# Maths

National Curriculum 2014 – Y5/6
‘Teachers should use every relevant subject to develop pupils’ mathematical fluency. Confidence in numeracy and other mathematical skills is a precondition of success across the national curriculum...Pupils should apply their geometric and algebraic understanding.

Teaching in geometry and measures should consolidate and extend knowledge developed in number. Teaching should also ensure that pupils classify shapes with increasingly complex geometric properties and that they learn the vocabulary they need to describe them’

Pupils should be taught to:

Number
• interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers through zero

Geometry
• illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius’

Phase One
• 'Common Era (CE)' and 'Before the Common Era(BCE)’ - Introducing negative numbers
Pupils could be introduced to negative numbers by investigating a number line and relating it to the years before the ‘Common Era’ (BC) and after the ‘Common Era’ (AD). Simple problems could be set by pupils for each other; E.g. How many years were there between 300 BC and 400 AD? L&T Strategies Pair work (5a) Snowballing (15).

Phase Two
Shape and pattern are important to the three Abrahamic faiths. In Judaism the six pointed star of David is the recognised symbol of Jewish Identity. Geometric star and circle patterns are also important as a form of ornamentation in Islam most often as tile patterns. Tile patterns are common place in Christian places of worship.

• Six pointed star patterns – linked with Art – an opportunity to explore the relationship between mathematics and art. L&T StrategyThink / pair / share (5)

The following activities provide opportunities for the revision of the properties of a circle (re visit the words, radius and circumference) and the use of isometric grids. L&T Strategy Solo (2)

• Instructions for creating a star pattern
1. Set your compass to 5cm - keep it the same all the time
2. Draw a circle
3. Place your compass on a point on the circumference A and make a small mark where the pencil crosses the circumference of the circle
4. Move the point of the compass to that mark and again make a small mark where the pencil crosses the circumference of the circle. Continue around the circumference marking off the points A to F as in the diagram

Diagram A
Use a ruler to connect point A to each of the other points

Diagram B
Repeat instruction 5 for points B to F

Diagram C
Can your pupils see the first six pointed star? What other shapes can your pupils see? Can they think of another way to make a six pointed star?

Extension
Can pupils make a smaller six pointed star using the points on the hexagon inside the star?

Diagram D
Ask your pupils to colour their star design. How many geometric shapes can they see?

Instructions for creating more star patterns using isometric grid paper (as Diagram E)

Triangular or an isometric grid template can be used to make patterns of hexagons and six pointed stars.
Putting a clean sheet of paper over the grid (and securing it), will enable pupils to use the grid as a guide, allowing the pattern to develop without the grid becoming too much of a distraction. The grid can be used horizontally or vertically depending on the pattern being created.

For a simple design, a small hexagon of six triangles can be coloured, then a triangle added to each side of the hexagon that makes a six pointed star. The star can then be enclosed by adding six diamonds. A bigger star and a bigger hexagon can then be made.

What repeating patterns can pupils find?

Diagram E
Phase Three
• Tessellation patterns – linked with Art– an opportunity to explore the relationship between mathematics and art

Pupils could look at the photographs of tile patterns from the Baptistry of the Santa Maria del Fiore, the Santa Croche in Florence and the Duomo (Cathedral) of Siena – Christian Tile Photos – before creating their own tessellated designs, noting colours, shapes and how they fit together.

The following activities provide opportunities for the revision of tessellation.

• Instructions for creating tessellated patterns
1. Pupils could draw their own square, triangle and/or parallelogram templates to create identical cut out shapes in a limited selection of colours to arrange in their chosen design.
2. The shapes could be arranged and stuck onto contrasting coloured paper – using the background as part of the design.

• Circle patterns – linked with Art– an opportunity to explore the relationship between mathematics and art
Pupils could look at circle designs from search engine ‘image’ results of Islamic circle patterns and the Islamic Art video clip. Identify where circles have been used as a basis for the pattern. Revisit the words radius and circumference.

The following activities provide opportunities for the revision of the properties of a circle.

Instructions for creating patterns using Compasses

Provide pupils with a pair of compasses; a ruler, a sharp pencil and a large sheet of paper (at least A3); some scrap paper to practise on and coloured pens and pencils.
1. Place the point of the compass in the centre of the paper and draw a circle.
2. Place the point of the compass anywhere on the circumference of the first circle and draw another circle. (Always try to be as accurate as possible). The new circle should pass through the centre of the first circle.

Diagram F
Always keeping the radius the same, move the point of the compass to one of the two places where the second circle has cut the circumference of the first circle and draw a third circle.

Diagram G

Move the point of the compasses to the new point on the circumference of the first circle and draw another circle. Repeat making circles round the edge of the first circle until you get back to where you started. If the drawing has been accurate the last circle passes through the centre of the original circle and through the centre of the second circle drawn. Link to Maths – Why are there exactly six circles round the edge of the original circle?

Diagram H

Now continue creating new circles, still with the same radius, round each of the circles you have drawn so far, until they go over the edge of the paper.

Diagram I

Pupils could use coloured pens/pencils to create patterns. Pupils may struggle to produce accurate drawings for this activity so they could be provided with a prepared sheet Worksheet Circle Patterns. Encourage pupils to be methodical and find repeating patterns on the sheet.

Extension
Pupils draw in parallel lines as shown in diagram below. This is more of a challenge as there are so many lines and circles!
Worksheet Circle Pattern with parallel lines

Religious Calendars

The Jewish and Islamic calendars are used to determine religious days and festivals and are based on the phases of the moon. The date for the Christian Easter is also determined by the phases of the moon.

The Christian calendar or Gregorian calendar, also known as the Western calendar, is the internationally accepted civil calendar.

Teachers may wish to investigate the relationships between the three calendars and the lunar cycles.