 30.  For each number write down the factors of that number.

Tip: Once you reach 'halfway' in a number, the only next available factor is the number itself.  E.g. the last 2 factors of 30 are 15 and 30.

Here is a game to help you revise factors...

Highest common factors
If you take 2 numbers, such as 16 and 24, you can often find factors that go into both numbers.
For example
Factors of 16: 1,2,4,8,16
Factors of 24: 1,2,4,6,12,24

In these two numbers some factors are common (the same). 1,2 & 4
4 is the highest of these factors so....

...The highest common factor of 16 and 24 is 4

Find the HCF of the examples written on the board.

Here is a game to help you revise highest common factors


Least common multiple

Another way of exploring relationships between numbers is to look for the least common multiple of those numbers.

A multiple is any number in a particular times table.
For example, 
Multiples of 5 are...5,10,15,20,25,30, 40, 45, 50 etc. 
Multiples of 4 are...4, 8, 12, 16, 20, 24, 28, 32, 36, 40 etc

You can see that 20 and 40 are common to both the 4 and 5 times tables.  Since 20 is the smaller number, it is called the 'Least Common Multiple'

Find the least common multiple (LCM) of the numbers you have been given.

Here is another fruitshoot game to revise your understanding of LCM
Or, if you prefer something different, have a snowball fight!

Pie Charts

Last week we created surveys and collected data about any question we liked.
You can review your questions and data again by looking at our edmodo maths page.

A great way to display the data you collect is by using a pie chart.


This pie chart shows the results of a survey that was carried out to find out how students travel to school.

Questions:
a) What is the most common method of travel?
b) What fraction of the students travel to school by car?
c) If 6 students travel by car, how many people took part in the survey?

Activity
Write 3 more statements that you can tell are true by looking at this pie chart.

Now you can use your own data to create a pie chart.  If you didn't finish your questions then ask a buddy if you can use their data,

Take a screenshot of your finished pie chart
Write 3 more statements that you can tell are true.
Publish your pie chart and statements to edmodo.

Surveys and Percentages

Finding equivalent fractions, decimals and percentages
Another game

Today we will look more at percentages.

Percentages are very useful when comparing answers to a survey or poll.

Click on this link and complete the quick poll...

If you check the results, you will see the percentage of people who agree or disagree with you.

Today you will create your own quick poll and collect the results.  We will then plot these results into a pie chart.

Click here to visit easypoll

You will need the username and password you have been given (or you can create your own account if you prefer)

Create your poll with a , save your poll and copy the link to your poll onto an Edmodo note for others to use.

Then look at other peoples polls and answer their questions!

Next we will look at turning the results into a pie chart...

Finding Fractions or Percentages of Numbers

Today we will look at finding fractions of numbers.

If we want to find 1/2 of 10 we just divide by 2
If we want to find 1/4 of 8 we divide by 4
If we want to find 1/10 of 20 we divide by 10

But what if we want to find 3/10 of 20?

First we divide by 10, then we multiply by 3

Solve these sums, note that questions 6 to 10 require you to add or multiply decimal numbers:

1) 3/4 of 8 =                                 6) 3/10 of 15 =
2) 4/5 of 15 =                               7) 4/10 of 23 =
3) 5/6 of 24 =                               8) 11/100 of 200 =
4) 7/8 of 80 =                               9) 7/100 of 120 =
5) 2/3 of 18 =                              10) 14/100 of 50 =

You can practice more of these questions here

Questions 8,9 & 10 are fractions over 100.  11/100 also means 11%

So, 11/100 of 200 is the same as 11% of 200

Now find the answer to these questions:
11) 10% of 150                           16) 12% of 1200
12) 20% of 200                           17) 15% of 300
13) 25% of 100                           18) 90% of 900
14) 30% of 150                           19) 17% of 200
15) 40% of 200                           20) 36% of 500

And, of course, you can have percentages more than 100
If 100% of 10 is 10, then 200% of 10 is 20
Find the answers to these questions
21) 200% of 17
22) 150% of 20
23) 250% of 50
24) 300% of 120
25) 1000% of 52.5

Socrative Quiz

Fraction Bingo

Rounding Decimals

Today we will practice rounding decimal numbers up or down to the nearest whole number, tenth or hundredth.

Here are a couple of games to practice this concept

Scooter Quest            Soccer Shoot                Decimal Sharks

Rounding decimals can have lots of uses.  Sometimes we just need to estimate amounts.  Like if we want to know how much our groceries will cost or if we are 'pricing-up' a DIY job.

Make a shopping list of 10 items and find the exact prices of these objects on the countdown website.  Write down the price of these objects in your books.

Next, round the prices up or down to the nearest dollar and add up the total.

Next round the price up or down to the nearest 10c and add them up.  Is there much difference?

Finally, add up the actual price using the exact prices.  How different are the prices?

Tenths and Hundredths in whole Numbers

We will look today at converting decimal units

Decimals Warm Up (Flash player required)
Decimals Warm up 2

Imagine you were buying some chips that cost $2.40 but you only had 10c pieces.  Lots and lots of 10c pieces!  How many would you need to buy the chips?

If you think of 10c as a tenth of $1 then you could say that the number 2.4 is made up of 24 tenths.




How many tenths in each of these numbers?
1) 3.5                 2) 7.1              3) 12.5             4) 103.9             5) 12.51

Number 5 is a little odd:
12.51 has 125.1 tenths.

How many tens in all of the number
6) 140                   7) 1450               8) 132             9) 17.1         10) 7
     

Practice more of these on the socrative quiz that has been set up for you


If a scientist measures something, then accuracy is very important.  They often use small units like mm.

If a goatfish is 147mm long, how many cm exactly is it?

Convert these lengths
11)   125mm = ____ cm                                   12) 290mm = ____ cm
13) ______mm = 41.2cm                                  14) _____mm = 132.6 cm
15)  7mm = ____ cm

Activity
Now, find some objects in the class to measure.  Write down the precise measurement in mm and then convert this measurement into cm.
For example:

Pencil   125mm = 12.5cm

Changing Fractions, Decimals and Percentages

We will begin by ordering some fractions with different denominators

Ordering Fractions

We have already looked at how you can turn a fraction into a percentage (and vice versa)

Today we will look at how to covert fractions into decimals

There are a few different ways to do this...

The first is to change the denominator into 10, 100, 1000 or 10000 etc. by multiplying it.  If you then multiply the numerator by the same number then you can easily work out the decimal number.

For example

Express 3/5 as a decimal.

3/5 = 6/10 = 0.6

or

6/8 = 75/100 = 0.75  (in this one, you must multiply the top and bottom number by 12.5)

You can revise this theory here - There are some questions at the bottom of the page.

You can also convert fractions that have a larger numerator

e.g.

Express 3/2 as a decimal

3/2 = 150/100 = 1.5  (multiply both numbers by 50)

Solve the Socrative questions on this subject

Here are a couple of games you can play to practice this skill

Puppy Chase!

Fruit Shoot!

Other fraction, decimal and percentage games

Fractions and Percentages

Today we will look at converting fractions and percentages
Begin by looking at fractions and percentages on a number line.

Equivalent Fractions Practice


It is easy to turn a percentage into a fraction.  Percentage means, 'Parts of 100' so 35% means 35/100

But we can simplify this fraction by dividing the top and bottom by 5

35/100 = 7=20

So 35% = 7/20

Use Socrative.com to practice some questions on this topic.

Practice with this matching game...

Ordering Fractions

Today we will look at fractions and ordering them in ascending order. (Smallest to Largest)

Sometimes it is easy to work out which is smaller,

Like

1/4    <    3/4


But what about

5/8    and   3/4


In order to solve this, we need to change the denominators (bottom number) so they are both the same.  We can turn a 4 into an 8 by multiplying by 2.  So if we multiply both numbers in the fraction 3/4 by 2 we will end up with 6/8.

Now we have
5/8   &    6/8
So obviously 6/8 is larger.

Convert the fractions on the board so they have the same denominator.  Then use the correct symbol to say which one is larger.


Order these fractions

Plotting positive and negative data onto a graph

Yesterday we looked at the difference between the hottest and coldest temperatures of many cities from around the world.

We found that sometimes the coldest temperature was below zero and to calculate the range it helped to think of a number line.

If the coldest temp was minus 12 degrees and the hottest temp was positive 28 degrees then the difference between these two temperatures would be 40 degrees.

Today we will create graphs to show how the temperature changes over a year.

Click here to visit the weatherbase website again.  Find a city from anywhere in the world but make sure that the temperature goes below freezing (0 degrees) at some point in the year.

Now draw a chart.  The x-axis will be labelled with the months of the year and the y-axis will have the temperature.  Make sure your y-axis lets you go below 0.

1) Plot each point accurately in your book.  Use a coloured pencil to join the dots.
2) Plot a second city using a different colour.  For an interesting comparison, choose 1 city from the Northern Hemisphere and 1 from the Southern Hemisphere.

Your finished graph should look something like this...

The above graph was made using this website.  Try it out for yourself and download a finished graph as a picture.  You can also use Excel if you have it installed on your computer.

WALT find the difference between + and - numbers: Temperature range

In Auckland we have some warm days and some cool days.  Some countries get extremely hot weather and some countries get extremely cold weather.  There are even some countries that get extremely hot and extremely cold weather.

Today we are going to find out where these countries are and just how hot and cold they get.

Take a look at this site

You can find almost any city in the world that you would have heard of.  See if you can find Auckland- Newmarket.  You should bring up a page of data that looks like this...

MONTHLY - WEATHER AVERAGES SUMMARY   [ Show All Data ]

[ °F ]   °C

Average Temperature

		ANNUAL		JAN		FEB		MAR		APR		MAY		JUN		JUL		AUG		SEP		OCT		NOV		DEC
C		15.7		19.7		20.3		18.9		16.7		14.5		12.4		11.5		11.9		13.2		14.5		16.1		18.1

Average High Temperature

		ANNUAL		JAN		FEB		MAR		APR		MAY		JUN		JUL		AUG		SEP		OCT		NOV		DEC
C		18.7		23		23.5		22.1		19.8		17.4		15.3		14.4		14.8		16.3		17.6		19.2		21.4

Average Low Temperature

		ANNUAL		JAN		FEB		MAR		APR		MAY		JUN		JUL		AUG		SEP		OCT		NOV		DEC
C		12.5		16.4		17		15.7		13.6		11.5		9.4		8.5		9		10.1		11.5		12.9		14.9

February has the warmest average 

 What is the average temperature in February?  

But within any day, it gets warmer and colder depending on what time it is.

What is average highest daily temperature in Feb?  What about the average low daily temperature?

What is the difference between these two temperatures?

23.5 - 17 = 6.5 °C

Which month has the warmest average temperatures?  Which month has the coolest?

What is the difference between these temperatures?

23.5 - 9 = 14.5 C

Now look at Moscow (Asia/ Russia/ Moscow) and answer these questions...

1) What is the warmest month and what is its temperature?

2) What is the coldest month and what is its temperature?

3) What is the difference between these temperatures?

Now find some more cities.  We are looking for cities that have extreme temperature ranges so find ones that get below freezing in winter and get really hot in summer.  Answer the 3 questions above for each city you find.

To prove you can find the difference between + and - numbers, submit 1 city (the one with the most extreme temperatures) and the answers to the 3 questions via Edmodo.  

Order Decimals to 3dp...and beyond!

Welcome to Mr Miller's Maths Class!

Today we will begin with a game...Guess the number

WALT: Ordering decimals to 3 decimal places...

Look at these 3 numbers:   2.01      2.1       2.001
Which is the biggest and which is the smallest?

What about these:
2.001     2.01     -2.1
(Notice the negative sign next to the 2.1)

Try the examples on the board:

Now we will use Socrative to practice what we have learned.

Getting the hang of it?  Well try ordering numbers at speed: Click here