# Archive for August, 2010

## 2 great books to kick off the school year

In the beginning of the year, one of the first things you want to do is set a context for numbers.  Two great books to do this are

Used Any Numbers Lately (prek-2nd) and Math Curse (3rd grade and up).

Used Any Numbers Lately is a great abc book that explores numbers in our world.  It does a great job of making math connections to real life.  For instance, E is for elevator numbers and H is for house numbers.  As an extension, I would have the class use this as a mentor text and then create their own abc’s of how they use numbers in their lives.  They can illustrate it and put it with their class big books.

Math Curse is the story of an upper elementary child who wakes up and finds that he can’t get his mind off numbers.  He wonders about the numbers involved in his breakfast, he is mesmerized by numbers on the bus on the way to school and then bombarded by the math that whirls around him all day long. As an extension activity, I would have the students do a mural of the many ways they encounter numbers throughout their school day.

Focus Questions for the Discussion:

(Before reading) How do we use numbers in our daily lives?

(After reading) Can you all think of other ways we use numbers in our daily lives?

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## Number Bonds/ Fact Families/ Complements of Numbers and Guided Math

Number bonds, fact families and complements of numbers basically are names for the same concept. They describe the relationship between pairs that make up a number. So for instance, 1+4, 2+3, 0+5 are all number bonds of five. For children to develop automaticity with number facts they need to learn their number bonds up to 18. They should learn these first through 5, then through 10, then through 18  cut and paste this url to arrive at this page…http://www.primaryresources.co.uk/maths/pdfs/number_bonds_to_10_rp.pdf

The key component to this is to build understanding at the three levels: concrete, pictorial and abstract. Too often math textbooks jump right to the abstract level, asking students to make connections that they don’t really understand. I have written a post on fact families and ten frames but I would like to discuss this idea further here (be sure to see those posts for further discussion).

1. Use a 5 frame and two sided markers. So students can see the relationships of building numbers that build five. They toss the markers and see the different ways to make five.

2.  Use snap cubes.  For example, I would use 2 green snap cubes and 3 blue ones.  I would then lead the students through activities where they explore the relationships.

3. Explore other numbers up to ten.

4. Use a 10 frame and two sided markers.

5. This is an excellent site that shows how to build through the 3 levels:

http://www.montgomeryschoolsmd.org/schools/oaklandes/mathstudentworkpages/gr1un2page6.html

Pictorial- The children follow the steps above but then color in their answers on the templates.

At the pictorial level have them make cards that illustrate the bonds: http://www.mathcats.com/explore/factfamilies/printaddcards.html

Some printouts that are colorful and engaging. http://www.sparklebox.co.uk/1211-1215/sb1213.html

http://www.sparklebox.co.uk/1571-1575/sb1571.html

http://www.sparklebox.co.uk/1386-1390/sb1389.html

Abstract – At this level, add the number sentences. You can also add the fact family triangle. Superfun Power Point Game: http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/851/Hitthebuttonv7.swf http://scratch.mit.edu/projects/MrShah/63856

Interactive Powerpoints:  (All these power points you have to cut and paste the url to see…they can all be found on this website http://www.primaryresources.co.uk/maths/mathsC1.htm)

These you can link to instantly:

http://www.amblesideprimary.com/ambleweb/mentalmaths/numberbond.html www.sparklebox.co.uk/md/addsub/bonds.html (great visuals some at pictorial and some at abstract level)

Practice sheets: Great Booklet to Make:

Great Links  cut and paste http://www.primaryresources.co.uk/maths/mathsC1.htm (most of the links above come from this site –there are tons more here…I just organized them and highlighted the ones I like)

http://homeschoolmath.blogspot.com/2007/09/number-rainbows-to-learn-subtraction.html

http://home-ed.info/maths/number_bonds.html

Also in this blog search:

ten frames, ten frame, fact families

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## Animoto and Guided Math Lessons

Animoto is a web 2.0 tool that offers lots of possibilities for introducing math concepts.  It is something you would use to springboard into the conversation.  It is free, easy to make and filled with potential!  The educator edition offers even more film time for free (http://animoto.com/education). You simply upload images, video, text and music and voila!  You have yourself an Animoto!  I made three to show you how they might look as an introduction to a math mini-lesson.  I would use these with the whole group as well as when I pull small groups.  These make great discussion starters and remember that a key element in guided math is about getting students to communicate their ideas about math:)

Introducing Numbers:

http://tinyurl.com/animotonumbers

Introducing Multiplication:

http://tinyurl.com/animotox

Introducing Fractions:

http://tinyurl.com/animotofrac

Discussion Starter Questions:

1. What did you see in this Animoto?

2.  What do you think we are going to be studying?

5.  How shall we find some more stuff out?

P.S.  I invite you all to make Math Animotos and send them to me.  I will make a space for a Math Animoto library on this site so together we can all have a fantastic resource!

Happy Mathing,

Dr. Nicki

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## Decimal Squares in Guided Math Groups

Decimals is a tough concept for many of our students.  It is so important that we spend some time building conceptual understanding and problem solving as well as the procedural fluency.  I think a great way to start is based on the work of Dr. Bennett from the University of New Hampshire (http://www.decimalsquares.com/).  Decimal squares is a way for students to visualize what they are talking about and to develop conceptual understanding.

tinyurl.com/decimalsq  (look for decimal squares)

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## Guided Math Contest Winners!

We have 3 winners: Nicole, Heather, and Sharon!  I will be emailing you about your book requests and mailing your books this week!  Thank you to everyone and please keep commenting.  We will be doing a Manipulatives Raffle in September!

Happy Mathing,

Dr. Nicki

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## Guided Math Blog Contest #1

Hello fellow educators! In preparation for back to school, I am doing a contest.

Rules:  The first 3 people to respond to at least 5 blog posts (any post from any month) will win a back to school math book bundle.  This will be 3 books targeted at the grade level that you teach! The contest starts today and ends on Saturday, August 28th.   Winners will be announced as soon as selected.  I will mail your books right away so that you have them for the beginning of the school year!

Happy commenting,

Dr. Nicki

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## 25 Things to do with the Hundreds Grid in a Guided Math Group or Math Center

25 Things to do with the Hundreds Board

The hundreds board is a great tool for teaching a variety of math concepts.  Some boards start with 0 and others start with 1.  Every student should have their own number grid.  Remember in terms of differentiation, everybody is not necessarily on the same page.  For example, some students might be working on a number board that goes up to 20 while another could be working on a number grid that goes up to 200.  Number grids are great for teaching a variety of concepts including addition and subtraction strategies, reading number words and ordering numbers.  See the list below for some ideas.

2. Subtracting -1

4. Subtracting +10

5. Teaching compensation with +8 facts

6. Teach compensation with  + 9 facts

7. Reading Number Words. Students pull a number card and mark that number word on the grid.First person to get 4 in a row vertically, horizontally, or diagonally wins.  Each player uses their own mat.

http://www.teachingideas.co.uk/maths/files/hundredsquarewords.pdf

8. Number Hunt. Teacher calls out a numeral and the students find it.  This is a great way to reinforce vocabulary because the teacher can call out numerals such as 10 less than 25 or 1 more than 64 etc.  Also, the teacher can call out the numeral in terms of place value.  For example, find the number that has 2 tens and 7 ones.

9. Number Grid Puzzles

http://mathwire.com/100board/100board.html

10. Fill in the Missing Numbers –

Take a number grid and white out some of the numbers.  Do this according to readiness levels- so some students have 5 numbers whited out while others have 25 missing.  Then put this grid in a sheet protector and have the students fill in the missing numbers.

http://mathwire.com/numbersense/blankhundredchart.pdf

http://resources.oswego.org/games/DogBone/gamebone.html

http://mathwire.com/100board/hbpuzzles.pdf

http://www.teachingideas.co.uk/maths/files/missinghundredsquare2.pdf

http://www.teachingideas.co.uk/maths/files/missinghundredsquare1.pdf

http://www.teachingideas.co.uk/maths/files/missinghundredsquare3.pdf

http://www.teachingideas.co.uk/maths/files/missinghundredsquare4.pdf

http://www.kidzone.ws/math/jungle/t_math.asp?gr1-series100.html

http://www.kidzone.ws/math/farm/t_math.asp?gr1-series100.html

http://www.kidzone.ws/math/ocean/t_m ath.asp?gr1-series100.html http://www.teachingideas.co.uk/maths/files/hundredsquarewords.pdf

11. Pull a Number and Round it to the Nearest 10. Use the Number grid to check your answer.

12. Talkin’ bout Numbers! Look at the number grid and discuss the numbers we use in daily life.

13. Skip Counting – Color in the Skip Counting Sequence or fill in missing number patterns.

http://www.apples4theteacher.com/math/games/100-number-chart-one.html

http://www.abcya.com/100_number_grid.htm

http://www.teachingideas.co.uk/maths/files/numbersquaregaps.pdf

14. Build a Grid

15. Find complements of 100

16. 100 Chart Picture Designs

http://www.jmeacham.com/games.htm

17. Everyday each student fills  in the number of the day of school on a blank grid and discuss how many more days until the 100th day.

18. Numbergrid races. Students race against themselves or others to put the hundred board back together.  This can be cut up into various degrees of difficulty.  For example, some puzzles can be cut into horizontal strips, others into vertical strips, others into squares or rectangles and still others into varying odd shapes.

19. Race to 100

20. Race from 100

21. Highlight odd and even numbers

22. Hundreds grid Number Stories

23. Mystery Numbers
http://www.oswego.org/ocsd-web/games/DogBone/gamebone.html

24. Multiple patterns

25. Money – The hundred board is great for teaching money.  Start by having students landmark the nickels, dimes and quarters and then give them problems where they have to use these landmarks to add money.

Web Resources:

Be sure to check out this website for 25 other things to do the number grid: http://letsplaymath.net/2008/09/22/things-to-do-hundred-chart/

http://www.fuelthebrain.com/Guides/view.php?ID=151

http://www.squidoo.com/hundredboard

http://illuminations.nctm.org/LessonDetail.aspx?ID=L303

http://www.mathwire.com/100board/hbpuzzles.pdf

http://karolyeatts.com/Math/The%20Wonders%20of%20the%20Number%20Chart%20revised.pdf

http://www.apples4theteacher.com/math/games/100-number-chart-50.html

http://standards.nctm.org/document/eexamples/chap4/4.5/

http://www.teachingk8.com/archives/integrating_math_in_your_classroom/from_one_to_one_hundred_by_michael_naylor.html

http://www.learnnc.org/lp/pages/3865

http://departments.bcsd.com/cipd/Mastering%20Math%20Facts.pdf

http://www.helpingwithmath.com/printables/tables_charts/cha0301_hundreds_chart01.htm

Print Resources & Games

http://www.rainbowresource.com/prodlist.php?sid=1271872984-71811&subject=10&category=2357

http://www.marcycookmath.com/chartbks.htm

http://www.amazon.com/Hundreds-Board-Activities-Computation-Measurements/dp/B000P1NUPQ

http://nzmaths.co.nz/resource/hundreds-board (click on the bottom of the page attachments in this site to get the activities after you read the page)

http://www.istemnetwork.org/resource/educational/lessondetail.cfm?lessonid=30

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## Digital Learners and Guided Math: A way to reach them

The students we teach are called Generation Z.  Prensky has named them the “digital natives” (http://www.marcprensky.com/writing/).  Here are 3 ways to tap into your students enthusiasm digitally when teaching math.

1. http://mathtrain.tv/ – A very interesting website with math videos, podcasts, screencasts and more that teach math concepts – often made by the students.  These are great instructional aids.  They also are great examples so students can make their own videos.

2.  http://edu.glogster.com/ – YOU MUST CHECK THIS OUT!  This has great instructional potential as well as group project potential.  Look under the category of math to see relevant examples….i.e. http://qvmsmathgirl.edu.glogster.com/properties/

You can make these and then show them to your class as well as post on your class blog or website.

3.  Harvey’s Homepage.  This is a great website for anybody who has a Smartboard.  Harvey is the man to know!  He can get you where you need to go!  His material is standards based, rigorous and totally engaging.

Please write me back and let me know how you like the websites and how you are using them in your classrooms.  I’d love to hear from you!  Also, be sure to send us great websites that you come across in your travels on the internet:)

Thanks,

Dr. Nicki

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## Tally Marks and Guided Math

Tallies: A special way to skip count by 5’s:

Building Conceptual Understanding: As a mini-lesson to introduce counting by tally marks  I read Tally O’Malley http://www.stuartjmurphy.com/books/level_2/detail.php?level_id=2&book_id=26. When introducing tallies, I have the children come up in groups and they count off. Every fifth student makes their arms like a tally mark across the other 4. We pull numbers or roll a big number or dotted die to decide which number we will make. The children have great fun and they are getting to see, feel and experience the tally first hand.

After this, we begin to practice toothpick tallies. First we do it in partners and then we do it individually.  In partners, one person rolls and the other person counts out the toothpicks and represents them as tallies. The partner has to agree or disagree. They then glue down what they have decided is the correct representation of that number.  They take turns playing this game for several rounds.   After they play in  groups,  they start to work individually.  I differentiate the whole process by giving different pairs and inidividuals different number ranges to represent. Finally, we play this same game, but we do it by drawing the tallies with crayons. The fifth tally is always represented by a different color, whether with toothpicks or drawings.

Practicing on the Pictorial and Abstract Level: We sing the tally song for reinforcement (see Mrs. Jones Tally song- we make up our own tune) http://www.mrsjonesroom.com/songs/tallymarks.html.   See examples of tally mark cards on Enchanted Learning. You can make your own or sign up for membership and download them from this site. I have found this site to be worth the \$20  dollar investment each year (http://www.enchantedlearning.com/math/tally/ )  Another idea can be found here (http://www.aimeeasher.com/shoppe/product.php?productid=3143).   I also download these tally dominos and have the students match the number to the corresponding domino.  I also have the students play comparing games with them.

http://lrt.ednet.ns.ca/PD/BLM/word_files/number/number_match_tally.doc

Tally Mark Resources: See the template below for a great way to practice procedural fluency. The children each have a template and they take turns rolling and tallying until someone finishes (http://www.mathwire.com/games/100tallygame.pdf http://www.mathwire.com/games/ktallyho.pdf)

http://www.oblockbooks.com/tec3225.pdf

http://www.brainpopjr.com/math/data/tallychartsandbargraphs/grownups.weml

http://www.abcteach.com/free/t/tallymarks2.pdf

http://www.kidzone.ws/math/gr1-tally1.htm

http://www.kidzone.ws/math/jungle/gr1-tally2.htm

http://www.kidzone.ws/math/ocean/gr1-tally3.htm

You should do some sort of tally chart for your daily routine.  For example you could tally the amount of teeth lost every month or any other data that students decide to collect.  jmeacham.com has some great templates for this …see  http://www.jmeacham.com/calendar/calendar.binder.htm

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## Skip Counting by 5’s in Guided Math lessons

Skip counting by 5’s is an essential skill.  It builds an important foundation for multiplication.  We have to make sure that our students are doing more than just skip chanting.   There are several activities we can do to build conceptual understanding, procedural fluency and problem solving skills.

Building conceptual understanding:

1.  I have the children stand up in front of the classroom and we skip count their hands by fives.  We then make this into a hand skip counting poster.  In small guided groups we build snap cubes into towers of five and then skip count them.  In follow up centers the children have several cards that they have to build in towers of five to represent and skip count the number.  On a concrete level, the students can get blank scaffolded organizers where they have to line the bears up in rows of five.

Pictorial Representation

After the children have plenty of opportunity to practice with physical objects I have them show the representation with drawings.  They can color in snap cube pictures or bears to represent the skip count.

Abstract Level

On the abstract  level,  we sing songs and do chants ( http://www.havefunteaching.com/songs/song-lyrics/counting-by-fives-song-lyrics.pdf).

http://www.songsforteaching.com/jackhartmann/countby5s.htm

Students also practice with number grids by coloring or circling by 5’s.

There is also a center where the skip counting by five cards are all mixed up.  The students use a timer and race themselves to put the cards in skip counting order.

In terms of daily routines, you should add a nickel each fifth day to reinforce counting with money.

Another way to practice is to do dot to dots.

http://www.education.com/worksheet/article/skip-count-dot-to-dot-IV

(See Post: Tallies: A special way to skip count by 5’s).

Resources for Skip Counting by Fives:

http://www.mathwire.com/strategies/count5.html

http://www.harcourtschool.com/activity/number_patterns5_10/

http://www.printactivities.com/Mazes/CountingBy5s-Mazes.shtml (there are tons of sheets for practicing skip counting by fives on this site…they offer plenty of opportunities to differentiate).

http://www.education.com/worksheet/article/count-by-fives-first/