How to Master Multiplication Without Learning the Tables
One Methods:Understand why you need it
Steps
Understand why you need it
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1Multiplication is learned thorough repetition, committing to memory a pair of digits (factors) and its result (product).The factors should range from 2 to 9 but it is customary to add 0, 1, 10 to the times tables; by crossing out these three unnecessary tables and then applying the commutative property of multiplication we can reduce the products to 31 and the pairs of factors to 36 ( see further down the display of factors and products cards) . Kids can learn these cards easily thorough drills and games either in teams and/ or on their own but, how can we start giving them and ourselves such helping hand ? Read on to find out.AdAd
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What you need
- highlighters
- big square paper
- packs of white card files
- paper clips
- Scissors
- Timers that count down in seconds
- A thick red and blue crayon
How to set about it
Let's review some basic notions and trim down the multiplication grid.
- 10 times table
Kids can become familiar with counting by tens easily.They easily realize that multiplying by ten is just adding a zero to the right of the original number; consequently the 'ten times' column and row can be crossed out . Accordingly 40=4x10 is not a valid answer in this project, whereas 40= 5x8 is.
- Product Zero
Any number repeated zero times or multiplied by zero equals zero; consequently product zero is always zero; in good logic we can cross out the column and row of zeros.
- Product One
Any number repeated one time equals the original number.Anything multiplied by 1 is that anything itself. Once our kids understand this, we can we can cross out the one times table: column and row.
The Squares
- A square is the result of multiplying any number by itself; 1x1=1; 1 is the square of 1; 2x2=4; 4 is the square of 2; 9x9=81; 81 is the square of 9.
- Write the list of squares that start by 4 and end at 81.
- Represent the 8 squares we're working with in your big squared sheet of paper. A square that has 4 units,(or 4 little squares ) is the square of...2 ( its sides measure 2 units each)...and similarly the square of 3, 4, 5....up to the square of 9.
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Find the squares within the grid. Get a different highlighter and color them. They're easy to find because they're are next to one another... on the diagonal of the grid.
Commutative Property
- The order of the factors doesn't change the product. 5x4=20; 4x5=20 so 5x4=4x5.
Besides the squares, which are, needless to say, square-shaped, the rest of products of the grid can be represented by rectangles.
- Ask the kids, using big square paper to draw and color some rectangles, for instance 2x3 (three times two) pink//4x3 (three times four) green and 5x6 (six times five) light blue.
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Ask them to write the notations on their rectangles and squares :For example 5x4 or 4x5 etc * Cut them out and compare the shapes obtained them with their classmates.
In a few moments,having it their way, they'll stumble upon the commutative property of multiplication which they can apply to the rest of the 36 products.
- Go back to the diagonal of squares that divides the grid into two halves
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Ask the kids to locate some number ( product ) in one half and the the same number ( product ) in the other half.After a few drills locating identical products, chances are some kid will say that both halves are the same...so... if they're the same, we'll be much better off crossing out the lower half,( for no other reason than to have a neat design) because both halves are identical.
The Final Touches to the Grid
Looking closely at the squares and remaining products in our neat triangle-shaped half, we notice that five products are repeated...because they have 2 pairs of factors each.
- 12=2x6=3x4 //16=2x8=4x4 //18=2x9=3x6 // 24=3x8=4x6 //36=4x9=6x6
- 16 and 36 are squares, and so, located in the diagonal.
Accordingly we cross out one of each pair of the five repeated products,We leave the diagonal of squares intact.
All along the project, the pair of factors are in this order: small x big , just for simplicity sake.
Making the Cards
- Open a packet of files and cut off the top right corner, ( 2cm= 0,8" each side)
of 31 cards.Write in blue crayon each of the products adding to the right some clues (x= one pair of factors; xx= two pairs of factors, a little square meaning a pair of same factors).
On the other side of the cards write the corresponding pair/s of factors
Basic Drilling
- Factors to elicit products
As teamwork or on their own kids are asked to give the product for the factors shown on a card.( Time: 10-15 sec.). Use kitchen timers or online countdown watches ).
If the product & time are correct the kid keeps the card, if not the right answer is called out and the card goes to the bottom of the pack.When all the cards have been dealt with, the kid with the largest number of them is the new dealer
There are plenty of occasions for a kid to work on his factors cards. Of course, no timer necessary and failed cards can be put at a right angle with the pack, to be done again.
- Products to elicit factors
To be carried out in a similar way.The kid helped by the clues on the product side, has to give the corresponding pair/s of factors. A different order of factors is, of course,considered valid: 15= 3x5 ; 15= 5x3 . After a few drills the team/s can work on their own.
Further Info
- Skip counting is a powerful tool to master simple-digit multiplication. Adopt your kids ways if they're used to finishing by tens:4,8,12,16,20,24,28,32,36,40
- Classroom and Internet material can be worked on thru this project's approach.
- For the kids' benefit this project is not intended to contradict the School's ways but to complement them.
- In connection with Home Schooled Children this is a short autonomous alternative to the traditional Times Tables.
- See also How to Master Multiplication Thru Drills and Games
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