Crops mentioned in the UK games are: Oats, beans, barley, wheat, groats and hops; pease (peas) not mentioned as such.
Wheat is mentioned in only two counties, Staffordshire and Isle of Wight- in the past, wheat was an exceptional crop, village people living on oatmeal and barley bread.
Gomme's III from Northants is interesting, possibly old, but the spelling is not explained.
III.
Does you or I, or anie one knowe
Where oates and beanes and barlie growe?
Where oates and beanes and barlie growe?
The farmer comes and sowes ye seede,
Then he stands and takes hys ease,
Stamps hys foote, and slappes hys hand,
Stamps hys foote, and slappes hys hand,
And turnes hym rounde to viewe ye land.

Waiting for a partner,
Waitng for a partner,
Open the ringe and take mee in,
Make haste and choose youre partner.

Now you're married you must obey,
Must be true to alle you saye,
Must bee kinde and verle goode,
And helpe your wife to choppe ye woode.

Perhaps a game of the fairs, before it came down to children.