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!

Fractions

This week we did some division with remains. Tammy struggled a bit with this, so we used the number line and piled the threes / fours onto the right spots: 3, 6, 9, 15 etc. She could then easily count how many threes there were in 28 etc. The remains were always expressed as a fraction e.g. 16/3 = 5 and 1/3. In the beginning she confused 1/3 and 2/3 but she soon caught up and "loved" this work.
However, I picked up that her tables were a bit rusty. This surprised me, because she really knew them exceptionally well: not only in sequence, but also when asked at random. Anyway to make "math" a bit easier we are back onto multiplication, but this time "longer" multiplication e.g.
27
x5
135

We converted miles to kilometers. (1 Mile = 1.6 km). She liked this. This was necessary to understand High School Musical 3 better and also to help her prepare for the U.S. trip and in any case it is problem solving and practice in multiplication and decimals.

She is busy writing a letter to Zac Efron. Formulating questions is still very difficult for her, but we are working on it. Spelling and reading ability are improving by the day, but she still needs a lot of guidance with comprehension. (There has been a vast improvement, but she still needs considerable practice before she will really be able to read a book on her own just for fun.).

Other new activities include water aerobics and swimming lessons and guitar lessons. In all of these she shows promise. (I will blog about these activities later.) Right now we are waiting for her guitar instructor. She has just had her 3rd swimming lesson. After lunch break she came up to finish her Zac Efron letter, but since I started blogging during break (and thus occupy the computer), I asked her to start on the multiplication homework work sheet so long. Guess what she said? "I would like to do division by 3...!"

She has done 3 multiplication problems while I've been typing this paragraph, but she forgot to add the tens, so I'd better stop babbling and help her.

Homeschooling is great! Have a great week.

Fractions

This week we went to the gym every day except Friday. Although we still take it slowly, Tamerin is already showing signs of increased fitness. We just have to keep at it. I have not yet spoken to the "bio". She took the abs class on Monday and was going to show me more apparatus after our workout on the floor (cardio), but I must confess: I was just too bushed after the cycling, rowing etc. to go and look for her to do more... Next week we will let her show us around first and then we'll work out!

None of us has lost weight yet: in fact I have gained!! But it does leave us with feeling good about ourselves.

The trips to the gym are spent doing oral math's. Tammy asked to do 1/4 fractions. She gets confused at times, but understands that to get to a 1/4 you have to divide into 2 and then into 2 again. She generally gets it right and even knows that 1/4 of 10 is 2.5: with R10 one can buy four items of R2.50 at our old school's tuck shop.

Sometimes Tamerin has to buy groceries or stationery. She has an excel file marked "Daddy's Money" where she keeps record of expenses, what the balance of the cash box should be and then of course we have to count the money. She thinks it is so cool to drag formulas. Excel is real fun.

Progress in math's

Amy knows most bonds very well and yet she can sometimes get stuck on something simple e.g. 8 + 6. If she does get stuck, I ask her which bond she knows (usually the double e.g. 8+8) and then she has to work backwards or forwards until she gets the answer: i.e. 8+ 8 = 16, 8+7 = 15, so 8+ 6 is.....! She is grasping this method more and more and it is rewarding to see how her insight improves!

We have also started with carrying over - both working out the sum on paper (counting the ones and then the tens) and by doing mental arithmetic. We started with adding 0 + 3, 10 + 3, 20 + 3, 30+3, 40+3 etc. until 100 + 3. Then we would take another set e.g. 3+4, 13+ 4, 23 + 4 etc. I always asked the sums in sequence and never skipped a set! She soon caught on and can now mentally calculate how much is 18+ 7, 58+ 7 etc. I no longer have to ask them in sequence. She understands!! She sometimes forgets to carry over (58 + 7 = 55), but such mistakes get less and less. It is so wonderful to be able to help her discover math's at her own pace. It is so much easier to drill sums verbally, than to only do worksheets. Homeschooling is the best!!

We have also done some fractions: 1/2 and 1/4. I focus on practical fractions e.g. of 100 and 50 and 60 and 30. The reason for this, is for general measuring and also for understanding time better. I have started to teach her to read the time last year, and she is quite good at it, but we until this month, we always read time in full minutes e.g. it is 8:55 (eight fifty five). We have now started to use the terms "past" and "to" e.g. 8:55 is five to nine. (8:15 and 8:45 involve "quarters" and therefore the focus on fractions.) When she asks the time I give her both versions of saying the time. On some days I leave at 13:15, and she now asks if I am leaving at "Thirteen fifteen" instead of "One fifteen". International time still requires some thinking, but she knows what it is all about!

Today we focussed on measuring again. How long is a metre? We measured from her right shoulder to her left fingertips (nearly a meter), the window (99 cm), and her steps (75 cm). We tried to give one metre steps: we put the measuring tape on the floor and stretched our steps. In the process, she lost her balance and we had a good laugh. I think she now has a better idea of what a metre is though. (It all came about because of an E-mail she received about a 17 foot shark that befriended a man. How long is a foot? How many "rulers" (30 cm) are there in a metre etc. )

I find often that opportunities for math's and reading present themselves as life itself happens. Amy is usually very interested - I believe it is because she senses the importance of such skills or knowledge. Weighing herself and measuring her waist are important to her. She is a bit overweight due to the fact that her medication stimulates her appetite too much. Weighing herself has two functions: to be aware that if you drink out 2l of Coke all by yourself, there will be consequences, and to become familiar with measuring concepts.

Homeschooling is fun!