Year 5 MathsWeek 9 – Ratio (1)

Week beginning Monday 25th May

We are learning to:

• Identify all factors and common factors of two numbers;

• Explain what is special about prime and square numbers.

• Understand the concept of ratio as a way to show the relative sizes of two quantities;

• Solve simple problems involving ratio.

Follow the learning journey on this PowerPoint; it has a break down for each day from Monday to Friday. There will be a task each day which

could be introduced in a video from our YouTube channel, a link to a different website, a worksheet or an open-ended challenge. If you want

to, you could upload your work to Purple Mash so that your teachers can see how hard you’ve been working.

Day 1

Monday 25th May 2020We are learning to find all factors of a number and use this knowledge to identify

square and prime numbers.

Watch today’s video (click here to access the FOJS YouTube channel) and complete

the task at the end. If you are unable to access the video, see the next slide for a

visual representation of today’s learning and slide 5 for a copy of today’s task.

From Input:

Factors are the whole numbers you multiply together to get another whole number.

factor x factor = product

Apart from in a few special cases, factors come in pairs. If

you work systematically, starting with 1, then you will be able

to identify all factors of a given number.

Finding factors of 24:

From Input:

Numbers with an odd number of

factors are called square numbers.

Numbers with only two factors (1 and

themselves) are called prime numbers.

Numbers that are not prime are called

composite numbers.This is because a number multiplied by

itself is a square number, as demonstrated visually below:

4 has three factors

1, 2 and 4

9 has three factors

1, 3 and 9 16 has five factors1,2, 4, 8 and 16.

1 is not a prime number as it only has 1 factor.

2 Is the only even prime number (factors are 1 and 2).

Some other examples of prime numbers are 3, 5, 7, 11,

13, 17 and 19.

TODAY’S

TASK:

Day 2

Tuesday 26th May 2020We are learning to identify common factors.

Watch today’s video (click here to access the FOJS YouTube channel) where we will

go through the answers of yesterday’s task. You can mark your own work.

If you have made a mistake and are not sure where you went wrong, please upload

your work to the blog so that one of us can check it for you.

Then watch the next part of the video with an input on common factors and

complete the task at the end.

EXAMPLE: Common factors are numbers that are factors of 2 or more numbers.

We talked about common factors briefly when we learnt about fractions.

We can use a Venn diagram to find common factors of a number, e.g. to find the common factors of 12

and 15:

Factors of 12 Factors of 15

1

2

3

4

5

6

7

8

9

10 11

12

13

14

15

The common factors of 12 and 15 are 1 and 3.

TODAY’S TASK:

Day 3

Wednesday 27th May 2020We are learning to understand the concept of ratio.

Watch today’s video (click here to access the FOJS YouTube channel) to check your

answers from yesterday.

Today’s input introduces the concept of ratio.

There are some key points on the next slide, followed by today’s task.

An introduction to ratio:

There are 2 chocolate cupcakes and 1 vanilla cupcake.

The ratio of the number of chocolate cupcakes to the number of vanilla cupcakes is 2 : 1.

We read this as 2 to 1.

We could also say, ‘for very 2 chocolate cupcakes there is 1 vanilla cupcake’.

In ratio, the first and second numbers refer to the first and second quantities. Order is very important!

The ratio of the number of vanilla cupcakes to the number of chocolate cupcakes is 1 : 2.

An introduction to ratio:

The numbers in a ratio could also be written in terms of equal groups or sets.

Greg the Grocer has 2 trays of pears and 3 trays of apples. There is an equal number of pieces of fruit

in each tray.

The ratio of the number of pears to the number of apples is 2 : 3.

The ratio of the number of apples to the number of pears is 3 : 2.

In this case, the numbers in the ratio do not represent the number of pieces of fruit.

An introduction to ratio:

Ratio does not only compare items in term of quantity but also in terms of mass, length, capacity etc.

I have 9kg of potatoes and 5kg of rice.

The ratio of the mass of potatoes to the mass of rice is 9 : 5.

The ratio of the mass of rice to the mass of potatoes is 5 : 9.

9kg 5kg

We do not include units in a ratio

(e.g. Kg) because we are comparing

the relative sizes and not the actual

mass. However, when writing two

quantities as a ratio, they must be in

the same unit.

We can use a comparison bar model

to represent the ratio visually.

Problem Solving:

Today’s Task:

Day 4

Thursday 28th May 2020We are learning to express equivalent ratios.

Watch today’s video (click here to access the FOJS YouTube channel) where we go

through the answers of yesterday’s task.

Then watch the rest of the video for an input on equivalent ratios.

There are some examples from the video on the next slides, followed by a copy of

today’s task.

Equivalent Ratios

2 trays of 2 chocolate doughnuts4 trays of 2 strawberry doughnuts

There are 4 chocolate doughnuts and 8 strawberry doughnuts.

The ratio of the number of chocolate doughnuts to the number of strawberry doughnuts is 4 : 8.

I put two doughnuts of the same flavour on each tray:

There are 2 trays of chocolate doughnuts and 4 trays of strawberry doughnuts.

The ratio of the number of chocolate doughnuts to the number of strawberry doughnuts is 2 : 4.

1 tray = 1 unit

Continued on next slide...

Equivalent Ratios continued

Next she puts 4 doughnuts of the same colour on each tray.

There is 1 tray of chocolate doughnuts and 2 trays of strawberry doughnuts. The ratio of the number of chocolate doughnuts to the number of strawberry doughnuts is 1 : 2.

The three ratios 4 : 8, 2 : 4 and 1 : 2 compare the same number of chocolate doughnuts and strawberry doughnuts.

These ratios are equivalent ratios:

4 : 8 = 2 : 4 = 1 : 2

1 : 2 is a ratio in its simplest form.

2 trays of strawberry doughnuts1 tray of chocolate

doughnuts

1 tray = 1 unit

Concrete Representation:

The ratio of the number of

red bricks to the number

of green bricks is 6 : 12. The ratio of the number of red bricks to the

number of green bricks is 3 : 6.

3 groups of

red bricks

6 groups of

green bricks1 group of

red bricks

2 groups of

red bricks

The equivalent ratios are 6 : 12, 3 : 6 and 1 : 2.

In these equivalent ratios, the ratio in its simplest form is 1 : 2.

Abstract:

Today’s Task:

Day 5

Friday 29th May 2020We are learning to

See today’s videos for the answers to yesterday’s task.

Then watch us begin to tackle the problem in today’s task.

At the end of the video there is an assessment activity (it is also available on the final

slide). Please complete this activity and, if you like, you could upload your work to

your work folders on Purple Mash for your teacher to see.

Today’s Task comes from the nrich website. You can find it by clicking here or visiting www.nrich.org and searching for ‘Rod Ratios’. If you do not have access to a computer, a copy of the problem is printed below.

This problem involves using Cuisenaire Rods. The nrich website has an interactive set of rods for you to use. Alternatively you can print out your own sets of rods

or even make your own! The colours and relative sizes are shown on the slide after the problem.

Assessment:

Have a great weekend!

From the Year 5 Team