Introducing algebra

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

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