# Maths

### Facts you need to know!

Below is a copy of the fact sheet sent home with your child. They need to have a good grasp of these facts in order to help them achieve the expected standard for a Year 6!

### Factors, Multiples and Prime Numbers

This week, Sycamore have been looking at factors, multiples, prime numbers, square numbers and composite numbers. Below are 3 videos. The first is Jacob explaining some of these terms; the next is Charlotte demonstrating how every integer (whole number) is a product of prime factors; the last video, with Anya and Milo, is a tricky maths problem involving some of these terms - remember, if you would like time to work it out, then please press pause before the answer is revealed. Good luck!

## A tricky maths problem - go on, see if you can unlock the treasure!

Applying maths to real life situations!

After the pressure of SATs, Sycamore Class unwound by applying maths to real life situations. The class were split into 3 activity groups. The first group had to look at the maths between different free kicks. The second group looked at how to make an infinite chocolate bar and the third group had to look at what makes the perfect cucumber sandwich.

### Football free kicks

Pupils looked at and performed different free kicks, including power free kicks, curled free kicks and dipping free kicks. These groups calculated that to hit the perfect free kick over the wall and into the back of the net, a player (9 metres away from the wall) must hit the ball over the wall (approximately 2 metres with a jump) at an angle of 13 degrees. They also discovered that the harder you hit the football, the less time a goalkeeper has to react. Typically, if the speed is constant and hit hard (like Stuart Pearce), by the time the goalkeeper sees the ball, with his own, internal brain reaction time, he'd only have three sevenths of a second for his body to react and move towards the ball.

We also discovered that a 'dipping' free kick is called a parabola, which references the trajectory of the ball and the shallower the ball is hit, the shallower the curve of the ball, like Drogba's free kick (see below).

A curling free kick is simple to explain as a player strikes the ball on one side, the air rushes quicker on the opposite side, allowing the ball to spin and effectively 'curl' through the air. This is called the Magnus Effect.

## Stuart Pearce

This free kick shows how angles, speed, distance and reaction times all play a pivotal role within football.

## Didier Drogba

This video shows the parabola free kick in action.

## Kevin Sheedy

This video shows the Magnus Effect in action from a free kick.

### The Infinite Chocolate Bar

One group was given a big bar of chocolate and asked to investigate how Mr Wallace can eat one piece of chocolate and the chocolate bar remains with the same area and perimeter?

This took a lot of problem solving and this group eventually came to the secret (that we won't be sharing) but it can be done, thus making a chocolate bar infinite. If you'd like to know how it is done, then you'll have to ask either Eveline, Lorna, Ruby or Jess. Please see the photographs below.

### The Perfect Cucumber Sandwich

Some groups were asked to work out the dimensions and proportions of the perfect cucumber sandwich. After much deliberation, the group realised that the overall volume in a perfect cucumber sandwich is 15.072 cm cubed. During the task, they had to calculate areas or squares and circles; volumes of cylinders and cuboids; measure accurately and use Pi. Take a look below at these groups in action.

## Post SATs Maths Fun Pictures

3-D Shapes

This week, Sycamore Class have been looking at 3-D shapes. We have identified them, stated their properties, and even made nets. Have a look at the photographs below, especially the one where Jake, Arron and Jack discovered that a cuboid could have completely different nets but still look exactly the same, as long as the net has the same dimensions.

Geometry

Sycamore have been looking at geometry this week and rotation in particular. The class had to remember to keep shapes congruent (the same size) when they rotated different shapes.

Below are Holly's and Ruby's work from this week. Holly was rotating shapes about a point on a vertex and Ruby was rotating about other points and applying this to her coordinate work.

Applying Ratio and Proportion

Sycamore have been understanding ratio and proportion this week. This has ranged from identifying ration and proportion or amounts, using these skills to help calculate recipes and applying these techniques to other problems. Below is an example from Charlie of how he solved this problem:

Tom was born in 1988.

Ben was born in 2000.

Tom and Ben have the same birthday. The ratio of Tom's age to Ben's on their birthday in 2001 was 13:1. In what year was the ratio of Tom's age to Ben's age 3:1?

Applying Division Methods

At the beginning of year, Sycamore looked at formal and informal methods of calculation, including column subtraction & addition, long multiplication and long division. Below is an example of how we apply these methods.

Lewis used his division skills to calculte how long it takes for light to reach each of the planets in our solar system. He then applied his division skills once more to write down the answers in minutes and hours rather than seconds.

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