- Times Tables: encourage playing around with times tables in order to more easily memorize them. 9 times tables: finger method.
- Confidence is a central issue in mathematics. So is perseverance.
- Loop Card Games: card numbered 1- number of card players (children). 'I have 8, Double me' I have 16, subtract 4…..loop back to something that ends up being 8. Easy to make, easy to execute, easily adaptable (doesn't have to just be +-x/). Good for use of mathematical vocabulary.
- Resources: coffee sticks (plentiful + easy to pinch). Spray one side orange. Pick up sticks and count those that fell orange side-up and plain side up.
- Maths is something you must do. Less specialists in primary maths teaching therefore more sympathetic, good teaching so better quality of maths teaching than in secondary.
- Chinese Number Puzzle.
- Gelman's Counting Principles:
Stable Order
1-1 relationship
Cardinal Principle
Abstraction
Order is irrelevant (counting sets in different orders)
One-to-one relationship between words and objects. Must learn the names of the words and their order first. That the last number they use (ordinal value) also gives the cardinal value of the group (i.e. how many of them there are). That as long as they apply the 1-1 relationship, they can count in any direction they want to (breaking the linear pattern of numbers). In order to count and out it all together, children must know a lot of things. Lots to be confused by (our system is not so logical, especially between 10 and 20).
Also must learn our place value system.
- Be careful with mathematical language. Make them talk in subject.
- Decomposition in a subtraction sum :
(53 - 17). Cash in (borrow) 10 from the tens column for the units column.
- Equal Addition is another (older) method. One fro mnought, you can't. Ten to the top. Pay back in the tens column at the bottom. Carry on.
- Kyle's Method: Take the difference of the units then the difference from the tens and then the difference from the difference. (Effectively dealing with negatives).
53
-17
4
40
----
36
- Complementing numbers to 9:
7,532,617 - 4,123,546
Magic number is making 9 out of the smaller number
e.g. 6 needs 3 to make 9 - - - - - - 3
4 needs 5 to make 9 - - - - - 5 3
5 needs 4 to make 9 - - - - 4 5 3
etc.
Eventually you get 5,876,453.
Add 7,532,617 to the magic number = 13,409,070. you have to carry the 1 all the way to the end = 3,409,071.
- The Number Line:
53 - 17:
17 - 20 - . - . - 50 - 53
+3 +10+10+10 +3 = 36
- Return to things you know, but that you don't know how you know it. Figure it out. If you don't know why you're doing it, why should you remember it?
- Circles
Circumference is just another word for Perimeter in Circles.
Measuring circumference of circles with a bendy ruler (or a piece of string): you will find that the circumference is always about 3 and a bit (i.e. 3.14 = Pi). So the formula of Pi x r(adius) is correct [3 and a bit / Pi x radius).
- Number Card Games (Number Cards Cat @ Pictorial Charts Educational Trust w13 0ud)
Set of number cards 0 -9. Sheet of paper with hundreds, tens, units. Each player draws 3 cards and the player with the largest number wins. element of chance (gambling by putting a 7 in the tens column if you draw that first).
Extend the game by using just one pack to change game dynamics.
Or, calculate the difference and use that as a measuring stick for who wins/loses.
Or, nasty variation: you make your partner's number.
- Grid System for Multiplication
42 x 27
The Elegant Solution/System:
42
x27
-----
Why do we add a 0 on the second line? Because you're multiplying by 20, not 2.
When multiplying by 10s and 100s, the decimal point never moves to the right. It is the numbers that move to the left. (This is Place Value)
The Grid System plays proper respect to place value
X 40 2
20 800 40 840
7 280 14 294
--------
1134
Multiplication is just repeated addition. Hence, 6 pencils at 12p is calculated as 12 + 12 + 12…= This method is fine until you come across a problem like 6 pencils at 9p: 9 + 9 + 9 doesn't simplify the problem at all. 9 x 6 is the best way of looking at it.
-Chunking in Long Division
4276 / 13 = ?
4276
1300 13 x 100
2976
1300 13 x 100
1676
1300 13 x 100
376
260 13 x 20
116
65 13 x 5
51
26 13 x 2
25
13 13 x 1
12
= [13 x ] 328 (reminder 12)
Lots of work but allows the child to make the decisions, in control. There is a rough system they can work with. There is no precise method: there is no right way. There are shortcuts and techniques (multiplying by 10 or 100, halving etc). They use other number facts that are totally idiosyncratic to them depending on age, ability + confidence. Maths is precise but the working out doesn't have to be.
Problem (strength?) is that there are a lot of operations going on.
Danger with Yr 6 is that they have been brought up with one way and then they are given a new system or method that is alien and throws them.
- Addition Techniques
Grouping to 10 when adding 4, 5, and 6:
(4 + 6) + 5 = 10
Doubling when adding 3, 6, 9:
3 + 6 is 9, doubled is 18.
Sequences: Take the middle number and multiply by the number of numbers in the sequence (as long as the gap stays consistent).
e.g. 1, 2, 3, 4, 5. Sum of these is 3 x 5 = 15
e.g. 1, 2, 3, 4, ,5, 6. Sum of these is 3.5 x 6 = 21. (Where there is a sequence that ends in an even number, it will always be multiplied by a .5 number.
-Number Grid
Have the grid set up with any kinds of numbers: sequence of 1-9 in different patterns, the 4 times tables etc.
Allow the kids to see the grid for a split second then quiz them on different things:
Position Numbers - e.g. What's the middle number?
Addition - e.g. Multiply the first number in the middle row by the last number in the middle row.
Swap top left and bottom right and add the new bottom row.
- Algebra
Multiplication tables are anchor for sequences + algebra.
Patterns and sequences (in number) are what make algebra work. It is sequences that we are interested in, not patterns.
Making a sequence under cardboard boxes using everyday objects.
Medallions with numbers on for each person: organized into 2,4,6,8 etc… and 1,3,5,7. Therefore to calculate the number of the 30th person, 2 x position = 2 x 30. For the odds sequence, it is (2 x position) - 1.
5 8 11 14 17
3 6 9 12 15
therefore formula can be 3n + 2.
This is an arithmetic sequence (going up in consistent quantities).
Area: measure of surface (area that something takes up). Kids can begin to understand the concept of area by dressing up in parent's clothing (too big), covering tables with newspaper, examining how many beans it takes to cover one leaf or another. Becomes increasingly sophisticated until you are counting squares in a rectangle.
Careful when you call one side of a rectangle a 'width' and another a 'length' (what happens when they come up against a square?).
- Instrumental and Relational Learning (Skemp- see handout)
Learning to drive and manipulating the gear stick and pressing the pedal too is instrumental learning. This kind of learning in schools in dodgy.
Relational learning is making connections i.e. You can easily tell if someone has learned something if they can translate that to another situation.
Using sequences in everyday school life
Taking register in numerical not alphabetical order. Organising groups according to these numbers.
Tasks
Read Skemp
Do Maths Audit
No comments:
Post a Comment