## Using Unifix Cubes in Guided Math Groups

Unifix cubes are ubiquitous in U.S. classrooms. They can be used for a variety of math concepts, including number sense, algebra, geometry, measurement and data and probability. The following activities can be done in small guided math groups. Small guided math groups give you the opportunity to talk with the students and it gives them the opportunity to talk with you. As teachers, we want to ask targeted questions and listen for the answers. During the conversation we want the students to connect with each other and talk math. We want them to use the manipulatives to prove, to represent, to justify and to explain their thinking. Manipulatives should provide a springboard into deeper content conversations.

*Numbersense*

Unifix cubes can be used to explore **equivalent names** http://www.maththeirway.com/BLACKLINES/001-061/028-032.pdf

http://www.hubbardscupboard.org/Unifix_Cube_Sheets.PDF

They also make great manipulatives to use to tell addition and subtraction stories using different story mats. They also are great for just practicing basic facts. Here is a counting video http://www.uwosh.edu/facstaff/video/mindsongmath/videos/base-10-1-2nd-grade-working-with-unifix-cubes

Here is a counting assessment using unifix cubes http://www.beaconlearningcenter.com/Documents/2967_02.pdf

Also look on uen.org and look under lesson plans…type in unifix cube fact family template.

Have students to take cups and handfuls of unifix cubes and first **estimate **and then actually count the total http://www.sde.ct.gov/sde/lib/sde/Word_Docs/curriculum/mathgoal/Book_Grades_3-5/Chapter_9_Word_Problem_Estimation_References/Teacher_Guide.doc

You can use them to **illustrate even and odd numbers**.

You can also use them to **represent fractions**.

*Algebra: Patterns*

Unifix cubes are great for **sorting.** Have cupfuls and bagfuls and have the children sort them by color. Scroll down and look at Video 7 http://www.learner.org/resources/series32.html

Unifix cubes can be used to explore patterns. Jmeacham has great pattern mats already made. Remember to teach students how to make growing patterns as well. Have students to copy, match, create, extend and name unifix patterns. http://www.jmeacham.com/docs/math.centers/unifix%20patterns%20AABB.pdf

http://www.jmeacham.com/docs/math.centers/unifix%20patterns%20AB.pdf

http://www.jmeacham.com/docs/math.centers/unifix%20patterns%20ABC.pdf

http://standards.nctm.org/document/eexamples/chap4/4.1/index.htm#applet

http://prekinders.com/math-patterns/ (click on picture of unifix cubes)

You can also use them to **represent comparison** stories.

*Geometry*

Have students explore** area** and **perimeter** with unifix cubes on inch grid paper.

(scroll down to picture about teaching area) http://www.kindergarten-lessons.com/teaching-measurement.html

http://www.edb.utexas.edu/faculty/wstroup/Gen_Act_Web/I03/zga03.html

*Measurement*

Have the students practice basic measurement activities with the cubes. Also have the students to estimate how many cubes long something is before they actually measure it out. They can explore length and height. http://www.beaconlearningcenter.com/documents/4459_3981.pdf

*Statistics*

Have the students to grab cupfuls of unifix cubes and then to graph the contents. Have them to make frequency tables, tally graphs, pictographs as well as bar graphs.

*Probability*

Fill different containers with different amounts of different colors. Then discuss the probability of choosing particular colors. Also play games where someone pulls a certain amount of cubes from a bag, recording the colors and then based on that data guesses the probability of pulling out certain other colors.

**Virtual Unifix Cubes**

http://ssrsbstaff.ednet.ns.ca/jrenouf/virtualmanipulatives.htm

**Just for fun:**

A history of the Unifix Cube: http://www.didax.com/newsletter/archive.cfm/NewsletterID/15.cfm

(An article with really great ideas)http://www.mylinkstolearning.com/nctm.htm

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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## 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

http://www.youtube.com/watch?v=Y0m3SxaQVI8

http://www.youtube.com/watch?v=fkPhj48qlpg&feature=related

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/

http://math.about.com/library/Worksheets/Countingby5e.pdf

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## Math Picture Book of the Day: One Red Dot

This book by David A. Carter is great for teaching Plus 1 facts. It is this fantastic pop-up book, that counts all these amazing things that pop off the pages, plus one red dot. We follow up with a 3 level lesson.

Concrete level: Students roll the dice and count out the unifix cubes and build a tower. They then add 1 red unifix cube.

Pictorial level: Students then draw a picture of their tower.

Abstract level: Students add the number sentence.

Follow- Up: Get red dots from Staples. Students roll the dice and then draw that many squares. Then they add one red dot. We also make our individual and class versions of One Red Dot.

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