I have a work in my classroom that deals with the properties. I have each of the different properties printed up on avery self stick labels and small cardstock. I then have 4-5 problems for each type of property on those same labels and a background of cardstock. It's all laminated. It becomes a matching work where they have the properties and then all the problems underneath. I find it's easier to see the distributive when you see it with all the properties. I can take a picture of it tomorrow so I'll be easier to see.
I am not sure that teaching distributive property to 3rd graders is appropriate. If I were using it to help them with their multiplication facts I would probably use it as a way to anchor a number to "add on to" to find the desired product.
For example if the fact I wanted them to understand was 8 x 6, I might start with 6 is the same as 5 + 1. Since I know that 8x5 = 40 and that 8x1 = 8, then I know that 8 x (5+1) = 48.
third grade is taught the distributive property means that 8x7 is the same as 8x3 plus 8x4. I tried this for two years, and it confused the daylights out of my students.
This year in 6th, a friend told me to put them in groups of different numbers (such as 7 and 6), and distribute 2 skittles to each member of each group. Add them up and multiply, or multiply and add them up, you get the same number.
When I work with small groups of 4th grade students struggling with these properties, I make them part of the demonstration like trishg1. Unlike trish1g, I have each group member select a card or other object from a set where each object has a different positive integer. Letís say Ann got 1, Bob got 2, Cal got 3, and Dee got 4 to start off easy.
For the commutative (ordering) property of addition, we add the numbers individually 1 + 2 + 3 + 4 first and get 10. Then Ann and Cal trade place and we add each studentís number in the new order getting 3 + 2 + 1 + 4 = 10. Now Cal and Bob trade places and we sum in order again getting 2 + 3 + 1 + 4 = 10.
For the associative (grouping) property of addition, we again add the numbers individually 1 + 2 + 3 + 4 first and get 10. Then Ann and Bob group their numbers to get 1 + 2 = 3, and Cal and Dee do the same to get 3 + 4 = 7. Adding Ann and Bobís total and Cal and Deeís totals together, we get 3 + 7 = 10. Now Bob and Cal add their numbers to get 2 + 3 = 5. Adding Annís number, Bob and Calís total and Deeís number together we get 1 + 5+ 4 = 10. Sometimes someone will suggest that we add Ann and Deeís numbers together providing an opportunity to reinforce the commutative property and how it is different than the associative property.
Finally, for the distributive property of multiplication over addition, the team gets 2 skittles times the total of each team memberís numbers. First each member determines how many skittles his/her number is worth and we add them together getting (1 X 2) + (2 X 2) + (3 X 2) + (4 X2) = 2 + 4 + 6 + 8 = 20. Could we just add the numbers together and multiply by 2? Well, (1 + 2 + 3 + 4) X 2 = 10 X 2 = 20. Does it always work? Try some more and see.
(Trying more examples canít prove that it always works, but advanced students may be able to come close to proving it using the definition of multiplication plus the commutative and associative properties of addition.
1 X 2) + (2 X 2) + (3 X 2) + (4 X2) =
(1 + 1) + (2 + 2) + (3 + 3) + (4 + 4) =
1 + 1 + 2 + 2 + 3 + 3 + 4 + 4 =
1 + 2 + 3 + 4 + 1 + 2 + 3 + 4 =
(1 + 2 + 3 + 4) + (1 + 2 + 3 + 4) =
(1 + 2 + 3 + 4) X 2
While this may be beyond most students, it may be a way to differentiate for those who already know the properties or master them more quickly than the rest. If you chose the numbers correctly, an easier extension is sharing the skittles equally among the team members.)
Wow--maybe you ought to change your name to lifechanger--because you are gonna . prop and i think i will extend it by having them make examples for the class to share by using other numbers like 18 or 24.
Careerchangers idea is what I was suggesting only she did a much better idea of explaining it. My idea was using objects, such as blocks, to represent each number, but her way works well too. If they don't see it with just the numbers try using her number ideas and then have objects to correspond with each number.
I've used cookies & the problem was 2(11 + 13)...the 11 were the number of girls in my class...the 13 was the number of boys...I gave the boys the 2 cookies each & the girls weren't happy about it...helped them understand the process of applying it to that kind of problem.
We use arrays as a tool to teach multiplication and division. You can use these also to teach distributive property to kids. Have them make an array with counters or square tiles and ask them to list all the facts they can see. For example if they make a 4x6 array (4 rows of 6) for 24 they can manipulate the array to see1x6+3x6 or 4x2 + 4x4 or2x6 +2x2 +2x4 etc. Hope this makes sense. If not I can send a picture example.
It is quite effective because it is the children discovering the ways multiplication can be broken up, not just the teacher telling them.
We recently completed a unit written by Cathy Fosnot, which teaches the concepts of multiplaction, and allows students to intrinsically discover the properties of multiplication. Works beautifully. Takes a month to get through even though unit is written as "10 days." Unit is called, "Groceries, Stamps, and..." can't recall the rest of the title off the top of my head. :-)