To cook the rice, put the rice and water in a medium sized saucepan. Bring the water to the boil and then reduce the heat to a simmer (gentle bubbles), cover with a lid and set your timer for 20 minutes. Take off the heat.
Meanwhile, spoon the sugar into a bowl, add the vinegar and salt and stir until the sugar has dissolved (disappeared). Pour the dressing over the hot, cooked rice and stir, leave the rice to cool.
Tip: Read the cooking instructions on the packet of sushi rice before you cook it, but the method here is how most sushi rice is cooked so it’s likely to be similar.
To make the sushi rolls
Put a sheet of nori seaweed on a sushi mat. Wet your hands in a bowl of cold water and use your hands or a spoon to cover two-thirds of the seaweed with rice, leaving a strip along the top of the seaweed sheet, furthest from you without rice. Press the rice down so that it is quite flat and evenly spread out.
Using the bridge cutting technique, cut the beetroot into thin strips – hold the beetroot between a thumb and finger of one hand to make a bridge, hold a table knife in the other hand, put the blade under the bridge and cut downwards through the beetroot to make strips.
Peel the cucumber into strips. Grate the carrot – hold the handle of the grater with one hand and then push the carrot downwards over the grater teeth. Always keep your fingers away from the teeth as they’re sharp.
Put a row of each of the veg along the middle of the rice. Pick up the edge of the mat closest to you and roll up the seaweed and its filling into a big sausage. Use the mat to help you roll up the seaweed neatly.
Squash the roll to make the sushi nice and compact, then unroll the mat. Do this again with the remaining sheets of seaweed, rice and filling.
Using the bridge cutting technique, cut the sushi in half, then into quarters and then cut each quarter in half to make 8 pieces of sushi. Repeat with the rest of the rice, seaweed and veg.
To make the sushi balls
Hold an avocado half between a thumb and finger of one hand to make a bridge, hold a table knife in the other hand, put the blade under the bridge and cut downwards through the through the avocado half to make strips. Squeeze over a little lemon juice to stop the avocado from turning brown.
Cut a beetroot into thin circles using the bridge cutting technique. Sit a piece of avocado or beetroot in the middle of a piece of greaseproof paper. In a little bowl, mix the mayo and wasabi together and dot a little on the veg.
Take a small ball of rice and mould into a ball with your hands and then sit it on the mayo. Bring the paper up around the veg and rice and squeeze to shape into a ball. Repeat with the remaining rice and veg.