Kids mind is amazing. They think so fast and absorb everything not even thinking about it. That's why it's important to behave properly when they are around.
But I am not here to learn you what to and not to do. I will simply tell you just a bit about three years old kids like the one little teddy bear I have at home.
I believe ever since the child's birth, you have watched him grow and develop. You watched and acknowledged his height, weight, and when you first looked, when he first rose to his feet, watched his first steps and listened proudly to his first words. You will surely have a great deal of experience with him.
That's why daily rituals are very important. Routine and schedules within the family give a sense of security to them. Try to include numbers and colors in daily conversations. "You wore a blue shirt," or "We made 6 cookies."
Encourage the child to perform the activities as freely as possible and trust him to carry them out on a daily basis. Thus, he will begin to rely on himself and rely on his power.
Give the child a lot of sensory experiences for learning and developing coordination - dancing, painting with fingers, puzzles ...
And a game like this I prepared for my boy and his mates in kindergarten for his birthday. A simple game made in no time which will encourage the young mind to think. Hope I gave you a good idea to motivate your kid. Have fun playing!