Yup. The hens will regulate their own calcium intake. Just make it available to them and they'll choose when they want it. Dried, crushed egg shell also works well. I use a mixture.
FYI- This method of feeding/calcium has many advantages over using layer feed. No issues with too much...
You may be having an issue with a hidden nest. The girls may have found a nice, safe place that you aren't aware of and have been piling up eggs there.
Mostly correct. Age will reduce, but not eliminate egg production. Mine lay best for 2 seasons, reduce ~20% in year 3 and are clearly less productive by year 4. I have a 7 year old barred rock that still lays periodically.
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@Charlotteandfriends - Do you still have the tag on the Layena...