Explaining, convincing and proving

Can you crack these cryptarithms?

Can you deduce the perimeters of the shapes from the information given?

A colourful cube is made from little red and yellow cubes. But can you work out how many of each?

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Join pentagons together edge to edge. Will they form a ring?

Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

Can you maximise the area available to a grazing goat?