Year 4 Maths - Westcott Primary

Year 4 Maths

Times table practise: All week

6, 8, 9’s

Lesson 1I can multiply three-digit

numbers by a one-digit number using formal written layout

Multiplication methods we already know:To multiply, you know you need to use your times table knowledge. There’s also another method you have used to help multiply… partitioning!

This means, we know 34 X 5 could be partitioned into 30 X 5 and 4 X 5. We could do this in our heads, written down like shown above or using the grid method…

X 30 4

5 150 20

34 X 5 = 170

I also know that 3 X 5 = 15 so then I know that 30 X 5 = 150. By knowing this fact it makes it easier to multiply.

I can also use place value counters to represent multiplication when partitioning.

521 X 3 =

Step 1: partition 521:

521 = 500 + 20 + 1 521 = 5 hundreds + 2 tens + 1 one

521 X 3 = Step 2 and 3: gather three sets of 521, multiply the hundreds, tens and ones and recombine:

5 hundreds X 3 = 15 hundreds2 tens X 3 = 6 tens1 one X 3 – 3 ones

521 X 3 = 500 X 3 + 20 X 3 + 1 X 3 =

1500 + 60 + 3

521 X 3 = 1563Step 4: regroup the hundreds into thousands and hundreds.

15 hundreds = 1 thousand + 5 hundred

521 X 3 = 1000 + 500 + 60 + 3 = 1563

Now we are going to look at how to use short multiplication using an abstract method. If you need to use counters or concrete objects, you can do this to help you.

Now you have seen an example of how to use short multiplication. Practise using this method yourself to complete the multiplication problems on the worksheet labelled ‘Activity 1’ (this will not need printing as children can write out using the short multiplication method).

Lesson 2I can multiply three-digit

numbers by a one-digit number using formal written layout

Recap of yesterday’s lesson:

Yesterday you practised using the short multiplication method to multiply 3 digits by 1 digit. Today’s aim is to use this method to problem solve.

Spot the mistake:

Have a look at identifying what is wrong with this problem?

Spot the mistake:

Instead of regrouping the ten, after 3 X 4 = 12, they have placed it in the tens column. Therefore making the number a lot bigger than it should be.

The answer should be:

7 3

X 4

2 9 2

Problem solving:

Harvey has five hundred and ninety-four packs of buns for a party. Each pack contains three buns. When Harvey is preparing for the party, he drops eighteen buns. How many buns are left?


Step 1- find the key pieces of information.Step 2- complete the first part of the problem. (594 X 3 = )Step 3- Complete the final part of the problem. ( 594 X 3 = __________ - 18 =? )

5 9 4

X 3

1 7 8 2

Step 2: Step 3: 1782 – 18 =

1 7 8 2

- 1 8

1 7 6 4

594 X 3 =

Answer:

There would be 1764 buns left for the party.


Task:

Complete the questions on activity 2 sheet, use your multiplication skills and knowledge to help you to complete the problems.

Lesson 3I can divide by a 2 digit

number

This lesson is going to focus on division!

Key vocabulary to remember and use:

Dividend divisor = quotient

60 10 = 6

We know:6 2 = 3 = 2. so that means we also know 60 3 = 20.

If 12 4 = 3, what does 120 4 = ?

120 4 = 30

One four is one each. That’s four.Two fours is two each. That’s eight.Eight divided between four is equal to two each.So, each child gets two sticks.

Four tens are one ten each. That’s forty.Eight tens are two tens each. That’s eighty.Eight tens divided between four is equal to two tens each.

Three tens are one ten each. That’s thirty.Six tens are two tens each. That’s sixty. There are two tens left over.Eight tens divided between three is equal to two tens each, with a remainder of two tens.

Six tens are two tens each. That’s sixty. There are two tens left over.Eight tens divided between three is equal to two tens each, with a remainder of two tens.

Two tens and one one is equal to twenty-one ones.

Three ones are one each. That’s three.Six ones are two each. That’s six…Twenty-one ones are seven each. That’s twenty-one.Twenty-one ones divided between three is equal to seven ones each.

Sometimes when we divide there will be remainders, as the number is not fully divisible by another.

Such as 3 divided by 2. 3 buttons shared by 2 people. They would both get 1 button, but there would be one left over. So the answer would be 1 r 1. r = remainder

Seven tens divided between three is equal to two tens each, with a remainder of one ten.

One ten and three ones is equal to thirteen ones.Thirteen ones divided between three is equal to four ones each, with a remainder of one one.

Each child gets twenty-four marbles; there is one marble left over.

84 sticks are shared equally between 4 children. How many sticks does each child get?

Step 1- write the divisor and the divided

Step 2- sharing the tens

8 tens divided by four tens is 2 tens.

Step 3- sharing the ones

4 ones divided by four is equal to 1 one.

Step 4- summarise (3 different methods shown)

Each child gets 21 sticks.

Task: Activity 3

Use the methods previously shown to work out the division problems.

Lesson 4I can divide by a 2-digit

number by a one digit number using formal written layout

Recap: Yesterday’s lesson we looked at how to divide 2 numbers using different representations.

https://www.bbc.co.uk/bitesize/topics/z36tyrd/articles/zgxdfcw

Key vocabulary to remember and use:

Dividend divisor = quotient

60 10 = 6

Today we will look at using short division. As shown yesterday,

84 4 = 21

Step by step breakdown: 84 4 =

• First write the divisor, which is 4.

• Then draw the frame. • Then write the dividend, 84. • Now divide, starting with the tens: 8 tens divided by 4 is equal to 2 tens: write 2 in the tens column.

• Then move to the ones column. 4 ones divided by 4 is equal to one one. Write 1 in the ones column.

72 ÷ 3 =

Step 1 – write the divisor and the dividend:

72 ÷ 3 =

Write ‘2’ in the tens column…

72 ÷ 3 =

… and write ‘1’ to the left of the ones digit of the dividend to make twelve ones.

72 ÷ 3 = 24 r 1

Sometimes when we divide, there will be remainders as discussed previously.

Write ‘2’ in the tens column…

Task: Activity 4

Using the method just shown, practise dividing 2 numbers by 1.

Lesson 5I can solve multiplication and

division problems

Using the methods you have learnt this week. Practise solving multiplication and division problems, using activity 5 for guidance.https://www.bbc.co.uk/bitesize/topics/z36tyrd/articles/zgxdfcw

Times table practise: All week

7, 11, 12’s

Lesson 6I can recognise and show, using diagrams, families of common equivalent fractions

Fractions. What are they?Fractions are a small or tiny part, amount, or proportion of something.

Equivalent fractions are fractions which have the same value, even though they may look different.

numerator

denominator

What fraction is represented?


6 one-sixths = six-sixths


3 one-tenths = three-tenths

What fraction is represented?4 one fifths = four tenths

Task: Complete activity 6

Lesson 7I can recognise and show, using diagrams, families of common equivalent fractions

Recap- Fractions. What are they?

Fractions are a small or tiny part, amount, or proportion of something.

Equivalent fractions are fractions which have the same value, even though they may look different.

numerator

denominator

Equivalent fractions, may look the same physically, but when written into a fraction will be different.

21

51

84

42

21

42x 2

x 2

How to find equivalent fractions?

You can make equivalent fractions by multiplying or dividing both top and bottom by the same amount. You only multiply or divide, never add or subtract, to get an equivalent fraction.

53

106

x 2

x 2

31

124

x 4

x 4

21

126

x 6

x 6

42

84

x 2

x 2

If we need to work backwards to find an equivalent fraction, instead of multiplying, we would need to divide.

104

52÷ 2

÷ 2

10 ÷o = 5

93

31

÷ 3

÷ 3 9 ÷o = 3

63

31

÷ 3

÷ 3

62

31

÷ 2

÷ 2

84

42

÷ 2

÷ 28 ÷o = 4

84

42

21

÷ 2 ÷ 2

÷ 2÷ 2

Fraction walls are a great way to help us visualise equivalent fractions. Using the fraction wall on the next page, can you identify any equivalent fractions?

Lesson 8I can calculate quantities, and fractions to divide quantities,

including non-unit fractions where the answer is a whole number

Unit and non-unit fractions.

A unit fraction has a numerator of 1. Such as ½, or ¼ .

A non-unit fraction has a numerator greater than 1, such as 2/4 or 4/6.

34

Circle of the oranges.The whole is divided into four equal parts and we have three of them.

Use the following stem sentence to identify the fraction that each part is of the whole.

The whole is divided into ___ equal parts. Each part is ___of the whole.

E.g The whole part is divided into 6 equal parts. Each part is 1/6 of the whole.

1/6 of 12 = 2

How many parts has the whole been split into?What fraction of the whole does each part represent?

Each part is !"

of the whole; !"of twelve apples is two apples.

Finding quantities How could I find !

"of fifteen?

How could I find !"of fifteen?

To calculate !"we need to find #

"first

then multiply by 3. 15 divided by 5 = 3 #"= 3 3 X 3 = 9 !

"= 9

Use the previous method to calculate the fraction of the next quantity.

4/7 of 14

Step one: find 1/7 of 14.

14 divided by 7 = 2. So 1/7 = 2.

Step two: Multiply 1/7 by 4. 2 X 4 = 8.

4/7 of 14 = 8

Lesson 9I can calculate quantities, and fractions to divide quantities,

including non-unit fractions where the answer is a whole number

Recap yesterday’s learning, looking back at strategies used to find fractions of quantities.

Finding quantities How could I find !

"of fifteen?

How could I find !"of fifteen?

To calculate !"we need to find #

"first

then multiply by 3. 15 divided by 5 = 3 #"= 3 3 X 3 = 9 !

"= 9

If this question was turned into a word problem, such as..

“If a bag had 36 items inside it and 2/3 of the items fell on the floor, how many items would still be in the bag?” The first step, we would need to find out what fraction of the objects would still be in the bag, which would be 1/3. So then we know we need to find out, 1/3 of 36. (36 divided by 3 = 12) We can check this answer, by multiplying 12 by 3, as the fraction is thirds (3 parts). 12 X 3 = 36. There are 36 items in the bag in total. So the answer, 12, is correct.

Task 9: Use your knowledge of how to find quantities of fractions to complete the problems on page, ‘activity 9’.

Lesson 10I can add and subtract fractions with the same

denominator

Adding and subtracting fractions

Top tips to remember in today’s lesson:• When adding fractions with the same denominators, just add the numerators.• When subtracting fractions with the same denominators, just subtract the numerators.• Addition and subtraction of fractions are the inverse of each other, just as they are for whole numbers.

Look at the representations below:

An apple is divided into eight equal parts.Callum eats three-eighths of the apple.Joel eats two-eighths of the apple. How much of the apple do they eat altogether?

The sum we are needing to work out is…

When we add 2 fraction together or subtract, we only look at the numerator (top number of fraction)

The previous slide showed different ways of adding two fractions. This could also be represented how we would normally add two whole numbers together.

Subtracting 2 fractions:There is eight-ninths of a full box of biscuits.Each biscuit is one-ninth of a box.If three biscuits are taken, what fraction of the box remains?

Look at the next 3 slides to see 3 methods of subtracting fractions.

Using a diagram

Number line

Verbally

Task: Using the methods shown, choose your preferred method and practise adding and subtracting fractions (activity 10).

Year 4 Maths - Westcott Primary

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