Here are some resources to practice with patterns!
www.mathplayground.com/functionmachine.html pbskids.org/cyberchase/math-games/stop-creature/ www.abcya.com/number_patterns.htm www.funbrain.com/games/number-cracker-game www.topmarks.co.uk/Flash.aspx?a=activity01 www.free-training-tutorial.com/sequences-games.html www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.PATT&ID2=AB.MATH.JR.PATT.PATT&lesson=html/object_interactives/patterns/use_it.html www.sheppardsoftware.com/mathgames/earlymath/BalloonPopPatterns.htm www.mathgames.com/skill/3.57-multiplication-input-output-tables-find-the-rule
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Distributive, Associative, and Commutative Properties In order to really help kids understand the properties, we stress that the "equals sign" does not mean "and the answer is..." and instead represents two balanced sides, like a scale. Commutative Property We remember the Commutative Property as the one that "Changes Order" (the C and O in COmmutative). For example, 5 + 3 = 8, but if I change the order of my two addends, my sum is the same 3 + 5 = 8. This property works for both addition AND multiplication. 5 x 3 = 15 and 3 x 5 = 15 Also, if you know what a commute is (a trip to school from home, for example) the commute to home from school is the same exact trip and same distance, but you just change the order of your commute (instead of going from home to school, you go from school to home). Associative Property To remember this property, just remember the term "associate," which means to be together with another person or group as friends. You can almost thing of the parentheses ( ) as the hug friends give to each other as they associate with one another :) In the associative property, we associate numbers differently, but the answer will be the same if we change the groupings. Example: We have three friends in class, Susie, Patty, and Diego. At recess one day, Susie and Patty decide to hang out and Diego plays by himself. Either way, we still have the same 3 friends. (Susie + Patty) + Diego. The next day, Patty and Diego hang out and Susie plays by herself. (Patty + Diego) + Susie. Both are the exact same three friends, just grouped differently. Let's look at this with numbers. If we have three numbers we want to add together, 2 + 3 + 4, it won't matter if we group: (2 + 3) + 4 or 2 + (3 + 4) No matter which number associates with another number, the sum will be the same in both cases- 9. Same goes for multiplication: 4 x 3 x 5 is the same as (4 x 3) x 5, which is the same product as 4 x (3 x 5)= all equal 60. Distributive Property The Distributive Property is a fantastic way to multiply large numbers together. It allows you to "break apart" a number into easier-to-multiply numbers and then arrive at an answer faster than going through lattice or the standard way. Here is an example: This is an array for 4 x 8 (4 rows with 8 dots in each row): Instead of figuring out 4 x 8, we can break this array into two, easier to multiply arrays: Now we have a 4 x 5 and a 4 x 3. We didn't get rid of or add any dots, just broke them down into a different configuration.
Now we can multiply: 4 x 5 = 20 and 4 x 3 = 12. We add the products together, 20 + 12 = 32, and there is our answer! Obviously we don't really need to use the distributive property for simple numbers like this, so here is a more abstract example. EXAMPLE) Let's say we are asked to multiply 3 x 46. Instead of having to figure out my 46 times tables, I can break it into a simpler problem. I can break 46 into 40 + 6, since those two numbers add up to 46. Then, all I have to do is multiply those two numbers times 3. Here is it written down: 3 x 46 \/ 3 x (40 + 6) -or- 3( 40 + 6) When we see the number on the outside of the parentheses without an operation symbol, we know it means to distribute and multiply times what is inside the parentheses. The multiplication sign isn't necessary. EX) 3(6) = 3 x 6 or 4(5) = 4 x 5 Now that we have 3( 40 + 6) we can finish the problem. We multiply the 3 times what is inside the parentheses: (3 x 40) + (3 x 6) \/ \/ 120 + 18 \/ 138 Websites for practice and extra info This site explains the three properties (also known as "laws") http://www.mathsisfun.com/associative-commutative-distributive.html Step-by-step distributive property info sheet Info on the properties http://coolmath.com/prealgebra/06-properties/index.html Videos on the three properties http://www.brainpop.com/math/numbersandoperations/ https://scratch.mit.edu/projects/98514731/ http://www.mathgames.com/skill/6.15-distributive-property http://henryanker.com/Math/Algebra/Distributive_Property_1.swf http://www2.gcs.k12.in.us/jpeters/distributive%20property.htm Here is a video I created to help my friends who are still not completely comfortable with the distributive property. I hope this helps! |
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