Getting out of math’s mud

The past month hasn’t been much fun – we mostly did math – stole from other subject periods to finish the previous day’s homework… Tammy really struggled with most of the math we did – especially problems like converting recipes. But she has nevertheless shown much improvement in all areas. Here are a few examples of the types of problems we did:

Time calculations e.g.

• On Saturday Tammy went to bed at 21:30 and she woke at 5:15. How long did she sleep?
• Nick Jonas wants to phone Tammy on her birthday at 19:00. What day and time will it be in California then?” “Lana wants to phone Tammy at 21:00 on her birthday. What day and time will it be in Australia then?
• The April holiday starts on 16 April and ends on 3 May. How many weeks/ days is that? (She calculates this without a calendar and then checks on the calendar to see whether she is right. These sums involved much subtraction, adding and division by 7.)
• Why time calculations? Because it is important in every day life as well as tourism and geography – two of her subjects. Whereas other people just pick up these skills, Tammy has to practice a method for everything.

Adding or subtraction e.g.

• Tammy invited 25 guests to her birthday party. 4 said they could not come. How many guests can she expect?
• Tammy received 14 gifts. She has already opened 6 gifts. How many more gifts must she open?
• Why? She still struggled with such basic problems, although we did a lot of them last year. I am convinced though that if we keep on practicing these, the ability to apply mathematical solutions to a variety of problems will emerge.

If one then multiply, if many then divide problems:

• The following recipe is enough for 6 people. How must Tammy change the recipe so that it is enough for 25 people? (Divide ingredients by 6 and multiply with the number of guests. Round the answer – you cannot use 3.75 chicken or measure 7.33 ml salt or 990 ml sauce.)
• Shaen will take 5 photos of each guest. How many photos will he take when there are 20 / 25 / 30 guests?
• If one plate costs R25, how much will the dinner for 30 people cost – i.e. how much will 30 plates cost?
• For the problems we whisked out the abacus and number line again. We drew pictures and real objects. And we practice and practice and practice. The conversion of recipes is part of lesson 1 of Grade 10 mathematical literacy, and both of us are determined to crack it – not only for the lesson, but forever!

Multiplication and division

• How to multiply with 25: Since 25 = 1/4 of 100, divide by 4 and multiply with 100. These problems also took several exercise sheets, before she could do it. Once she got the hang of it, it was fairly easy, but then she would apply the same “recipe” when multiplying 10 x 25! Of course you can divide 10 by 4 and multiply the answer with 100, but it is so much quicker to just add a zero!
• Besides the 1-12 tables, to also be able to count in 15’s and 25’s. To know the answers to 60/4, 4 x 15, 3 x 15, 45/ 3, 75/ 3, 3 x 25 100/ 4, 1000/ 4 etc. etc. This is much more fun and she loves it, if she “gets” me, i.e. if she can give the answer very fast!
• Percentages: this is nothing new, but it requires continuous practice. Also to understand what it meant when you run at 50%, 80% and 100%! (Water aerobics)

There is still a massive elephant to be eaten and for Tamerin the bites can never be too small. I am just grateful for the few mouthfuls that she has been able to digest. Let’s pray that these skills will stick forever!

Long division has started!

While we worked out fractions, I realised Tamerin's ability to divide is not so good: She doesn't know what is 20 divided by 5, but when given a prompt i.e. what times 5 gives you 20, she answers without hesitation! She knew her tables well, but division practice was sorely needed!

This week we spent a lot of time on long division, using 6 every time as the divider. Tammy likes to follow a given method and she managed the long division quite well: we marked the number line with the six times table to help her count the sixes, but after a day, it was no longer needed. I realised that her knowledge of tables would kick in again, but it took some frustrating time before it happened.

What I found frustrating (and where I had to remind myself that she is "slow" and I need to be very patient) is when she had to deduct e.g. 20 - 18: For most of the week, she would do the deduction the "long method": She would say 0-8; no it can't, so I take a ten and cross out the 2 and make it a 1. 10 take away 8 is 2. 1 take away 1 is zero....! She couldn't just "see" that 20 - 18 is 2 or that 30 - 28 is 2.

But - praise the Lord - by today she started to take short cuts: 20 minus 18 is 2! Long division is the only division she can do: even 606 divided by 6 is done the long division way, but I figure, it doesn't matter, the short cuts will come with time.

We never have remainders - remainders are calculated as decimal fractions until the 2 decimal. It was good to see that 39 / 6 = 6.5. She knows very well that .5 is 1/2 and could see that the remainder of 3 is half a six.

Reading and other exercises are a bit on hold, until we really crack long division. She has made giant leaps through taking many, many, many baby steps! Tammy has had a very bad cold, so we did not go to gym this week - that's too bad, but on the other hand, it left us with more time to do math.

Today we spent most of the morning, making a computer scrapbook page for mother's day. She has a nifty programme called "Scrapbook factory", but I am not very familiar with it, so we struggled a bit, but in the end the page came out quite successfully. Next year, I'll make sure she takes more pictures of her mom. There were actually very few pics of mom on the computer. (Guess who takes most of the holiday photos?!) Tammy has a camera, but today the batteries were flat.

Our vision is that she will work in an office one day. My dilemma is now: is it better to practice to do this type of thing on computer, or should she get more practice using a ruler, scissors and glue? Which type of activity will be more beneficial in the long run? I am not too sure about this one. Either is fun: she loves working on the computer and the end result is neat. But cutting, pasting and painting are fun too!

Have a Happy Mother's Day!