Problem Solving

The best way for the Porritt Maths Blasters to practise the strategies of doubling/halving, place value partitioning, rounding/compensating, reversibility and using basic facts is to solve word problems.

Word problems help us by placing the problem in an understandable way that makes sense - more real than just an equation (number sentence).
We can imagine the situation (context) easily and logically apply strategies to help solve the problem.

The most important thing we need to remember is that if you can't solve the problem with one strategy try another and another until you do - perseverance - something Albert Einstein knew something about:

A Great problem solving web site is: http://resources.woodlands-junior.kent.sch.uk/maths/wordproblems/index.html

Finding the Easy Way!

As mathematicians - YES we all are, we are always looking for patterns and easy ways to solve problems.  The Porritt Maths Blasters know that mathematicians like tidy numbers eg: 10, 20, 50, 100 etc.. and we are just a little bit lazy because we like solve problems quickly and easily.   This all comes down to strategy and number knowledge.

Today we were working on a multiplication problem:
If we have four boxes of chocolate and each box has 24 bars of chocolate inside, how many bars do we have altogether?

1. What is the maths? 4 x 24 (we say 4 groups of  instead of 4 times because it makes more sense to us and we can image (picture) in our heads what that looks like)
2. The next step most of us took was to simplify our problem by breaking 24 into 20 and 4 and multiplying each by 4 so 4 x 20 = 40 (we used 4 x 2 and then multiplied by 10)  and  4 x 4 = 16 (some of us knew the multiplication fact and some used doubling ie: 4 + 4 doubled)
3. Then we added together the answers to 4 x 20 = 80 and 4 x 4 = 16 to get the total 96.  The fancy name for this process is called place value partitioning.
4. Then we put the maths back into the problem and completed the problem by saying: There are 96 bars of chocolate altogether.

Then one clever cookie maths blaster said:

• "Hey 24 is only one less than 25 and I know that 25 is a quarter of 100 so if I have 4 groups of 25 and that makes 100 then 4 groups of 24 must be 4 less than 100 which is 96!"

I got my clever cookie maths blaster to draw a diagram on the white board and it looked something like this:

We were all amazed at how easily and simply she solved the problem by using her knowledge of what makes up 100 as well as rounding and compensating. 

Maths Investigation: How Our Families Use Maths Everyday.

This week we had to find out how the adults at home use maths in their everyday lives.  This was to show us that maths isn't just a subject at school but a part of our everyday lives.

Sylvia's Dad dyes carpet and he has to be very careful about measuring how much dye to use and calculating whether to add more dye or less depending on the shade of colour you want.
Sylvia also discovered her parents use maths to work out:  if they have enough money in their bank before they buy something (subtraction),  how much money to hand over to buy something and how much change you should get back (addition and subtraction),

Kellie's parents use maths when baking, using a tape measure and the distance and time it takes to get somewhere (measuring) and also when shopping (adding and subtracting, multiplying and dividing).

Lashana's, Courtney's and Kassia's Mums use maths when baking, cooking,  using the oven/microwave, filling the jug, making dinner, telling time (measuring), on the computer and money (adding, subtracting, multiplying and dividing) . 

Kassia's Dad is a truck driver and Kassia discovered his whole job is about maths! He measures freight to see how much it will cost to transport it as well as how much it will weigh the truck down. He works out how much petrol he needs to get from one place to another so he doesn't run out. (measuring)  He uses addition, subtraction, multiplication and division for paying wages to his staff, paying bills and using the computer.  He also has to work out the right amount of road users charges so he can drive on the road without getting tickets from the police.

Cameron's Dad uses geometry to calculate the radius from a known diametre of product, addition to work out the difference between a full roll and what's left of a roll of product, division to see how much product can be made out of a roll, multiplication to work out how much product you need to cover hours in a day and days in a week.  He also uses lots of measurement.

Isn't it amazing how our everyday lives are full of maths.  A very special thanks to the fantastic parents who took the time to talk about maths in their world.

Games Are Great For Basic Facts

Maths Games are an awesome way to learn our basic facts.  Today we had a go at the games listed on our blog.  These are some of our favourites. 

Justus and Courtney especially liked Ghost Blasters to practice number bonds. 
Sylvia, Kassia and Lashana especially liked Swimming Otters because they could compete against each other using multiplication. 
Capri and Cameron especially liked Tutpup because is was a fun way to practice multiplication and adding. 
Kayla liked Memory on because you got good at remembering where the shapes were pretty quickly. 

We had lots of fun and felt pretty good when we improved our score and awesome when we won a game.

The Nifty Nine Times Table

Today we explored how amazing the 9x tables are.
We discovered how to use our fingers to do our 9x tables:

Put your hands in front of you and spread out your fingers.
For 9 x 3 bend your third finger down. (9 x 4 would be the fourth finger etc...)
The fingers to the left of the folded finger are the tens ie: 2 fingers are 2 tens = 20
The fingers to the right of the folded finger are the ones ie: 7 fingers are 7 ones = 7
So the answer is 27.

The 9 x Table
1 × 9 =  9

2 x 9 = 18

3 x 9 = 27

4 x 9 = 36

5 x 9 = 45

6 x 9 = 54

7 x 9 = 63

8 x 9 = 72

9 x 9 = 81

10x 9 =90

 

Look at the answers on the right-hand side of the table above. Notice how the tens go up

but the ones go down.

All the digits in the 9 × table add up to 9.

18 = 1 + 8 = 9

27 = 2 + 7 = 9

36 = 3 + 6 = 9

Look at the pattern to the right: the ones column goes down one at a time and the tens column goes up.  You can see how the 9 x table reverses itself!

(1 × 9) 09 ~ 90 (10 × 9)

(2 × 9) 18 ~ 81 (9 × 9)

(3 × 9) 27 ~ 72 (8 × 9)

(4 × 9) 36 ~ 63 (7 × 9)

(5 × 9) 45 ~ 54 (6 × 9)

(6 × 9) 54 ~ 45 (5 × 9)

(7 × 9) 63 ~ 36 (4 × 9)

(8 × 9) 72 ~ 27 (3 × 9)

(9 × 9) 81 ~ 18 (2 × 9)

(10 × 9) 90 ~ 09 (1 × 9)

You can see the pattern the

9 x table makes on the 100's board 

We were amazed at how easy the 9 x are to learn once we discovered the patterns the numbers make.

Number Bonds

Number Bonds are number partners that add up to 10.  They are tidy numbers.  We used hand shapes to show number bonds because we have 10 fingers.  We can also show number bonds on the abacus. (Justus, Sylvia, Brayden and Kirsty)

Card Games are Great for Maths

A pack of cards can be very useful for learning maths knowledge and strategies.  Here is a picture of us playing Number Bond Fish.  Number bonds are pairs of numbers that make 10 eg: 5+5, 3+7, 2+8 ...
We have to try and get pairs of cards that add up to 10.

There are lots of ideas for games on the internet.  Just Google maths card games for kids.  Any good ones we find we will put a link on our blog.  If you find any good ones please let us know.