## More RTI Math Resources

Here is the IES guide to RTI (federal gov) in Math. It outlines the interventions very clearly, with a discussion about the research findings of each recommendation. Well worth using as a study guide in PD sessions. Everybody that works with students in math should be aware of the information in the packet! Here are the research based recommendations:

Recommendation 1. Screen all

students to identify those at risk for

potential mathematics difficulties and

provide interventions to students

identified as at risk.

Recommendation 2. Instructional

materials for students receiving

interventions should focus intensely

on in-depth treatment of whole

numbers in kindergarten through

grade 5 and on rational numbers in

grades 4 through 8. These materials

should be selected by committee.

Recommendation 3. Instruction during

the intervention should be explicit and

systematic. This includes providing

models of proficient problem solving,

verbalization of thought processes,

guided practice, corrective feedback,

and frequent cumulative review.

Recommendation 4. Interventions

should include instruction on solving

word problems that is based on

common underlying structures.

Recommendation 5. Intervention

materials should include opportunities

for students to work with visual

representations of mathematical

ideas and interventionists should

be proficient in the use of visual

representations of mathematical ideas.

Recommendation 6. Interventions at

all grade levels should devote about

10 minutes in each session to building

fluent retrieval of basic arithmetic facts.

Recommendation 7. Monitor the

progress of students receiving

supplemental instruction and other

students who are at risk.

Recommendation 8. Include

motivational strategies in tier 2 and

tier 3 interventions.

Happy Mathing,

Dr. Nicki

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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).

**Concrete: It is important to start with concrete materials. **

**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. **

**http://www.teachervision.fen.com/addition/graphic-organizers/44567.html**

**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****)**

(http://www.primaryresources.co.uk/maths/powerpoint/Making_10_2.ppt http://www.primaryresources.co.uk/maths/powerpoint/numberbonds_to10_SP.ppt http://www.primaryresources.co.uk/maths/powerpoint/number_bonds_to_10_partyhats.ppt http://www.primaryresources.co.uk/maths/powerpoint/numberbonds_to10.ppt

**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**:

**(Again you have to cut and paste these urls into the browser to arrive at exact page)** http://www.primaryresources.co.uk/maths/docs/Number_Bonds_Booklet.doc http://www.primaryresources.co.uk/maths/docs/number_bonds_to_10_strips.doc http://www.primaryresources.co.uk/maths/pdfs/SFnumbersearch1.pdf http://www.primaryresources.co.uk/maths/pdfs/SFnumbersearch2.pdf http://www.primaryresources.co.uk/maths/pdfs/nbonds10PDF.pdf http://www.primaryresources.co.uk/maths/pdfs/3easyadd.pdf http://www.primaryresources.co.uk/maths/pdfs/LH_making10and20.pdf http://www.primaryresources.co.uk/maths/docs/number_bonds_to_10_LD.doc http://www.primaryresources.co.uk/maths/pdfs/LH_numberbonds.pdf http://www.primaryresources.co.uk/maths/powerpoint/numberbonds_to20.ppt

**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)

*Other Links*

http://letsplaymath.net/2007/01/13/number-bonds-better-understanding/

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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## 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.

*1. **Adding +1*

*2. **Subtracting -1*

*3. **Adding + 10 (http://www.ictgames.com/100huntplus10.html)*

*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

**and discuss how many more days until the 100**

*in the number of the day of school on a blank grid*^{th}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.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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## Role of Flexible Grouping In Guided Math Instruction

Guided Math Groups are organized according to the common needs of a specific group of students. The goal is to engage in depth with those students around a particular instructional goal, with intensive practice. Guided Math Groups are Flexible-meaning that they change over time. As the teacher notices that students achieve particular knowledge and skill sets, they move the students around. Also, students can be in different groups based on the content strand. For instance, Carlos could be a great geometrical thinker and yet not have much fact power. So Carlos would be in the novice group for fact power but perhaps in the expert group during the geometry unit. This is why ongoing assessments are essential to the effective implementation of Guided Math Groups

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