Tips Archive » Content » Math

• Math Manipulatives (14 tips)
• Simulations & Stimulations (12 tips)
• Shortcuts (4 tips)
• Real Life Math (1 tips)
• Miscellaneous (4 tips)

Math Manipulatives

Transparent Protractors

From Sue Kast, a fifth grade teacher at Vintage Hills in Pleasanton, California:

"Each year before I start my geometry unit I run off a class set of protractors made on transparencies. I lay the protractors right on the glass of the Xerox machine and copy them onto the transparency film. I can usually fit seven on a page. I cut them out and give them to my class. This way everyone has one and if it is lost, it can easily be replaced. They are small enough to be used to take measurements right in their books and since they're transparent, they are much easier to read."

Memorizing Math Facts

From Susan Hopkins, a second grade teacher at Piru School in Piru, California:

"I've finally hit on a system that works for helping my students memorize math facts. I give each student a manila envelope and once a week we go over a set of ten to twelve math facts. I cut scratch paper into small pieces, the students copy the facts and put the answers on the back. For a few days, I give them a five-minute time slot to study. Then I go around and have students who think they're ready, tell me the answers. I mark the ones they know by heart with a mini stamper marker. That child then staples the marked cards together to take home and returns the others to the envelope. The students that know all the facts can then go around the room checking and marking other students' cards. This system allows us to keep adding harder problems and not have an avalanche of small pieces of paper falling all over the place."

EGG-citing EGG MATH

From Mary Alice Shackelford, a kindergarten teacher at Lake Placid Elementary, Lake Placid, Florida:

"I use the opportunity of spring to utilize colored plastic eggs in math for several days. Using egg cartons cut to make 'tens frames,' we estimate, count, tally, sort, classify by color and size (some eggs have smaller eggs inside), and calculate money (pennies, nickels, and dimes). We extend the activity by using grocery sale ads from newspapers to read how many cents items cost. We even become smart shoppers by determining which store has eggs on sale for the best price. We culminate the egg unit with an egg hunt. Each child has to tally total number of eggs found and they earn prizes from the treasure box based on accuracy."

Shape Boxes

From Karen Kinyon, a second grade teacher at Franklin Elementary in Manitowoc, Wisconsin:

"I ask my students to save empty laundry boxes. I especially like the ones with handles. I send the boxes home with white butcher paper to be wrapped. The students and the parents wrap them so that the lid may still be opened and shut. When they're returned, I place a geometrical solid into each box and ask the children to take them home and look for things that have this same shape. They bring the objects back for everyone to observe. We discuss the shapes and the mathematical terms that are assigned to each object."

Bean Bag Count

From Verlee Henry, a language arts and math teacher at Middle Township Elementary in Cape May Court House, New Jersey:

"I use a bean bag for my students to throw and catch as they count. It's also useful when counting by 2's, 5's and 10's. The beanbags keep the students' interest and make learning fun. This is also good for problem solving because if they drop the bag, they have to start over. Pretty soon they figure out that they should toss it to the person closest to them. It's fun to see them figure out these everyday problems on their own."

Constructing Geometrical Forms

From Joe Cooley, a geometry teacher at Trenton Central High School:

"For an engaging and dramatic geometry unit, my students construct large models out of tightly rolled newspaper struts. The struts must be clipped at the ends where there are weakest and it's best to use full format newspapers and roll them tightly from corner to corner. I use masking tape to make the connections. I've been able to construct tetrahedral prisms and 3-D Sierpinsky prisms up to eight feet high. Making measurements of height, slant height and base area is a challenging and interesting problem that makes the study of surface area and volume more of an active concrete exercise."

Subtracting on a Measuring Tape

From Sharon La Fee, a second grade teacher at Woodland Elementary School in Flint, Michigan:

"I have used many different manipulatives to teach addition and subtraction but this year I came across a really clear way to teach subtraction after just completing a unit on addition. Give each child a measuring tape and use the side of the tape with inches. Have them put their thumb on the first number, such as 12. Then have the students move their other thumb toward zero. They should move the number of inches that they are supposed to take away. This seems to stick with them a little longer than moving blocks, beads or other manipulatives. I think it is because it is one step away - but not so far away - from the concrete."

Rounding Up with Meter Sticks

From Karen Morrill, a third grade teacherthi at Mt. Ranier Elementary School in Mt. Ranier, Maryland:

"This week I was trying to help my students understand rounding to the nearest ten. I noticed they kept looking up to the number line I have on the wall. Then I got the idea to give each pair of students a meter stick at their desk. It really worked well. One would find the number and the other would see which ten was closest. On the meter stick the numbers 10, 20, 30, etc. are larger and darker. We even used it for rounding to the nearest hundred by adding a zero to each number. The only trick is the need for lots of meter sticks."

Teaching 1,000

From Stella Bock, an elementary teacher from Orange Avenue School, Cranford, New Jersey:

"When trying to teach my children the concept of 1,000, I tried to think of an item I could collect 1,000 of that would be cheap and practical, as well as renewable. I came up with the idea of collecting the plastic tabs from bread and English muffin wrappers. I also save caps from my milk and juice bottles. They're free, don't take up much space, and can be used over and over again. Just put out the word to your parents, and you'll get dozens. I still have parents from years ago periodically dropping off caps and bread tabs. All of my students have their own zip lock bags of counters for place value lessons, multiplication and division, and loads of other uses. You can also assign each color cap a money value and use those in your money lessons."

Counting Coins

From Sandy Bockhorst, a second grade teacher in Vista, California:

"I teach my students to count coins by counting coins to equal the number of days left in school. I then adapt to ask them the largest number of coins to equal that number as well as the smallest number. We are a year round school and right now are starting our second block. The kids really seem to be grasping and counting change. Next we will have to go shopping!"

Math Bath

From Sharon L. Morgan, a second grade teacher at South Penn Elementary School in Cumberland, Maryland:

"Each year during our study of liquid measurement I encourage parents to obtain plastic measuring cups, spoons, and containers for their children to practice measuring. The children respond to this homework because we call it 'Math Bath.' In their assignment notebooks each night we write 'take a bath' in the math block. The children are to take their plastic containers to the bathtub and practice measuring (ex: How many teaspoons are in a cup?) The children love to surprise their parents with the silly assignment and they really do practice their measuring skills!"

Place Value with Playing Cards

From Eric A. Yerington, a substitute teacher in Muscatine, Iowa:

"When I did my student teaching I used a game to help students with place value. It's easy to make and play. Simply get enough decks of cards so that each child can have 3 or 4 cards (depending on whether you want to study to 100s or 1000s). Take out the jacks, queens, and kings.Then make gameboards containing spaces for 4 or 5 cards. Label one space 'Toss Out.' After giving each child a gameboard and the cards, the teacher signals for the students to turn over one card. The objective is to create the largest (or smallest) number possible. They place the first card on a space. Once placed it cannot be moved. When all cards are placed, we see which student has the highest (or smallest) number. (The toss-out space does not count.) You can also do other activites such as finding the difference between the highest and lowest numbers, etc. I used this in fourth grade and the children always wanted to play."

Using Old Calendars, Part I

From Eileen Durgin-Clinchard, a retired teacher, now an adult educator from Omaha, Nebraska:

"When I taught first grade, I used outdated calendars that had big numbers to have the children cut the numbers apart (practice with scissors). Then I shuffled the numbers and had the students paste them down again in their own number lines (to ten or 20 or 30). Or they could paste them in a column and find same number of some object to paste beside each number. Or they could draw objects belonging to the same category (two pets, three dishes, four different kinds of balls, etc.) Or they could paste the numbers on three by five cards with a card with the same number of objects drawn on it. They take their 'decks' home to teach the game 'Concentration' to their families. This way each child has their own deck of cards as well as a way to involve parents in reinforcing number concepts and recognition. You can do several variations on this using catalogues and phonics activities."

Using Old Calendars, Part II

From Eileen Durgin-Clinchard, a retired teacher, now an adult educator from Omaha, Nebraska:

"To teach problem solving when learning about calendars, I used outdated calendars. I asked students to cut the calendars apart and cut the names of the months off, so they were left with separate sheets of one month each with no name. Working in groups, students' task was to construct a calendar for the new year using the old months, correctly re-naming them. When they finished, each group reported out, answering these questions:

1. What problems did they run into?
2. Did they think about these in advance or did they discover them as they went along?
3. Were they able to complete the task using one previous year or did they need more?
4. What other challenges can they think of about constructing a calendar?
5. How would they make a universal calendar, good for any year?"

Simulations & Stimulations

Beat That Time

From Stella Bock, a third grade teacher from Orange Avenue School in Cranford, New Jersey:

"When teaching multiplication tables, I print out flashcards from http://www.multiplication.com and give each child a copy to put in a Ziploc bag. The students take daily timed tests, starting with 30 facts and work their way up to tests of 100 facts. The students must pass each test twice before going on to the next level. This way each child is working at his own level and speed. They have 5 1/2 minutes to complete each test. As tables are memorized, the children drop that flashcard into a bucket and concentrate on the ones left in their bag. We make up jingles and memory aids for some of the more difficult ones. When 75% of the class can complete 100 facts in 5 ? minutes, we have an ice cream party. They are always encouraged to compete with themselves, beating their previous time or finishing a test."

Real Life Math

From Stella Bock, a third grade teacher from Orange Avenue School in Cranford, New Jersey:

"I have a math activity that I just started and it's been very successful so far. I recently had to purchase a major appliance, so I did some comparison-shopping. I talked to my class about this, and when I finally did make the purchase, I told them what I saved. I started thinking about all the real life examples of how we use math every day, so we've started a regular part of our math lesson called 'Real Life Math'. I tell my children how I used math during the previous 24 hours, and they volunteer ways they've used math too. We chart the results and we've gone through 2 pages of chart paper already! They actually remind me to ask them when I forget. One day they helped me figure out what I saved by catching a mistake on my shopping receipt. I feel it's very important for children to see a practical application of what they learn in school, and this activity has been a winner!"

Story Problems

From John Pitrelli, a fourth grade teacher at Perry Elementary School in Perry, Ohio:

"Here's a math enrichment tip. Each month my students write an original multiple step problem-solving question using a theme. For example, in October they can make up a problem about Halloween. The students submit their story problems without the answers written on them. They type them and can add a graphic if they like. Toward the end of the month I collect the problems and make a booklet for each child. On the last day of the month, I give them the booklets and ask them to solve their classmates' problems. After solving, they go to the author to see if the answer is correct. Both my kids and their parents love this enrichment project."

City Math

From Karen Isola Green, a 6th grade teacher at Spring Creek Middle School in Spring Creek, NV:

"While studying geometry, my kids create a city on four tables at the rear of my classroom. Some students are assigned the responsibility of creating the natural features like lakes, hills, and rivers by placing construction paper where they are located. Others design roads, bridges, and consider the use of other modes of transportation. Some work on the development of the business areas, while still others design needed municipal services, recreational areas, and housing. At home, the students create a 3-D building or facility to place in the town. After the city has been created, I ask my students to provide a written mathematical description of the building they designed. They are expected to use geometric descriptions using area, perimeter, volume, angles, measurements of distances, etc. The kids have very interesting discussions about placement of the buildings, modes of transportation and how they impact development, and other issues cities grapple with as they develop. My students voted this their favorite activity of the year. The cross-curricular connections with this are numerous."

Bingo Math

From Anonymous, a second through fourth grade special education teacher at Regional Day School in Atco, New Jersey:

"I give all my students a bingo card. I call out an addition or subtraction problem and if the students have that answer, they mark the number on their card. The first student to get bingo wins. This can also be a multiplication or division skill lesson as well."

Counting Combinatorics

From Todd Braun, a math teacher at Wisconsin Dells High School in Wisconsin Dells, Wisconsin:

In a mathematics course that I teach, there is an advanced unit in counting combinatorics. As a cooperative assessment, I give the kids the odds against being dealt all possible five-card hands in a game of poker. Their job is to prove those odds complete with a detailed explanation. I do this in groups of three and the discussions that lead them to their solutions are very interesting. This activity usually takes the students three fifty-minute class periods but the students really enjoy the challenge. It has been a rewarding experience."

Pokemath

From Joyce King, a third grade master teacher at May Elementary in Las Vegas, Nevada:

"To get one of my students interested in math, I had him bring his Pokemon cards to school and write math word problems using the characters and information. After writing the problems, which also included an additional ABC order section and draw your favorite character, I typed them and made copies for all my students to complete as a homework assignment. The student that made up the problems checked the papers and returned them to the class. This student is ready to do more and has loads of volunteers eager to assist. Email me if you'd like a copy of the worksheet."

Positive and Negative Numbers

From Susan Parramore, a University School Associate Professor at Florida A&M University Developmental Research School in Tallahassee, Florida:

"Teaching operations with positive and negative numbers is a difficult activity in math. I use a card game to help my students grasp the concept. I draw two cards at random and hold one up on each side of my face. Red cards are negative and black cards are positive. Tens and face cards are worth ten, aces are one, jokers are zero and all others are at face value. I call out addition, subtraction, multiplication or division and remind the students to go from left to right as they read. They must write the equation and answer while I count quietly to five. The students have very lively discussions over their responses because they must justify their answers. Often the problems lend themselves to good explanation."

Floor Circles

From Pam Luckenbaugh, a sixth grade math teacher at Herbert Hoover Middle School in Edison, New Jersey:

"When teaching parts of a circle, pi, area and circumference, I use a tool we all have readily available?the floor! I use washable overhead markers and draw a large circle, which covers about 1/3 of my floor. I tape a piece of string to the center of the floor and tie the marker to the other end, which works as a compass to make a perfect circle. I draw the diameter, a radius and a chord. My students 'walk' each part as we define them. To understand pi, the students walk the diameter and the circumference or the circle. Then we count their steps. Once we display the data on a chart, it's easy to see that the walk around the circle took about three times as many steps as the walk across the circle. I find that kids don't forget what pi means, since they literally walked it!"

Calendar Math

From Clare Delano, a fourth grade teacher:

"At the beginning of each month I cut out shapes according to the season or the holiday. Every day we write a number on a shape and place it on the wall around the perimeter of the room. We count each day of school this way. To add a little math to the beginning of the day, we do some quick calculating. For example, 'How many days has it been since day 100, How many days until the end of school, What is 23 + 123, What is 23 x 123, What is divided by 23?' In some instances, the level of multiplication or division has not been taught. Regardless, I put the problem on the board and we work it through. Now, having reached long division, several students know it already just by doing our daily math."

Place Value Town

From Donna Berry, a second and third grade Title 1 teacher at Mabel Wilson School in Cumberland Center, Maine:

"I developed a mat to help my students finally understand place value. I created a city block called Place Value Town. Reading Road, at the top of the mat, is a one way street from left to right. The street at the bottom of the mat is Placement Parkway, a one way street from right to left. Two cross streets are Comma Cut on the left of the block and Decimal Drive on the right of the block. There are three houses on this block called H, T and O for hundreds, tens and ones. There is also one house on the other side of Comma Cut called TH for thousands. This visual helps my students see that a number is read only one way but the numbers are placed in reverse order. This established the place. The value referred to the number of people who live in the house. For example, 105 means that one person lives in house H, five people live in house O but, just because no one lives in house T doesn't mean the house isn't there. The house on the next block, TH, is there so they can begin to understand higher numbers as well. I gloss over the decimal point by talking about the decimal point in money. This satisfies them as well as prepares them for future math."

Playing the Stock Market

From Steve Jantz, a seventh and eighth grade teacher in Wilbur School District, Wilbur, Washington:

"In our classes we are having a friendly competition using the stock market. Using the web site 'E-trade' students invest approximately $30,000 in several types of stocks. Each day we check their market action and buy or sell at least three times a week. In our math class we discuss the importance of percents, fractions, decimals and other areas of math and how they relate to the market. I have found students to be highly motivated with this lesson, mainly because it is dealing with money and class competition."

Shortcuts

Tricky Twelves

From Karen Evans, a fifth grade teacher in Old Saybrook, Connecticut:

"A student taught me the 12's trick a few years ago when multiplying numbers two through nine by twelve."

Here it is: 12 x 2 = 22 + 2 = 24
12 x 3 = 33 + 3 = 36
12 x 4 = 44 + 4 = 48
12 x 5 = 55 + 5 = 60
12 x 6 = 66 + 6 = 72
12 x 7 = 77 + 7 = 84
12 x 8 = 88 + 8 = 96
12 x 9 = 99 + 9 = 108

McDonalds Division

From Cassandra Hamilton, a Title I math teacher at Tyler Elementary School in Hampton, Virginia:

"When teaching long division, I use the DMSCBS acronym. The sentence we use is: Does McDonalds Sell Cheeseburgers & Shakes?

D-Decide Where to Place (The first digit goes in the quotient and then divide.)
M-Multiply
S-Subtract
C-Compare
B-Bring Down
S-Start Over Again

I make a chart showing a hamburger with all the fixings to represent the steps."

Memorizing Multiplication Facts

From Jay Edwards, a resource specialist at Hemet Elementary School in Hemet, California:

"I write out the multiplication facts (0x0 to 12x12) on the chalkboards; that's 169 problems in all! Then I tell my students to copy them all down and that for homework they'll be tested on those facts shortly. You can imagine the complaints! I remind them that math is filled with patterns and ask them if they can discover any patterns in the multiplication problems. Pretty quickly, someone spots that any number times zero equals zero. I erase 25 problems from the board and we're off and running! They quickly teach themselves the rules for multiplying by ones, twos, fives, tens, and most of the elevens. Someone notices that 3x4 is the same as 4x3 and that there are others like that, so the remaining duplicates are eliminated. What we have left are a paltry 23 multiplication problems that they have to write down and learn (far less than the 169 we started with). We practice a few each week, knowing that distributed practice is how students learn their facts, and within a couple of months, all of the second graders know their multiplication facts through the twelves!"

Families and Long Division

From Laraine Reisner, a 4th grade teacher in Los Angeles, California:

"When I teach long division I have the children write DMSCB on the top of their papers. I tell them it stands for Daddy, Mommy, Sister, Cousin, and Brother. In reality they learn it stands for divide, multiply, subtract, compare, and bring down. I have found this is a tremendous help to students who forget the proper order of division. I also always refer to it when I am doing a directed lesson. To bring humor to the lesson I will sometimes refer to the family name. 'You forgot the Mommy.' Children really appreciate having this little learning trick!"

Real Life Math

Teaching Life Skills

From Anna Campagna, a special needs teacher at Perry High School in Perry, Ohio:

"I instruct students in linear measurement by creating a biscuit quilt. The students are first introduced to the ruler and how to measure to the inch. Upon mastery, they are given the directions for making their quilts. Now the fun begins! They have to read directions, figure out amounts of fabric, make a list of all the items needed, prepare a budget, and plan a trip to the fabric store. Careful thought must go into the selection of fabric, as they have to coordinate at least three designs. Precise measurement is critical, as they need to create a template for each square and figure out how to correctly measure the boarders. They have no directions. All they have are their measuring skills and the knowledge gained based on the experience of making the quilt. It's fun watching them account for seams and boarders! During the quilting process, the students learn important life skills such as following instructions, planning, cooperation, patience and many others. After the quilts are finished, they challenge themselves further by creating pillows with the left over fabric. Many students give their quilts and pillows to their mothers for Mother's Day. Feel free to email me for the directions."

Miscellaneous

Protecting Worksheets

From Darlene Roker, a fifth grade teacher at Vermont Avenue Elementary in Los Angeles, California:

"I like to use math worksheets in directed class lessons by having students answer the questions/problems on another paper, and then give out the same worksheet as independent homework. The trouble is that students sometimes forget my admonition and write directly on the worksheet while we're in class. Now I place each worksheet in an inexpensive sheet protector while in class. For homework, I just hand them the uncovered worksheet that's neat and not written on!"

Permanent Graphing Grids

From Carol Jacobs, a primary special education teacher in East Ramapo School District:

"For permanent graphing grids, I laminate a grid chart and use it as a whiteboard would be used. I just wash it off under the faucet when I'm finished."

Geometry Through Poetry

From Michael Szewczyk, a fourth grade teacher at Berkeley Terrace School in Irvington, New Jersey:

"I work at having my students recognize and appreciate contrast. Teaching geometry through poetry? Yes, it works, it reinforces concepts, and it's fun. Here's an example of one I personally penned."

Symmetry

Symmetry, hey symmetry,
find the line that divides
the reflective beauty
in both you and me.

We each have a side left.
We each have a side right.
We use symmetrical eyes
to give us clearer sight.

We stroll with symmetrical legs
that stand on either side
Or help us pedal bike pedals
when we choose to ride.

We are blessed with a left hand
and one that's symmetrical right
that keeps us balanced at the desk
when we're asked to write.

Now our nose is in the middle,
smack dab on symmetry,
but it has two holy nostrils
for blowing after a sneeze.

Sweet symmetry gives form to me.
I can run a straight line in track,
but ours is between side to side
and not measured front to back.

Symmetry, hey symmetry,
find the line that divides
the reflective beauty
in both you and me.

---

Odds and Evens

From Bev Goodwin, a second grade teacher at Northside School in Elizabeth City, North Carolina:

"I teach even and odd and have less confusion with this technique. On even dates on the calendar the girls go first and on odd dates the boys go first."

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Math Songs

From a high school special education math teacher in Columbus, Georgia:

"I was tutoring a student, and I came up with a song to help her remember how to handle integer operations. I had found such a song for addition/subtraction on the Internet. We made up one for multiplication/division. It is sung to the tune of "Brother John, Are You Sleeping?"

Multiplying and dividing,
Use same sign, use same sign.
You will get a positive,
You will get a positive,
And you'll be fine, you'll be fine.

"In case you have not seen the addition/subtraction song, it is sung to the tune of "Row, Row, Row Your Boat."

Same sign, add and keep.
Different sign, subtract.
Take the sign of the higher number,
Then it'll be exact.

"I am planning to use these songs with my Pre-Algebra students as we begin to learn how to handle integers. We will also do hands-on work and will walk the "line" on the floor. But we will also sing every day, until they can sing this song in their sleep. Remembering how to handle integer operations is the place where my students falter, and often fall down."