Year 7 Maths

Higher Tier

Ark Globe Academy

Remote Learning Pack

Phase IV

Monday 8 June – Friday 19 June

Name ………………………………………………………………

Teacher ………………………………………………………………

Year 7 Maths Pack IV

Day

Title Objective Resource provided

Outcome On-Line Support

1 Factors and Multiples

To be able to identify and list factors and multiples

Annotated resources on the VLE and Questions in pack below

Do now and practice questions completed

2 Prime factorisation

To be able to express numbers as a product of their primes

Annotated resources on the VLE and Questions in pack below

Do now and practice questions completed

3 LCM To be able to use prime factorisation to find the LCM

Annotated resources on the VLE and Questions in pack below

Do now and practice questions completed

4 HCF To be able to use

prime factorisation to find the HCF

Annotated resources on the VLE and Questions in pack below

Do now and practice questions completed

5 Worded

problems To be able to interpret and answer worded HCF and LCM problems

Annotated resources on the VLE and Questions in pack below

Do now and practice questions completed

6 Equivalent

fractions To be able to identify and calculate equivalent fractions

Annotated resources on the VLE and Questions in pack below

Do now and practice questions completed

7 Simplifyin

g fractions To be able to simplify fractions

Annotated resources on the VLE and Questions in pack below

Do now and practice questions completed

8 Improper

fractions and Mixed numbers

To be able to convert between improper fractions and mixed numbers

Annotated resources on the VLE and Questions in pack below

Do now and practice questions completed

9 FDP To be able to convert

between fractions decimals and percentages

Annotated resources on the VLE and Questions in pack below

Do now and practice questions completed

10 Comparing

and ordering FDP

To be able to compare and order 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

Examples – Video tutorials

Check out Year 7 Higher week 1 annotated resources on the VLE ! Or Scan the QR codes below and follow the link Factors Multiples

Factors fit in, Multiples are massive! Factors are all the integers a value is divisible by without a remainder e.g. 2 is a factor of 10 as it goes into 10 exactly 5 times without a remainder. 3 is not a factor of 10. - The smallest factors of any number is 1 - The largest factors of any number is itself Example The factors of 18 are 1, 2, 3, 6, 9, 18 Prime numbers are integers which only have 2 factors, one and itself - 2 is the only even prime number Example The factors of 17 are 1 and 17 Multiples are the product of a value and another integer. They are the times tables of a number. Examples The first 6 multiples of 2 are 2, 4, 6, 8, 10, 12

The first multiple of 5 is 5 x 1 = 5

The fifth multiple of 5 is 5 x 5 = 25

- The smallest multiple of any number is itself

Practice

Example

Extend

Day 2- Prime factorisation

Do Now

Examples – Video tutorials

Check out Year 7 Higher week 1 annotated resources on the VLE ! Or

Prime numbers Product of prime factors

Scan the QR codes below and follow the link

Prime factorisation is when you write a number as a product of its primes. To start you break the number down using a prime factor tree. See step by step example below. The prime numbers you circle are then written as a multiplications in index form e.g.

154= 4 x 4 x3 x 3 = 𝟒𝟐 × 𝟑𝟐 You can check your answers by doing the calculation e.g. 4 x 4 x 3 x 3 does equal 154

Example

Practice

Example

Extend

Day 3- Lowest Common Multiple

Do Now

Examples – Video tutorials

Check out Year 7 Higher week 1 annotated resources on the VLE ! Or Scan the QR codes below and follow the link

Product of primes LCM

Example

Lowest common multiple (LCM)is the smallest number which is in both values timetable. When the numbers are large, when finding the LCM instead of writing out their times tables until we find a common value we use prime factorisation and a venn diagram Step 1: Write each value as a product of its primes Step 2: Complete a venn diagram of the prime numbers (remember if a number appears in both prime factorisations it goes in the middle on the venn diagram) Step 3: Multiply all the numbers in the venn diagram together ; Example

Practice

Extend

Day 4- HCF

Do Now

Examples – Video tutorials

Check out Year 7 Higher week 1 annotated resources on the VLE ! OR Scan the QR codes below and follow the link

Product of primes HCF

- The highest common factor is the largest integer which is a factor of both

values. - This can be found by listing factors or by using prime factorisation - When using prime factorisation you follow these steps Step 1: Write each value as a product of its primes Step 2: Complete a venn diagram with the prime factors Step 3: Multiply the values in the intersection of the venn diagram Example

Practice

Example

Extend

Day 5- Worded problems

Do Now

Examples – Video tutorials

Check out Year 7 Higher week 1 annotated resources on the VLE ! Or Scan the QR codes below and follow the link Product of primes HCF Product of primes LCM

Example

Practice

1) Tom and Claire both like do short exercise that involve small breaks.

Tom does a short burst of exercise every 2 minutes, and Claire does

hers every 3 minutes. If they start doing their exercise at 9:00am, when

do they both do their exercises again?

2) The 90A bus and the 95B bus both stop at the bus station at 12:00. 90A

stops there every 20 minutes and 95B stops there every 8 minutes. When

do they both stop there again?

3) Train A and Train B stops at Swindon as 10:30. Train A stops every 12

minutes and Train B stops every 14 minutes. When do they both stop at

Swindon again?

4) There are two loaf cakes. One is 35cm long and one is 27cm long. They

want to cut the cake up and sell the slices, but all the slices must be

equal. What is the largest slices that they can cut them into?

5) Florence wants to invest money abroad. Florence is aware that France

generally has a recession every 6 years and America generally has a

recession every 8. in the year 2005, both France and America were in

recession. Florence needs to work out the next time they will both be in

recession. When will this be?

6) An artist uses different types of paper to create her masterpieces. She

has shiny metallic paper and pink glittery paper. The shiny paper

comes in lengths of 24 inches and the glitter paper in lengths of 36

inches. She wants to make sure she can cut her paper into equal sizes

but doesn’t want them to be too small. What’s the largest size she can

cut them into without any waste?

Extend

Super stretch

Day 6- Equivilent fractions

Do Now

Examples – Video tutorials

Check out Year 7 Higher week 2 annotated resources on the VLE !

Or Scan the QR code below and follow the link

Equivalent fractions

• A division can be written as a fraction. If the division is 𝒂 ÷ 𝒃, this can be written as 𝒂

𝒃.

• A fraction is made up of a numerator (top number) and denominator (bottom number).

• Some divisions give the same answers, for example, 𝟏𝟎 ÷ 𝟓 = 𝟐 and also 𝟖 ÷ 𝟒 = 𝟐. This means that 𝟏𝟎 ÷ 𝟓 = 𝟖 ÷ 𝟒 as they both give the same answer. These calculations are known as equivalent as they are equal to each other.

• When calculations of the same value are written as fractions these divisions are

known as equivalent fractions. For example, 𝟏𝟎

𝟓=

𝟖

𝟒

• Equivalent fractions have the same value, for example 𝟏

𝟐 has the same value as

𝟐

𝟒.

• To generate equivalent fractions, you take your original fraction and multiply the numerator and denominator by the same amount. Example

• To work out a missing value in an equivalent fraction, look for pairs of numerators, or denominators, and work out what you multiply one by to get the other. Then do the same for the other value.

• Example

Example

Practice

Extend

Day 7- Simplifying fractions

Do Now

Examples – Video tutorials

Check out Year 7 Higher week 2 annotated resources on the VLE !

Or Scan the QR codes below and follow the link Simplifying fractions

• If the denominator and numerator share a common factor then the fraction can be simplified

• To simplify a fraction you divide the numerator and denominator by their highest common factor

• Fractions cannot be simplified if the HCF of the numerator and denominator is 1. This usually means one of them is a prime number.

Example

Practice

Example

HCF is 1 so it cannot be simplified

further

4 and 11 their HCF is 1 so it cannot

be simplified further

Extend

Day 8- Converting improper fractions and mixed

numbers

Do Now

Examples – Video tutorials

Check out Year 7 Higher week 2 annotated resources on the VLE ! Or Scan the QR codes below and follow the link

Improper Fractions to Mixed Numbers Mixed Numbers to Improper Fractions

• Improper fractions are called top heavy fractions, when the numerator is greater than the denominator so they have a value greater than 1.

• Mixed numbers are values which have an integer and fraction part

• To covert improper fraction to mixed numbers you need to:

• Step 1: Divide the numerator by the denominator

• Step 2: The whole number of times the denominator goes in becomes the whole number part of the mixed number, the remainder becomes the new numerator

• Step 3: The denominator remains the same ( unless the fraction part can be simplified)

Examples

• To change a mixed number into an improper fraction you have to :

• Step 1: Multiply the denominator by the whole number

• Step 2: Add you answer to the numerator. This becomes your new numerator.

• Step 3: The denominator stays the same ( unless it can be simplifies) Examples

Practice

Example

Extend

Day 9- FDP

Do Now

Examples – Video tutorials

Check out Year 7 Higher week 2 annotated resources on the VLE ! Or Scan the QR codes below and follow the link

FDP equivalence

- All values can be represented as fraction, decimals and percentages Fractions to decimals - To covert fractions to decimals you want to make the denominator a power of 10 e.g. 10,

100 or 1000, - You then write the numerator to that place value e.g. if you have 3/10 that’s 3 tenths so

o.3 Examples -

Fraction to percentages - Percentages are out of 100, so the aim is the make the denominator 100, then the

numerator is the percentage

Examples

Decimals to percentages To convert decimals to percentages you just multiply by 100 To convert percentages to decimals you divide by 100 Examples

Example

Practice

Extend

Extend

Day 10- Comparing FDP

Do Now

Examples – Video tutorials

Check out Year 7 Higher week 2 annotated resources on the VLE ! Or Scan the QR codes below and follow the link Ordering FDP

- To compare fractions, decimals and percentages you need to write them in the same

representation - Just pick which format, decimal, fraction or percentage, is easiest and convert all values

into that Example Order 0.4, 2/5 and 35% in ascending order

Practice

Example

Final answer should be as the values

were written in the question

Extend

END OF PACK