Teaching young children math
ruth beechick talks about this in her book 'an easy start in arithmetic"!
The best way to begin teaching a young child math is with manipulative, such as bugs, rocks, pennies, marbles, m & ms, socks, any objects you can count with. It can be taught anytime throughout your day, when your doing laundry, putting socks together, counting them, setting the table, counting the silverware, glasses, plates etc. Remember to make it fun for you and the child!!
Using manipulative like this, the kids can then figure out some very hard problems! Just holding and seeing the objects clicks in their young brains. When most kids are young they don’t think of a math problem as we do 1+3=4 , they need something more hands on so they can touch it and feel it to understand its value, once they learn this way of doing math the other steps wont be as hard. This is the first step of how other types of math will be understood.
After the child gets use to using the manipulative she/he will be able to picture the things in their head, he/she will be able to see them and work out the easier problems. When he/she is ready to move on to the next step, you’ll know because the child will not be using the manipulative as much, she/he will start picturing the problem in her head, finding a faster way to figure math problems out!!! Then it’s on to step 2!!!
From ruth beechick booklet "an early start in arithmetic'
Levels of thinking about (example 3 + 2 = 5) or any other numbers
Manipulative mode-
Real objects, with touching and moving: three plates or spoons, marbles, jacks, rocks, bugs etc, put two more with them. now there are five
Real objects, with only sight: 3 jacks in this group, 2 jacks in another group, there are 5 all together
Transition-
Pictures: picture of 3 jacks in a group and 2 in another group. 5 total
Symbolic pictures: 3 dots in this group and 2 in another group. 5 total
Mental image mode-
Touchable objects: think of 3 jacks and 2 jacks. they make 5 all together. (story problems)
Non-touchable ideas: a team won 3 games and lost 2 games. they played 5 games all together.
Symbolic mode-
Digits only: 3 and 2 are 5
Digits and signs: 3 + 2= 5
Showing posts with label math. Show all posts
Showing posts with label math. Show all posts
Can't Memorize the Times Tables?
Hi!!!! just had to put this here, shes one of my favorite writers and educators!
this is a really good article by ruth beechick and it works!
Problem: Can’t memorize the times tables.
Solution: Don’t blindly memorize; teach meaning instead.
Teaching Tips
April 1, 2009
How To Master the Times Tables
by Ruth Beechick
Here is an easy solution to what has become a major problem among homeschoolers.
Problem: Can’t memorize the times tables.
Solution: Don’t blindly memorize; teach meaning instead.
This article explains how to teach meaning. Meaning stays with children for life; blind memorizing does not last long without constant review. Meaning fascinates and engages the mind; blind memorizing bores the mind.
Begin the meaning route by giving children a good mental picture of our number system. Make a hundred chart for this.* This is a chart of squares, ten by ten. In the top row of squares print the numbers 1 to 10. In the second row print the numbers 11 to 20, and so on to 100 in the bottom row. Children could make this chart as a large poster.
Now, forget for a while that you’re on multiplication. Just work at first to build understanding of the number system. Have your child point on the chart with his finger or a short pointer everything you ask him to do. First show that adding is nothing more than counting forward.
• Point to 4. Add 3 squares. Where do you land?
• Point to 14. Add 3 squares. Where do you land?
• Point to 54. Add 3 squares. Where do you land?
Repeat with similar examples a few times each day. These examples each remain on one row in the chart. Stay at that level until you see that the child sees clearly that adding counts forward in the numbers. Then switch to subtraction, or take-away if your book uses that term. Subtraction is simply counting backward. Remember to have the child always point off squares on the hundred chart. This builds his inner visualization of the number system and that’s what you’re after here, not simply answers. When the above addition and subtraction problems are mastered, pose some problems that move from one row to the next. This is called bridging, bridging from one decade to the next.
• Point to 8. Add 6.
• Point to 18. Add 6.
• Point to 38. Add 6.
Later you can mix up the problems and not stay with one pattern like adding 6. When your child masters moving down the rows, begin counting by fives. Make him point, always point as he counts and says “5, 10, 15, 20, 25” and so on through the chart. Then:
• Count by 2s. (Every count is an even number.)
• Count by 10s.
Counting by fives, twos, and tens is relatively easy compared with other counting jumps. But if your child can do it try counting by fours. That’s twice the jumps of 2. If he does this enough he may catch on that in one row the counts end with 4 and 8, and in the next row the counts end with 2, 6, and 0. Then it’s back to 4 and 8 again. That two-row pattern continues all the way to 100. Your child should be seeing patterns everywhere by now. That’s part of the understanding he’s building. When all the above is extremely easy for your child, try doing multiplication problems, still having him point out everything on the chart. Count by twos as above. Then:
• Show me two 2s. Where do you land? (Points to 2 and 4.)
• Show me three 2s. (Points to 2, 4 and 6.)
• Show me four 2s. (2, 4, 6, 8)
• Continue to ten 2s.
When the child does this well, have him write 2 x 2 = 4 horizontally, or vertically if that’s the way his book does it. Then write 3 x 2 = 6 and the others all the way to 10 x 2. He should refer to the chart when needed. This is not a memory assignment or memory test. He’s learning to visualize the number system any time he refers to the chart. Count by fives to 50. Then:
• Show me two 5s. (5, 10)
• Show me three 5s. (5, 10, 15)
• Continue up to ten 5s.
Try teaching what is called the law of commutation: Show me two fives. Now show me five twos. Oh, the same answer both ways. Write both on your paper.
Another example: show me three fives. Now show me five threes. Oh, it’s 15 both ways. Write both on your paper. Either way you turn the numbers, the answer is 15.
Write the table of fives in a list from 2 x 5 = 10 all the way to 10 x 5. Beside it write a list that commutes the numbers, beginning with 5 x 2 and 5 x 3 all the way to 5 x 10. Do similar double lists with the twos and with the tens.
By this stage a child will know quite a few multiplication facts and he hasn’t spent any time with straight, boring memory. He spent his time thinking and understanding what goes on with the numbers. Now when he gets to larger numbers that he can’t visualize easily, he at least understands what happens when he multiplies them.
Some larger multiplication facts are easy if you relate them to already known facts. For example, teach the table of nines by relating it to the tens. What is 9 x 6? First think that 10 x 6 is 60, so subtract one 6 and get 54. Another example: What is 9 x 4? First think ten fours is 40, so subtract one 4 and get 36. Try a few each day until the nines are easy. Remember to commute when it helps. If a problem is 8 x 9, turn it to 9 x 8 and proceed by relating to 10 x 8.
After the nines are mastered, use the same system with the sixes. Relate each to the fives. For 6 x 4, think 5 x 4 plus another 4. For 6 x 7, think 5 x 7 plus another 7. Adding that 7 requires bridging, so those early steps of addition are necessary now for multiplication. To add 7 to 35, most people probably visualize that 5 takes them up to 40, then 2 more makes 42. If your child has trouble with this, go back to practice bridging on the chart. That’s adding a number that requires moving from one row to the next. Children who catch on easily to the meaning system will figure out more meaning for themselves and you don’t have to teach everything. For children who don’t catch on, go back to the early stages and teach again, moving slowly.
After a child masters the practices described above, he could fill out a sheet (don’t call it a test) that has all the multiplication facts. Don’t push for speed, and tell the child he can skip ones he does not know. By this time there should be only a few he skips, if any. He can learn those few by relating them to nearby facts. Or he can memorize them. It will be a small memory task, nothing like if you had started by saying, “Now you must memorize the times tables,” and you drilled and drilled each day. Children taught only by memory may have no way to figure out a fact they forget. Children taught by meaning can always find an answer some way or other.
It used to be important to achieve high speed in multiplying, but in our calculator age, speed does not matter in life applications. Use your judgment on how much speed to aim for.
For children near the early stages of multiplication, use the suggestions in this article in order and slowly and thoroughly. For children further along in their arithmetic book who bump into multiplication problems, use a part or parts that will iron out those problems. Careful teaching in basic arithmetic carries through life and helps immensely with all higher math.
this is a really good article by ruth beechick and it works!
Problem: Can’t memorize the times tables.
Solution: Don’t blindly memorize; teach meaning instead.
Teaching Tips
April 1, 2009
How To Master the Times Tables
by Ruth Beechick
Here is an easy solution to what has become a major problem among homeschoolers.
Problem: Can’t memorize the times tables.
Solution: Don’t blindly memorize; teach meaning instead.
This article explains how to teach meaning. Meaning stays with children for life; blind memorizing does not last long without constant review. Meaning fascinates and engages the mind; blind memorizing bores the mind.
Begin the meaning route by giving children a good mental picture of our number system. Make a hundred chart for this.* This is a chart of squares, ten by ten. In the top row of squares print the numbers 1 to 10. In the second row print the numbers 11 to 20, and so on to 100 in the bottom row. Children could make this chart as a large poster.
Now, forget for a while that you’re on multiplication. Just work at first to build understanding of the number system. Have your child point on the chart with his finger or a short pointer everything you ask him to do. First show that adding is nothing more than counting forward.
• Point to 4. Add 3 squares. Where do you land?
• Point to 14. Add 3 squares. Where do you land?
• Point to 54. Add 3 squares. Where do you land?
Repeat with similar examples a few times each day. These examples each remain on one row in the chart. Stay at that level until you see that the child sees clearly that adding counts forward in the numbers. Then switch to subtraction, or take-away if your book uses that term. Subtraction is simply counting backward. Remember to have the child always point off squares on the hundred chart. This builds his inner visualization of the number system and that’s what you’re after here, not simply answers. When the above addition and subtraction problems are mastered, pose some problems that move from one row to the next. This is called bridging, bridging from one decade to the next.
• Point to 8. Add 6.
• Point to 18. Add 6.
• Point to 38. Add 6.
Later you can mix up the problems and not stay with one pattern like adding 6. When your child masters moving down the rows, begin counting by fives. Make him point, always point as he counts and says “5, 10, 15, 20, 25” and so on through the chart. Then:
• Count by 2s. (Every count is an even number.)
• Count by 10s.
Counting by fives, twos, and tens is relatively easy compared with other counting jumps. But if your child can do it try counting by fours. That’s twice the jumps of 2. If he does this enough he may catch on that in one row the counts end with 4 and 8, and in the next row the counts end with 2, 6, and 0. Then it’s back to 4 and 8 again. That two-row pattern continues all the way to 100. Your child should be seeing patterns everywhere by now. That’s part of the understanding he’s building. When all the above is extremely easy for your child, try doing multiplication problems, still having him point out everything on the chart. Count by twos as above. Then:
• Show me two 2s. Where do you land? (Points to 2 and 4.)
• Show me three 2s. (Points to 2, 4 and 6.)
• Show me four 2s. (2, 4, 6, 8)
• Continue to ten 2s.
When the child does this well, have him write 2 x 2 = 4 horizontally, or vertically if that’s the way his book does it. Then write 3 x 2 = 6 and the others all the way to 10 x 2. He should refer to the chart when needed. This is not a memory assignment or memory test. He’s learning to visualize the number system any time he refers to the chart. Count by fives to 50. Then:
• Show me two 5s. (5, 10)
• Show me three 5s. (5, 10, 15)
• Continue up to ten 5s.
Try teaching what is called the law of commutation: Show me two fives. Now show me five twos. Oh, the same answer both ways. Write both on your paper.
Another example: show me three fives. Now show me five threes. Oh, it’s 15 both ways. Write both on your paper. Either way you turn the numbers, the answer is 15.
Write the table of fives in a list from 2 x 5 = 10 all the way to 10 x 5. Beside it write a list that commutes the numbers, beginning with 5 x 2 and 5 x 3 all the way to 5 x 10. Do similar double lists with the twos and with the tens.
By this stage a child will know quite a few multiplication facts and he hasn’t spent any time with straight, boring memory. He spent his time thinking and understanding what goes on with the numbers. Now when he gets to larger numbers that he can’t visualize easily, he at least understands what happens when he multiplies them.
Some larger multiplication facts are easy if you relate them to already known facts. For example, teach the table of nines by relating it to the tens. What is 9 x 6? First think that 10 x 6 is 60, so subtract one 6 and get 54. Another example: What is 9 x 4? First think ten fours is 40, so subtract one 4 and get 36. Try a few each day until the nines are easy. Remember to commute when it helps. If a problem is 8 x 9, turn it to 9 x 8 and proceed by relating to 10 x 8.
After the nines are mastered, use the same system with the sixes. Relate each to the fives. For 6 x 4, think 5 x 4 plus another 4. For 6 x 7, think 5 x 7 plus another 7. Adding that 7 requires bridging, so those early steps of addition are necessary now for multiplication. To add 7 to 35, most people probably visualize that 5 takes them up to 40, then 2 more makes 42. If your child has trouble with this, go back to practice bridging on the chart. That’s adding a number that requires moving from one row to the next. Children who catch on easily to the meaning system will figure out more meaning for themselves and you don’t have to teach everything. For children who don’t catch on, go back to the early stages and teach again, moving slowly.
After a child masters the practices described above, he could fill out a sheet (don’t call it a test) that has all the multiplication facts. Don’t push for speed, and tell the child he can skip ones he does not know. By this time there should be only a few he skips, if any. He can learn those few by relating them to nearby facts. Or he can memorize them. It will be a small memory task, nothing like if you had started by saying, “Now you must memorize the times tables,” and you drilled and drilled each day. Children taught only by memory may have no way to figure out a fact they forget. Children taught by meaning can always find an answer some way or other.
It used to be important to achieve high speed in multiplying, but in our calculator age, speed does not matter in life applications. Use your judgment on how much speed to aim for.
For children near the early stages of multiplication, use the suggestions in this article in order and slowly and thoroughly. For children further along in their arithmetic book who bump into multiplication problems, use a part or parts that will iron out those problems. Careful teaching in basic arithmetic carries through life and helps immensely with all higher math.
Learning Math Facts X + --
What I do to help the kids memorize Math facts
is make it into a game,
i write the facts
(1x2, 2x1, you can do this with subtraction or addition also, etc)
on recipe cards
(i only do 0-3 at first and then add more facts as they need, and take out the easiest ones)
and play a game called concentration.
Its where you take turns turning over the cards to find matches, it works so good!
You can start where the child is, like the older kids i start at 3s or 4s since most of them know the other facts.
Be sure to write the facts 4x2 and 2x4 also 1x8 would be a match. I stack them when i write them out instead of side by side but either way works!
You can play this game with all the kids no matter what age really, even younger ones ( just to be include they learn something)
is make it into a game,
i write the facts
(1x2, 2x1, you can do this with subtraction or addition also, etc)
on recipe cards
(i only do 0-3 at first and then add more facts as they need, and take out the easiest ones)
and play a game called concentration.
Its where you take turns turning over the cards to find matches, it works so good!
You can start where the child is, like the older kids i start at 3s or 4s since most of them know the other facts.
Be sure to write the facts 4x2 and 2x4 also 1x8 would be a match. I stack them when i write them out instead of side by side but either way works!
You can play this game with all the kids no matter what age really, even younger ones ( just to be include they learn something)
More ideas to teach our young kids!!
More ideas to teach our young kids!!
These games and crafts are fun to play with the younger kids and will keep them busy while you teach another child. Of course you’ll have to have some one playing with the child and helping him/her. I have one of the older kids do this if I need to help another child. I used these games and crafts on my kids.
Matching ABC game!
Make a matching alphabet game! Make out of recipe cards, print small case letters and upper case letters on the cards. If you can see through the backs of card just color with a crayon. Now mix up the cards and lay them face down 5 across and 5 down or anyway you want, then have child and you take turns turning over and matching uppercases with lower case letters !! Be sure to have the child say the letters! Give a prize at the end of game!
What letter is in the bag game!!
Fill a bag with different things that start with sounds you want to teach your child. Things like ball, book, pin, doll, car, rock, apple etc. now show the child all the items in the bag, put them back in the bag. Next tell the child to find something in the bag that starts with an A in the bag and ask the child what sound(s) the A makes. Let the child reach in and try to find the Apple by touching it only, not by seeing. ( if the child doesn’t know the sounds tell him/her)
Counting around the house!
Find a bunch of stuff you can put in a bag and count! Like buttons, rocks, pins, pencils, spoons, paper clips, erasers, etc. then let child dump bag out on tray or table and count how many objects of each there is. This is good for younger children especially, helps them put a number with objects.
ABC Bingo!
Make your own bingo cards with construction paper. Write the ABC’s on it like in a bingo game. Use upper case and lower case letter also can mix in numbers! Learn two things in one game! Now to play the game call out the letter or number and the child can put a marker on the letter or number you call. When the child calls out bingo you can give the kids a prize! This also works with states and capitals or times tables.
Tissue paper letters
Using a large poster board draw a letter on the board and let the child tear up tissue paper and decorate the letter. Also can use finger paints to paint a letter on the poster board! Nice and messy!
Counting Book!
This is fun, make a counting book together. Buy one of those blank books at the dollar store or make your own with construction paper stapling the pages together or lacing them. On each page have the child trace or print a number. Now have the child draw that many items on the page! Also fun to find items and glue them on the page. These can be make of material also, just use hot glue. Also if you have a large family you can use pictures of the family to use as objects to glue on the pages! Also can do this with the ABCs!
A B C collage!
Buy a large piece of poster board(1$ at dollar store) and look through magazines, pictures, newspapers, etc for letters that begin with a,b,c,d,etc. make it a month long project! By looking for a letter a day and then paste them on the poster board with the letter under it! Hang it on the wall so everyone can see it. Also works with newsprint.
These games and crafts are fun to play with the younger kids and will keep them busy while you teach another child. Of course you’ll have to have some one playing with the child and helping him/her. I have one of the older kids do this if I need to help another child. I used these games and crafts on my kids.
Matching ABC game!
Make a matching alphabet game! Make out of recipe cards, print small case letters and upper case letters on the cards. If you can see through the backs of card just color with a crayon. Now mix up the cards and lay them face down 5 across and 5 down or anyway you want, then have child and you take turns turning over and matching uppercases with lower case letters !! Be sure to have the child say the letters! Give a prize at the end of game!
What letter is in the bag game!!
Fill a bag with different things that start with sounds you want to teach your child. Things like ball, book, pin, doll, car, rock, apple etc. now show the child all the items in the bag, put them back in the bag. Next tell the child to find something in the bag that starts with an A in the bag and ask the child what sound(s) the A makes. Let the child reach in and try to find the Apple by touching it only, not by seeing. ( if the child doesn’t know the sounds tell him/her)
Counting around the house!
Find a bunch of stuff you can put in a bag and count! Like buttons, rocks, pins, pencils, spoons, paper clips, erasers, etc. then let child dump bag out on tray or table and count how many objects of each there is. This is good for younger children especially, helps them put a number with objects.
ABC Bingo!
Make your own bingo cards with construction paper. Write the ABC’s on it like in a bingo game. Use upper case and lower case letter also can mix in numbers! Learn two things in one game! Now to play the game call out the letter or number and the child can put a marker on the letter or number you call. When the child calls out bingo you can give the kids a prize! This also works with states and capitals or times tables.
Tissue paper letters
Using a large poster board draw a letter on the board and let the child tear up tissue paper and decorate the letter. Also can use finger paints to paint a letter on the poster board! Nice and messy!
Counting Book!
This is fun, make a counting book together. Buy one of those blank books at the dollar store or make your own with construction paper stapling the pages together or lacing them. On each page have the child trace or print a number. Now have the child draw that many items on the page! Also fun to find items and glue them on the page. These can be make of material also, just use hot glue. Also if you have a large family you can use pictures of the family to use as objects to glue on the pages! Also can do this with the ABCs!
A B C collage!
Buy a large piece of poster board(1$ at dollar store) and look through magazines, pictures, newspapers, etc for letters that begin with a,b,c,d,etc. make it a month long project! By looking for a letter a day and then paste them on the poster board with the letter under it! Hang it on the wall so everyone can see it. Also works with newsprint.
Teaching young children math
Teaching young children math
Step 1
The best way to begin teaching a young child math is with manipulative, such as bugs, rocks, pennies, marbles, m & ms, socks, any objects you can count with. It can be taught anytime throughout your day, when your doing laundry, putting socks together, counting them, setting the table, counting the silverware, glasses, plates etc.
Remember to make it fun for you and the child!!
Using manipulative like this, the kids can then figure out some very hard problems! Just holding and seeing the objects clicks in their young brains. When most kids are young they don’t think of a math problem as we do 1+3=4 , they need something more hands on so they can touch it and feel it to understand its value, once they learn this way of doing math the other steps wont be as hard.
This is the first step of how other types of math will be understood.After the child gets use to using the manipulative she/he will be able to picture the things in their head, he/she will be able to see them and work out the easier problems.
When he/she is ready to move on to the next step, you’ll know because the child will not be using the manipulative as much, she/he will start picturing the problem in her head, finding a faster way to figure math problems out!!! Then it’s on to step 2!!!
debbie
Step 1
The best way to begin teaching a young child math is with manipulative, such as bugs, rocks, pennies, marbles, m & ms, socks, any objects you can count with. It can be taught anytime throughout your day, when your doing laundry, putting socks together, counting them, setting the table, counting the silverware, glasses, plates etc.
Remember to make it fun for you and the child!!
Using manipulative like this, the kids can then figure out some very hard problems! Just holding and seeing the objects clicks in their young brains. When most kids are young they don’t think of a math problem as we do 1+3=4 , they need something more hands on so they can touch it and feel it to understand its value, once they learn this way of doing math the other steps wont be as hard.
This is the first step of how other types of math will be understood.After the child gets use to using the manipulative she/he will be able to picture the things in their head, he/she will be able to see them and work out the easier problems.
When he/she is ready to move on to the next step, you’ll know because the child will not be using the manipulative as much, she/he will start picturing the problem in her head, finding a faster way to figure math problems out!!! Then it’s on to step 2!!!
debbie
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