Archive for April, 2010
The New Core Math Standards are out! They look good. Finally, we as a nation are sitting down and agreeing about a common set of standards, saying that yes indeed there should be a baseline that all students know from Hawaii to Alaska, California to New York and Illinois to Texas! Oops, did I say Alaska and Texas? They are the only two states who have not agreed to the standards. Oh well, maybe they’ll eventually come along. But, everybody else has voiced approval with some reservations. The team consisted of the nation’s governors, state commissioners of education, school administrators(Council of Chief State School Officers)and others. These standards are suggested for all states but as of yet not mandatory, although President Obama has spoken about tying them to Title 1 spending. It is expected that most states will have them in place within 3 years. The big idea behind the standards is GOING DEEP! LESS IS MORE! YEAAAH! Finally, our children have a chance to learn something really well.
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Fact Families are really important for students. There are many ideas that you can teach with them. Here are 5 concepts to teach with fact families and some great websites to do it!
1. Fact families can help to reinforce the basic facts.
2. Fact families can help to teach the concept of equality.
3. Fact families help to teach turn around facts (commutative and anticommutative property of addition and subtraction and multiplication and division).
4. Fact families help to teach inverse facts.
5. Fact families help to practice the missing addend concept.
When teaching fact families, always start with concrete materials. Then next, show it visually on the cards. Finally, teach it at the abstract level with the fact triangle house and cards.
Concrete level…Pull out the plastic bears and tell stories. At this point, I don’t show the cards. I tell the stories and we act them out with the manipulatives. I tell the students that we are going to look at a special way to record the stories in a few day. The first few days we just tell stories.
Story 1: There were 3 green bears in the park. Then 5 blue came. How many are there in total?
Story 2: There were 5 blue bears in the park. Then, three green ones came. How many are there in total?
Story 3: There were 8 bears in the park. 3 bears left. How many stayed in the park?
Story 4: There were 8 bears in the park. 5 bears left. How many stayed in the park?
Story 5: There were 8 bears in the park. 5 bears were blue. How many were green?
Story 6: There were 8 bears in the park. 3 were green. How many were blue?
Story 7: There were 8 bears in the park. Some went away. 5 stayed. How many left?
Story 8: There were 3 bears in the park. Some more came. Now there are 8. How many came?
These are all story types based on the work by Carpenter, Fennama and Franke (1996), Cognitively Guided Math Instruction.
Also see this site by NCTM for teaching fact families at the concrete level with macaroni….http://illuminations.nctm.org/LessonDetail.aspx?ID=L120
Mathcats has some great ideas… You can actually print the Fact Family cards out and then have the children draw or illustrate them as pictured below. Check them out at http://www.mathcats.com/explore/factfamilies/printaddcards.html
|You can have the children draw bears, unifix cubes, paste stickers, paste pattern block pictures etc.|
There is a great song on songsforteaching.com by Carl Sherril about fact families http://www.songsforteaching.com/carlsherrill/factfamilies.htm
This blog http://cityteacher.wordpress.com/2007/09/09/using-triangles-to-teach-fact-family/ has a very detailed version of how one teacher teaches fact families all year long. This teacher has made it a part of her daily routine and so the children do them everyday and become quite comfortable with the various concepts.
This is a great, detailed planning map for fact families: http://www.childrensengineering.org/technology/Math_Fact_Family_Map.pdf
When I am teaching this concept at the abstract level, I actually draw a house with a triangular roof. I put the largest number on top and the other two numbers in the sides. Then, I draw 4 windows and a door. In the top two windows I put the addition facts…each one underneath the corresponding number in the triangle…so for example under 5 would be 5+3 and then under 3 would be 3+5 and then on the door I put the larger number again and I remind the students that we are going to use the big number to subtract. So, in the two windows on either side of the door, I put the subtraction facts. On the door, I put a – sign as the doorknob. This reminds them to subract. I have found this to be a very helpful tool for introducing fact families at the abstract level (see picture: fact family picture1).
Here is a picture of a great center idea. I would either buy this or make my own. http://www.oblockbooks.com/shoppingcart/html/pages/CreativeTeachingPress_ctp4695.htm
Another great website that talks about teaching with domino fact families and dice fact families: http://www.education.vic.gov.au/studentlearning/teachingresources/maths/mathscontinuum/number/N17501P.htm#a1
There are some great domino fact families and dice fact families information atHere is a great template for recording fact family math resources at the Utah Education Network’s website:
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