Constructing in the Math Center at Choice Time

In my combined first and second grade classes, children’s self-initiated learning took place during Choice Time. Much enthusiastic activities took place in the construction area of the Math Center. These concrete experiences serve as a background for gaining new insights and understandings – therefore, opportunities for increasing their cognitive development.

Materials supplied  for constructing were: 5 small paint buckets, each one ½  full of Cuisenaire Rods; 1 inch wooden colored cubes; dominoes; Base Ten Blocks; and Unifix Cubes.

Building all kinds of structures were most popular – buildings, towns, roadways, and towers, supplemented with various other materials such as 1 inch cubes, dominoes, pegboards, etc.

There were times when too many structures were knocked down because someone carelessly walked by. So there was an agreed upon class rule that excluded anyone from the math center for a few days if they knocked anything down – even if it was a complete accident. The number of days agreed upon varied with each class, but usually it was two or three days. No blame was attached, and it was amazing how carefully children walked through or by the buildings after that. From then on, there were few accidents.

Constructing allows opportunities for developing concepts necessary for good achievement in abstract math. A good math student is able to conserve, recognizing that two amounts are equal even though one is a different shape or size than another – that five Cuisenaire Rods or five rulers are five. Building in the math center, children constantly see various arrangements of numbers of objects.

It is also an opportunity for overcoming egocentrism. An egocentric child cannot see or understand another viewpoint. An aid to overcoming this is continually looking at all sides and angles of each structure built. Success in math requires a good mental image of numbers of objects in many different configurations including the various shapes, sizes, and dimensions of these objects.

Children must have concrete experiences before they can abstract. While children were constructing, they were constantly sorting and classifying while looking at balance, design, and structure. These were opportunities for developing seriation plus spatial and numerical relationships eventually leading to paper and pencil math, no longer needing objects.

Read more about the math program and the Math Center in my book, Early Childhood Programs: Opportunities for Academic, Cognitive, and Personal Success. Included is a web site where programs and activities can be downloaded for use in a classroom. Also, see 7 reviews on www.amazon.com

Beginning Readers’ Success

In my classroom, each successful beginning reader after being offered materials and guidance and support, in one way or another, taught herself to read. She may have participated fully in all parts of the program offered, or perhaps only in part of the designed program with special attention unique from anything offered. But she, and every beginning reader, made choices along the way, perhaps unaware of making those choices, but choices never-the-less about how she learned to read. She chose to use phonics or avoided them because innately, she knew a better way. It was always hoped that during and after learning how to read, these choices allowed her self-confidence to grow, leading to continued motivation, responsibility, and independence – that she knew the purposes for learning how to read and enjoyed many different books, stories, and articles.

Read more about programs for beginning reading in my book, Early Childhood Programs: Opportunities for Academic, Cognitive, and Personal Success, beginning on page 38.  Also, see 7 reviews on www.amazon.com

A Game for Learning Letters

A bingo-type game for learning the names of letters was very popular. There were boards 6” x 6” with nine squares, each containing a letter. There was a pile of cards, face down, each containing one letter. A child would pick up a card, say the name of the letter, and place a poker chip or some marker over the letter if it was on his board. When these games were first made, one child would be the caller with the pile of cards. Well, why were some games so popular and why did some entail big arguments? Because no child could be a caller for others! That caused the rumpus. As soon as each child picked up her own card – peace!!! Live and learn! There was a rule that a letter could not be covered up without saying the name of it.

Read more about games and activities  in my book, Early Childhood Programs: Opportunities for Academic, Cognitive, and Personal Success, beginning on page 49. Also, see 7 reviews on www.amazon.com

Warm Fuzzies and Cold Pricklies

TA for Tots and Other Prinzes by Alvin Freed was printed in 1973 and is still available today. It was used in the beginning of every year with my combined first and second grade classes.  TA stands for Transactional Analysis, a system for personal growth and change. It’s about feeling warm fuzzies and cold pricklies and feeling that they are prinzes instead of frozzes (his unisex terms for princes, princesses, and frogs). The two terms were easy to understand and simplified discussions about getting along and during conflicts. “Are you feeling some good warm fuzzies today?” Or “I know you’re having cold pricklies right now. How can you change that?”  Children loved the book and used the terms easily with one another.

Read more about children’s personal development and social interaction in my book, Early Childhood Programs: Opportunities for Academic, Cognitive, and Personal Success, beginning on page 134. Also, see 7 reviews on www.amazon.com

Symmetry in a Combined First and Second Grade

A visual experience during a study of symmetry broadens children’s awareness of their world. It helps in facilitating their understanding with the patterning of numbers. As children become more familiar with symmetry, they also become aware of transformations and spatial relationships, directly related to geometry and science.

In my combined first and second grade classes, a study of symmetry lasted at least half a year and more often all year. Library books were used for referral. Children noticed or were exposed to symmetry in their own world, inside and outside the classroom. They found symmetry in letters, people, animals, and kites and in nature with plants, flowers, leaves, and snowflakes.

Building in the math center produced many symmetrical designs using Cuisenaire Rods, 1” cubes, and many other manipulatives along with geoboards, pegboards, and pattern blocks.

Palindromes were quite a challenge such as “madam” and “aha”. Some classes found many three letter words such as “pop” and “eye”. They were fascinated with some phrases I found such as “a man, a plan, a canal – Panama” and “never odd or even”, etc.

There were many designs made using pieces of folded paper with paints and scissors. One, two, or three colors of paint were placed in a construction paper fold, then folded and pressed gently before opening and revealing the symmetry. A little more complicated was using thin paper folded once or multiple times before cutting a design, while retaining some folded parts so it stayed together after opening. Of course, making snowflakes was very popular.

Read more about teaching Math with other supplementary activities and games in my book, Early Childhood Programs: Opportunities for Academic, Cognitive, and Personal Success, beginning on page 113. Also, see 7 reviews on www.amazon.com

Practice Counting by 10s to 100 with The Bean Game

“The Bean Game”, a very popular one for my combined first and second grade, reinforced an understanding of counting by 10’s to 100. Four game boards, each in a different color, were made on 9” x 12” oak tag. A tongue depressor is traced around 10 times on each board.  To play the game, there were about 50 tongue depressors with 10 beans glued on each one, a pile of beans, and a pair of dice.

A child would roll the dice and pick up the number of beans indicated by the sum of the dice. When a player had 10 or more beans, he picked up a 10 bean tongue depressor and placed it on his game card. He then returned 10 of his beans to the pile and kept what was left over to use with the next 10. The winner, of course, was the first one to fill his card.

Read more about teaching Math with other supplementary activities and games in my book, Early Childhood Programs: Opportunities for Academic, Cognitive, and Personal Success, beginning on page 113. Also, see 7 reviews on www.amazon.com

A Measuring Activity for First and Second Grades

Children measure each other working in pairs – using a ruler and/or a tape measure. If metric measurement is preferred or added, they would use a meter stick and a metric tape measure.

Each pair has the following list:  length of foot, hand span, head, neck, waist, wrist, arm span, height

An interesting discovery was made when children were asked to compare the measurement with outstretched arms, of the distance from finger tip to finger tip to that of their height. (It is about the same!)

Read more about teaching Math with supplementary activities and games in my book, Early Childhood Programs: Opportunities for Academic, Cognitive, and Personal Success, beginning on page 113. There is a web page available with a work sheet for this activity including a diagram of a person that can be printed for classroom use, in Appendix M. Also, see 7 reviews on www.amazon.com

Four Models of Multiplication

Learning the four models of multiplication enables children to fully understand multiplication used in problem solving, various operations, and in everyday life.

Sets: within each of some sets, an equal number of objects

Array: an equal number of columns and rows.

Cross Product: every item in one set of objects combining with each item in another set.

Measuring: on a number line of objects, skipping an equal number of times across the line.

After explaining the four models, examples should be presented. It takes a while for children to realize that the numerical answer is not the answer – you want to hear which model it is. The following are some examples, first for a mother with a child or two and then for a teacher with a class:

Mother, for sets: there are 3 bags of candy. There are 6 pieces of candy in each bag. How many pieces of candy are there?

Mother, for array: on our cookie tray, we put cookies in 3 rows and 4 columns. How many cookies are we baking?

Mother, for cross product: if 4 butterflies landed on each of 3 flowers, how many landings were there?

Mother, for measuring: Mary took a walk. On every 3 blocks, she took a drink of water. She drank water 4 times. How far does she walk?

Teacher, for sets: we will listen to 5 children read 2 stories each. How many stories will we hear?

Teacher, for array: we need 3 rows of chairs with 4 chairs in each row. How many chairs do we need?

Teacher, for cross product: Jane has 4 skirts that can go with 3 different blouses. How many outfits does she have?

Teacher, for measuring: on a number line, Susan put a marker on every 3rd number, 4 times. What number did she end with?

Again, it takes practice for children to answer which model it is. But when children are easily able to give the correct model, they will fully understand the use and purpose for multiplication.

Read more about teaching Math in my book, Early Childhood Programs: Opportunities for Academic, Cognitive, and Personal Success.  Included is a web site where programs and activities can be downloaded for use in a classroom. Also, see 7 reviews on www.amazon.com

Models of Subtraction

Learning the four models of subtraction enables children to fully understand subtraction used in problem solving, various operations, and in everyday life.

Take Away: taking a small set from a large set.

Separating: 2 small sets within a larger set.

Missing Set: empty spaces in a large set.

Matching Sets: comparing 2 separate sets

If sets are not clearly understood, group/s can be substituted for set/s. After explaining the four models, examples should be presented. It takes a while for children to realize that the numerical answer is not the answer – you want to hear which model it is. The following are some examples, first for a mother with a child or two and then for a teacher with a class:

Mother, for take away: Katie has 5 brothers.  Two brothers went outside to play.  How many brothers are still in the house?

Mother, for separating: There are 6 red and blue balls. Two of them are red. How many are blue?

Mother, for missing set: The table is ready for 4 people for dinner. One person is already sitting down. How many more people can sit at the table?

Mother, matching sets: There are 3 chickadees and 2 blue jays at our feeder. How many more chickadees than blue jays are at our feeder?

Teacher, for take away: There are 20 children in our class. 5 children are going to the library. How many children are left in the class?

Teacher, for separating: There are 6 children in the library. 4 of them are girls. How many are boys?

Teacher, for missing set: There are 8 chairs at a table. If 5 chairs are occupied, how many more chairs are empty?

Teacher, for matching sets: There are 5 children reading and 4 children writing.  How many more children are reading than writing?

Again, it takes practice for children to answer which model it is. But when children are easily able to give the correct model, they will fully understand the use and purpose for subtraction.

Read more about teaching Math in my book, Early Childhood Programs: Opportunities for Academic, Cognitive, and Personal Success, beginning on page 113. Also, see 7 reviews on www.amazon.com

Models of Addition

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Learning the three models of addition enables children to fully understand addition used in problem solving, various operations, and in everyday life.

Putting Together: two separate sets meet in one location.

Adding On: one set moves to join another set.

Separating: adding together 2 stationary sets.

If sets are not clearly understood, group/s can be substituted for set/s. After explaining the three models, examples should be presented. It takes a while for children to realize that the numerical answer is not the answer – you want to hear which model it is. The following are some examples, first for a mother with a child or two and then for a teacher with a class:

Mother, for putting together: Sam is in his bedroom and Julia is in the living room. Their mother calls both of them to meet her in the kitchen. When they arrive in the kitchen, how many people are there now?

Mother, for adding on: Lizzy is by herself in her house. Jane and Tom are playing outside. Lizzy asks them to come inside to play with her.  How many children now are playing inside?

Mother, for separating: There are two green cars parked on the side of the street.   Two red cars are parked in a parking lot.  How many cars are parked?

Teacher, for putting together: There is a program in the assembly.  Mrs. B’s class leaves their room and Mr. F’s class leaves their room and both go to sit in the assembly. How many children are in the assembly?

Teacher, for adding on:  Our class is in our room and we invited Ms. Green’s class to come and see our play.  How many are in our class now?

Teacher, for separating: Five children in Mrs. T’s class are wearing red today. Seven children in Ms. Smith’s class are also wearing red. How many children are wearing red?

Again, it takes practice for children to answer which model it is. But when children are easily able to give the correct model, they will fully understand the use and purpose for addition.

Read more about teaching Math in my book, Early Childhood Programs: Opportunities for Academic, Cognitive, and Personal Success, beginning on page 113. Also, see 7 reviews on www.amazon.com

   Teaching Young Children © Peggy Broadbent 2011 - All Rights Reserved