Almost all of the children of William Charles Hapgood and Clara Ann (Newton) went to Kin Kin Junction State School. Jeffrey Gordon Hapgood appears to have been too old for school by the time the family moved to Kin Kin from NSW in 1913. A listing of Kin Kin Junction School Admissions lists  the following Hapgood family enrolments, and their pupil numbers:
1913: 60 Clarice Hapgood; 61 Jane Hapgood (Iris Jane) 62 Mona Hapgood; 63 Ina Hapgood
1915: 86 Gwendaline Hapgood
1917: 107 Stella Hapgood
1924: 166 Olga Hapgood
Also listed are the Waddells:
1916: James Waddell (who married Ina Hapgood above), Patricia Waddell (my grandmother), and Jessie Waddell.
As mentioned in the last post, Olga Hapgood wrote a wonderful memoir of her early life growing up in Kin Kin. She talks in particular about the Kin Kin Junction State School, which was the heart of the little community and very influential for both the Hapgood and Waddell families.
Many farms were established in those early days, so the tiny Kin Kin Junction School was opened in 1909 and so it was that in 1924 I commenced school there as my sisters before me had done, I must confess that I never liked school but of course loved the company of the other children. Practically the whole of my school days were spent under the beady watchful eyes of a headmaster commonly known as “Old Adam”, who was intensely disliked by us all. Our school was a tiny one roomed building set high from the ground so we were often cramped for room and spent a lot of time on the veranda being taught by the older scholars. Despite this we were really taught to read and spell very well.
Many of the children rode horses to school, but fortunately I only had a short distance to walk.Olga Hapgood Memoirs, 1918-1942
Olga was pupil number 199 at the Kin Kin School. A book on history of the Kin Kin Junction State School prepared for the 75th Jubilee celebrations has a few other comments about the “Old Adam” Adam Douglas, who taught at the school from 1928 . A student Ruby Sorenson in the same year as Olga (pictured above) recalled in 1991 that he was very fond of roses and carefully pruned the old rose bushes on the school grounds. She tells an anecdote of Olga Hapgood and Adam Douglas:
Adam Douglas was, apparently, very protective of his roses. When Olga Hapgood picked one, for instance, he sent her outside with a glue pot, giving her instructions to restore the flower back to the bush. She spent her whole afternoon in this futile attempt at corrective surgery!From Kin Kin Schools Past and Present by JD Dale 
The Kin Kin Schools book by JD Dale  also has a section by Ina Waddell (nee Hapgood) who attended from 1913 to 1923. Ina wrote:
I came to Queensland with father, mother, brother and sisters early in 1912. My father bought a farm not far from the school (nearly all standing scrub).
The school had been opened a few years before I started there. My first teacher was Miss Sedgman… I don’t think Miss Sedgman taught for long. The next teacher was a Miss Pilcher whose home was in Gympie. She boarded with my parents and rode her horse to Cooran after school each Friday and caught a goods train to Gympie coming back to Cooran by train Monday morning and riding out to school.
I started school 23rd September the day I was 5 years old. The school was a small wooden building – there were four long desks either side of the room, a teachers table in the front, a press in one corner where books were kept and a few book shelves on the other side. The school was high off the ground with partly used verandahs front and back where we hung out school bags and hats. We used slates to do our homework on – not very hygienic. The toilet was a big hole dug in the ground with a wooden toilet built over it (horrible). Diptheria broke out in the school on two occasions and as I can remember two pupils died. There was always a nice harden – the boys gardened while the girls had sewing lessons.
Games – we mostly played rounders, prisoners base, red rover, and the older boys played cricket. A game the girls loved and played a lot was what we called “Jacks” played with 5 marbles on short grass or a mat.
We went into school 9.30am and came out at 3.30pm. The highlight of the year for me was Arbor Day and Picnic Day at the end of the year; also Pomona show. Arbor Day was a picnic where mothers and fathers came and we had a basket lunch and planted trees. I remember I always had a new dress and hat for picnic day. The committee members made sandwiches and the mothers brought cakes. Each pupil received a book and we played games and had races.
We had sewing lessons twice a week and learned useful sewing. We worked a sampler with lots of lovely fancy stitches. The older girls made clothing. When the First World War started in 1914 Miss Pilcher knitted socks to send to the soldiers and she taught us (boys and girls) to knit socks and knee pads. The Comforts Fund supplied the wool and instead of sewing lessons we had two half hours a week knitting. Some of the boys were really good at knitting. Miss Pilcher stayed for a few years, then resigned and went to the Church of England School in Toowoomba.Ina Hapgood (later Waddell), January 1991 for 75th Jubilee. 
Ina’s best friend in school, Jessie Moffat, and lifelong friend, also wrote an entry for the Kin Kin schools book, and wrote:
A little girl, Ina Hapgood, the daughter of a farmer started school the same day as I did and we have been friends ever since. We sat in class side by side and now in our 83rd year are still friends. After the little Methodist Church was erected close by the school we were able to observe the weddings of my special friend’s sisters, Phyllis Johnston and Iris Bentley. Weddings were usually on week days at that time.Jessie Moffat school memories, 1991 . Phyllis and Iris were older sisters of Ina and Olga Hapgood.
Kin Kin was a small town and all of the families were connected with the school(s) in the districts. There is a terrific photo of the “Local Ladies” who supported the school in 1929, which includes 4 of Olga’s sisters, her Mum and her Aunt.
The Kin Kin Junction State school opened in 1909 , There is a photo of the students of the Kin Kin Junction school a few years later in 1916, with all the kids lined up on the balcony and the steps. This features several of Olgas sisters (Iris, Mona, Ina, Gwen Hapgood) and several of her future sisters-in-law from the WADDELL family: Patricia Waddell (married Olgas eldest brother Jeffrey – they were my grandparents), Jessie Waddell, Jim Waddell (who later married Ina Hapgood) and Jean Waddell. The Hapgoods and the Waddells were inter-twined in Kin Kin right from their earliest school days, and so the fact that there were two weddings — Jim Waddell and Ina Hapgood, and Jeff Hapgood and Amy Patricia Waddell – meant that the families were linked together permanently.
In later years the Kin Kin Township school opened, and the Waddell kids were enrolled there.
Update: Another photo of the Kin Kin School has popped up on the Gympie School Archives facebook page, taken about 1930. It shows the main school building but also a bit of the other building (teachers residence) and the paddock and trees. All the kids are lined up along the fence, and you can almost imagine the excitement and commotion of this photo being taken. Olga Hapgood is presumably in this photo, somewhere….
 “Kin Kin Schools Past and Present” by JD Dale. 1991. https://trove.nla.gov.au/work/8412964
 Gympie School Archives, and facebook page: https://www.facebook.com/schoolarchives/posts/153486689619098