Mathematics planning: Year 5 Autumn 2: Multiplication and DivisionNational Curriculum objectivesMultiply and divide numbers mentally drawing upon known facts.Multiply and divide whole numbers by 10, 100 and 1000.Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers.Recognise and use square numbers and cube numbers and the notation for squared (2) and cubed (3)Solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes.Know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers.Establish whether a number up to 100 is prime and recall prime numbers up to 19

LI Introduction/hook

Fluency Reasoning and problem solving

Mathematical talk

To identify multiples of known tables

Fluency – find all multiples of a certain number and identify the imposters in another.

How do you know – Identify multiples of a number and develop a rule for finding them.

Rolling of the dice – children get two dice, roll then and multiply the number. The resulting number can be writing into a blank multiplication grid for those working towards expectations. For those working at or above, they and draw their own grid, deciding on what would be suitable eg a six by 6 grid.

Number cards 0-9.Children in in the multiplication grid, identifying where a number is a multiple of more than one x table.

What do you notice about the multiples of 2? What is the same about them, what is different?Look at multiples of other numbers; is there a rule that links them?

Intervention: Notes:Building on their times tables knowledge, children will find multiples of whole numbers. Children build multiples of a number using concrete and pictorial representations e.g. in an array.array.

To Identify all factor pairs of

Fill in missing factors of 24. Can they find a link between 24

Factor arrays - Place more than twenty counters on the desk so children have to reason that they do not need all of them.How many different ways can they make

Kayla’s method – Have a chat about Kayla’s method. Is it particularly good. Why?

Efficient

How can work in a systematic way to prove you have found all the factors?Do factors always come in pairs?How can we use our multiplication and

Mathematics planning: Year 5 Autumn 2: Multiplication and Divisiona number and common factors of two numbers.

and finding the missing factors of 42?

an array. Children to draw the arrays in their book and label them, writing all of the factors for twenty.

Circle the factors of 60 – explain why they are and discover which factors are missing.

Finds all possibility Systematic etc

Complete the task and explain what happens when you get to a number that is commutative. Why do we not need to write it down again?

Abundant or not abundant, that is the question – complete the example with the children and add the word to your working wall. Children who finish this task could explain the difference between abundant and not abundant.

division facts to find factors?

Intervention: Notes:Children understand the relationship between multiplication and division and can use arrays to show the relationship between them. They know that division means sharing and finding equal groups of amounts. Children learn that a factor of a number is the number you get when you divide a whole number by another whole number and that factors come in pairs.(factor × factor = product)

Identify common factors of two numbers.

Find common factors of 35 and 60. What is the highest common factor and why?

Counter factors – give children the counters (multilink can work here as well). Can children make arrays systematically which mean they find common factors?Try this for 12 which is a small number and 15.

True or false – how well do children know multiples and factors. Provide children with key vocab to help them explain their reasoning using correct mathematical language.

How can we find the common factors systematically?Which number is a common factor of any pair of numbers?How does a Venn diagram help to find common factors? Where are the common factors?

Mathematics planning: Year 5 Autumn 2: Multiplication and Division

Again, encourage systematic working out. Find all 2 digit numbers with a digit total of 6 and work their way through the rest of the question.

Intervention: Notes:Using their knowledge of factors, children find the common factors of two numbers.They use arrays to compare the factors of a number and use a Venn diagram to show their results.

To recall prime numbers to 19 and to identify a method for finding prime numbers to 100.

Explain why 5 is a prime number.

Allow children time to investigate. If they do not know what a prime is, can they use their previous learning to work out multiples and factors to

Give children counters or multilink and allow then time to investigate the arrays for the following numbers. What do they notice? What do they think these numbers are called and how could you possible tell all prime numbers?

Composite and prime carroll – Explain what a prime number is and a composite. Allow children time to write the definitions in their book for future ref. Fill in the diagram allowing children time to using counters and multilink to investigate.

Find it! Prove it! – Give children the following rule for finding a prime number to 1006n + 1 or 6n – 1Can children work out all of the numbers and decide if they are prime or composite? Children should find that unless the number is 49 or ends in a 5 it will be a prime. The reason all numbers ending in 5 are not prime is because they are all multiples of 5.

How many factors does each number have?How many other numbers can you find that have this number of factors?What is a prime number?What is a composite number?How many factors does a prime number have?

Mathematics planning: Year 5 Autumn 2: Multiplication and Division(This lesson may run over into two)

surmise what a prime may be? Task 2:

Children working towards will simply stay at this point and investigate. Those working at greater depth may move on to identifying numbers past 100.Explain the following rule and ask children to find out if it is true.

Try this:Add the numbers together to find the digital root2 + 8 + 1 =And2 + 8 + 3 =Can you divide the answer 3?If you can, then it is not a prime number. What happens if you can’t?

Intervention: Notes:Using their knowledge of factors, children see that some numbers only have 2 factors and these are special numbers called Prime Numbers. They also learn that non-primes are called composite numbers. Children can recall primes up to 19 and are able to establish whether a number is prime up to 100 Using primes, they break a number down into its prime factors.

Mathematics planning: Year 5 Autumn 2: Multiplication and DivisionTo recognise square numbers and use correct notation.

Match the square with the calculation.What do children notice about each representation?

What does the array show? – a grid which is 3 x 3 but also a square.

Make 36 – allow children time to make arrays using 36 counters or cubes. What do they notice? Do any of the arrays make a square? Which one? What do they notice about that calculation?

Find it, prove it – can children find the first 12 square numbers by making them, drawing them into their books and writing the number sentence to go with them.

Why are square numbers called ‘square numbers’?Is there a pattern between the numbers?True or False: The square of an even number is even and the square of an odd number is odd.

Intervention: Notes:Children will need to be able to find factors of whole numbers.Square numbers have an odd number of factors and are the result of multiplying a number by itself. They learn the notation for squared is 2

To recognise cubed numbers and use correct notation.

children to use the multilink on their table to form different sized cubes. Encourage them to make the smallest as this may be easier to explain using a multiplication sentence. Ask children to TTYP what a multiplication sentence is so that they are aware what they are writing down.Show children the animated section by clicking the mouse once. This will give children an extra challenge if they feel they have worked out the first question quickly.Spend 10 minutes on this and move on to the task.For example: the children can make a 2 x 2 cube which would give them 8 cubes in total. They should work out that 2 x 2 x 2 equals 8. Some greater depth children may realise, if given the algebraic

Go through Sasha’s explanation of how you find a cubed number. Bring up my incorrect response and ask children to make the cube to prove who is correct and where I have made the error.Display the other animations which ask children to think about which cubed number comes before 8 and which cubed number will come after 8. Can children make them to prove their answers?

Children should now be able to confidently work out the first 3 cubed numbers but they will have to talk to their partner about ways in which they could find cubes using larger numbers. Encourage children to uses column method for larger numbers as there will come a time when building cubes would just be too much.Task: children to stick the table into their books and complete all sections. The

Children have these sheets to stick into their books. Children working below ARE will require some support and use of the hundred square. Provide them with clues such as: Could you work out all of the cubed numbers and square numbers to see which one is the same. They can problem solve but just require extra support.Children at greater depth will naturally lead on to the more challenging tasks which also require them to understand balancing equations and prime numbers.

How are squared and cubed numbers the same?How are they different?True or False: Cubes of even numbers are even and cubes of odd numbers are odd.

Mathematics planning: Year 5 Autumn 2: Multiplication and Divisionformula, what they have to do. only cube that is not on the display is 6

cubed which they will have to work out abstractly.Allow children time to work these out and then mark with children using pink pen.

True or false answers are:1 – true 27 + 8 = 35 and 8 x 5 = 40 – 5 = 352) First 3 cubed numbers are 1, 8 and 27 and they total 36. 6 x 6 is 36 so this is true.3) 5 cubed equals 125 which cannot be a prime because it is a multiple of 5.

Intervention: Notes:Children learn that a cubed number is the product of three numbers which are the same.If you multiply a number by itself, then itself again the result is a cubed number.They learn the notation for cubed is 3

To multiply and divide numbers mentally drawing upon known facts and inverse operations.

Complete the fact family. (Clarify what a family is.

Missing numbers – complete the missing number calculations.

Balancing – complete the balancing equations

Why is it useful to know multiplication is the inverse of division?How do our multiplication and division facts link to multiples and factors?If I double the number I am multiplying by, what will happen to my answer?

Intervention: Notes:

Mathematics planning: Year 5 Autumn 2: Multiplication and DivisionGo through the second reasoning and problem solving question with the children as they could assume they are talking about the cars and bikes and not the wheels they have.

Children use their knowledge of the times tables up to 12 × 12They solve problems using their understanding of the inverse and represent times-tables in a concrete and pictorial way.

To multiply by 10, 100 and 1,000

Correct the calculations that are incorrect.

Place value calculations – provide children with a place value grid and allow them time to make the number and move the counters to where they need to be.What are they doing – correct misconceptions of just adding a 0.

Balancing – complete the balancing equations.

Which direction do the digits move when you multiply by 10, 100 or 1,000?How many places do you move to the left?When we have an empty place value column to the right of our digits what number do we use as a place holder?Can you use multiplying by 100 to help you multiply by 1,000?Explain why.

Intervention: Notes:Children recap multiplying by 10 and 100 before moving on to multiplying by 1,000. They look at numbers in a place value grid and discuss how many places to the left digits move when you multiply by different multiples of 10

Mathematics planning: Year 5 Autumn 2: Multiplication and DivisionTo divide by 10, 100 and 1,000

Correct the calculations that are incorrect.

Place value calculations – provide children with a place value grid and allow them time to make the number and move the counters to where they need to be.What are they doing? – correct misconceptions of just taking away a 0.

What happens to the digits?How are dividing by 10, 100 and 1,000 related to each other?How are dividing by 10, 100 and 1,000 linked to multiplying by 10, 100 and 1,000?What does ‘inverse’ mean?

Intervention: Notes:Children look at dividing by 10, 100 and 1,000 using a place value chart. They use counters and digits to learn that the digits move to the right when dividing by powers of ten.

To find multiples of 10, 100 and 1,000.

Complete fluency calculations which help children unpick misconceptions about adding and taking away 0s.

If we are multiplying by 20, can we break it down into two steps and use our knowledge of multiplying by 10? How does using multiplication and division as inverses help us use known facts?

Mathematics planning: Year 5 Autumn 2: Multiplication and Division

Intervention: Notes:Children have been taught how to multiply and divide by 10, 100 and 1,000. They now use knowledge of other multiples to calculate related questions.

Intervention: Notes:

Intervention Notes

Intervention: Notes: