# Relationship between multiplication and division ks2

### Multiplication and Division KS2 : angelfirenm.info

The tasks in this collection encourage upper primary children to look deeper at multiplication and division. Multiplication and Division. Rules to help! Multiplication and Division are opposites. See the Family of Facts: 4 x 3 = 12 ÷ 3 = 4. It's all about Groups. This is a complete lesson with teaching and exercises about the relationship between multiplication and division, meant for third grade. They are opposite.

This representation not only assists in understanding the process, but provides a visual image for children to draw upon as they begin to use and memorise the basic number facts. Using arrays to explore larger numbers Arrays can be helpfully used to explore calculations such as 13 x 5 where the array can be split into useful chunks such as 10 and 3.

## Multiplication and Division KS2

This means that children can use their known number facts to work out calculations. After a while drawing all the dots can get very tedious! The blank array then becomes a very useful tool for helping children model their thinking and work out how to do more complex multiplications in an informal way. Here's a child using the blank array, as a thinking tool, to help them work out 15 x The blank array helps children to use other strategies, such as compensating, when carrying out multiplication.

Here, to work out 34 x 9, the child has decided to do 34 x 10 and then take off the 34 x 1. Beyond the blank array this 'dividing the multiplication into easy parts' strategy can be formalised into the grid method.

The children can see how the 'abstract' grid method overlays the array and formalises the blank array into a standard form. Division as the Inverse Operation of Multiplication Of the four operations, division is the most troublesome for young students.

Full understanding of division tends to lag well behind the other operations. For many children opportunities to explore the concept with concrete materials are curtailed well before they perceive the relationships between division and the other four operations. One such relationship, the inverse relationship between division and multiplication, can be effectively illustrated using arrays.

Language clearly plays an important role in being able to express the mathematical relationships and the physical array supports this aspect of understanding by giving the children a concrete image to talk about.

Placing the mathematics into a real-life context through word problems can facilitate both understanding of the relationship and its expression through words.

### Relationship between Multiplication and Division

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse? Mystery Matrix Age 7 to 11 Challenge Level: Can you fill in this table square? The numbers 2 were used to generate it with just one number used twice.

Use 4 four times with simple operations so that you get the answer Can you make 15, 16 and 17 too?

- The Connection Between Division and Multiplication
- Maths KS1 / KS2: The relationship between multiplication and division

Multiplication Squares Age 7 to 11 Challenge Level: Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only. Factor Lines Age 7 to 14 Challenge Level: Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Can you make square numbers by adding two prime numbers together? We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

Which is quicker, counting up to 30 in ones or counting up to in tens? Can you put the numbers 1 to 8 into the circles so that the four calculations are correct? Odd Squares Age 7 to 11 Challenge Level: Think of a number, square it and subtract your starting number. How do the images help to explain this? One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

Carrying Cards Age 7 to 11 Challenge Level: These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers? Multiples Grid Age 7 to 11 Challenge Level: What do the numbers shaded in blue on this hundred square have in common?

What do you notice about the pink numbers? How about the shaded numbers in the other squares? Age 7 to 16 Challenge Level: This game can replace standard practice exercises on finding factors and multiples.

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time? What's in the Box? This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Factor-multiple Chains Age 7 to 11 Challenge Level: Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers.

**Math Antics - Integer Multiplication & Division**

How about the largest possible numbers? Four Go Age 7 to 11 Challenge Level: This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row? Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

Choose a symbol to put into the number sentence. In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time? Explore Alex's number plumber.

## Arrays, Multiplication and Division

What questions would you like to ask? Counting Cogs Age 7 to 14 Challenge Level: Which pairs of cogs let the coloured tooth touch every tooth on the other cog?

Which pairs do not let this happen? Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights? Follow the Numbers Age 7 to 11 Challenge Level: What happens when you add the digits of a number then multiply the result by 2 and you keep doing this?

You could try for different numbers and different rules. Ip Dip Age 5 to 11 Challenge Level: Curious Number Age 7 to 11 Challenge Level: Can you order the digits from to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Factor Track Age 7 to 14 Challenge Level: Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules. Square Subtraction Age 7 to 11 Challenge Level: Look at what happens when you take a number, square it and subtract your answer.

What kind of number do you get? Can you prove it? Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether! What do you think is happening to the numbers? These practical challenges are all about making a 'tray' and covering it with paper.

Multiply Multiples 1 Age 7 to 11 Challenge Level: Can you complete this calculation by filling in the missing numbers?