## Number Focus Group

Term 3 Week 1

These lessons are focused on multiplying and dividing decimal numbers by multiples of 10 which will address the Australian curriculum content (ACMNA130) Multiply and Divide decimals by powers of 10.

To divide a decimal by a whole number multiple of 10, move the decimal point left one place for each zero in the multiple of 10.

To divide by 10, move the decimal point one place to the right 1.975 ÷ 10 = 0.1975

To divide by 100, move the decimal point two places to the right 1.975 ÷ 100 = 0.01975

To divide by 1000, move the decimal place three places to the right 1.975 ÷ 1,000= 0.001975

If there are not enough digits after the decimal point, add a zero 1.975 ÷ 10,000 = 0.0001975

These lessons are focused on multiplying and dividing decimal numbers by multiples of 10 which will address the Australian curriculum content (ACMNA130) Multiply and Divide decimals by powers of 10.

**Dividing decimal numbers by multiples of 10 i.e. 10, 100, 1000**To divide a decimal by a whole number multiple of 10, move the decimal point left one place for each zero in the multiple of 10.

To divide by 10, move the decimal point one place to the right 1.975 ÷ 10 = 0.1975

To divide by 100, move the decimal point two places to the right 1.975 ÷ 100 = 0.01975

To divide by 1000, move the decimal place three places to the right 1.975 ÷ 1,000= 0.001975

If there are not enough digits after the decimal point, add a zero 1.975 ÷ 10,000 = 0.0001975

**Multiplying decimal numbers by multiples of 10 i.e. 10, 100, 1000**

What you should already know -

A quick way to multiply a

**whole**number by a multiple of 10 is to add as many 0's to the whole number as there are in the multiple of 10.

e.g. to multiply a whole number by 10 add one zero 24 x 10 = 240

to multiply a whole number by 100 add two zeros 24 x 100 = 2400

to multiply a whole number by 1,000 add three zeros 24 x 1000 = 24000

**Multiplying decimals by multiples of 10**

To multiply a decimal by a multiple of 10, move the decimal point right one place for each zero in the multiple of 10.

To multiply by 10, move the decimal point one place to the right 10 x 0.975 = 9.75

To multiply by 100, move the decimal point two places to the right 100 x 0.975 = 97.5

To multiply by 1000, move the decimal place three places to the right 1000 x 0.975 = 975

If there are not enough digits after the decimal point, add a zero e.g 10000 x 0.975 = 9750

This can also be demonstrated on the place value chart below. You can create your own place value chart in Pages to help you.

Follow this link to practice multiplying by powers of 10 - Multiplying by powers of 10
Still confused? Visit this link to explain more - Khan academy Extension - Develop a game that will test multiples of 10. This can be a card game, a dice game or a computer game. Be creative and we'll play them in class. |

**Prime Numbers Wednesday 11th June****TASK 1**:

- As a class we will complete Eratosthenes Sieve. The instructions can be found below.
- Make a list of the prime numbers you have discovered.

**TASK 2**: Investigation -

**Two Primes Make One Square**

Can a square number be created by adding two prime numbers together?

You will need to complete the task for the square numbers for 2-10

**example**-

Start by squaring the number - 2 squared is 4

Using your list of PRIME numbers do two prime numbers equal 4?

2 is a prime number - 2 + 2 = 4

So in this case, two prime numbers when added together equal 2 squared.

Try with the squares of the numbers between 3 - 10

Did you find any square numbers which cannot be made by adding two prime numbers together?

**TASK 3**: Find all the different pairs of primes which add to 98.

**TASK 4**: This task is a 4 part question

- Write each number from 6 to 30 as a sum of 3 primes. Use the list you have created using Eratosthenes sieve - Here are the first three:

6 = 2+2+2

7 = 2+2+3

8 = 2+3+3

Record your findings and anything you think might be of interest.

Tuesday 10th JuneTuesday 10th June

Some numbers have special or interesting properties. Investigating these numbers helps you to understand them better.

**Prime numbers**are a very interesting set of numbers that have practical application in nature (lifecycles) and everyday life such as cryptology (password protection).

**What is a Prime Number?**

A prime number is a whole number

**greater than 1**that can only be divided evenly by 1 or itself.

They have been recognised since at least 300 BC, when they were studied by the Greek mathematicians Euclid and Eratosthenes.

Today we will investigate the prime numbers under 100

Download this file - Eratosthenes Sieve and complete the task. Please see me if you have any troubles opening the file.

1. Follow the instructions below which show how to use the Sieve of Eratosthenes to identify prime numbers to 100. Remember that a prime number can be divided only by itself and one and 2 is the smallest prime.

The sieve gives you a simple method for finding prime numbers.

Cross 1 out.

Then starting from 2, circle 2 but cross out every multiple of 2 from your sieve. Starting with 3, circle 3, but cross out every multiple of 3 from your sieve.

Starting with 5, circle 5, but cross out every multiple of 5 from your sieve. Starting with 7, circle 7 but cross out every multiple of it.

Do the same with all the primes that you know already. The numbers that are crossed are not primes, because they are multiples of other numbers. The numbers that are circled are primes. They should have no divisors apart from themselves and 1.

Make a list of your primes.

**Extension**-

1. Extend your sieve to 200 and find the prime numbers less than 200.

2. Identify the numbers that were sieved by 11 and 13 but not by the lower prime numbers (such as 2, 3 etc.)

3. Identify the first times there are gaps of 4, 6 and 8 between new prime numbers.

**Class discussion**: What do you notice about the prime numbers?

**Please drop your BIDMAS presentation to me - under the 'Other' tab**

Password

Password

__Dreambig135____Maths Symbols__

Decimal Challenges

Decimal Challenges

Please click on the links in order and work through these to build your understanding of decimals. You will need your Education Department details to access these.

Easier:

1. Wishball Challenge: hundredths

2. Wishball Challenge: thousandths

3. Wishball Challenge: ultimate

4. Wishball Challenge: tournament

Harder:

1. School Canteen #1

2. School Canteen #2

3. School Canteen #3

4. Swamp Survival

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1. Calculator puzzles!

2. How to solve large division problems

3. Party Time! (Problem solving and budgeting)

__Adding and Subtracting Fractions__

Work through the following websites in order to help you understand how to add and subtract fractions with related, the same and unrelated denominators. You will need to use your Education Department username and password. Work through at your own pace and remember to ask for help if you need it!

1. Adding with related denominators

2. Adding with unrelated denominators

3. Park fractions

4. Simplifying fractions

- watch the video from Mrs Russell and learn about how to simplify fractions, to get the lowest possible way of writing that fraction. Then complete the following tasks by answering these questions in your maths books: easy then hard. Then you may complete these online games about simplifying fractions. First then second.

__Order or Operations: BIMDAS__

Refer to this presentation if you need help with remembering how to work out problems with many different operations. Then click on this link to practise BIMDAS and click on the operation that must be completed first.

__Mental Maths with whole numbers__

Click on this link to be directed to complete your mental maths activities. You need to select an appropriate level to be working on - the numbered levels do not correlate with your year level. If you are finding it too hard, choose a level lower. Too easy? Choose a level higher.

Simplifying Fractions Flipbook

Click on the image below to download your Factors and Multiples Chart. Once it has been downloaded, you must open it in Finder and right click. Select open with pages and start your work.