Learn Russian: Мама рада: папа дома.

In Russian, the present tense of the verb 'to be' is almost never used. So instead of saying 'Mum is glad', you simply say Мама рада (Mum glad). The same goes for the second part: папа дома literally translates to 'dad at home'.

Why is the word for glad рада instead of рад?

рада is a special type of short adjective that changes its ending based on who is feeling the emotion. Since Мама is feminine, we use the feminine form рада. If dad were the one who was glad, it would be the masculine form: Папа рад.

Dad is masculine, so why does папа end in an 'a' like a feminine word?

A small group of Russian nouns refer to men but have feminine-style endings, like папа (dad) and дедушка (granddad). Even though they end in 'a', they are still grammatically masculine words.

I thought the word for house or home was дом. Why is it дома here?

дом is the noun for a physical house or building. However, when you want to say the location 'at home', you use the fixed word дома. Think of it as a location word answering the question 'where?' rather than just naming a building.