Heuristics For Math

With final exams looming next week, I try to be calm and composed when encouraging Big Bee to revise her work. I am a firm believer in constant revision, and not last-minute cramming, so as not to stress the child (although I was the direct opposite when I was a student as I operate much better under adrenaline rushes, haha!). I also believe in regular revision so my child will not be put off by this entire concept and philosophy of examinations. 

Besides, with longer days at work due to a new but exciting portfolio, Big Bee and I typically have less than an hour of revision each night, as I also set aside time for fun bonding, which is a lot more important than aggressive mugging for examinations. I want my kids to associate me with loving fun and not as a kiasu mum worried about exams results!

Hence, I am thankful that Big Bee is rather self-motivated (can be improved further, though!). I give her homework to do before I leave home for work, and she usually completes them when I am back in the evenings. I am also highly grateful that my Mum is around in the day to keep an eye on Big Bee, although the latter usually takes advantage of her nice granny whenever I am not around, thus resulting in a frustrated granny! She is a lot more disciplined and well-behaved with me around though! 

I am also heartened that Hubby is entertaining Little Bee to the max as I focus on revising with Big Bee these couple of weeks. Teamwork is indeed a fundamental key in a successful marriage. 

I am digressing actually. I meant to write about a couple of interesting Math sums in an exercise that I am currently marking after Big Bee had completed it. These Math sums are quintessential demonstrations of the heuristics and modelling methodology that most parents complained about (many very much prefer algebra that we had been used to). 

On the contrary, I had begun to truly appreciate the beauty of heuristics when explaining such sums to Big Bee - as they are a lot more logical and visual, hence, much easier to understand, compared to the remote concept of algebra (although they will be acquainted with good old algebra very soon!).

Kids take to heuristics and modelling very well. It is also not rocket science for parents, and I learned the methods myself, just by browsing through her textbooks. However, this evening, as I was working through a problem sum with Big Bee, she came up with the solution much faster than me, much to my amusement! I used to be embarrassed if I could not solve a problem in front of my child, but these days, I will graciously tell the Bees that I am learning from them too. Parenting is all about learning from our children as well, and our children will definitely love it if they know they can help us. 

Anyway, here are the problems: 

1. Carena and Megan save some money every day. Each day, Carena saves the same amount of money, and each day Megan saves $1 more than Carena. After several days, Carena saved $18 and Megan has saved $27. How much does Megan save in 1 day? 

2. Alice, Susan and Jane have 270 buttons. Alice has twice as many buttons as Susan. Jane has 3 times as many buttons as Alice. How many more buttons does Jane have than Susan? 

(I know it is just sooo tempting to use algebra on this - I did use it at first! - but bear in mind the kids don't know algebra!)

3. Ali has 3 times as many marbles as Bala. After Ali lost 4 marbles and gave Bala some marbles, the two boys now have the same number of marbles. Bala has 22 marbles now. How many marbles does Bala have at first?