200 Records: Understanding The Limit - http://boldsparks.com/200-records-understanding-the-limit/

AccountTrigger.cls

trigger AccountTrigger on Account (after update) {

// make a set of all account ids that are not active but previously were active
Set<Id> accountsSetToInactive = new Set<Id>();
for(Account acc : trigger.new) {
    if(!acc.Active_Checkbox__c && trigger.oldMap.get(acc.Id).Active_Checkbox__c) {
        accountsSetToInactive.add(acc.Id);
    }
}

// get all the related contacts and set them to inactive
if(!accountsSetToInactive.isEmpty()) {
    list<Contact> contactsToSetInactive = [SELECT Id,Active_Checkbox__c FROM Contact WHERE AccountId in :accountsSetToInactive];
    for(Contact con : contactsToSetInactive) {
        con.Active_Checkbox__c = false;
    }
    update contactsToSetInactive;
}

}

ContactTrigger.cls

trigger ContactTrigger on Contact (before update) {
    runCounter.contactTrigger++;   
    
    for(Contact con : trigger.new) {
        con.Batch_Size__c = String.valueOf(trigger.new.size());
    }

    system.debug('@@@ Contact Trigger Ran: ' + runCounter.contactTrigger + ' times.');
    
}

execAnon.cls

list<Account> accounts = [SELECT Id,Active_Checkbox__c FROM Account WHERE Name LIKE 'Account '];
for(Account acc : accounts) {
    acc.Active_Checkbox__c = False;
}
update accounts;

runCounter.cls

public class runCounter {

    public static integer contactTrigger {
        get {
            if(contactTrigger == null) {
                contactTrigger = 0;
            }
            return contactTrigger;
        } set;
    }

}