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Bookmark Monday: Medieval Math

So sue me, I like corny math story books. But with a title like Sir Cumference and the King’s Tens, you’re not just that wee bit curious of the content?

Noticing that the King has been rather gloomy of late, Lady Di of Ameter suggests to her husband, Sir Cumference the idea of hosting a surprise birthday party for the King. Which is a great idea, except now the castle is burgeoning with guests and more are arriving by the minute, and Lady Di needs a way to figure out how many lunches she needs to tell the cook to prepare.

With the help of the Knights of the Round Table – Sir Kell, Sir Tangent and Sir Lionel Segment, Sir Cumference and Lady Di of Ameter must quickly figure out the most time-efficient and accurate method of counting the total number of guests.

How do we do it?

Line them all in a straight line and count?….Too slow….

Form small circles and total the sum of parts? …Too exhausting…

What next?

Cindy Neuschwander cleverly introduces “place value” in an entertaining and engaging way as the story makes use of tents to illustrate the concept by separating the 9,999 guests that show up for King Arthur’s party into nine groups of one thousand, nine groups of one hundred, nine groups of ten and nine single guests, divided into four tents or number neighbourhoods.

I’ll be keeping an eye out for the rest of the Sir Cumference series now.

Huzzah for more corny math storybooks!

Bookmark Monday: Are you smarter than a third grader?

xyz + yz + z = yyz

What is x, y and z? Solve.

We were asked this question on Saturday night by one of the cousins; it was from a primary school math textbook.

Parents of Singapore primary-school age children from West to East, North to South, have been overheard cracking their heads over the logic of the  Heuristics methodology in the syllabus scope for Primary 3, at the office water-cooler, on public transport and in the midst of cracking their favourite chilli crab pincer. 

“Heuris-whats? Can it be eaten?”

Yes it’s waaaayyyy before my time as a mother of but two preschoolers.  But I’d eventually have to face it so I was curious enough to go look it up.

Heuristics – as defined by the Merriam-Webster online dictionary
: involving or serving as an aid to learning, discovery, or problem-solving by experimental and especially trial-and-error methods ; also : of or relating to exploratory problem-solving techniques that utilize self-educating techniques (as the evaluation of feedback) to improve performance
— heu•ris•ti•cal•ly \-ti-k(ə-)lē\ adverb

Hm. And this relates to Bookmark Monday how?

Well, we found this cute and clever book on an ordering booklist. Knowing nothing about it save for what we’d read on the short introductory synopsis, we ordered a copy and excitedly perused through it last night when it arrived.

The left brain of me couldn’t help succumbing to the temptation of subjecting myself to mental athletics at the sprightly hour of midnight, whilst the right half violently protested and loudly orated the surely-more-logical-and-reasonable option of succumbing to the comforts of a feather pillow.

Left brain won. (I know, I know, geeky geek…)

Frankly it will be some time before we pull this book out to share with our kids.  But Singapore math syllabus, Model method and homework woes aside, if you are looking for a more enjoyable resource with a no-tears formula for exploring heuristics and developing problem-solving techniques, I have to admit “Math Potatoes: Mind-Stretching Brain Food” comes pretty close.

That…and seriously? Can you resist checking out a book series with titles such as “The Grapes of Math” and “Math-terpieces”?

Now that we’ve got ourselves this copy, my attention is piqued enough to be on the lookout for the rest of the titles by Greg Tang, especially the ones for the younger preschool set – Math Fables and Math for All Seasons.

By the way, have you figured out the values of x, y, and z?

Yes? Give yourself a thump on your back – you are smarter… 😉
Not yet? Keep calm and crack on.

Bookmark Monday: Love, Family and Chinese Characters

Learning Chinese is an academic rite of passage almost every child in Singapore must go through sometime in their preschool life.

As parents, admittedly, DH and I aren’t incredibly disciplined (or rather, that should readare incredibly ill-disciplined‘) in our efforts to develop an appreciation for Mandarin with as much fortitude as we do for English. And so it is that we keep reminding each other that we “really must do something”, “really must read to them”.

Adding to this is the challenge of my having never studied Chinese, and so at my present age in life, it’s a tremendous mental obstacle.  I don’t want, don’t feel like doing it, but I must.  The inadequacy burns me most fiercely especially when they come home from school, singing Chinese songs and repeating random phrases they’ve learnt, to me, which I can’t decipher, and can’t repeat accurately to DH, when he returns from work, so that he can actually do something with them. 😦

So anyway.  Start somewhere I must.

So DH has been looking for some story books on Chinese characters, where the artwork is based on the shape of the Chinese character itself, (sort of like a Chinese version of Word Art 🙂  ) demonstrating the etymology of the word, i.e. how it evolved from the original pictogram representation to the regular traditional or simplified script that is commonly taught in schools today.

Personally, I like these, because by understanding the etymology, it helps me remember the character a little better. Some books are more artwork than story though, so we were glad when we found The Magic Brush, written by Kat Yeh and illustrated by Huy Voun Lee; as it is rich, both in storyline and illustrations.

The artwork for this book was created with cut-paper collages, known as jian zhi.  A Chinese folk art, passed down from generation to generation, jian zhi uses paper cutouts to create symbolic representations of words, showing the inspiration from where the character design originated.

A heartwarming story steeped in key tenets of Chinese culture – love, traditions, filial piety, and respect; and an effectively constructed introductory primer to first level Chinese characters, The Magic Brush is about a little girl named Jasmine, and her baby brother, Tai Tai, and of how their grandfather, A-gong comes to stay with them in spring and introduces Jasmine to a beautiful world of imagination and wonder through Chinese calligraphy.

All through spring and summer, they paint and write and dream wonderful worlds, created through the pictorial representations of the Chinese characters A-gong teaches Jasmine to write, bounded only by the limits of Jasmine’s imagination.

However, A-gong falls ill in the autumn and eventually passes away. Day after day, Jasmine mourns his passing.  But when one afternoon Tai-Tai abandons his nap and finds his sister sitting in the chair where their grandfather always sat, holding A-gong’s paintbrush, Jasmine decides to introduce Tai-Tai to the calligraphy that A-gong taught her, and together, with A-gong’s paintbrush, they recreate magic…just as their grandfather had said.

Bookmark Monday: One Grain of Rice

First, a note of thanks to our readers who have provided encouraging feedback and comments on Bookmark Monday – I really hope we continue to find and review good books, and that you’ll continue to share your thoughts with us.

On the back of the positive feedback we’ve received on our review of the Warlord series, I wanted to share this other mathematical folktale – One Grain of Rice, written and illustrated by Demi.

We discovered this author and her series of books in the local library, and have put in an order to purchase our own copy of “One Grain of Rice”. While it’s early days yet for our children to be learning squaring of numbers, it’s an investment that we’ll be keeping in store for our own family’s future “math enrichment” fun that one can’t get from doing school workbook assigned pages of sums. 😉

While she is more well-known for folk tales with moral lessons built into the storyline, such as “The Donkey and The Rock”, “The Greatest Power”, and “The Hungry Coat”, we feel that “One Grain of Rice” is an absolute gem because it combines moral lessons about justice, greed and selflessness, with a mathematical theme around squaring and exponential growth.

In the book, there is a chart showing how a single grain of rice, doubled every day for thirty days, results in a haul of 536, 870, 912 grains by the thirtieth day. Added up all together over thirty days, more than a billion grains of rice were delivered. Also, below are some website links I’ve found with math lesson plans themed around the book.   If you do give it a try, I’m always interested to hear how it went for you. 🙂

Synopsis extracted from the book:

Long ago in India, there lived a raja who believed that he was wise and fair. But every year he kept nearly all of the people’s rice for himself. Then when famine came, the raja refused to share the rice, and the people went hungry. Then a village girl named Rani devises a clever plan. She does a good deed for the raja, and in return, the raja lets her choose her reward. Rani asks for just one grain of rice, doubled every day for thirty days.
Through the surprising power of doubling, one grain of rice grows into more than one billion grains of rice — and Rani teaches the raja a lesson about what it truly means to be wise and fair.

Edible Math: Addition, Subtraction and Fractions

I apologise that we’re a little behind on our Wordcraft activities. As you know, we do all our brainstorming for our crafting activities at night. But in the past few nights, I’ve just completely knocked out the moment my head hits the pillow…so…I haven’t been logging on to the pc much.  But I promise we will get this back on track, soonest possible.

In the meantime – I wanted to show you something fun to do with leftover cupcake liners.  (I didn’t discover this, DD did.)

We’d just finished three mini cupcakes for tea.

After eating them, DD folded the cupcake liners into half and half again. She then arranged them on the plate. I think it was more for the aesthetic, than the mathematical angle, as the strawberry, vanilla and chocolate colours look very cheery.  

But arranged that way, each of those liners look like quarters that make up a circle! 

Below are some questions we walked through in a simple math-based game.  🙂

  1. How many cupcake liners do you have on the plate?
  2. How many cupcake liners do you think it takes to form a full circle? (Manoeuver the shapes around the plate to work out the answer. If your child is old enough to understand, you can introduce the concept of quarters, halves and wholes.)
  3. How many more cupcake liners will you need to make a whole circle? 
  4. What shape do we get if we take away one of the cupcake liners? (Half a circle).

If you do try it out, I would be very grateful if you’d let me know how it goes, and I’d be interested to know if there are other variations of questions you come up with as well.

Have fun!

Mommy Musings: CM

Lately, I’ve been reading up snippets of Charlotte Mason defined education. I first heard of it from some homeschooling friends.

Not that we are about to embark on homeschooling (the thought of being solely responsible for the children’s education fair frightens me), but some of the principles strike a chord with me.

So I am mustering up the courage and energy to challenge myself to go beyond what I have been doing with the kids so far, into a more focused and disciplined approach.

More information on this link here, but this summary of the principles around a CM education is extracted from the Ambleside Online website:-


  1. Narration, which consists of the child telling back a story.This takes the place of composition in the early years.
  2. Copywork, or the transcribing of a well-written piece of literature as handwriting practice.
  3. Nature study with an emphasis on close, focused observation of creation as a means to knowledge of God.
  4. Outdoor life is necessary to teach nature first-hand, which means plenty of time spent out of doors each day in all weather and in different environments for students of all ages. “School” for children younger than six consisted almost entirely of time spent outdoors.
  5. Habit training as a discipline of the child’s will and behavior. Children are trained to develop the will, which is manifested in a strong resolve to act in a right manner.
  6. Living Books rather than textbooks to convey ideas. Living books, whether fiction or non-fiction, are more than just interesting books that make a topic come alive. A true Living Book has the best material, from the best minds, or at least the real story from someone who was there or has a real interest in their subject.There is a high standard in literary excellence and, while she advocated the use of many books, quality is to be preferred over quantity.
  7. First-hand exposure to great and noble ideas through books in each school subject, rather than rote memorization of dry facts. Besides books, children are exposed to great minds through art, music and poetry, which was read to the child daily.
  8. Memorization was used, not to assimilate facts, but as a means to have material to meditate on, so her students memorized scripture and poetry.
  9. History is taught with primary sources and well-written history books.
  10. Literature is taught along with history. For example, if one is studing the Civil War, one would at the same time read works of American literature written at that time.
  11. Once children are able to read fluently, they read the lessons themselves, except for books that need editing like Plutarch’s Lives.
  12. Reading instruction was primarily based on sight vocabulary, but did include use and teaching of phonics. Even beginning readers, she thought, ought to have something interesting to read, like nursery rhymes, rather than dull first readers, so she taught the sight words necessary to allow them to read real books.
  13. Schooling is teacher-directed, not child-led, though the child can pursue any number of personal interests during their free time, and her students had all afternoon free.
  14. Short lessons with an emphasis on excellent execution and focused attention and variation in the day’s scheduled activities so as not to over-stress the brain on one task.
  15. In the teaching of mathematics, the ability to reason is emphasized over “working sums”, so emphasis is placed on story problems and working with numbers that are within the child’s comprehension, therefore, a manipulative-based instruction is desirable.
  16. Charlotte Mason encouraged proficiency in at least one other language, specifically French, as well as study in Latin.
  17. Charlotte Mason set aside time each day for some form of physical fitness routine which included daily walks and a “drill” which included stretching, breathing exercises, calisthenics, dancing, singing, and games.
  18. The knowledge of God, as found in the Bible, is the primary knowledge and the most important.


To that end, where time allows, we have decided in our family to do the following:-

  • In language – to encourage vocabulary development, introduce some sight recognition of basic words, and supplement with phonics exercises (rather than making phonics the major focus).    Starting from last week, you would have observed that we’ve attempted to be more focused in our Wordcraft activity by trying (as far as possible) to connect the theme for the week, with a book.  Where we are able to, we try and obtain those on prescribed reading lists or written by recommended authors.
  • In art – to aim to provide exposure to books with notable illustrations, so their minds and skills can be challenged to explore new techniques, media and improve on existing skills. More visits to the library!
  • In exercise and time outdoors – to set aside a disciplined time every day if possible, to bring the children out to the playground, or to ride their tricycles. (Rainy evenings have not been helpful in this regard, but try we must!)
  • In the area of proficiency in another language – to be more diligent in speaking and reading of the Chinese language (this is a personal admonition to myself to stop beating about the bush, and start getting serious about it!)
  • In developing knowledge of God – to start doing family devotions, and learning hymns and songs regularly together.

It’s interesting to look back in time to when I first began this blog, and how it started out from a desire to just spend time together on something fun to do with the kids – largely unscheduled and unstructured – into where we want to get to from here.

It feels like a very small start, and very definitely mere tip of the iceberg. But at the same time, it’s an incredibly ambitious plan for two full time working parents with mostly only alternate evenings to spare. *phew*

But. Every journey begins with a single step, and we are called to be faithful stewards of the young lives God has carefully placed in our hands…so…

…off we go. 🙂