We start close to home, which is exactly right on day one. Arusha National Park sits under Mount Meru, forty minutes from town, and it is the gentlest introduction to a safari there is: no lions, so you can get out of the vehicle, and a walking trail among giraffe, zebra, buffalo and waterbuck. Black-and-white colobus monkeys throw themselves between the trees overhead, and the Momella lakes are pink with flamingo. Short drives, no early start, and children can move about. Dinner and overnight in Arusha.

After breakfast we drive south to Tarangire, arriving in time for a picnic lunch under the acacias. Tarangire is the elephant park, and this is the day the safari becomes real for children: in the dry season the herds gather along the river in their hundreds, and calves the size of a sofa walk past the vehicle close enough to hear breathing. The baobabs here are over a thousand years old, which is a fact worth telling a nine-year-old. A full afternoon of game driving, then we climb to Karatu. Overnight in Karatu.

The big one. We descend six hundred metres down the wall of the Ngorongoro Crater — an extinct volcano that collapsed in on itself and is now a bowl twenty kilometres wide, full of animals that never leave. Lion lie in the open. Black rhino, elephant, buffalo and hippo share the floor with thousands of zebra and wildebeest, and flamingo line the shallow soda lake. It is a small enough space to see a great deal without hours of driving, which suits children perfectly. Picnic lunch. Overnight in Karatu.

A gentler day. Lake Manyara is a short drive from Karatu and it is small, green and full of things happening close to the road: baboon troops squabbling in the groundwater forest, blue monkeys overhead, hippo wallowing in the pools, and flamingos out on the soda lake beneath the Rift Valley escarpment. Manyara is also famous for its tree-climbing lions, which nobody has ever fully explained. After a morning game drive and lunch, we drive back to Arusha. Dinner and overnight in Arusha.

The day the children have been waiting for. We drive east from Arusha to Chemka, where a natural hot spring rises out of the ground and forms a pool of astonishingly clear turquoise water under a canopy of fig trees, warm enough to swim in all day. There is a rope swing. Bring a towel and a swimsuit and expect to have to argue them out of the water. After a picnic lunch we drive on to Kilimanjaro International Airport for your flight home, or back to Arusha.