Archive for July, 2010
It is really important when we are teaching odd and even numbers that we spend some time developing the concept. Oftentimes we teach it as this abstract concept when students must have multiple opportunities to build their knowledge base. Here are a few ideas of how to do that in guided math groups.
I use this template to have students build conceptual understanding about odd and even numbers odd-or-eventtemplate1.
Step 1: Roll dice and record number. Step 2: Build a picture with mosiacs, toothpicks, stickers or some other type of manipulative. Step 3: Group in twos and decide if it is odd or even.
Pictorial And Abstract Level
After students have explored odd and even numbers, next I want them to have more opportunities using drawing as a way to prove whether a number is odd or even and then opportunities to explain their reasoning. I use this template Odd or Eventtemplate2final.
Step 1: Roll dice and record number. Step 2: Build a picture. Step 3: Group and decide if it is odd or even. Step 4: Explain why.
Here is a traditional way that students practice odd and even numbers. They color them on the number grid. However, remember this is an abstract way to practice identifying the actual numerals. Students need to understand the concept first:) Circle all the odd numbers in blue
Adding Odd and Even Numbers
After students understand what odd and even numbers are, the next step is to teach the properties of adding odd and even numbers. Again this should be done through experiences that build understanding. Students should be allowed the opportunity to explore the concept by actually adding odd and even numbers and thinking about the results. Here is a template that helps them to do that Odd or Eventemplate3final
Great Websites with Games and Activity Sheets
Some great books to use when teaching about odd and even numbers:Read Full Post | Make a Comment ( None so far )
Children should practice skip counting in a variety of ways. Here are some center ideas based on Gardner’s (1983;1993) theory of Multiple Intelligences.
1. Linguistic– Make a book center where they read and write skip counting stories.
2. Logical Mathematical– (NCTM Story) (Skip counting cards); Also filling in number lines and number grids on sheets or at the computer and dot to dots:
3. Visual/Spatial– Number Collages/ Dot Paint
Several Powerpoints: http://math.pppst.com/skipcounting.html
4. Musical– Chants and Song- Skip Counting Song
5. Interpersonal activities: Have students play skip counting games in partners or groups.
A. Skip counting card shuffle
B. Skip counting chart color in pages
C. Computer skip counting games (listed above and here)
6. Intrapersonal activities
Be sure to give your students the opportunity to practice these activities by themselves.
7. Bodily-Kinesthetic Activities:
A. Centers where they build the skip counting sequence with bears and snap cubes. One center I use is toothpicks for skip counting by tallies. I read the book Tally O’Malley and then I have the students roll or pull a number and then show that number with toothpicks. In the whole group we make a human tally by generating a number and then having the students come up and stand in a row, with each 5th student making a diagonal with their arms across the other 4. I differentiate the number generators by readiness levels. I also do this same center by having the students roll and draw out the tallies. We go from concrete to pictorial to abstract. The abstract is where they are actually naming the number.
B. I put out counting bags with instructions.
Task Card: The lollipop factory is bagging candies. Here is the box of candies. Put 5 in each bag and then skip count to find out how many bags of lollipops they can make from this box. I also give the students bags of toothpicks and say tell me how many are in this bag but skip count it out by making bundles of ten. I differentiate the amount that is in each bag.
C. I put out playdoh and tell the children they are in a bakery. They can make cakes or cookies and then skip count how many “raisons” or “beans” or “candles” are on top of each item.
This center is a chance where students get to look around the room and in magazines and books for things to practice skip counting. I also have the students counting nickels and dimes in this center because it is part of our everyday environment. They use the number grid as an abstract scaffold for this activity.
Gardner, Howard (1983; 1993) Frames of Mind: The theory of multiple intelligences, New York: Basic Books. The second edition was published in Britain by Fontana Press.
Great Multiple Intelligence Resources:Read Full Post | Make a Comment ( None so far )
Calendar Math is really important. Calendar Math can help to reinforce those everyday skills that students need to work on throughout the year. You can do calendar math in a whole group and differentiate the instruction by having the students to have individual calendar folders where they do varying levels of work. I would also look at these folders with students during individual conferences sometimes, just to do a check in about their understandings. You most certainly could pull small groups every so often to do some calendar binder work with them. Here are four featured sites with calendar math ideas.
1. J Meacham has some wonderful ideas. See http://www.jmeacham.com/calendar/calendar.htm. Be sure to look at the individual binder examples because she has posted the templates in both word and pdf documents http://www.jmeacham.com/calendar/calendar.binder.htm. In terms of differentiation, I give some children 2 or 3 pages in their binder whereas I give other students 4 or 5 pages, depending on their readiness level. Be sure to label all the parts of any graphs you do.
2. Scholastic has a great ideas page http://teacher.scholastic.com/fieldtrp/k2/calendar.htm. One of the best ideas is to visit http://richardphillips.org.uk/number/ and to click on the number of the calendar day and you get tons of information about that number. Very cool!
3. Math Their Way has terrific calendar ideas http://www.center.edu/pub/docs/Chapter4.pdf. Again remember to be clear and precise about the different types of graphs you are doing. If it is a pictograph, be sure to have a symbol. Often times we graph the object such as a dog, cat, or bird. But on most state exams, the pictograph has one symbol that the students use for all the votes, for example a smiley face. Furthermore, on the bar graph remember to label both axes, not just the categories and the numbers. You have to give the categories and the numbers names such as Types of Pets and Number of Votes. Also be sure to put titles on your graphs. Then have the students make noticings about the graphs and put those on bubbles around the graphs. This is a great way to reinforce vocabulary.
4.Incredible stuff here at Mathwire http://www.mathwire.com./routines/morning.html. This morning routines page has great pictures http://www.mathwire.com./routines/photos.html . Be sure to look at the coins for the date display because this will reinforce money concepts. I always have the students draw two ways to make the money in their journal starting at the middle of first grade.
GREAT Smartboard Activity: http://www.softschools.com/math/calendar/activities/calendar_game/
Great Commercial Program I’ve seen used quite effectively in some schools: http://www.greatsource.com/store/ProductCatalogController?cmd=Browse&subcmd=LoadDetail&division=G01&ID=1003600000006164&frontOrBack=&nextLevel=4&sortProductsBy=SEQ_TITLERead Full Post | Make a Comment ( 8 so far )
Dyscalculia is a math learning dis/ability. We don’t talk about it much here in the states, although awareness is growing. Dyscalculia is more than just having a little trouble with math. It is when a student is severely struggling to pick up concepts. Learning Disabilities Online describes it in the following way “Dyscalculia is a term referring to a wide range of life-long learning disabilities involving math. There is no single form of math disability, and difficulties vary from person to person and affect people differently in school and throughout life.” There are various interventions that help to scaffold the learning. I have listed some of the key sites that have information and interventions for specific aspects of dyscalculia. Guided Math groups are an excellent opportunity to work with students who have this dis/ability.
There is also a book called the Dyscalculia Toolkit.Read Full Post | Make a Comment ( 4 so far )
Here are some great websites with templates to use in guided math groups. Browse these pages for a variety of things from place value grid paper to woozle cards.
Featured link: Woozle cards (great for having students sort into attributes and justify their reasoning).
Featured link: More or less cards (Have the students pull a card with a number and then pull a more or less card and follow the instructions. This builds flexibility with adding and subtracting. Also the addition and subtraction recording blanks are a great visual for noting place value).
Featured links: More, Less, The Same Pictures ( Have two students roll the dice and build towers and then choose which card matches their scenario) and Two sided Number Bean Station Records (These are great for having students toss two-colored beans to find the equivalent names of numbers: just spray paint some beans if you don’t have the lakeshore or eai (great online teacher store) version); Names Numbered Squared (One game I play with these is t0 have the students pull a card and get a starter number…and then place it somewhere on the blank grid and build in a 100 grid from there. This builds great flexibility with adding and subtracting 1 and 10). Also the Unifix number station templates are great for having students build number towers or to find all the equivalent names of numbers.
Featured links: Add and Subtract cards: Builds flexibility with adding and subtracting (1. Have students pull a number card. 2. Have students pull an add or subtract card. 3. Have students roll a number and then add or subtract that number from original number.) Also look at the number match cards (dominos, numerals and tallies). Be sure to see the extensive number charts going up to 999!
Featured Links: The Adding 9 and 8 cards – an absolute must for building conceptual understanding through pictorial representation.
Summer Blackline Masters by Grade from Ceres Unified:
(You just have to browse through but their are some interesting templates;)Read Full Post | Make a Comment ( None so far )
Linguistic Intelligence – These are the students who get it through words. They like to hear it told to them. They understand through verbal explanations. Teaching with picture books and through songs, poems and chants helps them to learn. Also telling stories about the math and talking it through grabs and keeps their attention. In small group lessons you will be explaining and listening to these students “talk it out.” Here is a sample math workshop addressing the needs of the linguistic learners:
Mini-Lesson: Starts with a story, song, poem, chant; Math Think Alouds where the teacher makes the thinking process transparent;
Guided Math Group: Math think alouds; Sharing around the table; Each person explaining what they are doing; these students live for the individual math conferences because they get to talk about what they are doing and talk out their goals and talk out their challenges….
Math Centers: Provide opportunities for students to share their math with each other as they are learning
Share: There is an opportunity for these students to come up and share their thinking with the class. Play microphones (either the echo ones or the toy ones with a battery amp really engage these learners…they will come up and talk forever about the math)…
see the booklist in this blog
see conference protocols in this blogRead Full Post | Make a Comment ( 2 so far )
I saw some really great stuff today at ISTE (the International Society for Technology in Education). Some highlights:
www.educationcity.com – great website teaching subjects through cartoons…math stuff looks great…school site licenses are very affordable and they give free trials…
www.professorgarfield.org – Check out the Knowledge Box section….some math…all free…and site is expanding
www.cyberchase.com….pbs stuff for free and they said they are currently in development of much more math stuff
www.bizworld.org I also saw this great program by a nonprofit group that teaches math through having children create real businesses on campus…even 3-5th graders (bracelet and movie businesses)….they supply everything in a kit for $45….
http://mathworld.wolfram.com/ and http://www.wolframalpha.com/ …this is a good site to generate interesting numbers in real life… you enter a date, a name, anything and the numbers come up for that topicRead Full Post | Make a Comment ( None so far )