Families Affair

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Addition/Subtraction: So, why should you spend a lot of time combining and breaking apart numbers with your child? We know that there is a lot of mathematics that is developmental. You would never expect a one year old child to run a race or learn to type because their bodies and brains aren't ready to do those tasks. It's the same with concepts in mathematics. There are certain ideas and procedures that are difficult (if not impossible) for children to understand until they're ready. Remember hearing about the psychologist Piaget's work with conservation of number? He would set out 7 tiles in a row touching each other and 7 tiles in a row but separated from each other. When he asked young children which row had more tiles, they would say that the spread out row had more. As children grow, they learn that the quantity stays the same even when the tiles are spread out. There are all sorts of milestones like this in the mathematical growth of a child. If you try to push your child to do problems that they aren't ready for, all you'll get is frustration!

Here's an example of what happens when children aren't ready for a concept: Ask any first grade teacher which kinds of problems are the hardest for first graders and they'll tell you that it's the 5 + __ = 8 kind of problems. Children who aren't ready for this kind of problem will answer 13. If you insist that they do those kinds of problems (which they don't understand because they aren't ready for them yet), they'll start memorizing the right answer. DANGER DANGER This is the first step to trouble in algebra nine years down the road. Mathematics has to make sense. If math becomes memorization, they'll do fine for a while but at some point the memorization won't work anymore and math will become impossible.

What's a parent or teacher to do? Play games and do activities like the ones in this kit. Work on the 5 + ___ = 8 problem using color tiles, rocks, pennies, or bowling balls. Talk about situations where a problem like this might turn up ("I need 8 lemons and I have 5 in my bag. How many more do I need?" "You have 5 candies and your sister has 8. How many more does she have than you?"). The task for you is to provide experiences for your child to allow them to work on seeing the parts of 8 (and all the other numbers, too!). As your child develops a sense of number, they will also be developing the neural connections that will help them zoom through those developmental milestones.

What about multiplication? As your child builds the multiplication facts, help them take them apart and put them back together. The goal is to understand multiplication so well that, even when you forget the fact, you have another way to find the answer. For example, 6 x 7. Who can remember that answer? Six times six, however, that's easy. If you can remember that 6 x 7 is really (6 x 6) + 6 or even (5 x 7) + 7, you can reconstruct the answer whenever you need it.

Use the tiles to make a very nice multiplication table. If you click here, you'll open a window that has a sheet of 1 inch squares on it. Print two of them and then trim and tape them together so you have a 10 by 10 grid. Fill in the numbers as shown here, leaving the upper left hand corner blank.

Now you and your child are going to use the tiles to create a multiplication table. Choose any problem. For this example, we chose 4 x 5. Build the array (rectangle measuring 4 tiles by 5 tiles) right on the table, starting in the upper left hand corner.

When you count the number of tiles, you'll find that the answer is 20. Write that number in the square that is diagonally down and to the right of the bottom right hand corner of the array.

Here's another example showing the array for 7 x 5. Help your child explore the idea that the same array gives the answer for 5 x 7 by rotating the array 90 degrees. Also help your child find all the patterns that exist in the multiplication table. Finding patterns and using them will make math easier and more fun.