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Try out all the daily maths challenges from Maths Week Scotland 2024

Problem 1 is all about working out the dimensions of a domino within a larger rectangle.

Problem 2 is all about working out the distance, speed and time of two runners.

Problem 3 is all about working with decimals and fractions.

Problem 4 is all about working out averages.

Problem 5 is about shapes and working out areas.

Challenge 6 is all about finding different combinations.

Problem 7 is all about number patterns.

You might not always need or be able to give an exact answer to a calculation, Sometimes an approximate answer is good enough. You can give an approximate number by rounding up or down.

When adding and subtracting numbers it's important to be consistent with positive and negative values. Remember that two plus signs or two minus signs make a positive. One plus and one minus make a negative.

In the column method of addition and subtraction, numbers are written so their place values line up vertically forming columns for ones, tens, hundreds, thousands etc.

Place value is the value of each digit in a number, for example ones, tens or hundreds. Decimal place values include tenths, hundredths and thousandths. The value of a digit goes up by ten as it moves to the left.

When adding and subtracting decimals it is important to keep place values consistent. Remember to be careful when using positive and negative values.

Both positive and negative numbers can be multiplied and divided using rules. Two signs the same gives a positive answer. Two different signs give a negative answer. More difficult multiplication can be carried out using the grid or column method. Division can be worked out using short or long division.

Multiplying a decimal by a whole number uses the same method as multiplying two whole numbers. When multiplying by 10, 100 or 1000 you need to move each digit the correct number of places to the left.

Dividing decimals by whole numbers works the same way as dividing whole numbers except, just like addition and subtraction of decimals, the decimal point must be kept in line. When dividing by 10, 100 or 1000, remember to move all digits the correct number of places to the right.

Multiples are numbers that can be divided by other numbers. Common multiples can be divided by two or more numbers. The lowest common multiple is the smallest number that two or more numbers can divide into.

A factor is a number that divides into another number exactly. A common factor is a number that two numbers can both divide into exactly. The highest common factor is the largest number that divide into two numbers exactly.

Prime numbers are numbers that can only be divided by themselves and one. If a number is a multiple of any other number, then it is not a prime.

A factor is a number which divides exactly into another number. 1 is a factor of every number and every number is a factor of itself.

Many maths problems involve using multiples and factors to find the answer. If you are set a word problem you should look at the key information given to see if you need to use factors or multiples.

A power is a way of writing a number that is multiplied by itself. A root is the opposite of this. It is a way of writing a number that can be divided into another number multiplied by itself.

You can evaluate powers yourself or with a calculator by multiplying the number by itself the number of times shown by the power or index. Finding the root is often easiest using the root button on a calculator.

Fractions are a way of expressing parts of a whole or equal parts of an amount. The number on top is the numerator and shows the number of parts you are dealing with. The number on the bottom is the denominator and shows the total number of equal parts that something has been divided into.

Fractions are calculations involving a portion of a quantity, shape or object. Equivalent fractions allow cancelling (also known as simplifying) to simplest form.

Mixed numbers are made up of a whole number and a fraction. Any whole number can be written as a fraction where the numerator is a multiple of the denominator. So a mixed number can also be written as an improper fractions where the numerator is bigger than the denominator.

Adding and subtracting can be applied to mixed number fractions. Each has its own method that helps make sure the numerator and denominator are treated correctly.

Per cent means 'per 100'. If 70 per cent of the population own a pet, this means that 70 out of every hundred people own a pet. The symbol % means 'per cent'.

Calculating a fraction of a number can be done by multiplying by the numerator (top number) and dividing by the denominator (bottom number). Percentages can be worked out by multiplying by the percentage and dividing by one hundred.

When a quantity is increased or decreased by a percentage, you can calculate how much it has changed by and what the new amount is. You can also work backwards from a final number to find the original quantity (100%).

Ratios are usually written in the form a:b and are used to compare quantities which are measured in the same units. Given a ratio, quantities can be calculated and are in direct proportion when they increase or decrease.

Financial maths is needed for all jobs, from calculating wages to working out profit, loss and VAT. Knowledge of financial maths is also required to be able to understand bank statements and savings.

Budgeting is listing and planning estimated income and spending. This allows us to make informed choices regarding spending and saving.

Understanding the best value for money is important when looking at option or contract services, eg mobile phone deals.

Travelling abroad involves converting currencies into the currency of the country visited. To calculate the amount, exchange rates are used.

Calculations involving distance, speed and time can be worked out using formulae. When doing these calculations, the units used should be consistent.

Time has various units of measurement, eg seconds, hours, days. Knowing how to measure time is useful as it helps you work out when your favourite TV show is on, or how many days there are in a month.

A problem involving the ambiguities of language. Marcus du Sautoy sets a word puzzle.

Before measuring something, you need to know what unit to use. You can do this by estimating its approximate length, mass or volume.

Solving calculations of length, mass and capacity might involve converting between standard units. Understanding what kilo-, centi- and milli- mean will help you decide which number to multiply or divide by.

The perimeter of a shape is the total distance around its edge. To calculate the perimeter of a shape, you just have to add up the lengths of all of its sides.

When converting between metric units of area and volume, the numbers you have to multiply or divide by need to be squared for area and cubed for volume.

Two-dimensional shapes are flat. The perimeter of a 2D shape is the total distance around the outside of the shape. The area of a 2D shape is the space inside the shape. Compound shapes can be split into different shapes to work out total area.

An object’s volume is a measure of its total three-dimensional space and can be found using formulae. Volumes of composite objects can be found by breaking them down into simpler objects and adding the volumes together.

Marcus du Sautoy looks at the Arabic roots of the invention of algebra.

Numbers written in a specific order can form a sequence. Terms in a sequence can be related by patterns such as a common difference. Sequences where terms have a common difference are called 'arithmetic sequences.'

Learn about the nth term in a sequence and how to calculate it.

Algebra is part of maths where we use letters to represent unknown values or values that can change.

Algebraic expressions can be simplified by gathering like terms. Like terms are terms that feature the same variable, usually shown by a letter.

When you know the value for letters in an algebraic expression you can substitute these values into the expression and solve it.

An equation is a mathematical expression that features an equals sign. Solving an equation means finding a missing value, which is usually shown by a letter.

An equation is a mathematical expression that contains an equals sign. Creating an algebraic equation is a useful step to finding an unknown value. You can solve an equation by using inverse mathematical operations.

A formula is a mathematical rule that shows the relationship between different variables. A formula can be created and used for something that is calculated frequently.

2D shapes are flat, plane shapes. Triangles have three sides and three angles that add up to 180°. Quadrilaterals have four sides and four angles that add up to 360°.

Learn how to construct triangles using a pencil, a piece of paper, a ruler, a protractor and a compass.

3D objects have three dimensions - length, width and depth. Prisms are 3D objects with a constant cross section. Pyramids are 3D objects with a flat base and which taper to a vertex. Many three-dimensional objects can be constructed from 2D nets.

Angles are often described using three letters. Angles can be drawn and measured using a protractor.

Complementary angles form a right angle. Supplementary angles form a straight line. Parallel lines in shapes can form corresponding and alternate angles. You can use these properties to find missing angles.

Angles inside a shape are called interior angles. Interior angles in a triangle add up to 180°. Interior angles in a quadrilateral add up to 360°.

Parts of a shape on either side of a line of symmetry will be exact mirror images of each other. Different two-dimensional shapes have different numbers of lines of symmetry.

Similar figures are identical in shape, but generally not in size. A missing length on a reduction/enlargement figure can be calculated by finding its linear scale factor.

It is important to make sure any information you work with is robust. Things to look out for include validity of the source, scale used, sample size, method of presentation and appropriateness of how the sample was selected.

When carrying out an investigation, you will need to collect and record data from which you can draw conclusions.

Statistical information can be presented in diagrams, graphs and charts. The type you use will largely depend on the sort of data that you want to present.

Data is presented in different ways across diagrams, charts and graphs. These can be studied to find specific information or to identify patterns, known as trends, in whole groups of data. These findings can then be summarised and described in words.

An introduction to the four main colours of ink required to print a magazine.

Why you only need 35 people for it to be very likely that two will share a birthday.

Can you work out how many books there are in different boxes?

Can you work out how much the farmer weighs?

Can you figure out which nets can fold into cubes or dice?

Can you work out how much money Tam McTavish spent on a family shopping trip?

Can you figure out how many triangles in this diagram?

Can you solve this problem about sequences and finding missing information?

Can you calculate the average speed of a journey?

Can you solve this problem about visualising 3-D shapes and counting cubes?

Can you find out the missing prices to solve this problem?

Can you figure out measurements and calculate costs to solve this gardening problem?

Can you use different types of mathematical averages to find some mystery numbers?

Can you find all the possibilities for fitting dominoes in a box with this problem about space and volume?

Can you work out how many teachers are taking part in a meeting?

Can you work out where the missing lines in a diagram should go in this problem about mathematical relationships?

Can you solve this problem about numbers that read the same forwards and backwards?

Can you solve this problem about comparing different units of length and distances?

Can you work out the areas of different parts of triangles?

Can you solve this problem about using different lengths of rod to work out all sorts of measurements?

Can you solve this problem about powers and incides?

Can you solve this problem about using different taps to fill a water tank?

Can you solve this problem about equations with missing numbers?