3rd Grade - Multiply And Divide With 1 And 0

 
     
 
     
 
Newsletters:
 
     
 
 
3rd
Multiplication and Division
Multiply and Divide with 1 and 0
Understand the special properties of 0 and 1 in multiplication and division
Number Sense: Multiplication and division with 1 and 0 The ability to multiply by 0 and understand that the product is always 0. If a number is divided into 0, the answer is also 0. The ability to multiply by 1 and understand that the product will always be the other number multiplied. A number divided by 1 is always that number, as well.
 
 

Building Blocks/Prerequisites

 

Sample Problems

(1)

Any number multiplied by 0 or divided into zero is zero.

(2)

Any number multiplied by one is equal to that number. This is called the Multiplicative Identity Property.

(3)

Commutative Property: when two numbers are multiplied together the answer (product) is the same regardless of the order of the numbers.

(4)

Associative Property: the grouping of three numbers does not matter when multiplying. The answer will be the same regardless of what order the numbers appear.

(5)

A number times 1 will give you a larger answer than that number times 0. (Except when multiplying by 0; 0 x 0 = 0)

Learning Tips

(1)

Use multiplication flash cards with the problem on the front and the answer on the back.

(2)

Use manipulatives to show that one of that number is still that number. For example, a group of 7 gems is still a group of 7 gems because it is only one group of seven.

(3)

Children can listen to another story about Gnome Multiply and his adventures of 0 and 1. Gnome Multiply collected gems in the forest, as usual and instead of dropping the gems into his magic belt slots of 2, 3, 4, etc., he dropped the gems into the space in his belt before the number slots began. This space was 0 and unfortunately the gems fell right through the hole and back onto the forest ground. By the time Gnome Multiply got back to the Treasure House, there were no gems left. He had 0. Similarly, he dropped the gems into the next slot over, #1. This was a shallow pocket and there was only enough room for the few gems that Gnome Multiply would drop inside. Whatever he dropped in, that’s what he got out.

(4)

The child can write out the 0 times tables and the 1s times tables, while the parent draws attention to the emerging patterns (0 for all the answers in one column and a consecutive increase by one in the other column).

(5)

Allow your child to see how 0 and 1 can be the child’s very good “friends” when there are math problems to be done—because they save time! Children enjoy seeing little time-saving devices and there are several that concern 0 and 1. To start, help your child count out several stacks of pennies, buttons, or other small objects into sets of 10. Pull one set of 10 in front of you (you can call this work area “the learning pad” and encourage your child to write 10 (for the number in the stack) X 1 (the number of stacks). Count how many objects there are (10) and complete the equation: 10 x 1 = 10. Now, pull one more stack of 10 to the Learning Pad and write the new equation: 10 x 2=20 right below the first. Do this two more times so that the equations are stacked one below the other, and ask your child if he/she sees a pattern. The pattern will probably be obvious: When multiplying by 10, the answer is the number you are multiplying by in the 10s column, with a 0 in the ones column. Ask your child to predict if this will work for a really big number—maybe 542 x 10. What would you imagine that the answer is? Help your child use a calculator to see that the answer is indeed 5420; the number to be multiplied by 10, with a 0 at the end. What you are really doing, you can point out, using your Place Value Pad, is moving each of the numbers (the 5, the 4 and the 2 over to the number column place to the left, and placing a 0 in the ones spot, and your child has just proved to himself that this time-saver works, and why.


Similarly, you can start at the beginning again, substituting “1” for the 0 so that the rule your child creates is that any number multiplied by 1 is still the same number.


To test your child’s understanding, ask if the “rules” that you created in the two learning tips above work if you want to subtract 1. (It does not work, but if you want to subtract 0, you still have the number you started with.) If you want to divide by one? (A set of objects divided into one set of objects still have that same number of objects in it.) Can you divide a group of objects by 0? No, this is a problem with no solution possible because we do not have any way to divide up a group of objects by nothing. The smallest whole number group we can divide by is a group of 1, and that simply tells us that we have the same set we started with. It was in one group to begin with, and it is still in that one group.

Extra Help Problems

(1)

2 x 0 = (0)

(2)

1 x 5 = (5)

(3)

0 x 9 = (0)

(4)

9 x 1 = (9)

(5)

3 x ____=3

(6)

_____x 8=0

(7)

6,754 x ? = 6,754 (1)

(8)

10,000 x 0 = ? (0)

(9)

0 = 256 x ? (0)

(10)

0 ÷ 14 = ? (0)

(11)

? ÷ 256 = 0 (0)

(12)

89 ÷ 1 = ? (89)

(13)

9,900 ÷ 1 = (9,900)

(14)

? ÷ 1 = 501

(15)

0 x 0 = ? (0)

(16)

5,098 x 1 = ? (5,098)

(17)

1 x 897 = ? (897)

(18)

1 x 0 = ? (0)

(19)

77 x ? = 77 (1)

(20)

77 x ? = 0 (0)

(21)

100 x 0 = ? (0)

(22)

1 x 100 = ? (100)

(23)

300 ÷ 1 = ? (300)

(24)

9 x 0 x 9 = ? (0)

(25)

0 x 88 x 200 = ? (0)

 

Related Games

 
 

Copyright ©2009 Big Purple Hippos, LLC