__Curriculum Intent__

At Rice Lane Primary we use a scheme called Power Maths for our teaching and learning. This scheme has been produced by leading experts in the mathematics field. It is designed to improve and deepen mathematical understanding for all children. Please follow the links below to find out further information.

__Curriculum Implementation__

The Power Maths scheme is used across the school from Reception to Year Six. Children are encouraged to use mathematical vocabulary during their daily lessons to discuss and share their ideas. In order to deepen children's understanding of the maths concepts that they are learning we use a concrete-pictorial-abstract approach. Concrete is children using real objects to actually 'do' the maths by moving and manipulating things. Pictorial is using picture representations of objects to really 'see' the maths. Abstract is when children show an understanding of mathematical concepts, symbols and notation. These concepts can all be used at any time and with any age to support understanding. Each child has their own practice book in which they complete activities linked to the daily teaching activity. It is clear to see the progress that the children are making and any misconceptions can be quickly addressed.

__Curriculum Impact__

Power Maths lends itself to continual formative assessment within lessons. Teachers are able to identify children who are struggling with the concepts and put into place appropriate support immediately. Alongside this, each unit in the scheme provides a summative end of unit check for teachers to quickly and clearly assess each child's understanding.

Termly monitoring from maths subject leads in the school measures children's progress and highlights any children who are potentially at risk of falling behind.

__Calculating__

In order to help parents with their children's calculating at home we have added some guidance sheets, using the steps as taught through our Power Maths scheme. Please click on the appropriate year group below.

__Maths Dictionary__

Over the next few weeks we will be creating and uploading our own Maths dictionary, which we hope will help both our students and adults at home too. If anything isn’t clear or if you would like anything in particular added to our Maths dictionary please ask.

__Algebra__

Algebra is when we use letters to represent numbers.

If 2 + a = 3, we can figure out that that a must equal 1.

If 100 – b = 90, we can work out that b must equal 10.

Sometimes, we see a number and a letter directly next to each other. This means that the letter and the number must be multiplied together.

So 3c just means 3 x c. If 3c = 15, we can use our knowledge of times tables to find out what c is. 3 times something equals 15 and we know that 3 x 5 = 15, so c must be 5.

__Angles__

Acute angle: an angle less than 90^{0 }(it’s only small so it is ‘a cute’ angle!).

Right-angle: exactly 90^{0} degrees, like the letter L.

Obtuse angle: this angle is between 90^{0} and 180^{0}. Bigger than a right angle but never more than a straight line.

Reflex angle: a reflex angle is an angle that has started to fold back on itself. It is between 180^{0} and 360^{0}.

__Area__

Area is how much flat space something takes up. This is always measured and written in squared units e.g. 100m^{2}, 3cm^{2} or 20km^{2}.

Working out areas:

Squares: because all sides are the same length we can multiply the width by itself.

Rectangles: multiply the length by the width.

Triangles: multiply the length of the base by the height, then halve your answer (divide it by 2).

__Arrays__

Arrays are a way of visually representing Maths questions or statements in pictures or symbols, to make them easier to understand. Equal groups are shown in rows or columns. The example below is a way of showing 4 groups of 6 or 6 groups of 4.

__Averages__

Hey diddle diddle, the median’s the middle,

You add then divide for the mean.

The mode is the one that you see the most,

And the range is the difference between.

If we had the numbers: 5 6 6 8 and 10

The **median** would be 6 (the middle number when they are put in order). If there is an even number of values you find out what would be exactly half way between them.

For the **mean** we would add all of the numbers together 5 + 6 + 6 + 8 + 10 = 35. Then we divide by 5, because there are 5 numbers all together so 35 ÷ 5 = 7. The mean is 7.

**Mode** would be 6 because it appears the most often.

**Range** would be the biggest number take away the smallest, 10 - 5 = 5.

__BIDMAS__

BIDMAS is also known as ‘Order of Operations’. BIDMAS tells us the order in which to work out problems so that everyone who answers the same question will get the same answer.

Which of the following is correct? 2 + 3 x 5 = 30 or 2 + 3 x 5 = 17 ?

BIDMAS can help us figure out which one is right. Below we show what BIDMAS stands for as well as some examples of the different operations.

B Brackets ( 5 + 7 )

I Indices 3^{2}

D Division 90 ÷ 10

M Multiplication 6 x 7

A Addition 15 + 7

S Subtraction 7 – 4

If there is more than one operation in a question, BIDMAS is the order that we must work them out in. For the question 2 + 3 x 5 the operations are + and x. In BIDMAS Multiplication comes before Addition so we do the ‘times’ part first. 3 x 5 = 15. We then do the ‘add’ part so 2 + 15 = 17. So, the correct answer to 2 + 3 x 5 is **17**.

__Bridging Through 10 or 100__

Bridging is a way of adding that most of us probably do without thinking. In the question 9 + 6, for example, you might take 1 from the 6 to take you to 10 then add the remaining 5 to get the answer of 15.

In 28 + 4 you could take 2 from the 4 and add that to the 28 to take you to 30. You could then add the remaining 2 to get the correct answer of 32.

For 90 + 50 you could do it like in the picture below.

__Bus Stop Method __

‘Bus stop’ is a phrase that seems to really confuse adults when it comes to Maths. The bus stop method is just what we now call short division. It gets its name because it looks a bit like a bus stop. The sum 362 ÷ 7 set out using the bus stop method and worked out would look like this:

__Chunking__

Chunking is another method for working out division questions that we might not be able to do in our heads. It involves repeated subtraction. To be able to do chunking well, you need to be confident with your times tables.

Let's start with a nice simple one:

Now for a tough challenge! When working out 882 ÷ 6 we are seeing how many 6s go into 882. We could count up in 6s but that would take a long time so we can take some shortcuts. We could start by taking away 100 6s from 882. That would leave us with 282. Then we could take away 40 6s. This would leave us with 42. We know that 7 6s are 42 so we could then take that away. Altogether we have used 100 + 40 + 7. That means that 147 6s will go into 882, so 882 ÷ 6 = 147.

Tip- sometimes it helps to write out the times table of the number we are dividing by at the side of the page when doing chunking. If you can see on the page that 4 x 6 = 24 you could also use your Maths skills to work out that 40 x 6 = 240.

__Circles__

In a circle the **Circumference** is the distance around the outside. The **Radius** is the distance from the centre of a circle to the circumference. The **Diameter **is a straight line passing from one side of a circle to the other going through the centre point.

__Column Method__

The column method for addition or subtraction is just the way we set out our sums so they are easy to understand and to help prevent mistakes. We always start with the ‘ones’ or ‘units’ column and then move left to work out the tens, hundreds, thousands etc.

Column addition should look something like this:

Column subtraction should look something like this:

__Coordinates__

Coordinates tell us the position of something on a grid. Coordinates are always written in brackets with the two number separated by a comma. The first number tells us the position on the x-axis (horizontal or left to right) and the second number tells us the position on the y-axis (vertical or up and down). In the younger years of school the children might be told ‘in the house and up the stairs’ to help remember the order. Higher up the school the children use positive and negative numbers so they might be told ‘along the corridor and in the lift’.

__Division__

For easier division questions you can look at the entry under **Bus Stop Method**. **Chunking** is also a method that we can use for division, but another way that we need to learn is **Long Division**. Just the mention of long division can give people nightmares, but as long as you follow the correct steps all it takes is practice. Year 6 used the following funny video to help them master long division earlier this school year.

__Factors__

Factors are numbers that we can multiply together to make another number. Some numbers have a very small amount of factors and some have a lot. For example the number 12 has the following factors: 1, 2, 3, 4, 6 and 12. We can divide the number 12 by all of these numbers and not have any remainders. In pairs those numbers can be multiplied together to make 12.

1 x 12 = 12

2 x 6 = 12

3 x 4 = 12

__Fractions__

Fractions are normally written as one number over another number. We call the number on the top the **numerator** and the number on the bottom the **denominator**.

**Mixed numbers** are when we have a whole number with a fraction.

**Improper fractions** are when the numerator is larger than the denominator.

**Equivalent fractions** are fractions that might appear different but have the same value. By using a fraction wall we can see that 4/8, 5/10 and 6/12 all have the same value.

**Adding fractions**:

When **subtracting fractions **the process is almost the same as when adding. The only difference is that we take one numerator from the other.

**Multiplying fractions**:

**Dividing fractions**:

We should always try to put fractions into their simplest form. To do this we need to simplify. Here is another video, which Year 6 watched when they were **simplifying fractions**:

__Measure__

We use measure to find out the size or quantity of something. In school we almost always use metric measurements.

We need to be familiar with converting between different units of measure. Here are some units of measure and how they compare to others:

**Length**

10mm = 1cm

100cm = 1m

1000m = 1km

**Mass**

1000g = 1kg

**Capacity**

1000ml = 1l

**Time**

60 seconds = 1 minute

60 minutes = 1 hour

24 hours = 1 day

__Negative Numbers__

Negative numbers are numbers that are less than 0. When we are dealing with negative numbers we often have to count through zero. We can use number lines to help us with questions like this.

If the temperature is 5˚C degrees and then it drops by 8˚C what is the temperature now?

From 5 we can count back 8, which would take us to -3 ˚C.

Some handy tricks to remember with negative numbers are that when you multiply 2 negative numbers together the answer is always positive e.g. -3 x -6 = 18. When you multiply a positive number and a negative number together the answer is always negative e.g. -2 x 10 = -20 or 5 x -5 = -25.

__Opposite Angles__

When two straight lines cross at a point the opposite angles are always equal to each other.

The angles around a single point always add up to 360˚.

In picture above, if we knew that angle **a** was 100˚ we would also know that angle **c **would be 100˚. Knowing that **b** and **d** would have to take the total up to 360˚, and that they would be equal, we could figure out that together they (**b** and **d**) must add up to 160˚. Therefore, by dividing by 2 we would know that both **b** and **d** would be 80˚.

As well as this, the **angles along a straight line** add up to 180˚. So if we were told that one angle is 30˚ we know that the other must be 150˚ in order to take the total up to 180˚.

__Parallel__

Parallel lines are lines that always stay the same distance apart- a bit like train tracks. Even if the lines carried on forever they would never meet.

**Pictograms**

In pictograms we use pictures to represent numbers in a graph. Here we have a pictogram showing how many cupcakes a stall sold each day for a week. Each cupcake on the pictogram represents 6 cakes sold. We can then work out that on Monday 30 (5 x 6) cupcakes were sold. On Tuesday 15 were sold (2½ x 6). How many cupcakes were sold on Wednesday?

__Polygons__

These are shapes that have 3 or more straight sides. The image below shows a selection of **regular polygons**. In regular shapes all side lengths are the same and all angles are equal too. Irregular polygons have angles and side lengths which are different. The larger shape here is actually a hexagon because it has 6 straight sides. It has sides that are all different lengths and its angles are all different sizes so it is an **irregular polygon** (and an irregular hexagon).

__Quadrilaterals__

These are 4-sided shapes. There are a variety of shapes classified as quadrilaterals including: trapeziums (one set of parallel sides), parallelograms (two sets of parallel sides), rhombuses (4 sides all the same length, but all angles not equal) and squares (4 sides all the same length and 4 right-angles).

__Ratio__

Ratio is a way of showing the comparative value of 2 or more amounts. We write ratio as two numbers separated by a colon ( : ). We will look at a couple of examples and hopefully it will make sense!

In 6A the ratio of adults:children is 1:11. This means that for every 1 adult there are 11 children. In 6A there are actually 2 adults, which means that there are 22 children.

If the ratio of orange cordial:water must be 1:5 how much water should be mixed with 20ml of cordial? The ratio tells us that for every 1 part of cordial we need 5 parts water. We have 20ml of cordial so we need 5 times as much water to mix with it. We can multiply 20ml by 5 to tell us how much water we need, which is 100ml.

__Roman Numerals__

This is a number system that has been around for thousands of years, and is still visible around us today. In Roman Numerals different letters represent different numerical values.

Usually, the letters are written in descending order (highest value to lowest) e.g. CXV represents 100, 10, 5 or 115. If a smaller value letter is written before a higher value letter we subtract the smaller value from the higher one e.g. CIX represents 100, 1, 10 (100, 10 – 1) or 109.

__Scale Factor__

When we change the size of a shape in Maths we can give a scale factor so we know how much bigger or smaller it is going to be. Enlarging a shape by a scale factor of 3 means that every side of the shape will become 3 times longer. A scale factor of 0.5 means that each measurement of the original shape will become only half as long in the new version.

__Shapes__

We have already mentioned a lot of different shapes in other parts of the dictionary, here we can see some of the properties of 3-D shapes.

*Vertices is another way of saying corners.

__Symmetry__

Symmetry is when an object can be split in half by a straight line and each half is an exact mirror image of the other. The line that splits the shape in this way is called a **line of symmetry**. Shapes that can be split like this are called **symmetrical**. Some shapes have no lines of symmetry, whereas some have lots. The dotted lines below show the lines of symmetry for three shapes.

__Time__

Telling the time is an important life skill and in school we learn how to tell the time on analogue clocks, 24-hour digital clocks and on 12-hour digital clocks.

__Transformation__

Transformations are the different ways that we can move shapes in Maths.

**Reflection** is when something is reflected in a mirror line. Each part of the reflection will be the same distance from the mirror line as its corresponding original part.

**Rotation** is when a shape is rotated (either clockwise or anti-clockwise) about a point. Sometimes we use tracing paper to help us with this, although in SATs tests it’s not allowed. In this example the shape is being rotated 90˚ clockwise about the point.

**Translation** is when a shape is ‘slid’ from one place to another. It stays the same way up, but moves horizontally and/or vertically. In this example, the original orange shape has been moved 1 square to the right and 4 squares up.

__Triangles__

The main types of triangle that we need to be able to identify are:

**Scalene**- all sides are different lengths and all angles are different sizes

**Isosceles**- 2 sides are the same length and 2 angles are the same size

**Equilateral**- all 3 sides are the same length and all 3 angles are equal

**Right-angled**- has one angle which is 90˚ exactly

The interior (inside) angles of a triangle always add up to 180˚, this means that if we know what two of the angles are we can always find out what the value of the missing angle is.

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