OK Evil:
First you clearly have a computer as your on MN - so let me start off with your Kenya school kid complaint.
Did you consider typing in on a search engine:
school life in Kenya
because when I did I found: www.kids-4-kenya.org/learn-about-kenya/schools.cfm & www.bbc.co.uk/learningzone/clips/life-in-rural-kenya/4499.html - with a class clip from the BBC showing a Kenyan school.
Now you may have to help your child read this or explain some of the terminology - you will have to vet websites obviously - but there's a lot of information there to explain the similarities and differences between school in Kenya and in England - and that is of benefit to your child:
It's important to understand that not everywhere is like home.
This exercise might show that they are privileged that education is a right & free in England
(actually rather a recent advent historically - and that may be worth discussing)
gets children thinking about different approaches to education - is that fair that some children stop school at 13 because they can't afford to stay in school/ there family need the help financially/ maybe physically.
Genuinely - my approach to something like this is teaching those core research skills that ultimately will help your child achieve in Senior School & beyond.
Do I know anything about this? No - well then go find some facts (the web is brilliant for this - use a search engine, chose reputable sites and see what you find out).
Once you've gathered a list of facts (maybe set the limit at 10 or a dozen) - then consider how you want to present them.
England vs. Kenya?
So you could have each paragraph be about a fact and then discussing difference in England/ Kenya - i.e. school day length/ cost/ ages in school/ uniforms/ singing/ etc...
You may not particularly value learning about other countries - but it may be of interest to your child, it may spark an interest in your child and some of the unfairness in the world may just get your child interested in growing up and making the world a better place where every child can stay in school until 18 if they want to and girls aren't getting married at ages 12-14.
I agree fresh air and outdoor play is a wonderful thing - but I suspect this written homework you're complaining about (4 options out of 8) was over the term and not just for one night. So over a few days - perhaps 15 minutes on one website - reading it & making notes / 30 minutes on the BBC class clip web site & making notes/ 30 minutes planning the writing task and 30 minutes writing with possibly a last stage of you looking over the work and correcting some errors with your child (our classic is no punctuation/ lack of capitalisation) - all can be a really good thing and part of a very balanced childhood where learning more about things is also seen as a pleasurable activity.
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I agree that this is ambitious old stuff the Year 3 teacher is setting - but rather than seeing this as an unfair imposition on you - why not think of yourself as lucky. This teacher is instilling some really good research skills through very straightforward activities into your child.
DD1 has had no writing tasks in 7 years of primary school and now post SATs all homework has stopped. Getting her to write a letter of thanks to her grandparents for a present is literally World War III. She doesn't know how to set out the letter/ how to address the envelope. She doesn't know how to write out a date. She doesn't know how to spell sincerely. She doesn't know it should be capitalized - she argues that how can you have just one word for the sentence.... She gets angry that I suggest different punctuation or improving the wording. And we write thank you letters each Christmas/ Birthday - it was only by Year 5 that this settled down and she really knew what the task entailed and could do it swiftly - the point being that the practice was essential to mastering this skill/ task.
Trust me - on the cusps of DD1 going of the senior school I would have given my right arm for a Y3 teacher (Y4/ Y5 even Y6) who was interested in getting some writing/ research skills instilled in children early.
DD2 is in a new school (Y4) - and this style of homework (coupled with in class work as well - so maybe research at home/ write in school or visa versa ) is very common. The difference in my two DDs language skills at this age/ ability to work independently at their present ages (9 & 11) is night and day.
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I know homework can be annoying - but just as you might watch a tv programme because you enjoy history/ science/ nature - think of selecting homeworks (or your way of dealing with them) in terms of how they touch on your child's interests. Your child may have selected the Kenya option - because they're interested - and trust me part of the job description is grinning and bearing it and supporting their interests (I say this having stood in the rain for hours during football matches).
I suspect the teacher did not intend for you to cloister your DC indoors for hours finishing the 4 assignments in one go. I tend to approach these things in small defined bite-size pieces. So maybe research a few websites (2-3 separate events). Plan how you'll organise the facts you've gathered - preparing a writing outline. Write the essay. Check through the essay - maybe correcting glaring errors (missing punctuation/ capitals - but trying to leave it your child's own work). In this way - there should be more than enough time for your child to play outdoors and we find that by asking them to do homework whilst we're preparing dinner is a nice way of getting our DDs to see homework as part of the process of being a student, nothing to be upset or freaked out about, and sometimes very enjoyable. It is nice to learn new things.
HTH