**I wrote recently about the pros and cons of homework where I discussed my views on this divisive subject. One of the cons is that it eats into family time and chilling out time. A few nights ago, I spent about 2 hours, in and around making tea and a lemon drizzle cake, helping Delilah with her year 5 maths homework. The subject of the home was around multiplying 3-digit numbers by 2-digit numbers. But there was a catch – some digits were missing from the sums.**

I am not about to moan about the setting of difficult or challenging homework. This also isn’t a whinge at how much time it took, especially on her night off from dancing. Sometimes I enjoy a challenge, and for me, that challenge was explaining how to find these missing numbers to my daughter.

I had some concerns that maths seems to have leapt forward in her transition from year 4 to 5 so as well as Helen talking to her teacher I phoned and spoke to the head of school too to find out why. At this point, I need to just clarify that I have no issues with the way Delilah is being taught, with the teachers, or with the school – it’s a great school.

#### The change to the national curriculum

There’s a reason why year 5 maths is getting harder.

Having spoken with the school it’s now apparent what is going on. The national curriculum was changed in 2014 so there is a pre-2016 national curriculum and a post-2014 national curriculum. Up until the end of year 4, Delilah was being taught on the pre-2014 national curriculum. But, crucially, the government’s Department for Education had in mind a full adoption date. This happens to mean that when Delilah moved into year 5 she would now working to the post-2014 national curriculum.

To understand the changes to the national curriculum I found this BBC new article summarises it very well – How the National Curriculum Is Changing. For more reading on the changes click here.

Essentially the focus is on English, maths or science. The curriculum has been trimmed down in all other subjects at key stages 1 and 2. We’ve actually noticed this through talking to the girls about school. They have a daily routine that heavily focuses on English and maths, whereas looking at history, geography and art seem to have taken a back seat. But, the crucial thing to understand is that in those core subjects learning objectives have been pushed forward so that more advanced skills are being taught at a younger age.

If I am honest, I don’t like the changes. I like even less so that cohorts of children have been given a big step to climb – or as our head of school puts it “climbing a ladder with a missing rung”.

#### The maths homework challenge – part 1

Enough about my frustrations with the national curriculum, here’s an example of the type of question set in the homework.

The task is to work out the missing number on the top line.

The first thing to understand is that all the information needed is right there. I know that sounds obvious, but ensuring a 10-year-old, that is not confident with maths, understands this is vital. The second thing to understand is that, as with many mathematical conundrums*, there’s more than one way to go about this equation. A child might really grasp one way of doing it, but not the others. Sometimes the problem is that the national curriculum wants certain methods taught – but what if that is the method your kid just cannot grasp? *On a side note; I remember when Lydia was in year 3 and I taught her column addition to do some of her homework, but I was “told off” by her teacher as they no longer taught column addition – mental! *So I set about finding the method Delilah would understand the best.

##### Method 1:

The first method works on the fact that 2712 is the result of 4_2 x 6 and 13560 is the result of 4_2 x 30. So it simply a case of either doing either 2712 ÷ 6 or 13560 ÷ 30. Of course, without a calculator, this would require long division. I don’t know about you, but the mere mention of long division brings me out in cold sweats! Luckily, today kids are taught division by chunking and to understand this (if you don’t know it) check out this YouTube video that explains it:

Using division by chunking you would end up with something similar to this:

This results in 2712 ÷ 6 = 452, so the missing digit is 5. You could use the same method for 13560 ÷ 30 and get 452 also.

##### Method 2:

In this second method, we will work to reverse how a student would have calculated 4_2 x 6. As shown in the original equation, when multiplying a 3-digit number by a 2-digit number you first multiply the 3-digit number by the units (6) then the tens (30) of the 2-digit number. Then add those two results together to get your final answer.

So, we look at what we know and what we know we can calculate.

We know that the result of 4_2 x 6 is 2712. We also know that in long multiplication we multiply 6 by the units (2), tens (unknown) and hundreds (4) then add those results together to get 2712:

If we take the results we can calculate (12 and 2400) away from 2712 we are left with 300. We have then got the result of the unknown number multiplied by 6.

I then had to take some artistic license (or whatever the teaching equivalent is). I told Delilah that because the number we’re looking for is in the tens column we now divide 300 by 10. Or in other words – take a zero off the end. This leaves us with 30. Now it’s just a matter of knowing your 6 times table and knowing that 6 x *5* is 30. So the missing digit is 5.

#### The maths homework challenge – part 1

Of the various questions on her homework, many had the missing number in the 3-digit number and the methods I explained above work for all of them. But what if the missing number is in the 2-digit number? Let’s look at an example.

How do we go about solving this one?

##### Method 1:

My first method in this case, and it won’t work for all examples but simply highlights the importance of knowing your times tables, is as follows.

There is a rule that applies to these multiplications. The unit value from the 3-digit number multiplied by the unit value from the 2-digit number is the only one that affects the unit value in the answer. This means that the 1 in 981 is a result of 7 x {missing number}. We know that the missing number can only be 0 to 9, and therefore we also know that the only 7 times table result that ends in a 1 (going up to the 9 times table) is 21 when you multiply it by 3.

Therefore the missing number is 3.

##### Method 2:

You could use the division by chunking, as above, to calculate 981 ÷ 327. That’s quite a tricky one to do so you might try simplifying it.

Start by asking how many times does 300 (from 327) go into 981. That would be 3 times, leaving you with 81. Then you are left with the simpler division by chunking of how many time 27 goes into 81, and the answer is 3.

#### The importance of basic maths skills

It’s no surprise that the key to understanding how to solve these problems is having strong core maths skills. You require nothing more than knowing the following:

- column addition
- column subtraction
- long multiplication
- long division/division by chunking
- timetables from 1 to 10

Those 5 skills will see you through any mathematical issue, even when you tackle the dreaded algebra! The key to it, of course, is knowing how to apply them.

I hope my approach to this maths homework has been useful to you. Can you think of any other ways of solving these? Maybe I’ve missed a really obvious, much simpler way.

**Proving that every day is an education, I learnt about the proper plural word for conundrum. I won’t bore you with the Internet rabbit hole I fell down in order to find this out, but safe to say that the internet seems split as to whether it is conundra or conundrums! I chose to go with conundrums as I suspected this would be to more formally accepted plural.*

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