Maths

Y5 Maths

Key Stage 2

Year 5

Multiplication and division

In this lesson, we will refamiliarise ourselves with the concepts of multiples and factors. We will use the language of factors and multiples by giving examples, describing rectangular arrays and defining the terms. We will then model how to solve missing number puzzles requiring understanding of the language before letting you have a go independently.

Multiples and factors

In this lesson, we will be learning how to work systematically to identify the correct number of factors and factor pairs for given numbers, using the notion of factor bugs to help us.  We will then develop our learning further by proving that square numbers have an odd number of factors.

Factor pairs

In this lesson, we will explore numbers with only two factors and define these as prime numbers. We will then play a game that involves making arrays and identifying prime numbers up to 20. Our independent task to conclude the lesson will require all prime numbers up to 100 to be identified by using a range of clues based on multiples and factors.

Prime numbers

In this lesson, we will use our prior knowledge of multiples and factors to create chains, playing a game whilst investigating number patterns. We will then adapt the rules of the game to create alternative chains, being challenged to try and identify ever increasing lengths of chains.

Factor and multiple chains

In this lesson, we will be required to explain and demonstrate the process of multiplication and division by 10, 100 and 1000 using different visual representations. This understanding will then enable us to derive facts from known multiplication facts which we can represent and explain. The expectation is that by the end of this lesson we will be confidently able to explain and demonstrate how to multiply and divide by 10, 100 and 1000.


Multiplying and dividing by 10, 100, 1000

In this lesson, we will explain and model mental strategies for doubling and halving by using our understanding of multiplication and division. We will also use our doubling and halving strategies to multiply and divide by four and eight. By the end of this lesson, we would hope that everyone will be confident in explaining how to multiply and divide by four and eight by using strategies of doubling and halving.


Doubling and halving strategies

In this lesson, we will use our knowledge of multiplying and dividing by 10, 100 and 1000 to derive facts from known facts. We will then use the distributive law and derived facts to multiply by choosing the most efficient and effective representations.

Using derived facts to multiply mentally

In this lesson, we will learn to estimate using derived facts and then adjust them to calculate the answer. We will then be able to solve a range of problems selecting suitable strategies and giving reasons for our choices.

Calculating flexibly

In this lesson, we will using the formal written layout to multiply numbers with up to four digits by a single digit, looking at it with both pictorial, concrete and abstract representation. We will  then develop our strategy to understand how to use the same method to multiply by 2-digit multiples of ten.

Short multiplication

In this lesson, we will explore area models using Dienes blocks to represent multiplication. This is connected to the steps involved in long multiplication and we will then gain experience with the formal algorithm.

Long multiplication

In this lesson, we will begin by introducing the context of synchronized swimmers arranged in groups within squads to multiply three numbers in different arrangements. They use different factor pairs to solve the same problem in different ways. We will also look at distributive law can be represented using area models.

Using factors to multiply

In this lesson, we will explore dividing numbers by partitioning into multiples and dividing the parts. We will start with calculations that involve dividing by a single digit making links to the multiplication calculations in the last lesson. We will then find multiples of 2-digit numbers and use these to divide by partitioning into multiples in order to divide each part.

Using multiples to divide

In this lesson, we will solve division problems using short division and place value counters. We will start by exploring division by sharing and then division by grouping, showing how to record the formal method of short division whilst demonstrating each stage of the process using pictorial and concrete representations.

Short division

In this lesson, we will explore how to interpret remainders in the context of a problem. We will begin with very simple numbers we can calculate mentally, reasoning whether the answer needs to be rounded to the next whole number or not before moving onto numbers suited to a short division strategy.

Division with remainders

In this lesson, we will revisit some of the man learning concepts taught across the unit. We will be reviewing our understanding of multiples and factors; multiplying and dividing by 10, 100, 1000; mental strategies for efficient mental calculation and finishing off the lesson by consolidating our familiarity with formal methods of multiplication and division. At each section, problems and challenges will be presented and then discussed.

Key Stage 2, Maths, Multiplication and division