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!

Money Matters

Part of preparation to go to the U.S. is practising to convert $ to Rand. This involves checking the exchange rate every morning and while Tammy is going to do that for the next couple of weeks, I let her enter the data on Excel and insert a chart: since starting that at the beginning of the week, the Rand has steadily strengthened against the $ and it shows on her chart. This morning Tammy proudly announced today that the Rand has strengthened!

She then converts $1 - $10 dollars as well as $100 and $1000. In the beginning she has made lots of mistakes, but she has done 2 sheets without a single mistake.
Example:
R 8. 35
x 8 (How does one underline this on a blogpost?!)
66 . 80

Today she made 2 mistakes - both with adding e.g with the above calculation when she had to add 4 + 2 she wrote 7!! Tammy, Tammy....!

She loves these calculations and I love them too as they involve multiplication, adding and the use of the decimal point. She also has to estimate the answer before calculating it i.e. 8 x 8 = 64 and 8 x 9 = 72 so the answer must be between 64 and 72, but today it will be closer to 64 because 35c is closer to R8 than R9. Since estimating the answer, she has made far fewer mistakes! This is also what she will use if she has to convert $ to R without a calculator or pencil and paper.

The other money matters that we practice is rounding prices. I have started with it last year, but only now feels that she understands. So we go through newspaper ads and she reads me the real price and then what it "actually" costs. R69.99 = R70.00. Great fun.

We also count money. We have been doing it for a long time, but it is not easy and Tammy has to really focus on not confusing R and c.

This week I also let Tammy "pay" for stuff.
She first counts her money to establish how much she can pay.
Then she has to round the price e.g R35.99 = R36.
Then she gives me enough cash to cover the price, but not too much (e.g. 2 x twenty Rand notes, seeing that she has no R10 note or coins to make up R6).
Then she has to calculate how much change she would get. (R40 - R35 = R5 .... + the 1c, but seeing that we no longer use 1c coins, the shop would round it and give her 5c.)

She has also calculated discounts e.g. 50%, 25% and 10% discounts. Percentages are not new to her, seeing that she always has to calculate the percentage of her homework or test results and we used percentages a lot when we covered the elections.

She still needs lots of practice, but she understands what it is all about and is very determined to crack it. This is very practical, fun numeracy and works for us.

First days of 2nd Term: Elections!

Besides our school vacation, we have had many public holidays in April: 22 April was Election Day, 27 April was Freedom Day (to commemorate our first truly democratic Election 15 years ago) and Friday 1 May is Workers Day. Last week we had two days of school and then I took off the rest of the week to go to the sea with my children (after we first voted of course!). So this is our "2nd week" of school, but actually today has only been our 3rd day of school this term. We could get used to have so many days off!

Last week Tammy and I spent a lot of time calculating how many people would vote if the voter percentage was 80%, 70%, 60% etc. based on the actual number of registered voters. (23,180,000). The ruling party i.e. the A.N.C. had a 2/3 majority after the last elections and that meant that they could change the constitution by themselves. To ensure true democracy, it was hoped that they would not get a 2/3 majority again. We have a very high crime rate and service delivery throughout the country is deteriorating and in many places virtually non-existent. In these aspects, the country is a mess and change is desperately needed if we are not to share the lot of Zimbabwe.

Anyway, it was good talking to Tamerin about the importance of voting and how the parliamentary seats would be allocated. Today, we studied the real results ("results" and "statistics" were today's new words) and then Tamerin "practised" speaking about the results.

She again did a lot of % calculations - from very simple ones e.g. 10% of 100 and 10% of 200 to 65.9% of 17,680.729 i.e. the election results. The complicated ones she did with a calculator of course! She also calculated percentage the other way around e.g. 40/ 50 x 100 =80% . Here too she worked from very simple calculations to real election results i.e. 11,650,748 out of 17,680.729 (the A.N.C.'s results) and 2,945,829 out of 17,680.729 (the D.A.'s i.e. the main opposition's results) It was good to see that her calculations were the same as the official statistics!

So what did she learn in this theme?

• What elections are about and a basic understanding of how our government is put together.
• The importance of voting: the higher the voter percentage, the more votes are needed to get a seat in parliament.
• What an I.D. document is.
• The voting process
  
• To read figures that run into hundred thousands or millions. A million has six zero's!
  
• To calculate % and to have a basic understanding of percentages e.g. 50% is half.
• These % calculations helped to reinforce basic arithmetic: multiply and divide.
  

Tammy has been familiar with the term "percent" for a long time, as she daily records the weather forecast and it often includes 30% or 60% chance of rain. Since January, I let her calculate her homework results i.e. calculate how many sums she did, subtract the mistakes, and work out the percentage that she achieved. Working with percentages is not difficult, but an important life skill and I am thrilled with how well she copes with them. We can now go on to work out discounts and interest rates.

Thank you God for Tammy's good progress!

P.S. Tammy wrote (with help) on her blog about the election results. This helped her to verbalize her election information as she would explain it to her Ouma.