Rule 1: 1. كَيْ 'in order that'
كَيْ introduces a purpose and is followed by the imperfect. After كَيْ the final ḍamma of the verb becomes a fatḥa: يَقْسِمُ he divides but كَيْ يَقْسِمَ in order that he may divide. This changed ending is the first sign you meet of a mood of the imperfect that later lessons will treat fully; for now, simply remember fatḥa after كَيْ.
ذَهَبَتْ أُمِّي إِلَى السُّوقِ كَيْ تَشْتَرِيَ سَمَكَةً.
dhahabat ummī ila-s-sūqi kay tashtariya samakatan
My mother went to the market in order to buy a fish.
دَخَلَ الْقِرْدُ الْبَيْتَ كَيْ يَأْكُلَ.
dakhala-l-qirdu-l-bayta kay yaʾkula
The monkey went into the house in order to eat.
أَكْتُبُ الدَّرْسَ كَيْ أَفْهَمَهُ.
aktubu-d-darsa kay afhamahu
I write the lesson out so that I understand it.
جَلَسَتِ الْقِطَّةُ عِنْدَ الْبَابِ كَيْ تَدْخُلَ.
jalasati-l-qiṭṭatu ʿinda-l-bābi kay tadkhula
The cat sat by the door in order to get in.
ذَهَبَتَا إِلَى الْقِرْدِ كَيْ يَقْسِمَ السَّمَكَةَ بَيْنَهُمَا.
dhahabatā ila-l-qirdi kay yaqsima-s-samakata baynahumā
They (two) went to the monkey so that he would divide the fish between them.