Year 7 Maths

Foundation Tier

Ark Globe Academy

Remote Learning Pack

Phase IV

Monday 8 June – Friday 19 June

Name ………………………………………………………………

Teacher ………………………………………………………………

Please email Miss Bowers (e.bowers@arkglobe.org) if

you have any questions at all about anything in this

pack.

Year 7 Maths Pack 4

Day Title Objective Resource provided Outcome On-Line Support

1 Factors and Multiples

To be able to find factors and multiples of any number

Annotated resources on the VLE and Questions in pack below

Do now and practice questions completed

2 Types of

numbers To be able to identify different types of numbers including primes and squares

Annotated resources on the VLE and Questions in pack below

Do now and practice questions completed

3 LCM/HCF To find Lowest

Common Multiple and Highest Common Factor through listing

Annotated resources on the VLE and Questions in pack below

Do now and practice questions completed

4 Prime

factorisation To introduce method of writing numbers as a product of prime factors

Annotated resources on the VLE and Questions in pack below

Do now and practice questions completed

5 Prime

factorisation To consolidate and practise writing numbers as a product of prime factors

Annotated resources on the VLE and Questions in pack below

Do now and practice questions completed

6 Equivalent

fractions To be able to spot and find fractions that are equivalent

Annotated resources on the VLE and Questions in pack below

Do now and practice questions completed

7 Simplifying

fractions To be able to simplify fractions to express them in their simplest form

Annotated resources on the VLE and Questions in pack below

Do now and practice questions completed

8 Converting

fraction to decimals

To be able to convert fractions to decimals using place value

Annotated resources on the VLE and Questions in pack below

Do now and practice questions completed

9 Converting

fractions to percentages

To be able to convert fractions to percentages

Annotated resources on the VLE and Questions in pack below

Do now and practice questions completed

10 Converting

FDP To be able to convert fractions, decimals and percentages

Annotated resources on the VLE and Questions in pack below

Do now and practice questions completed

Day 1- Factors and Multiples

Do now

Go to the VLE and look at the annotated resources for Year 7 Foundation Week 1

In addition: Use these video tutorials

Optional 2: use these links:

Optional 1: hold your phone camera up to the screen, scan the bar code and click on link that appears Factors: Multiples:

https://corbettmaths.com/2012/08/24/factors/ https://corbettmaths.com/2012/08/11/1335/

Finding Factors: Factors are numbers that go into that number exactly Factors are the whole numbers that divide into that number without a remainder All factors of a number are either the number itself or smaller than that number For example: 2 x 5 = 10 1 x 10 = 10 therefore 1, 10, 2, 5 are all factors of 10 1 x 18 = 18 2 x 9 = 18 3 x 6 = 18 therefore 1, 2, 3, 6, 9, 18 are all factors of 18 Example question: List all the factors of 8: Think of all the numbers you times together to get an answer of 8 >> 1 x 8 = 8 2 x 4 = 8 therefore the factors of 8 are 1, 2, 4, 8

Independent Practice on Finding Factors:

Multiples:

Multiples are all the numbers that are in that number’s times table Multiples are all the numbers in the times table of that number and can go on forever All multiples of a number are either the number itself or bigger than that number For example: Multiples of 7 mean: list all the numbers in the 7 times table 7, 14, 21, 28, 35, 42, 49…. etc Multiples of 3 mean: list all the numbers in the 3 times table 3, 6, 9, 12, 15, 18…. etc Example question: List the first 6 multiples of 4: List the first 6 numbers in the 4 times table, starting with 4: 4, 8, 12, 16, 20, 24

Independent Practice on Finding Multiples:

Day 2- Types of Numbers

Do Now

Go to the VLE and look at the annotated resources for Year 7 Foundation Week 1

In addition: Use these video tutorials Prime numbers

Optional 2: use these links:

https://corbettmaths.com/2013/03/24/prime-numbers/

Types of Numbers: You need to be able to recognise different types of numbers. Here are some of the types that you might come across: Factors – go into a number exactly (Day 1) > Factors Fit inside Multiples – in the times table of that number (Day 1) > Multiples are Massive Odd numbers – whole numbers that cannot be divided by 2 > 1, 3, 5, 7, 9… Even numbers – whole numbers which have a factor of 2 > 2, 4, 6, 8…. Prime numbers – these are numbers that only have two factors: 1 and the number itself The first 10 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 (try to memorise these prime numbers, they will help you a lot!)

Independent Practice on Types of Numbers:

Optional EXTENSION: try if you can

Day 3- HCF and LCM Do Now:

Go to the VLE and look at the annotated resources for Year 7 Foundation Week 1

In addition: Use these video tutorials Highest Common Factor (HCF) Lowest Common Multiple (LCM)

Optional 2: use these links: https://corbettmaths.com/2012/08/24/common-factors-and-hcf/

https://corbettmaths.com/2012/08/11/lcm-and-common-multiples/

Finding the Highest Common Factor (HCF):

Factors are numbers that go into that number exactly

The Highest Common Factor of two numbers is the largest factor that they BOTH have

For example:

The factors of 10 are: 1, 2, 5, 10

The factors of 18 are: 1, 2, 3, 6, 9, 18

>> So the highest common factor of 10 and 18 is 2

Example question:

Find the HCF of 24 and 28:

1) List the factors of 24 (1, 2, 3, 4, 6, 8, 12, 24)

2) List the factors of 28 (1, 2, 4, 7, 14, 28)

3) Find the largest number that comes up in both lists

>>So the answer is 4

Independent Practice on finding the Highest Common Factor (HCF):

Finding the Lowest Common Multiple (LCM):

Multiples are all the numbers that are in that number’s times table

The Lowest Common Multiple between two numbers is the lowest multiple that they BOTH have

For example:

The multiples of 5 are: 5, 10, 15, 20, 25, 30, 35…

The factors of 6 are: 6, 12, 18, 24, 30, 36…

>> The lowest common multiple of 5 and 6 is 30 as it is lowest number in both lists of multiples

Example question:

Find the LCM of 10 and 12:

1) List the first 8 multiples of 10: (10, 20, 30, 40, 50, 60, 70, 80)

2) List the first 8 multiples of 12: (12, 24, 36, 48, 60, 72)

3) Find which is the lowest number that comes up in both lists

>>the answer is 60

Independent Practice on finding the Lowest Common Multiple (LCM):

Optional EXTENSION: Try if you can

Day 4 – Prime Factorisation

Do Now

Go to the VLE and look at the annotated resources for Year 7 Foundation Week 1

In addition: Use these video tutorials Prime numbers Product of prime factors

Optional 2: use these links:

https://corbettmaths.com/2013/03/24/prime-numbers/

https://corbettmaths.com/2012/08/20/product-of-primes/

Prime Factorisation:

Prime Factorisation is a method used in Maths to break a number down into its prime factors (its building blocks)

You might also be asked to: “write a number as a product of its prime factors£ (this means the same thing as prime factorisation)

You need to use a factor tree:

Example question: Write 18 as a product of its prime factors

Steps:

1) Draw two lines down from the starting number (18) 2) At the end of each line write two factors of 18 (numbers that times

together to make 18) > 3 x 6 (could also have been 2 x 9) 3) If any of these numbers are prime (2, 3, 5, 7, 11, 13…) you circle them and

the tree stops (so 3 is circled but not 6) 4) Keep going until all the numbers are circled (prime) 5) At the end write out all the circled numbers like this: 2 x 3 x 3 6) These are the prime factors

Example question: Write 36 as a product of its prime factors

Steps:

1) Draw two lines down from the starting number (36) 2) At the end of each line write two factors of 36 (numbers that times

together to make 36) > 4 x 9 (could also have been 2 x 18 or 3 x 12) 3) If any of these numbers are prime (2, 3, 5, 7, 11, 13…) you circle them and

the tree stops (non are prime in the first row) 4) Keep going until all the numbers are circled (prime) 5) At the end write out all the circled numbers like this: 2 x 2 x 3 x 3 6) These are the prime factors

Independent Practice on Prime Factorisation

Day 5 - Prime Factorisation (continued)

Do Now

Go to the VLE and look at the annotated resources for Year 7 Foundation Week 1

In addition: Use these video tutorials Product of prime factors

Optional 2: use these links:

https://corbettmaths.com/2012/08/20/product-of-primes/

Example question: Write 60 as a product of its prime factors

Steps:

1) Draw two lines down from the starting number (60) 2) At the end of each line write two factors of 60 (numbers that times

together to make 60) >> 2 x 30 3) If any of these numbers are prime (2, 3, 5, 7, 11, 13…) you circle them and

the tree stops (non are prime in the first row) 4) Keep going until all the numbers are circled (prime) 5) At the end write out all the circled numbers like this: 2 x 2 x 3 x 5 6) These are the prime factors

Independent Practice on Prime Factorisation

When the question asks you to “give your answer in index form” you need to write it out with index numbers: For example: 2 x 2 x 3 x 5 can be written as 22 x 3 x 5 (as there are 2 2’s times together) For example: 2 x 3 x 3 x 5 x 5 can be written as 2 x 32 x 52 (as there are 2 3’s and 5’s times together) For example: 2 x 2 x 2 x 3 x 3 x 7 x 7 x 7 can be written as 23 x 32 x 73

Independent Practice on Prime Factorisation

Optional EXTENSION: Try if you can

Day 6- Equivalent Fractions

Do Now:

Go to the VLE and look at the annotated resources for Year 7 Foundation Week 2

In addition: Use these video tutorials Equivalent fractions:

Optional 2: use these links:

https://corbettmaths.com/2013/02/15/equivalent-fractions/

Equivalent Fractions:

Always remember the GOLDEN RULE of fractions:

**Whatever you do to the top number (numerator), you do to the bottom number

(denominator)!**

To find an equivalent fraction you just need to TIMES the top (numerator) and bottom

(denominator) by the same number Example:

To the missing number in an equivalent fraction you need to see what number you

TIMES to get the new fraction and then do the same to the numerator/denominator by

the same number Example:

Independent Practice on Equivalent Fractions:

Optional EXTENSION if you can:

Day 7 – Simplifying Fractions

Do Now:

Go to the VLE and look at the annotated resources for Year 7 Foundation Week 2

In addition: Use these video tutorials Simplifying fractions:

Optional 2: use these links:

https://corbettmaths.com/2013/03/03/simplifying-fractions-2/

Simplifying Fractions:

To write a fraction in its SIMPLEST form you need to divide the numerator and

denominator by their HCF

Always remember the GOLDEN RULE of fractions:

**Whatever you do to the top number (numerator), you do to the bottom number

(denominator)!**

To simplify a fraction:

1) Find the HCF of the numerator and denominator

2) Divide both numerator and denominator by their HCF

3) Check you can’t simplify anymore

Examples:

Independent Practice on Simplifying Fractions:

Optional EXTENSION – try if you can:

Day 8 - Converting Fractions to Decimals Do Now

Go to the VLE and look at the annotated resources for Year 7 Foundation Week 2

In addition: Use these video tutorials Converting fractions to decimals:

Optional 2: use this link:

https://corbettmaths.com/2013/02/15/fractions-to-decimals/

Converting Fractions to Decimals:

To convert fractions to decimals, we need to review place value and remember what

each column is called:

If a fraction has a denominator of 10, 100, 1000 you just need to write in the correct column and add zeros For example 𝟑

𝟏𝟎 = 3 tenths = 0.3 (as you just write 3 in the “tenths” column)

𝟒

𝟏𝟎𝟎 = 4 hundredths = 0.04 (as you just write 4 in the “hundredths” column)

𝟏𝟐

𝟏𝟎𝟎 = 12 hundredths = 0.12 (as you just write last number (2) in the

“hundredths” column)

Independent Practice on Converting Fractions to Decimals:

If a fraction does NOT have a denominator of 10, 100, 1000 you need to:

1) Convert it to an equivalent fraction over 10, 100 or 1000 2) Write it in the correct place value column and add zeros

For example: -

Some more examples:

Independent Practice on Converting Fractions to Decimals:

Day 9- Converting Fractions to Percentages Do Now

Go to the VLE and look at the annotated resources for Year 7 Foundation Week 2

In addition: Use these video tutorials Converting fractions to percentages:

Optional 2: use this link:

https://corbettmaths.com/2013/03/29/fractions-to-percentages/

Converting Fractions to Percentages:

A percentage is a fraction out of 100.

For example:

𝟒

𝟏𝟎𝟎 = 4%

𝟏𝟏

𝟏𝟎𝟎 = 11%

𝟐𝟔

𝟏𝟎𝟎 = 26%

If the fraction is already written with a denominator of 100, you just write the

numerator as the percentage.

If the fraction does not have a denominator of 100, you need to:

1) Write it as an equivalent fraction with a denominator of 100

2) Write the numerator as a percentage

For example 𝟑

𝟏𝟎 =

𝟑𝟎

𝟏𝟎𝟎 = 30%

𝟑

𝟓𝟎 =

𝟔

𝟏𝟎𝟎 = 6%

𝟏𝟓

𝟐𝟎=

𝟕𝟓

𝟏𝟎𝟎 = 75%

Independent Practice on converting Fractions to Percentages:

Day 10- Converting Fractions, Decimals and Percentages (FDP)

Do Now

Go to the VLE and look at the annotated resources for Year 7 Foundation Week 2

In addition: Use these video tutorials Converting FDP:

Optional 2: use this link:

https://corbettmaths.com/2013/02/15/fdp/

Converting Fractions Decimals and Percentages:

You need to be able to confidently convert between Fractions, Decimals and Percentages. Here are some reminders about what to do: Fractions to Decimals: Write as a fraction over 10, 100, 1000 and put in the right column for place value (see Day 8) Fractions to Percentages: Write as a fraction out of 100 (see Day 9) Decimals to Percentages: Times by 100 Percentages to Decimals: Divide by 100 Percentages to Fractions: Write as a fraction out of a 100 (denominator) and then simplify

Decimals to Fractions: Write as a fraction from the place value

Example questions:

1) Write 𝟑𝟓

as a decimal and percentage:

𝟑𝟓

= convert to equivalent fraction over 10 (x2) = 𝟔𝟏𝟎

= 0.6

0.6 = 60% (you times by 100)

2) Write 0.85 as a fraction and percentage:

0.85 = write a fraction from place value = 85 hundredths = 𝟖𝟓𝟏𝟎𝟎 = Simplify if you can (÷

by 5) = 𝟏𝟕𝟐𝟎

0.85 = 85% (you times by 100)

3) Write 40% as a decimal and fraction:

40% = write as a fraction out of 100 = 𝟒𝟎𝟏𝟎𝟎 = Simplify if you can (÷ by 20) =

𝟐𝟓

40% = 0.4 (you divide by 100)

Independent Practise on Converting FDP:

Independent Practise on Converting FDP:

Fill in the missing values in the table:

Optional EXTENSION – Try if you can: