This one can be a challenge for children, who (hopefully unlike their parents) are pretty ego-centric. It is nice to form habits early that include prayer for others. It is scriptural and also practical.
We should always be mindful of the lost around us. We should also be quick to pray for anyone at any time, even in the store or in our neighborhood. If you encounter someone with urgent needs, I encourage you to stop and pray right then. It is very rare that someone will not accept an offer for prayer.
You can encourage your children to intercede on behalf of others by offering them opportunities. Things like prayer lists and bulletin boards can keep children mindful of the needs of others. And it helps even more when your first answer to a need they bring to you is to pray about it. Even a simple two sentence prayer can move mountains. Putting the needs of others before your own will develop children who are giving and loving. They will also see the scripture in Matthew played out in their lives, when Jesus said not to take care for your own needs, but to seek His kingdom first. They will see God’s blessing on their lives and it will increase their faith all the more.
Gal 6:2 Bear ye one another’s burdens, and so fulfil the law of Christ.
Jam 5:16 Confess your faults one to another, and pray one for another, that ye may be healed. The effectual fervent prayer of a righteous man availeth much.
Mar 13:33 Take ye heed, watch and pray: for ye know not when the time is.Luk 10:2 Therefore said he unto them, The harvest truly is great, but the labourers are few: pray ye therefore the Lord of the harvest, that he would send forth labourers into his harvest.