Month: October 2011

Completing multiplication number sentences

This maths worksheet is suitable for Year 5 children who have a good knowledge of the times tables and can manipulate numbers ‘in their heads’.

It is surprising the number of different strategies we use to calculate mentally. The same type of question can be processed several different ways, often depending on the numbers being use. If we look at some of the questions on this worksheet it will become clearer as to what I mean, as I try to explain how I go about answering them, although you may well have different (and better) alternatives.

Question 1: ? x 2 = 120

Looking at the question I immediately think that I have to halve 120 to get the answer. I do this by halving 12, which is 6 and multiplying by 10, making 60. This is all done in a split second, and I might be tempted to think I did it in one, but it is important to stop and think of the steps that you go through.

Question 3: ? x 4 = 48

I could have halved and halved, or divided by 4, but, in fact, I learned my 12 times table many years ago and I know, instantly,  that 12 x 4 = 48 so the answer of 12 came immediately.

Question 4: 41 x ? = 205

The answer was not immediately obvious. I looked at the unit (1) and the unit in the answer (5) and it struck me that I need to multiply by 5. A quick check that4 x 5 will give me 20 confirmed this.

These are just a few of the ways of working out the answers and it is well worth asking children how they go about finding the answers.

Complete multiplication number sentences (1)

 

Resource of the Week: Congruent shapes and scalene triangles

Today we look at two mathematical terms which are less commonly known. Firstly, congruent is a word to conjure with! In fact it has a very simple meaning. If two shapes are congruent then they are identical in every way, including size.

Whilst this is very straightforward, unfortunately people who design maths tests papers make this as difficult as possible, as children are expected to be able to spot congruent shapes even when one of a pair has been turned. By far the easiest way to spot two congruent shapes is to cut one out, or trace it and see if it fits exactly over the other – if it does it is congruent. On this worksheet the aim is to find pairs of shapes which are congruent, and as always, the answers are provided! I do recommend the tracing option!

The second term is scalene. Most people are familiar with equilateral triangles and isosceles triangles but the term scalene triangle is the one that is most frequently forgotten. Quite simply, a scalene triangle is one which has no sides the same length and no equal angles.

These two worksheets can be found in the Year 5, Shape and Measures category.

Congruent shapes

Scalene triangles

KS2 Maths Paper 2010 Question 13

This is question 13 from the 2010 SAT Paper A.

It is a nice little question to pick up two valuable marks, especially if near the level 3/4 or 4/5 boundaries, but one again, more than one calculation has to be made to reach the correct answer.

The first thing to do is work out that two of the lighter grey rectangles will total 40 cm. Then subtract 40 cm from 45 cm, leaving 5 cm which is the answer to 13a.

The second part can be worked out in several ways, including:

1. Subtract 5 cm from 20 cm, leaving 15 cm. (Here is the reason for the optional mark if the answer is incorrect as it shows an understanding of the problem.)
2. Work out that 3 of the light grey rectangles will total 60 cm. Subtract 45 cm from 60 cm which gives 15 cm.

One mark is awarded for the correct answer to 13a.
One mark is awarded to the correct answer to 13b.

Question 13 from SATs Paper A 2010

Question 13 answers and suggested method

Year 4 Calculating

Part of the site which is developing well and is well worth a look is the Year 4 Calculating category. There is much to be learnt in year 4, including adding three small numbers mentally and being able to add two 2-digit numbers ‘in your head’. There are a lot of strategies which need to be understood and become second nature to make this happen including partitioning numbers. It is also important to understand the relationship between addition and subtraction, which is very useful to use when checking answers.

Year 4 is a time for consolidating knowledge of tables but other ideas are also introduced including number sentences with more than one operation (later leading to BODMAS).

Division becomes much easier when times tables are known and a lot of the work on division in Year 4 involves remainders and writing remainders as fractions.

Why not have a look at our year 4 calculating worksheets? There are still more in the Four Rules section of the site.

Year 4 Calculating

 

Long multiplication worksheets

Here is a page of practice questions for long multiplication using the standard written method. Each question is laid out so that the answer can be completed in three parts.

Looking at 67 x 23, the three stages would be:

1. multiply 67 by 20. The easiest way to do this is to place a zero in the units column of the answer and then multiply by 2. Placing the zero has the effect of moving each digit one place to the left, hence ten times bigger.

2. multiply by the units (3) and place the answer below, making sure the units go in the units column etc.

3. add the two products.

Of course the units could be multiplied first, followed by the tens, but it is important to find one standard method and stick to it. Of course, tables to to be known to make this a quick process.

This worksheet, and others, similar can be found in the Four Rules section of the site, under Multiplication.

Long multiplication 2-digits by 2-digits