Perpendicular lines

perpendicular linesThe term perpendicular was usually introduced to children in the upper primary years and indeed into secondary school, but it is now thought that it should be introduced in year 3. At this stage children just need to be able to recognise two lines which are perpendicular to each other and to make it easier all the pairs of lines shown on the worksheet either cross or touch.

Of course, the key to being able to do this is to recognise a right angle and plenty of practice with recognising right angles must be done before going on to using the term perpendicular.   When the lines are vertical and horizontal it is quite easy to spot perpendicular lines but other placements make it more difficult to see just by looking and there is no harm in using the corner of a piece of paper to judge whether this is the case.

Perpendicular lines

Roman numeral clock faces (2)

roman numerals clock 2Our Roman numerals clock face worksheet has proved very popular so I thought I would post another similar page, but including quarter to and quarter past the hour times. I have also been asked why the clock face shows IIII for four o’clock rather than IV. In fact most Roman clockfaces do show the four Is and nobody is sure why.

One reason is that when looking at the numerals opposite to each other – all of them are in perfect balance, except for the ‘heavy’ VIII and the ‘light’ IV; optical balance is re-established by printing an also ‘heavy’ IIII.

Another reason which has been given is to do with the old casting process of the numerals; ‘ Since some numerals were cast out of metal, or carved out of wood or bone, you need 20 I’s, 4 V’s, and 4 X’s, even numbers of each, if you use four I’s for “four”. The molds would produce a long centre rod, with 10 I’s, 2 V’s, and 2 X’s on each side.’

A third possibility is that clocks use IIII rather than IV out of respect for the Roman God Jupiter, the king of the Gods,  whose name, in Latin, begins IV (the V being the U we now use, the I the J). Very old sun dials seem to use the IIII and early clocks followed suit; it has also been suggested that Wells Cathedral clock, one of the earliest cathedral clocks used the IIII and everyone copied this, and yet another reason is that Louis XIV preferred IIII over IV and ordered all clocks to be made in this way, and it has remained like this ever since.

Finally it has also been suggested that Romans were not great at subtraction so IIII was easier to work out than IV! I have no idea which, if any of these has the best claim to being true but interestingly Big Ben uses the IV convention.

Roman numerals clock  2

Mental division practice

being able to divide mentally is essential and is made much easier by knowing times tables.

Here is a follow up page to one published earlier, giving more practice with simple division. If children have a good knowledge of the 2x, 4x, 5x and 10x tables they should find these quite straightforward. The only potentially tricky ones are where the missing number is in the middle of the number sentence

eg 24 divided by ? = 6

This requires a good understanding of what the number sentence means, but all that is required to answer is a knowledge of ‘what multiplied by 6 makes 24’.

This worksheet can be found in our Year 3 Knowing Number Facts section.

Y3 division practice 2

Roman numeral clock faces

roman numerals clockOne of the new targets for maths in year 3 will be to, ‘tell and write the time from an analogue clock, including using Roman numerals from I to XII’. As I haven’t published any time sheets using Roman numerals I thought that now was the perfect opportunity; so here it is!
It is best that children are introduced to the Roman system of numbers before doing this worksheet, although it is interesting to understand that many adults do not look at the numbers around the clock, just the angle of the two hands and indeed many fashion watches fail to have numbers on at all, but we still manage to be able to tell the time.

This page sticks to just whole hours and half hours, although perhaps it should be pointed out that Julius Caesar and his chums would never had read the time in this way!!

Roman numerals: clock faces

Year 3 money problems: packed lunch

packed lunchBy year 3 children will be well acquainted with the pound and pence signs and should know that there are 100 pence in a pound. They should also be familiar with the way that we show money in pounds e.g. £2.34 where the decimal point separates whole pounds from pence and that the digits in first column after the pound sign represent 10ps and the second digit represents single pence.

This worksheet looks at some simple addition of money using both pounds and pence and involves working out answers using more than one operation or process; this always makes it harder.

Buying a packed lunch

Days, months and years

days months yearsAs children progress through year 3 and into year 4 it is expected that they get to know and number of facts to do with measuring time, other than just reading the time on a clock face. These facts include knowing that:

1 year = 365 days or 52 weeks or 12 months

1 week = 7 days

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds

hey should also be able to use a calendar and write the date correctly.

This will then progress onto knowing the number of days in each month. There are several ways of doing this. I prefer the ‘knuckle trick’ of putting both fists together , knuckles upright and then reciting the months going from left to right – tops of knuckles have 31 days, dips don’t.

The rhyme below can also be helpful:

30 days hath September

April, June and November,

All the rest have 31,

except in February alone

which has but 28 days clear

and 29 in each leap year.

Days months and years


Year 3: More missing numbers

I have had a number of requests for more pages similar to the ‘Find the Missing Numbers’ published in May, so here is another.

The questions are all similar:

e.g. Find a pair of numbers with a sum of 7 and a product of 12.

Pairs of numbers with a sum of 7 are:

1 and 6

2 and 5

3 and 4

(it is not necessary to go on to 4 and 3 etc) as these have already been found.

Pairs of numbers with a product of 12 are:

1 and 12

2 and 6

3 and 4

Look for the same pair and the answer is 3 and 4.

Find the missing numbers (2)

Year 3 Maths: Find the missing numbers

What looks like a very simple worksheet is actually rather tricky. There are six statements about pairs of numbers, along the lines of:

Find a pair of numbers with a sum of 8 and a product of 15.

Firstly, children need to know that the sum of two numbers is found by adding up. Secondly, they need to know that to find the product of two numbers they need to multiply them together.

It is then a matter of some ‘trial and error’ work, finding two numbers which meet one of the criteria and then seeing if they meet the other. For those who are good at times tables it is more efficient to start with finding products, as there are less possible answers.

Find the missing numbers 1

Measuring in kilometres

shape imageChildren in the UK get far less experience at using kilometres than most Euoropeans because we have decided to keep with the mile for most of our longer measuring. Of course this is a nonsense: to start with a system using mm, cm and metres and then switch to a completely different system ie miles does not make any sense at all! Until our road signs are changed there is little hope of any improvement in this situation.

Whilst there are 1760 yards in a mile the much simpler metric system has the easy to calculate 1000 metres in a kilometre.

At this stage children should be beginning to write half a kilometre as 0.5 km but 1/2 km is acceptable. This free maths worksheet concentrates on writing half kilometres as decimal fractions.

Free Y3 maths worksheet: Measuring in kilometres (pg 3)

Year 3 graphs

I have published a page on graphs for year 3 children today; thanks to urbrainy for this resource. The main difference with data handling from year 2 to year 3 is that the reading divisions becomes harder as they may no longer go up in ones. Hence children are having to find numbers half way between two others.

This graph looks at interpreting the data of a graph showing the most popular zoo animals. The second page  shows a blank tally chart so that children can collect their own data and then create their own graph.

Zoo animals graph