Short division of decimals (1)

Here is a page of practice on using the short method of division of decimals. The numbers being divided are just units and tenths which helps with getting the method correct.

There are arguments for and against putting the decimal point in before you start, or leaving it until you have reached that point in the question. it does not matter as long as it is inserted correctly.

One of the best ways to be fluent with this method is to talk it through out loud. If we look at question 2 which is 4.5 divided by 3, the verbal stages are:

a. How many 3s in 4?

b. 1 times 3 is 3 so there is 1 with a remainder of 1.

c. Place the 1 on the answer line, immediately above the 3.

d. Place the decimal point just above the answer line so it can be clearly seen.

e. The remainder 1 is placed just in front of the 5 (usually written smaller).

f. How many 3s in 15?

g. 3 x 5 is 15 so the answer is 5.

h. Place the 5 on the answer line, immediately above the 5 (tenths).

i. Answer 1.5

This page can be found in our Four Rules, Division category.

Division of decimals (1)

Year 5 subtraction worksheets

Here are two worksheets to help assess whether children have a good grasp of subtraction.

They revise the following concepts:

Subtraction is the same as taking away, finding the difference between, and complementary addition.

Subtraction is non-commutative.

When a larger number is subtracted from a smaller number, the answer is negative.

Subtracting a number from another makes it smaller.

Subtracting zero makes no difference to a number.

Subtraction is the inverse of addition.

By year 5 children should have good mental strategies for solving subtraction problems.

These pages, and other similar can be found in our Year 5 subtraction category.

Revise understanding subtraction (1)

 Revise understanding subtraction (pg 2)

8 times table practice

Here we have another in our series of Rocket tables sheets. This time it is the 8 times table, which is one of those tables that many children never really get to learn ‘off by heart’. This page makes a good check sheet to see whether the table is known: if it is then it will take little time to complete. If the table is not known then much more time will be needed.

It can be argued that the 8 times table can be derived from doubling the 2x table and then doubling again.Of course, this is true, but it just takes too long.

This can be found in our Maths Worksheets, Four Rules section.

8x tables space challenge

Year 6 maths worksheet: adding fractions

My first addition of fractions page was very popular and I have had  several requests for more, as it does take some time and re-inforcement to get the hang of this concept. I believe that adding fractions is one of the hardest topics for children to understand, mainly because it involves so many steps.

Remember, to add two fractions the denominator has to be the same: this requires a good understand of equivalent fractions, so make sure that this is fully understood before attempting addition. Once this has been done the addition is easy, as the denominator stays the same and just the top numbers (numerators) are added.

This will result in a vulgar fraction eg 14/10 which needs to be converted to a mixed number.

As there are ten tenths in one whole one this makes 1 and 4/10.

Finaly the fraction can be simplified: 4/10 is the same as 2/5 so the final answer will be 1 and 2/5.

This page can be found in our Year 6, Calculating category.

Adding fractions that total more than 1 (pg 2)

What maths should children know by the end of Year 6?

This is the final article in our series on what maths children should know, although I will be returning to this theme again and again in the future.
Much of the work carried out in year 5 eg addition and subtraction will need to be reinforced and is not covered in these targets for year 6. Please note that this is only a summary of the key areas of maths to be covered in the year. Some of the work here will be too difficult for many year 6 children: it is very much a set of targets published by the Primary Framework rather than a realistic review of what children can actually achieve. It does give you a good idea of what teachers are hoping to achieve with their children by the end of year 6.
I believe that if a child can successfully meet these challenges then they have a very bright future in maths ahead of them.

Counting and understanding number:

By the end of year 6 children should
• be able to add or subtract using negative numbers in contexts such as temperature.
(eg The temperature is -7 degrees. It rises by 3 degrees. What is the new temperature?)

• understand decimals up to thousandths and partition numbers.
(eg 4.567 = 4 units + 5 tenths + 6 hundredths + 7 thousandths.)

• round decimals.
(eg round 4.56 to the nearest tenth.)

• order decimals up to 3 decimal places and place them on a number line.
(eg order these numbers: 0.7, 0.77, 0.707.)

• understand and use improper fractions.
(eg recognise that 8 pieces of a 5-piece chocolate cake is 8/5 or 1 and 3/5.)

• simplify fractions by cancelling.
(eg 6/10 = 3/5.)

• write one quantity as a percentage of another.
(eg write £30 as a percentage of £300.)

• find equivalence between percentages, decimals and fractions.
(eg 1/10 = 10% = 0.1.)

• solve simple problems involving ratio and proportion.
(eg Sarah has 15 sweets. She gives Tasha 1 sweet for every 4 she keeps herself. How many sweets does Tasha get?)

Knowing and using number facts:

By the end of year 6 children should
• use knowledge of tables to multiply decimals.
(eg multiply 0.6 by 8.)

• use knowledge of tables to divide decimals.
(eg divide 4.8 by 8.)

• use knowledge of tables to work out square numbers up to 12 x 12.
(eg the square of 11?)

• use knowledge of tables to work out the squares of multiples of 10.
(eg the square of 30?)

• understand that prime numbers only have two factors and identify prime numbers up to 100.
(eg what is the next prime number after 17?)

• find the prime factors of 2-digit numbers.)
(eg find the prime factors of 12.)

• use various methods to check answers to calculations, including rules of divisibility.)
(eg if the sum of the digits of a number is divisible by 3 then so is the number.)

Calculating:

By the end of year 6 children should
• mentally add decimals.
(eg 4.5 + 3.2)

• mentally subtract decimals.
(eg 5.4 – 3.8)

• mentally multiply decimals.
(eg 3.6 x 5)

• mentally divide decimals.
(eg 4.5 divided by 9.)

• use efficient (standard) methods to add numbers, including decimals.
(eg £6.78 + £9.85)

• use efficient (standard) methods to subtract numbers, including decimals.
(eg £9.78 – £5.85)

• use efficient (standard) methods to multiply numbers, including decimals.
(eg 345 x 67)

• use efficient (standard) methods to divide numbers, including decimals.
(eg 456 /8)

• relate fractions to multiplication and division.
(eg 8 divided by 2 = ½ of 8 = 8 x ½)

• know the term quotient and state as a fraction or a decimal.
(eg 54 divided by 5 = 10.8 or 10 and 4/5.)

• find fractions of whole numbers.
(eg find 4/5 of 60.)

• find percentages of whole numbers
(eg find 60% of 48.)

• make sensible use of a calculator to solve multi-step problems.

Understanding shape:

By the end of year 6 children should
• classify 2-D and 3-D shapes according to their properties, including recognising parallel and perpendicular sides/edges.
(eg know the diagonals of a square intersect at right angles.)

• become increasingly accurate when drawing or making shapes.

• be able to reflect, translate and rotate shapes through 90 degrees or 180 degrees.
(eg sketch the reflection of a 2-D shape on a grid.)

• use co-ordinates in the first quadrant to draw and complete shapes.
(eg sketch the position of a triangle after it has been translated 2 units down.)

• learn to use a protractor to measure and draw angles.
(eg draw an angle of 45 degrees.)

• calculate the angles in a triangle.
(eg if two angles of a triangle are 60 and 70 degrees, calculate the third angle.)

Measuring:

By the end of year 6 children should
• choose and use to a suitable degree of accuracy metric units of measurement.
(eg measure 450 ml of water in a jug.)

• convert between units using decimals to two places.
(eg change 3750 ml to 3.75 litres.)

• recognise that measurement is approximate and decide on the necessary degree of accuracy when measuring.
(eg measure the length of a tray to the nearest 1 cm.)

• calculate the perimeter and area of rectangles.
(eg know the formula for finding the area of a rectangle.)

• estimate the area of irregular shapes by counting squares.
(eg count any square more than half covered as a whole square and any less than half as zero.)

Handling data:

By the end of year 6 children should
• use the language of chance or likelihood to describe and predict outcomes.
(eg answer the question; what is the probability of throwing a 5 with a 1 to 6 dice?)

• collect, sort, process and present data to solve a problem and interpret the results.
(eg find the most common period of time that goals are scored in the Premier League.)

• construct frequency tables, bar charts, line graphs and pie charts to show results of investigations.
(eg show frequency table for times of goals scored.)

• identify the difference between discrete and continuous data.
(eg draw a line graph in which intermediate values have meaning.)

• use the terms mode, range, median and mean.
( eg know that mode means the most common.)

Using and applying mathematics:

By the end of year 6, when investigating, children should
• choose appropriate operations to solve multi-step problems.

• decide whether to calculate mentally, on paper, or by calculator.

• use tables to show the steps taken.

• record results and check accuracy.

• suggest plans and lines of enquiry.

• review methods used.

• begin to use simple formulae in words and then symbols.

• explain orally, in words or diagrams their reasoning and conclusions.

Mangahigh free for schools

In a very exciting development, I have just heard that Mangahigh is going to be absolutely free from tomorrow for schools to use. In fact, going to the site, it is free now!! From tomorrow the mangahigh.com games-based resources will be completely free for UK and Irish schools. Previously Mangahigh charged for access but they feel that a free service is more attractive for teachers.

Toby Rowland, CEO and founder of mangahigh said,

‘We know that schools across the UK and Ireland are short on funding, and the situation may get worse before it gets better. That’s why we think it’s the perfect time to launch a completely free maths resource for schools.’

Incorporating more than 45000 maths questions and 11 unique maths games as well as powerful analytic tools it must be well worth a visit.

mangahigh

Know number facts in Year 2

A lot is expected of children in Year 2, especially what they should know off by heart when calculating. By the end of the year they should:

•    know all addition facts for two numbers up to a total of 10.      (eg 4 + 5.)

•    be able to derive subtraction facts for numbers up to 10.     (eg if they know that 6 + 3 = 9, they can instantly work out that 9 – 6 = 3.)

•    know all the pairs of whole numbers which total 20.    (eg 16 + 4.)

•    know all the pairs of multiples of 10 which total 100.   (eg 30 + 70.)

•    know the doubles of whole numbers up to a total of 20.  (eg double 7.)

•    understand that halving is the inverse of doubling and hence derive halving facts from their knowledge of   doubling.   (eg if double 8 is 16, then half 16 is 8.)

•    recall 2, 5 and 10 times-tables.  (eg know 5 x 6.)

•    work out related division facts.   (eg if 5 times 2 is 10, then 10 divided by 5 is 2.)

Now, that is quite a lot to know with instant recall, and they will need plenty of practice to achieve this. Why not go to our Year 2 Knowing and Using Number facts to help them on their way?

Year 2 Knowing Number Facts

Maths puzzle: Year 4 Handling data wordsnake

The Primary Framework for Mathematics has given each year group a set of mathematical words that they should know. This word snake contains words from the data handling section of year 4. There are only 8 of them but every letter in the grid is used once.

The words can be found by moving across or up and down (but not diagonally). The next word follows on directly from the first.

The first word (survey) is given to you so that you can get the idea. The first letter of next two words is also given, then you are left to find them with no help.

This is not easy: try it yourself. A great way to use some of the necessary language in a fun way.

This page can be found in our Maths Puzzles category.

Maths puzzles: Wordsnake year 4 data handling

Maths game: Three hexagon

Playing board games and card games from an early age is a great way to help children with their maths. Whether it is matching pairs, counting on or back or throwing dice, the participation involves calculating skills, predicting, seeing patterns and thinking logically.

Here we have a great little maths game for young children, thanks to MathSphere from its CD, ‘It’s All Figured Out!’

The rules are as follows:

This is a game for two people.

Each player has three counters.

The aim of the game is to get the three counters in a straight line.

The player going first places a counter on one of the circles.

The second player then places one of his/her counters on a circle. This continues until all the counters have been placed.

If neither player has got 3 counters in a straight line then the first player slides a counter along a line to a circle that is not already covered.

The other player then slides a counter to an adjacent circle.  Counters can only move along one line into an empty space. They can not jump over counters.

If a player can not move a counter she/he misses a go.

Is there an advantage in going first? By careful placement of the counters at the start of the game can you ensure that you will always win?

3 hexagon

Written methods of multiplication

In our Four Rules, Multiplication category we have a range of pages which look at written methods of multiplication. Parents seem to have been confused by what is taught in school, but it is really the process leading up to the standard written method which has changed: the standard method itself is very much the same as when parents were children and even when grandparents were children!

The worksheets take a brief look at moving towards the standard method and then we have worksheets on:

  • short multiplication: multiplying 2-digits by 1-digit
  • multiplying 2-digit numbers by multiples of 10
  • multiplying 3-digits by 1-digit
  • multiplying money by a single digit eg £3.45 x 4
  • multiplying decimals eg 3.8 x 7

On most of these pages there are clear explanations of how to do them, which have been very popular with both parents and teachers.

Why not go to our Four Rules, Written Multiplication section?