Archive for November, 2010
Throughout the month of November we have been discussing different mathematical manipulatives. I am going to start a series of posts on Base Ten Blocks. These are great mathematical manipulatives to use when working in small guided math groups. They are one of the most important manipulatives we have to teach place value, number sense, addition, subtraction, multiplication and division. Yet, they are very underutilized. These 3-dimensional blocks come in a variety of materials (plastic, wood, magnets) and colors. They are divided into cubes /units(one’s place) rods /longs(ten’s place) flats (hundred’s place) and blocks (thousand’s place).
I want to start by giving an example of the base ten centers that I set up for students in the primary grades when we are exploring representing numbers and their values. I will begin each lesson with a mini-lesson either using magnetic base ten blocks, overhead base ten blocks or an interactive base ten block game on the Smartboard. Then, I send the students to centers where they explore numbers.
I differentiate the centers by readiness- meaning I have students exploring different numbers. So for example, in the stamp center, the novices might have blocks through the hundreds and the apprentices and experts might have blocks through the thousands. I also use tic tac toe menus and dot cards during the place value unit (see http://daretodifferentiate.wikispaces.com/Choice+Boards and http://www.iu29.org/resources/Documents/ThinkDot.pdf ). Finally, after student activity time, I always end with a share where we make an entry in our class math journal about the math that we did for the day. We don’t just talk about what we did, but we talk about what the math was that we were practicing.
- Magnetic Base Ten Blocks – Partner A pull a card; Partner B show the representation on the white board with magnetic blocks
- Stamp Base Ten Blocks – Work as Individuals- Pull 2, 3 or 4 cards (depending on the group); Make the largest number possible and stamp it out; Then, make the smallest number possible and stamp it out
- Regular Base Ten Blocks – Pull a card (numbers are written in expanded form); Show the number
- Paper Base Ten Blocks – Roll a number (2, 3 or 4 digit based on group); Write the name, the number, the expanded form and show the number by gluing down the paper Base Ten Blocks.
- Base Ten Block Flashcard Set –This is a great set that I bought at Lakeshore. I like it because it has 4 representations of the number and you can give the experts all 4 cards to match up and the novices two. There is a picture, expanded form, standard form and word form. The students love to play this in groups. It is a cooperative game, where everybody is helping each other to find all the pairs.
- Computer Base Ten Block Game (various games)
- Draw out the number in Base Ten Block Representation (roll a number and represent it by drawing out the base ten blocks).
- Place Value Match Up Self Checking Puzzles (bought at Lakeshore)
Base Ten Block Mats:
Base Ten Block Paper
http://lrt.ednet.ns.ca/PD/BLM/table_of_contents.htm (scroll down to the base ten materials)
Be sure to look for the upcoming posts on using Base Ten Blocks!
Dr. NickiRead Full Post | Make a Comment ( 3 so far )
Geoboards are a great manipulative. They come in a square frame and a circle frame. You can either buy them or make your own. You use them with rubberbands/geobands. Always discuss the proper use of rubber bands and have consequences for folks who use them inappropriately. Be sure to give the students free exploration time before you give an assignment (as with any manipulative). Also be sure to have the students transfer designs back and forth between the actual geoboards (concrete level activities) and the dot paper geoboards (pictorial level activities). You can use geoboard to explore many different geometry concepts such as classify polygons, estimate and calculate the area and perimeter of a polygon, construct line segments and endpoints, draw congruent figures, explore angles and do coordinate grid work. Below I have listed a couple of great links to geoboard activities.
- Use your geoboard to make different shapes: polygon, quadrilateral, triangle, square, rectangle, pentagon, hexagon and an octagon.
- Use interactive geoboards to explore geometric shapes, describe their properties and develop spatial sense. http://standards.nctm.org/document/eexamples/chap4/4.2/
Exploring Symmetry and Congruence
Exploring Area and Perimeter
National Library of Virtual Manipulative Activities
(making 3-d shapes) http://nlvm.usu.edu/en/nav/frames_asid_129_g_1_t_3.html?open=activities
(circular geoboard grades 3-5) http://nlvm.usu.edu/en/nav/frames_asid_127_g_2_t_3.html?open=activities
(circular geoboard grades 6-8) http://nlvm.usu.edu/en/nav/frames_asid_284_g_3_t_3.html?open=activities
(coordinate grid activities 3-5)
(coordinate grid activities 6-8) http://nlvm.usu.edu/en/nav/frames_asid_303_g_3_t_3.html?open=activities
Many More Geoboard Activities
http://mathcentral.uregina.ca/RR/database/RR.09.98/loewen2.3.html (angles, perimeter and area)
*(Student Activity Sheet) http://www.mathinscience.info/public/cover_up/geoboard_activities.pdf
Blackline Masters of Geoboards
(circular geoboard) http://people.morehead-st.edu/fs/m.schack/circle_geo.pdf
(square geoboard) http://eclectichomeschool.org/pdf/10x10dot.pdf
(many paper geoboards) http://etc.usf.edu/clipart/galleries/math/geoboards.php
(scroll down to bottom of page to see picture of center) http://www.marcias-lesson-links.com/MathTubs.html
*(Teacher story of introducing geoboards) http://www2.scholastic.com/browse/article.jsp?id=3671
(an academic article) http://www.jstor.org/stable/30213962
*(a few ideas to make your own geoboard)
Dr. NickiRead Full Post | Make a Comment ( 5 so far )
Teddy Bear Math Counters have many uses including counting, operations, graphing, sorting, story telling, patterning, probability, fractions, ratio and estimation. Doing these types of lessons in guided math groups, allows the teachers to focus on each student. In these groups we have an unprecedented opportunity to talk with students and listen to them talk back! I can’t stress enough the idea of creating this space where students get to share their mathematical thinking. Below, I have listed some sites that have good tasks using teddy bear math counters.
Ten Frames and Teddy Bears: http://www.acoe.org/acoe/files/EdServices/Math/NumberRecTenFramesV2.pdf
Sorting: Scroll down for the Teddy Bear Sorting Organizers http://www.teachingheart.net/teddybear.html
For the word versions of these (so that you can simplify or complexify the patterns) go to this url and scroll down to pattern blocks (for some reason the bears are mislabeled) http://www.jmeacham.com/math/patterns.htm
Scroll down to the bottom of the page and print out the dot pattern cards and use them with the bears: http://prekinders.com/math-patterns/
Have the students write stories using the teddy bears to model what happened. http://www.abcteach.com/free/c/colorandwrite_teddybear_elem.pdf
Make up your own bingo by the different bear attributes…
Google ” Let The Probability Games Begin” for a great lesson on UEN.
Additional Resources:Read Full Post | Make a Comment ( 1 so far )
Number Tiles are a really great tool.
http://www.montessorimom.com/downloads/number_tiles.pdf (match the number tiles with the dot tiles below).
Great Dot Tiles:
Use for ordering numbers, adding and subitizing. http://www.montessorimom.com/downloads/quantity_tiles.pdf
Algebra Tiles (SUCH AN UNDERUTILIZED RESOURCE)
You can either make number tiles or buy them commercially. They come in foam, wood and plastic. They come as squares or rectangles. They also make overhead number tiles.
Dr. NickiRead Full Post | Make a Comment ( None so far )
We can use these 1″ plastic tiles in four colors to build models of math concepts, develop basic arithmetic skills and explore color and number patterns. Remember that in terms of a guided math lesson, you always want to think in terms of doing concrete activities, then pictorial activities and finally abstract activities. Spend time in small groups developing conceptual understanding as well as procedural fluency. We want our students to understand the math they are doing.
Here are some great general sites:
Exploring Prime and Composite Numbers
http://mapps.math.arizona.edu/sample_session.pdf (pages 15-24)
Addition and Subtraction of Integers
Also Google UEN lesson “Math 5 – Act. 29: Likely or Unlikely”
Google this UEN lesson as well- “How many ways can you represent a number”
Math Tile Video
Dr. NickiRead Full Post | Make a Comment ( 1 so far )
Ten frames are one of the top ten manipulatives that every elementary teacher should have! I have written before about this great tool, but here I am highlighting some instructional videos. Watch them for some fantastic ideas!
1. http://www.youtube.com/watch?v=p6RaMGDPfJg (good introductory video)
2. http://www.youtube.com/watch?v=h_xFBoSEyj8&feature=related (Look at these large ten frames! I like the size.)
3. http://www.youtube.com/watch?v=aQ0cpiD_dO4&feature=channel (Smartboard Lesson!)
4. http://www.youtube.com/watch?v=gZhsigFt-aA&feature=related (Teacher in action)
5. http://www.youtube.com/watch?v=vlrDL1qUdlA&feature=related (Missing Addend Lesson)
6. http://www.youtube.com/watch?v=XwPdVl7RpJk&feature=related (Kindergarten lesson using ten frames to compare numbers)
7. http://www.youtube.com/watch?v=OqUwc8yUsKg&feature=related (notice the use of two colors for the dots in these practice cards)
8. http://www.youtube.com/watch?v=FXMMfgiQ9RA&feature=related (notice the use of two colors for the dots in these practice cards)
9. http://www.eduplace.com/cgi-bin/schtemplate.cgi?template=/kids/mw/help/eh_popup.thtml&grade=2&chapter=2&lesson=5&title=Make+10+to+Add&tm=tmfc0205e (TEN FRAME VIDEO TO USE WITH STUDENTS)
10. http://www.youtube.com/watch?v=BRWSQFPvchc&feature=related (Look at these commercial ones, but you can just as well make your own student sets)
Here is a Ten Frame:
Be sure to see the other posts in this blog about ten frames. Do a search for ten frames, number bonds and fact families.
Dr. NickiRead Full Post | Make a Comment ( 3 so far )
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.
Unifix cubes can be used to explore equivalent names http://www.maththeirway.com/BLACKLINES/001-061/028-032.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.
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://prekinders.com/math-patterns/ (click on picture of unifix cubes)
You can also use them to represent comparison stories.
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
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
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.
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
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
Dr. NickiRead Full Post | Make a Comment ( 3 so far )
Two sided Counters! Everybody needs them. They are so great. You can use them to model all the operations. They are officially called Double Sided Math counters. They usually come as red on one side and either white or yellow on the other. You can also just make them by spray painting lima beans. You can also print out paper ones http://www.teachervision.fen.com/teaching-methods/printable/44640.html?detoured=1
5 Frames -Use them with 5 frames. Teach them in small groups with the actual frame and then move to the internet games. In the games on this site, you work on different strategies, such as counting, missing addend and adding with 5 as a landmark number. http://illuminations.nctm.org/activitydetail.aspx?id=74
10 Frames – Use them with 10 frames. Teach them in small groups with the actual frame and then move to the internet games. In the games on this site, you work on different strategies, such as counting, missing addend and adding with 10 as a landmark number. You also work on teaching the visual representation of using lucky 8 and lucky 9 otherwise known as compensation. Ten frames allow students to see what they are doing. http://illuminations.nctm.org/activitydetail.aspx?id=75
Addition -Students can use these counters to practice addition problems. Each color is a different addend. They model with the manipulatives. I also set up problems where they have to take an equation and build the model.
Equivalent Names – Students toss the beans and then color in the amounts on this Math Their Way bean template… http://www.center.edu/BLACKLINES/001-061/033-039.pdf. There are templates for equivalent names from 4-10. I have the students make equivalent name books. I also have the students to match different pictures with different equations. I also have them to use the mats to build the different equations.
Comparing– Students toss the counters and then compare the amounts of each color.
Patterning – Use the counters to make different patterns…abc, abab, abcd, ababbabbb, abc
Fractions– Have students toss the counters and then write the fractional part of each color. http://www.math-lesson-plans.com/support-files/day8fractionswithtwocolorcounters.pdf
Probability – Give the students one double-sided counter and have them flip the counter 10 times and record the colors. They discuss how many times it lands on each color and discuss the probability of each color coming up.
Two color counters come in plastic, in foam, as magnets, in circles, and in bean shapes.
Read Full Post | Make a Comment ( 5 so far )
Number lines are a great visual tool. There are many different types of numberlines that can provide a scaffold into deeper understanding. You want to use numberlines so that students have visual models and understanding of the relationships between numbers (see http://thinkmath.edc.org/index.php/Number_Line ). Numberlines provide visual scaffolds so students can picture what they are doing. Numberlines can be used to teach counting, skip counting, even and odd numbers, rounding, positive and negative integers, fractions, decimals and time. Here are a some links to a few good resources by category.
***(colorful, primary numberlines) http://www.sparklebox.co.uk/md/counting/lines.html
https://www.songsforteaching.com/math/kindergarten-firstgrade/addonemore.php (sing this song as students use a number line to figure out the answer)
(with negative values) http://www.helpingwithmath.com/printables/others/lin0301fraction02.htm
(intervals of 5 minutes) http://www.helpingwithmath.com/printables/others/lin0301number26.htm
(google: “wow how time flies” for a page to uen which has a pdf of an elapsed timeruler)
http://alex.state.al.us/lesson_view.php?id=26567 (scroll to bottom for word document of ruler)
(Make your own numberlines) http://themathworksheetsite.com/numline.html
(article about fraction numberlines) http://www.merga.net.au/documents/RP412008.pdf and http://www.cehd.umn.edu/rationalnumberproject/88_3.html and http://www.merga.net.au/documents/RP552007.pdf
Have fun! Write me and let me know how it’s going.
Dr. NickiRead Full Post | Make a Comment ( 2 so far )
This month we will be exploring different types of math manipulatives and how they help to build mathematical proficiency. We are going to start with Pattern Blocks. Pattern blocks are one of the most underutilized math manipulatives around. Pattern blocks are a wonderful math resource for the classroom. They come in 6 colors and shapes – yellow hexagons, green triangles, blue diamond shaped rhombus, red trapezoids, orange squares and a smaller beige rhombus. We tend to use them in the primary grades for patterning and then in the upper grades for a bit of fraction work.
In the primary grades we can use them to sort, pattern, to explore transformations, symmetry and congruency as well as compose and decompose shapes. In the upper grades we can use them to explore, add & subtract fractions as well as do angle work. You can use pattern blocks to teach number sense (counting, fractions, estimation), statistics (graphing) and probability, as well as geometry and algebra.
In this post I am going to talk about and list some great resources to take Pattern Blocks to the next level.
REALLY COOL STUFF! Let’s start with something super fun! Math and Music. Check out this cool Pattern Block Rock site: http://www.philtulga.com/patternblock.html
Pattern Blocks: Pattern Activities
Great primary patterning cards. The links are mislabeled so click bears to get pattern blocks. The great thing about the workmats on this site is that they come in word so that you can simplify or complexify them as needed: http://www.jmeacham.com/math/patterns.htm
Pattern Block Puzzles:
(scroll down to Pattern Block Pictures) http://www.kellyskindergarten.com/math/math_activities.htm
Pattern Blocks: Talking about shapes
Great Annenberg Lesson Plans (Be sure to click through entire sequence of lessons!) http://www.learner.org/courses/teachingmath/gradesk_2/session_02/section_01_b.html
Pattern Blocks: Talking about Symmetry
Pattern Blocks: Fraction Activities
Great pattern block fraction activities. Really creative work mats and rigorous thinking activities. Scroll down and print out the work maths: http://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/years7_10/teaching/frac.htm
Pattern Blocks: Angles
Printable Paper Pattern Blocks: Remember we want to move from the concrete to the pictorial and then the abstract. The paper pattern blocks provide an opportunity to work at the pictorial level. You can use these at any grade level.
Primary Pattern Block Activities:
Scroll down to the bottom of the page for some great game ideas: http://www.kindergarten-lessons.com/kindergarten-pattern-activities.html
Some Cool Pattern Supplies. I use these to make different types of centers.
I have pattern block stamps, stickers, giant floor size pattern blocks, foam ones, plastic ones, magnetic ones (regular size and gigantic ones), activity cards.