When raising Sabi, we often faced a common question: “How does Sabi juggle so many tasks at 7?” Our method? Think about how you organize your days as young adults, and we did something similar for her.

We have mass-printed weekly planners for Sabi. On the left side, we outlined essential tasks—like brushing teeth or practicing math. Beyond that? She got to fill in the rest, mapping out her week.

Each week, she used two sheets. Every Sunday night, she sketched out her ideal week. Then, as each day passed, she noted what she really did on a second sheet. She’d review her notes every morning, setting the tone for her day.

Notice the phrase “prepare for”? The planner has inculcated the habit to not just show up, but to plan ahead and make the most of from showing up.

Imagine a machine which is nothing more than a row of boxes that extends as far to the left. Let’s call it a “two-one machine” both written and read in a funny backwards way.

And what do you do with this machine? You put in dots. Dots always go into the rightmost box.

• Put in one dot, and, well, nothing happens: it stays there as one dot.
• But put in a second dot – always in the rightmost box – and then something exciting happens. Whenever there are two dots in a box they explode and disappear – Bhoom! – to be replaced by one dot, one box to the left.

We see that two dots placed into the machine yields one dot followed by zero dots.

Putting in a third dot – always the rightmost box – gives the picture one dot followed by one dot.

Let’s make a table and do it for all numbers till 10

Here is a visual way to look at it

Now, instead of playing with a 1 <- 2 machine, we could play with a 1 <- 3 machine (again
written and read backwards, a “three-one “machine). Now whenever there are three dots in a
box, they explode away to be replaced with one dot, one box to the left.

You can try this for different types of machine: 1 <- 4, 1 <- 5 and so on…

What are these machines doing?

Can you figure out what these machines are actually doing? Why is the code for two hundred and seventy-three in a 1 <- 10 machine, “273”? Are all the codes for numbers in a 1 <- 10 sure to be identical to how we normally write numbers. If you can answer that question, can you then also make sense of all the codes for a 1 <- 2 machine? What does the code 1101 for the number thirteen mean?

Both the above approaches, teaches the concept of binary (1 <-2) , tertiary (1 <- 3) and decimal (1 <- 10) number systems.

Puzzle: Consider you have squares of different sizes 1cm, 2cm, 3cm, 4cm and 5cm. How many minimum number of squares can be used to cover 7 x 7 matrix?

The most common answer that you will end up easily by trying different combinations of squares is 10. However, there are less than 10 squares that can fit it. Here’s the solution for it:

There are patterns even in daily objects arounds us. A book’s or any grocery product barcode may look like a bunch of random digits, but there is a secret mathematical code hidden in the barcode.

What pattern do you see in the Barcode below?

• There are alternate black and white vertical stripes
• Some stripes are thick and some stripes are thin
• It starts and ends with black color stripe.

Puzzle: Consider a 10cm barcode. How many different patterns can you create using combinations 1 cm or 2 cm (black and white stripe)

You can use paper cut outs of 1 cm and 2 cm and then place them in different combinations to find the patterns.

When Sabi was younger, we encouraged her independence. Simple tasks like choosing outfits or tying shoe laces were hers to tackle. One day, Sabi attempted to comb her hair, which is soft and tends to frizz. A mishap led to a tangled rubber band and we had to snip a bit of her hair. We advised her to wait until she turned 10 to tie her hair again. Yet, her curiosity persisted.

Last October, when her aunt inquired about a gift, Sabi’s initial thought was dolls. This took us aback, since dolls never truly caught her interest. A moment later, she wondered aloud if there were dolls with lifelike hair and accompanying combs. Sabi wanted to comb the doll’s hair to learn how to comb her own hair.

What is the difference between the two leaves?

• Gulmohar has Rounded leaves while Jacaranda has Pointed leaves
• …
• Gulmohar leaves are in pair of two, while Jacaranda leaves are in pairs of two with one single leave at the tip of the stem. Hence, Gulmohar leaves are 2n and Jacaranda leaves are 2n+1.