## Subitizing and Guided Math Groups: Part 2 Why it is so important!

Subitizing provides a basis for early addition skills. Different arrangements help children to see and discuss different ways to name a number. Ten frames are another tool to use to build subitizing skills. Subitizing is a fundamental skill in the development of students’ understanding of number (Baroody, 1987).  Clements  (1999) writes that students can use subitizing to develop understanding of number, conservation and compensation.

Here are some game ideas.  There are several others listed in the links below.  When you show your students the cards you should ask “What do you See?” This is different from “How many? because it frames the question in a way that they think about different number arrangements.  More question examples http://naturalmaths.com.au/numblocks/mr_subitization.htm

1. Quick image games where the teacher flashes dot cards and the students tell how many.

2. Give children a set of cards with equivalent names but one that doesn’t belong.  Have them select the one that doesn’t belong.

3.  Have students match the number with the dot card.

4. Have the students play matching games with cards that show equivalent names.

Great Resources for Subitizing:

There is a new video out by Marilyn Burns called Number Talks that shows a teacher using dot cards and ten frames.

http://teachmath.openschoolnetwork.ca/Subitizing.htm

http://www.acoe.org/acoe/files/EdServices/Math/NumberRecSubitizingV3.pdf

http://www.k-5mathteachingresources.com/support-files/dotcards1-12.pdf

http://www.k-5mathteachingresources.com/support-files/large10frames1-10.pdf

http://www.k-5mathteachingresources.com/ten-frames.html

References

http://en.wikipedia.org/wiki/Subitizing

http://teacherweb.com/wa/nachesvalleyprimaryschool/msclark/Subs.PDF

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## Subitizing and Guided Math Groups: Part 1

Subitizing is being able to look at a number and know how many without counting.  It refers to “rapid, accurate and confident judgments performed for small numbers of items. It comes from the Latin adjective subitus (meaning “sudden”)” and has to do with immediately knowing how many items one sees for a small set of numbers.  When we are talking about larger sets we often estimate or count.

There are two types of subitizing. Perceptual subitizing is looking at the number and knowing how many without any mathematical processes taking place.  Conceptual subitizing is based in mathematical processes, such as looking at the parts and the whole. An example of this iswhen you see the eight domino and you know that it is five on one side and three on the other and that makes eight.  Spatial patterns are just one kind.  Other patterns include kinesthetic ones such as finger patterns, rhythmic and spatial-auditory (Clements, 1999).

We usually teach students to subitize up to ten. See  http://www.poweroften.ca/index.php?option=com_content&view=article&id=37&Itemid=103

Spatial arrangements make subitizing easy or hard.  Rectangular arrangements seem to be the easiest followed by linear, circular and scrambled arrangements increasing in difficulty (cited Clements, 1999). You can use dot cards, domino cards, number-cube cards and ten frames to teach subitizing.  You can also use bingo chips and interlocking cubes.

Subitizing is a fundamental skill in the development of students’ understanding of number (Baroody, 1987).  Clements  (1999) writes that students can use subitizing to develop understanding of number, conservation and compensation.  In part 2 we will discuss this further.

Resources

http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdf

http://mathelem.sites.fcps.org/system/files/kordeliasGame.pdf

References

http://en.wikipedia.org/wiki/Subitizing

http://teacherweb.com/wa/nachesvalleyprimaryschool/msclark/Subs.PDF

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## Teaching Fact Families in Guided Math Groups

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

Pictorial level

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.

Abstract Level

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:

http://www.uen.org/k12educator/corelessonplans.shtml

http://www.reallygoodstuff.com/pdfs/151857.pdf

References & More Resources

http://www.mrsmcdowell.com/Number%20Families/Domino/domino5.pdf

http://www.mrsmcdowell.com/Number%20Families/numbers.htm

http://www.mathwire.com/strategies/matsff.html

http://teachingcontent.org/CK/resrcs/lessons/06_1_Dazzling.pdf

http://www.region10ct.org/regiontenmathpages/region10mathsitefaq/What%20is%20Cognitively%20Guided%20Instruction%5B1%5D.pdf

http://www2.scholastic.com/browse/article.jsp?id=10228

http://www.uen.org/Lessonplan/preview.cgi?LPid=10985

http://www.dpi.state.nd.us/title1/08fallconfhandouts/miaff.pdf

http://illuminations.nctm.org/lessons/howmanyfish/Fish-AS-FactFamilies.pdf

http://illuminations.nctm.org/LessonDetail.aspx?ID=L78

http://www.busyteacherscafe.com/worksheets/math/factfamilies.pdf

http://www.education.com/files/50201_50300/50201/file_50201.pdf

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## Guided Math with Dominos: More Ideas

When teaching a guided math lesson, you always want to think about providing concrete, pictorial and abstract activities. You want to make sure that you are asking questions that make students think mathematically and justify their answers.  These are the types of activities that build conceptual understanding but also help build automaticity.  When the students are counting the pips they are working on understanding the numbers and how they are represented.    But, when they are working on the fact sorts, they begin to build automaticity and fluency because they are thinking about the types of facts.  I call fact knowledge, knowing the Dolch words of math.  If students can look at a fact and recognize it as a double and then add fast, it gives them automaticity. If they recognize, “oh, that’s a plus 1 fact, I just count up one number” then they are building their fluency.  If they can recognize, “oh that’s a doubles +1 fact, I just double and add one more” then they can add fast without using slower strategies such as counting on their fingers or counting up.  Once children have conceptual understanding, we want them to have procedural fluency and automaticity.  Dominos is a great tool to build that.

Concrete Level Activities:  ACTIVITY A:  Students match number facts with dominos.  The good thing about using  dominos is that the children can count the pips.  I tend to have a wide assortment of dominos in the classroom.  ACTIVITY B:  Students create their own dominos with big dots (from Staples).  You can either give them a large construction paper template or have them make their own.

Pictorial level: ACTIVITY A: Students pick a domino and draw it on a blank template. They then write the number sentence.  ACTIVITY B:  Using the fact sheet (which is differentiated by readiness) students paste a paper domino with the correct fact.  They also play a domino match game, where the facts are on one side and the dominos on the other and they connect the ones that match with a line.

Abstract level: ACTIVITY A: Domino Fact Sort.  Students have differentiated sorting sheets and they sort the facts according to specific criteria.  For example, on one sheet students sort doubles dominos from all other dominos. ACTIVITY B: Domino Fact Sort Races.  Using a sand timer, students see how long it takes them to find and sort various facts on a template.

Domino Fact Sort

Domino Doubles Facts

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## Guided Math with Dominos

What does that fact look like?

In this activity, students receive a template with number facts.  They then have to find the fact domino that matches the number sentence.  I do this activity with novice mathematicians so they can begin to sort fact dominos and put the domino representation with the number model.  Students enjoy Domino Fact match.  I ask them how they know it’s correct.  I want them to justify their answers.  For the more advanced students we play a different version, where there is a missing addend.   Here is great link to domino math ideas and blackline masters:

http://mathwire.com/strategies/matsdom.html

Happy Mathing,
Dr. Nicki

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