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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: Downside up and back round again

If you like optical illusions and tessellations, you might find D.B. Johnson’s Palazzo Inverso fascinating.

A story about an apprentice named Mauk, his job is to help the Master design and build a grand Palazzo. Every day is the same, and on an ordinary day like any other, Mauk wakes up, and goes through the motions like he always does.  But something strange is afoot – the bricklayers are spilling bricks on the ceiling and workers are falling down stairs, the water in the fountain is falling up instead of down and everything appears all mixed up.

The Master blames Mauk for all the mayhem. But Mauk only sharpens the pencils, he isn’t allowed to draw.

Except…at times when the Master was looking out the window, Mauk might have turned the drawing round just a tiny bit and the Master never having noticed this, never realized what a strange Palazzo he was drawing.

This is a continuously looping story, which means you read it from the front to back, and then turn the book upside-down (and see what happens with the picture!) and read from the back all the way to the front again. Great fun!

Notes to the parent: 

  1. For more supplemental activities on optical illusions and tessellations, readers based in Singapore should check out the “Mathematics Everywhere and Everyday” and “The Mind’s Eye” sections at the Singapore Science Centre.
  2. You can also click here for an online version of the story.  But seriously – the print version is a lot more engaging, and allows you to take your time to pore over the intricacies of the pictures.  Which I still haven’t got enough of. 🙂

Excerpt from D.B. Johnsons’s website:

The apprentice Mauk is an entirely fictional character who takes his nickname and his inspiration from the work of Dutch artist M. C. Escher (1898-1972). Escher’s skill at playing with perspective and tricking people into seeing his version of three–dimensional space made him world famous.                   

In a work called Ascending and Descending, Escher drew stairs that lead down and around a building’s inner courtyard, yet appear to go back and end where they began. These endless loops going nowhere became his trademark. He was fascinated by stairs and realized that with a few carefully drawn steps he could take a person out of the real world and into his world of the impossible.    

Bookmark Monday: Who’s Theo LeSieg, it’s quite a clever nick!

So sue me for being behind time, but I just found out that Dr. Seuss has a series of books he wrote to be illustrated by others, and for those books, he used the name Theo LeSieg – his real name was Theodor Geisel, LeSieg is his surname, Geisel, spelled backwards.

We’re generally quite selective over the Dr Seuss books we pick. Some just have so many nonsense words, and our kids make up enough nonsense words in a day to rival the good doctor – there’s a limit to how many I can take!

But with our latest find from the library: “Ten Apples Up on Top!”,

I’m thinking that it might be worth checking out the rest of the LeSieg series.

Ten Apples is written with the usual synopsis of zany characters doing silly stuff in high action speed sequences, but it retains the signature rhyming style Seuss(?), Geisel(?), LeSieg(?) is known for.  I like the fact that the text uses simple – and real – words that’s approachable for beginner readers and also can be extended for teaching beginner arithmetic as well.

Click below if you’d like to watch a dramatized reading of the book.

Bookmark Monday: Press Here

In this era where interactive is associated with reliance (sometimes too much) on the iPhone or iPad and apps and all sorts of technological gadgetry, it is incredibly refreshing to find a book (a book!) that successfully achieves a true interactive, experiential engagement with the reader on print, the oldest media on earth.

This week’s Bookmark Monday review, Press Here by Hervè Tullet, was inspired by a friend of ours, who showed DH and DD this book when we visited their home on the weekend.

Absolutely captivating on several levels for the following reasons:-

  • Use as a teaching tool to reinforce basic language and mathematical building blocks – colours, numbers, counting, left, right, relative sizes and pattern recognition.
  • Perfect as a read-aloud with parent and child, or self-read.
  • Thoroughly engaging, and really, your imagination is the limit.

The cover is simply designed with a single yellow dot, inviting the reader to “Press Here”.

And when you do, off you go then, on this magical interactive journey, following the narration from first through to last page, every page a captivating change from the previous, reacting to whatever action you’d done in the prior page. 

Watch the dots multiply and move around the page as you tap, rub and blow on them, or tilt and shake the book. And watch them grow and shrink in reaction to single and multiple claps.

And watch your child’s face – it will be a priceless experience! 😉

Related activity:

Check out this link on Amazon to get a preview via a free printable to make your own Press Here mini-activity book, and some supplementary activity sheets as well.

Math at Play – Make your own number line

Credit for this post really should go to DD, because this was entirely her idea and effort.  I’m just the scribe. 🙂

So then, how to make your own number line or ruler.

(I think it’s brilliant!  I wish I had been that smart at four.  But it’s too late for me now, ha!)

1. Take out your number sticker pack.

2. Paste down the numbers from 1 till…hm, the last number that can fit on the sheet of paper.  Whichever way you arranged your paper to begin with.  So it ended with 18 on hers.

3. Using a pair of scissors, carefully cut out your number line/ruler.

4. Measure everything and everyone in close range.  Like baby bro’s face length. And Daddy’s. And Mummy’s.

5. Patiently entertain Mummy’s randomly made up math problems. Like whose face is longer – Di Di’s or hers…or how many units is Daddy’s face longer than Mummy’s….etc etc.


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: Shaken AND stirred.

On the weekend, we received an invite from a friend to join a school field trip to learn how to make ice cream at Scoop of Art, a gelato café located in the Marine Parade Community Centre.

Ice cream? Ooh, I don’t have to be asked twice. 😀

Have you ever tried making ice cream in a bag? I haven’t.  Hadn’t. But now that I have, I’m so inspired that I’m plotting the shortest distance route to the nearest NTUC supermarket to stock up on Ziploc bags, wahahaha!

Here’s what you’ll need for raw materials to make basic vanilla ice-cream (recipe from Scoop of Art):-

1 cup milk
5 ml vanilla extract
3 tablespoons sugar
Ice cubes
6 tablespoons salt
One sandwich size Ziploc bag, and one large Ziploc bag.

1. Measure out milk in a measuring cup, add sugar and vanilla extract, stir well.

2. Pour the mixture into the small Ziploc bag and seal tightly.

3. Fill the large Ziploc bag half full of ice and add 6 tablespoons of salt.

4. Place the small bag inside the big bag and seal the big bag tightly.

5. Shake for 15 minutes until the mixture solidifies.  (You might need mittens or a tea towel as the bag will be VERY VERY cold!)

6. Open the bags and enjoy your own home made shaken and stirred ice cream.

Home made! At almost zero cost! And only ever fifteen minutes away from it… ICE CREAM!


In the process, there were plenty of opportunities to:-

  1. Practise measuring liquids and dry ingredients with measuring cups and spoons.
  2. Count the number of ice cubes required to reach the halfway mark on the Ziploc.
  3. Identify start and stop points with the hands on a clock for the 15 minutes required to solidify the ice cream.

You can also explore the scientific angle, and discuss freezing and melting points, e.g.

  1. What is the purpose of adding salt to the ice?
  2. In the process of ice cream making, the milk mixture changes from ___ state to ___ state?
  3. How does the action of shaking the bag influence the result of liquid to solid state in the mixture?
  4. What then happens to the ice cream when it is left out in the open? It then changes from ___ state to ___ state?  Why?

I’d love to know if you decide to try it out and what results you got. 🙂

Oh, and if that Mars Bar and Sea Salt flavour looked tempting enough for you to pay a visit to Scoop of Art, you can find them at 278 Marine Parade Road #01-03 Marine Parade Community Club. Tel: 63456563.

And now, for those Ziploc bags. And some cocoa powder for chocolate ice-cream, mmm. Maybe some berries! And…

Bookmark Monday: The Warlord’s Series

Having done the letters of the alphabet in uppercase and lowercase in our Alphabet Wall series, we moved on to piece letters together in our weekly Wordcraft.  Now, as an extension to the recommended reading section in each Wordcraft post, we’re starting a new series called Bookmark Monday. 🙂

Here, we hope to be reviewing books that we have ourselves enjoyed as a family and we hope you’ll also explore the titles, or if you’ve also read the books, let us know what you think of them as well.

To kickstart our series, this is a collection of picture books we found in our local library titled The Warlord’s Series, written by Virginia Walton Pilegard. 

Set against the background of ancient China, each story is written as a mathematical adventure of two children who serve in the household of a Chinese warlord, and is coupled with simple craft instructions at the end of each book on how to create your own math tool that applies the concept and Chinese mathematical invention introduced in the story.  

The series is listed by the California State Department of Education as recommended mathematics reading for second grade. 

Not that that was the reason we picked it off the shelf – really, we were just intrigued by the math element and the fact that it provided an easy introduction to Chinese history and culture for our kids. 

At this stage, we’re just enjoying the book for the latter element, and appreciating time in the evenings reading together as a family.  No complicated preschool geometry going on in our home!  Haven’t actually tried out the crafts, but hmm…maybe we’ll get around to making a Chinese water clock some time. 😉 

Read all about Chuan and Jing Jing’s adventures and the following math concepts in:-

  • The Warlord’s Puzzle – Geometry and Early Chinese Tangrams

  • The Warlord’s Beads – Cardinal Numbers and the Chinese Abacus

  • The Warlord’s Fish – Magnets and Compasses used in 3rd Century B.C. China
  • The Warlord’s Puppeteers – Ratios and Chinese Puppetry
  • The Warlord’s Kites – Measurements and Chinese Kites
  • The Warlord’s Messengers – Velocity and Chinese Land Sailing
  • The Warlord’s Alarm, A Mathematical Adventure – Telling Time and Chinese Clock Inventions 


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!