Maths Plus You

The summer holidays are finally here! ☀️

There are so many fun packed activities planned for July and August!

If you would like to book a space on any of the workshops, or need more information, please DM me!

Want to polish up on your own maths skills? Try daily .coffee

Have a great summer 😊
Charn

It’s July!

The summer holidays are fast approaching and so is the 2023 11+ entrance test!

Naturally, the summer holidays are a time for fun and relaxation - a well deserved break for all students. However, if your child has been working hard getting prepared for their 11+, the summer slump can be demotivating.

With 10 weeks to go until the grammar school entrance tests, is your child fully prepared?

Does your child still struggle with certain topics and concepts?

Are you new to the 11+ and haven’t started any preparation?

The summer 11+ Accelerator Workshops may be just what you need!

They are designed to cover all aspects of the 11+ over 5 days.

Pick ’n’ mix topics as required or block book 5 days.

DM for prices and further information.

#11+

The first Maths Workshops of 2023 are here!

Book now for February half term.

These workshops are a great way to consolidate learning, learn new skills for 2023 and build confidence!

The activities are carefully designed to promote problem solving, collaborative work and stretch mathematical thinking. Here’s what’s involved:

Year 3 and 4 Maths.
Maths should always be engaging and fun, especially for younger years! We will be involved in practical activities and games, covering the breadth of core skills.

Year 5 11+ Maths.
Students will focus on the high level of numerical reasoning required for the 11+ grammar school entrance exams. We will target topics not covered in Year 5, like Algebra, Ratio and Probability.

Year 6 Maths and English SATs.
The Maths workshops are designed to consolidate learning and delve into 2 mark, multi-step problems. SATs English will cover all aspects of the English papers. The workshops can be booked together or separately.

GCSE Foundation revision.
If your child has a target grade of 5 (in Year 10 or Year 11), then this workshop is perfect. We will be diving into 3 and 5 mark questions, plugging any gaps in understanding and creating flashcards for revision. In this small group, there will be plenty of opportunities to ask questions.

Mindful maths.
Does your child get anxious at the thought of maths? Does this reflect in their grades and progress? The Mindful Maths program has been designed to incorporate many mindful techniques and pathways to ease frustration with maths. With a helpful guide for every step of problem solving, the problem/solution pathway could be just the thing your child needs to make progress with maths.

For more information, or to book a space for your child, send me a DM.

Hope to see you there!

Charn
Lead tutor
•
PS As a parent/carer, if you would like to practise your maths skills and help your child on their maths journey, then join me over on Insta .coffee
I organise weekly meet-ups and daily maths problems for you to try!
•

The first Maths Workshops of 2023 are here!

Book now for February half term.

These workshops are a great way to consolidate learning, learn new skills for 2023 and build confidence!

The activities are carefully designed to promote problem solving, collaborative work and stretch mathematical thinking. Here’s what’s involved:

Year 3 and 4 Maths.
Maths should always be engaging and fun, especially for younger years! We will be involved in practical activities and games, covering the breadth of core skills.

Year 5 11+ Maths.
Students will focus on the high level of numerical reasoning required for the 11+ grammar school entrance exams. We will target topics not covered in Year 5, like Algebra, Ratio and Probability.

Year 6 Maths and English SATs.
The Maths workshops are designed to consolidate learning and delve into 2 mark, multi-step problems. SATs English will cover all aspects of the English papers. The workshops can be booked together or separately.

GCSE Foundation revision.
If your child has a target grade of 5 (in Year 10 or Year 11), then this workshop is perfect. We will be diving into 3 and 5 mark questions, plugging any gaps in understanding and creating flashcards for revision. In this small group, there will be plenty of opportunities to ask questions.

Mindful maths.
Does your child get anxious at the thought of maths? Does this reflect in their grades and progress? The Mindful Maths program has been designed to incorporate many mindful techniques and pathways to ease frustration with maths. With a helpful guide for every step of problem solving, the problem/solution pathway could be just the thing your child needs to make progress with maths.

For more information, or to book a space for your child, send me a DM.

Hope to see you there!

Charn
Lead tutor

PS As a parent/carer, if you would like to practise your maths skills and help your child on their maths journey, then join me over on Insta .coffee
I organise weekly meet-ups and daily maths problems for you to try!

PROBLEM 56

Plans and elevations

No calculations for this one - just some simple observations.

Plans and elevations are 2D visual representations of 3D objects and structures.

Elevations are viewed from the side or the front. Plans are viewed from above - a bird’s eye view.

The correct 2D view of the 3D shape was C. None of the other sides would be visible when viewing the shape from the top.

Students learn about plans and elevations as part of their GCSE Maths course. They also form part of the non-verbal reasoning section, for secondary school entrance tests.

How did you get on with that one? ☕️🥐

Need some last minute gift ideas?

These suggestion might just help!

Humble Pi, by Matt Parker.
Can the smallest mathematical error make that much of a difference? It certainly can! The results are often alarming, comical and sometimes even tragic.

Mathlink Cubes by learning Resources.
Such a useful and fun maths manipulative! Help youngsters visualise addition, subtraction, fractions, shapes, times tables, division, measurement and so much more! My most used resource - highly recommend!

GCHQ Puzzles by GCHQ
Every family has at least person who loves solving puzzles! Puzzle solving creates interaction and collaboration. Great for competitive minds of any age.

David Walliams Card Games by Lagoon
Play traditional old-fashioned card games, with a twist! Based on the very successful stories, fans will be delighted with the fabulous illustrations from Tony Ross.

What’s the point of maths? By DK Books
Insightful, amusing and entertaining. Maths doesn’t have to be your favourite subject to enjoy this one. Where do our modern maths ideas come from? Delve into the origin of todays most important maths ideas. A good one to satisfy curious minds!

Rummikub Classic by Ideal
Suitable for 2-4 players, this board game is a much loved part of .Coffee sessions!

Players take it in turns to remove a group of tiles from their tile rack, in either a set or a run. A set must contain tiles of the same number, a run must contain tiles with consecutive numbers.

Sounds easy enough? You need plenty of logic, skill and strategy - never the same game twice!

Jigsaw Puzzles by Ravensburger
Always a treat to myself! Jigsaw puzzles develop skills in:
* Hand-eye coordination
* Visual perception
* Patience
* Fine motor skills
* Perseverance
* Problem-solving
* Team work
* Cognitive skills

Such a great way to spend some time with loved ones!

Hope this was useful. Enjoy your Christmas holidays with your friends and family.

Charn 🎄

PROBLEM 55

PUZZLES

Puzzles are a fast and fun way to practise maths.

At first glance, it seems as though this puzzle is impossible to solve.

There are 3 different types of shapes: triangles, trapeziums and a circle.

The value of each shape is unknown, however the relationship between the shapes is provided.

Line 1: 2 triangles = 1 trapezium

Line 2: 1 triangle + 1 trapezium = 60

Line 3: 1 trapezium - 1 circle = 30

Step 1 Start with the second row. Substitute the trapezium for 2 triangles.

Line 2 now shows 3 triangles = 60

If 3 triangles = 60 then 1 triangle must equal 20 (60 ÷ 3 = 20).

Step 2 Go to row 1. If 1 triangle equals 20, then the trapezium must be worth 40 (20 + 20 = 40).

Step 3 Go to row 3. Substitute all known values.
40 (trapezium) - circle = 30.
Therefore the circle must equal 10 (40 - 10 = 30).

▵ = 20

⏢ = 40

⃝ = 10

How did you do with that one? ☕️🍩

When did you last actively practise your maths skills?

Numeracy is the the ability to use maths in all aspects of daily life. The foundation of numeracy? Good basic maths skills.

Calculated Coffee is a weekly meet-up for anyone who would like to practise their maths (even pre-schoolers!).

This weeks Calculated Coffee session is taking place on Friday 25th November 10-12pm at Starbucks Telford Bridge.

Did you know that solving maths problems can help to:

- strengthen cognitive ability?
- develop skills in logic and reasoning?
- reduce feelings of anxiety?
- build confidence?

Small steps create big changes!

Hope to see you on the 25th!

Charn ☕️

PROBLEM 50 - PROBLEM 54

PROBLEM 50 - Graphs

The 4 examples show linear, exponential, quadratic and cubic graphs. A linear graph follows a straight line. An exponential graph rises/falls exponentially, creating that dramatic curve depicting growth or decay. A quadratic graph follows an approximate ‘U’ shaped curve, or parabola as it is correctly known. A Cubic graph has 2 turning points, a maximum and a minimum.

PROBLEM 51 - BIDMAS

BIDMAS (also known as BODMAS or PEDMAS) is an acronym that dictates the order in which mathematical operations are performed. The order is Brackets, Indices, Division, Multiplication, Addition and Subtraction. The correct answer is 202.

PROBLEM 52 - Real world numeracy

For this question you are required to calculate the change received from a coffee order, if you pay with £20. This is a common example of everyday numeracy. The correct change is £2.05p

PROBLEM 53 - Percentages

This is another great example of everyday numeracy! The handbag has been reduced by 20% in a sale to £896. This means that £896 is equal to 80% of the original price. The original price of the handbag (100%) is £1,120.

PROBLEM 54 - Fractions

If 3/5 of a number is 18, what is half of the number? For this question, calculate the value of 1/5 to figure out what the whole amount is. From here, you can calculate a half! One fifth equals 6. The whole amount is 30. One half of the amount is 15.

How did you do? 🤔☕️

PROBLEM 45 - PROBLEM 49

PROBLEM 45 - Circles

Which circle is labelled correctly? The answer is Circle B.

PROBLEM 46 - Probability

5 cards are removed from a pack of standard playing cards, including 2 aces. There are 52 cards in a standard deck of playing cards. This leaves 47 cards in the pack, including 2 other aces. The probability of randomly selecting another Ace is 2/47.

PROBLEM 47 - Speed, distance and time.

There are 2 parts to the car journey: 60mph for 1.5 hours and 48mph for 1 hour and 10 minutes. What is the total distance travelled?
Part 1 of the journey covers 90 miles, part 2 of the journey covers 56 miles. This is a total of 146 miles.

PROBLEM 48 - Shapes with unusual names.

An oblate spheroid looks like a sphere that has been squashed down at both poles. Planet earth, or an M&M candy are easily recognisable examples.

PROBLEM 49 - Arithmetic.

C is correct 328 ÷ 4 = 82 All the others are incorrect!

How did you do with those? ☕️🧁

PROBLEM 41 - PROBLEM 44

PROBLEM 41 - Bearings.

A bearing is an angle describing the position of one object in relation to another, using points of the compass. You may have come across bearings when planning journeys using maps. ANGLE B = 235°

PROBLEM 42 - Statistics, finding the mean.

Mean is the average value of a set of numbers. It is calculated using the formula sum of values divided by the number of values. The missing value was 12!

PROBLEM 43 - Area of circles

To calculate the area of a circle, use the formula πr². Using 3 as the value for π, Circle C is incorrect.

PROBLEM 44 - Conversion

Using the Exchange rate £1 = €1.16, how many Euros would you receive for £25? The answer is €29.

How did you do with those? ☕️🥐

PROBLEM 40 and SOLUTION

Algebra.

Solving 𝒙. Algebra is all about puzzle solving. You are given a problem with one missing piece. To find the missing piece you will need to move other pieces of the puzzle around without unbalancing the equation.

The equation stated 3𝒙 – 9 = 𝒙 – 8 The missing part of the puzzle is 𝒙.

When solving any equation, keep the equation balanced. Whatever you add, subtract, multiply or divide from one side of the equation must also be performed on the other side of the equals sign. The aim is to get 𝒙 on its own.

Step 1 Add 9 to both sides of the equation. The equation now becomes 3𝒙 = 𝒙 + 1

Step 2 Subtract 𝒙 from both sides. The equation now becomes 2𝒙 = 1

Step 3 Divide both sides by 2. The equation now becomes 𝒙 = 1/2

𝒙 = 1/2 or 0.5

To check the answer, substitute the value for 𝒙 back in to the equation.
3 x 0.5 - 9 = 0.5 - 8
Both sides of this equation equal -7.5. It is balanced. Therefore the answer is correct!

After geometry, algebra is probably my favourite topic. It encompasses everything I enjoy about puzzle solving - taking something seemingly impossible and reaching a solution. Of course, its not always possible to find a solution using a direct route, more often than not, you will need to try different pathways until you have solved the problem!

Many of my students feel anxious about maths. I have learnt over time that it isn’t the topic that builds anxiety, it’s the fixation on the correct answer. The magic of maths happens in the middle - that chaotic area between reading the problem and reaching a possible solution. The chaos deserves to be celebrated! As I tell all of my students, repeatedly attempting different pathways to a solution, builds resilience and skills for life ♥️

I hope you enjoyed that one!

Charn ☕️🥐

PROBLEM 39 and SOLUTION

Perimeter and geometry.

This is a multi-part problem. To begin, identify all of the ‘known’ facts.

·Perimeter is the outer edge or boundary of a shape.

·The shape consists of a pentagon and 5 identical isosceles triangles.

·A pentagon is a 5-sided 2D shape.

·An isosceles triangle has 2 sides of equal length and 2 base angles of equal size.

·The perimeter of the pentagon is 45cm.

·The perimeter of each triangle is 25cm.

Divide 45cm by 5 to calculate the measurement of each side of the pentagon.
45 ÷ 5 = 9 Each side of the pentagon is 9cm in length.

The side of the pentagon is also the base length of the triangle. It is known that the triangle is isosceles. To calculate the sum of the 2 missing sides subtract 9 from 25cm.
25 - 9 = 16. Divide 16 by 2 to calculate each individual side. Each side of the triangle is 8cm.

The outer star shape has 10 sides of 8cm.

The perimeter of the star shape is 8cm x 10 = 80cm

Always gather the facts before you begin - this helps to eliminate unnecessary steps and creates a clearer pathway to the solution!

Result!

Charn ☕️💪

PROBLEM 38 and SOLUTION

Pythagoras’ Theorem.

Perhaps the most recognised topic from high school maths! I hope it bought back some positive memories😬?

Pythagoras’ theorem describes a geometric relationship between the three sides of a right angled triangle (or a right triangle).

Although its use has been documented on tablets during Babylonian times and in ancient Indian texts preceding Pythagoras’ writings, he is the one that is credited with proving it.

The theorem states, in its most basic terms, that when three squares are added to the sides of any right angled triangle, the area of the largest square (c) is equal to the sum of the area of other two squares (a + b).

What is the theorem? a² + b² = c²

The dimensions of the triangle are 6cm and 8cm. The missing measurement is the hypotenuse - the longest side of the triangle. The other two sides are known as the legs of the triangle.

6² + 8² = c²

36cm + 64cm = 100cm

c² = 100cm (to find the actual measurement, find the square root of the number).

c = √100

c = 10cm

There are so many everyday uses of Pythagoras’ Theorem! It is used widely used in the construction industry to ensure buildings are square and staircases and structures like roofs have the correct length. The theorem is also used in air and sea navigation to calculate the shortest and longest distance between 2 points.

Even cartographers are able to use the theorem to calculate the steepness of hills and mountains.

How did you get on with this one?

Charn ☕️🧇

PROBLEM 37 and SOLUTION

Circumference.

The circumference of a circle is its perimeter - its outer edge or boundary.

The word originates from the Latin word circumferentia, meaning to carry around.

There are two ways to calculate the circumference of a circle, πd or 2πr.

Pi (π) is the ratio of the circumference of a circle to the diameter of that circle. Regardless of the size of a circle, the ratio will always equal Pi.

Pi is an irrational number, it has been rounded in this case to 3.14. This magnificent number deserves a post of its own!

There are two ways to calculate the circumference of a circle, πd or 2πr.

In this case the radius of the circle is 10cm, therefore the diameter is 20cm.

Diameter is twice the size of the radius. It is a straight line running thorough the centre of the circle from one edge of the circle to the other.

Radius is a straight line from the centre of a circle, to the edge of the circle.

πd = 3.14 x 20cm = 62.8cm
2πr = 2 x 3.14 x 10cm = 62.8cm

The circumference of the circle is 62.8cm

Good work everyone ! 🙌

Charn ☕️🧁

PROBLEM 36 and SOLUTION

Roman numerals.

Developed by the ancient Romans in the 8th to 9th century, the Roman numeral system consists of just seven capitalised letters.

The symbols are I, V, X, L, C, D and M.

I = 1

V = 5

X = 10

L = 50

C = 100

D = 500

M = 1000

From clock faces and books to plays and Olympic events, Roman numerals are still widely used.

As language and writing has evolved over the centuries, these Latin symbols have continued to survive! Did you notice that there is no null quantity?

The zero was defined by the Indian astronomer Brahmagupta in the 7th century, though it had been used as a concept before then. It didn’t reach Europe until around the 1200’s!

So, what does MCMXCIX represent?

M = 1000 CM = 900 XC=90 IX=9 The number is 1999.

The rules?

If a large number is followed by a smaller number, like XI, add the small number to the large number. For example:
XI = 10 + 1 = 11
MXIII = 1000 + 10 + 3 = 1013

If a small number precedes (comes before) a larger number, subtract it. For example:
IX = 10-1 = 9
CD = 500 - 100 = 400

Well done if you got that one ⭐️

Look out for Roman numerals on film credits, clocks, old buildings and sporting events. See if you can figure them out!

Charn ☕️🥐

PROBLEM 35 and SOLUTION

Decimal numbers.

A decimal number is a number that lies between two whole numbers.

For example, 1.5 is a number between 1 and 2.

A decimal number can be a positive or negative number.

1.2 , 87.925, 3.57, 0.00081 are all examples of decimal numbers. They have a whole part and a fractional part.

Every number to the right of the decimal point is a fraction of a number (or part of a number). Each number has a specific place value.

After the decimal point:

➡️The first number is worth 1 tenth (1/10)

➡️The second number is worth 1 hundredth (1/100)

➡️The third number is worth 1 thousandth (1/1000)

➡️The fourth number is worth 10 thousandths (10,000) and so on.

Partitioning decimal numbers.

As part of the national curriculum students are taught to partition (split) decimal numbers into their parts. This deepens their understanding of the value of the number.

1.2 partitioned is 1.0 + 0.2 which is 1 whole and 2 tenths. 1.2 has 1 decimal place (it has 1 number after the decimal point).

87.925 is 80 + 7 + 0.9 + 0.02 + 0.005 which is 8 tens, 7 ones, 9 tenths, 2 hundredths and 5 thousandths.

87.925 has 3 decimal places (it has 3 numbers after the decimal point).

Multiplying decimal numbers.

0.14 x 0.02

Step 1 Remove the decimals. The numbers now become 14 and 2.

Step 2 Multiply the numbers 14 x 2 = 28

Step 3 Place the decimal point back in.

0.14 has 2 decimal places, 0.02 has 2 decimal places. This means that the answer will have 4 decimal places after the decimal point.

0.14 x 0.02 = 0.0028

Using this method, we can see that OPTION B is incorrect, it doesn’t have enough decimal places in the answer. The answer should be 0.0036.

From completing homework with children to baking and building furniture - learning to work with decimals is a very useful skill!

Charn ☕️🍞

PROBLEM 34 and SOLUTION

A puzzle!

Puzzles and games are a great way to actively practise working with numbers.

In this puzzle, you are required to calculate the value of each fruit, using the total sum of each row.

In row 1, 3 identical pineapples are shown with a total of 45. Divide 45 by 3 to find the value of 1 pineapple.

45 ÷ 3 = 15

1 PINEAPPLE = 15

Using the known value of the pineapple, calculate the value of an apple.

2 apples + 1 pineapple = 55

55 - 15 = 40

2 apples = 40.

Divide 40 by 2 to get the value of 1 apple.

1 APPLE = 20

We now have enough information to find the value of the pear.

1 apple + 1 pineapple + 1 pear = 65

20 + 15 + 1 pear = 65

35 + 1 pear = 65

1 pear = 65 - 35

1 PEAR = 30

Well done everyone!

Charn☕️🍐

PROBLEM 33 and SOLUTION

Linear equations and graphs.

This was a challenging one!

This graph displayed various points plotted on to a co-ordinate grid (or Cartesian plane as it is properly known).

There were no curves, or dips in the line - it was a straight line.

The straight line indicates a constant linear relationship between two variables (x and y).

All equations of a straight line can be written in the form y=mx+c. This is a linear equation. It results in a straight line when plotted on a graph.

y is a co-ordinate determined by the x value.

m is the gradient of the line (how steep it is).

c is the y intercept - the point at which the line crosses the y axis.

When a value for x is put into the equation y = mx + c, a result for y is produced.

There were 3 choices of equation for the line.

A) y = 2x + 1
B) y = x
C) y = 3x + 2

This line graph intercepted the y axis at 2 when x = 0

Option A - the intercept was 1

Option B - the intercept was 0

Option C - the intercept was 2. This was the answer.

A new one for so many of you!

Charn ☕️

PROBLEM 32 and SOLUTION

Total surface area.

The shape is a square-based pyramid.

In Problem 31, we looked at different types of pyramids and this type of pyramid (square-based), is probably the most widely recognised.

Total surface area is the combined area of each face of a 3D shape.

In this case, the pyramid has 5 faces; 4 triangular and 1 square.

To find the total surface area, find the area of the square base and each triangle.

In Problem 19, we looked at how to calculate the area of triangles.

The formula is (Base x Height) ÷ 2 OR 1/2(Base x Height). Remember, always use the perpendicular height.

The area of the square face is 5cm x 5cm = 25cm²

The area of one triangular face is (5cm x 10cm) ÷ 2 = 25cm²

Multiply the area of the triangle by 4 as there are 4 triangular faces. 25 x 4 = 100

The area of all 4 triangles = 100cm²

The total surface area of the pyramid is 100cm² + 25cm² = 125cm²

Skills in calculating surface area are required when painting a wall, wrapping a present or even icing a cake!

Well done everyone for trying!

Charn ☕️🥐

PROBLEM 31 and SOLUTION

Geometry.

This 3D shape is an OCTAGONAL PYRAMID.

A pyramid is a 3D shape with these properties:
•a polygon at the base
•triangles around the sides
•the sides meet at a common apex (single point at the top of the shape).

A pyramid is a POLYHEDRON. A 3D shape consisting of polygons joined at their straight edges.

The octagonal pyramid has an octagon at the base (8-sided polygon) and 8 triangles around the sides. The triangles join at the apex of the shape.

An octagonal pyramid has 9 faces, 9 vertices and 16 edges.

The pyramid is defined by its base.

Pyramids can have any polygon at the base - I have included some examples for you to take a look at it.

My students will tell you that geometry is my favourite area of maths! I remind them of that fact many times 😅

Which topic has become your favourite?

Charn ☕️🍏

PROBLEM 30 and SOLUTION

Expanding brackets.

Expanding brackets means to multiply each term inside the brackets by the term or expression outside the brackets. This will remove the brackets from the expression or equation.

9(a-4) = 3(x+4)

9(a-4) has two steps:

9 x a and 9 x -4

9 x a = 9a

9 x -4 = -36

Together, this becomes 9a - 36

3(x+4) has two steps:

3 multiplied by x and 3 x 4

3 multiplied by x = 3x

3 x 4 = 12

Together, this becomes 3x + 12

The solution was choice C.

Lots of you got this one correct! 🙌

Keep going!

Charn ☕️❤️

PROBLEM 29 and SOLUTION

Geometry.

Taking a few minutes to understand a shape and its properties, can minimise the amount of steps it will take to solve a maths problem.

The shape is a PARALLELOGRAM.

Those of you that have persevered with the questions over 30 days (wow and thank you 👏) will have remembered some key facts about this shape.

Opposite angles are equal. Opposite sides are parallel.

This means that Angle B is equal to 110°.

Parallelograms have 2 pairs of Parallel lines.

Each side of the parallelogram contains a pair of co-interior angles.

Co-interior angles add up to 180°.

Angle A is a supplementary angle, it is part of a straight line, which measures 180°

180° - 70° = 110°.

Angle A must be 110°.

Charn ☕️🥐

PROBLEM 27 and SOLUTION

Measurement.

Maps and scales.

The map uses a scale of 1:100,000

Map scales are always shown as a ratio of two numbers.

This means that 1cm on the map represents 100,000cm in real life.

If 100,000cm = 1km then 700,000cm = 7 km

On the map, a distance of 700,000cm will be shown as 7cm.

Not a lot of maths behind this one, just recalling a very useful fact.

How did you do?

Charn ☕️🍩

PROBLEM 27 and SOLUTIONS

Percentages.

Calculating percentages mentally has got to be one of the most useful skills.

Percentage increases and decreases affect all of us, in so many different ways. From interest rates to exam results - percentages are everywhere!

Per cent means out of 100 and is Latin in origin.

Any amount can be expressed as a percentage, that is as an amount out of 100.

There are so many ways to find a percentage of an amount without a calculator - I have shown you 3 ways, but there are others!

The important relationship, and the key to solving most percentage problems, is the relationship between fractions, decimals and percentages.

12.5% is one half of 25%

Knowing that 25% is equal to 1/4 is the key factor in solving this problem!

12.5% is half of 25%, therefore as a fraction it is half of 1/4 which is 1/8.

The increase was £12 as this is 1/8 of £96.
£96 increased by 12.5% is £108.

A useful one to know!

Charn ☕️🍰

PROBLEM 26 and SOLUTION

Geometry.

This regular 7-sided polygon is a HEPTAGON.

The word originates from the ancient Greek word for 7-angled ‘heptagonos’.

It is sometimes referred to as a Septagon.

‘Septem’ is the Latin word for 7. You may recognise ‘septem’ from September - originally the seventh month of the ten month Roman year. Both names refer to the same shape.

A heptagon has 7 interior angles which measure approximately 128.57°

The sum of the interior angles is 900°

Each exterior angle of a regular heptagon measures approximately 51.43°

Have you seen any heptagons around?

The 50p and 20p coins are both heptagon shapes!

Always something new to learn.

Charn ☕️❤️

PROBLEM 25 and SOLUTION

Proportion.

This problem involves proportional quantities. The ingredients must be kept in proportion to each other. That is, if one ingredient is increased or decreased in value, the other quantities will be treated in the same way. The ratio will remain the same, regardless of the values.

The key fact to solving this problem is 120g of butter is needed for 8 servings. From here, we can adjust the ingredients in proportion to each other.

2 ways to calculate how much butter is required for 20 servings:

Solution 1

120g = 8 servings
60g = 4 servings

4 servings x 5 = 20 servings

60g x 5 = 300g

Solution 2

60g = 4 servings
120g = 8 servings
240g = 16 servings

16 servings + 4 servings = 20 servings

240g + 60g = 300g

Same answer, 2 different ways!

Which method did you use?

Have a great day!

Charn ☕️🥐