Early Math Concepts for Young Children

In my combined first and second grade, activities during Choice Time provided children with opportunities to make discoveries and achieve mathematical understanding through play. In the Math Center, while constructing, playing games, and pondering puzzles they were problem solving, using logic, and gaining various concepts of number. The Art Center also provided opportunities for expanding math concepts through creating constructions, collages which involve sorting and classifying, and carrying out ideas for patterning. And throughout the year, there were studies and emphases on symmetry and patterning. These concepts are assets for good achievement, enabling children to fully understand their math. Plus, new math concepts in the district-required math books always involved concrete experiences and manipulatives. Lots of them in various forms. Yes, it’s possible for children to manage correct answers in their books without understanding, but that guarantees from about third grade on – huge difficulties. I always hoped that they would know how and why they arrived at their answers and see the purpose of learning math in their daily lives. Then good abstract math would follow.

The children also understood that there may not be only one right answer in all circumstances. They should think about it. You know, a three-year-old once taught me that 1 + 1 = 1. It was a beautiful day outside when he was concentrating upon pouring a heavy pail of water into his pail of sand. When he finished and looked down at his pail of sand he was shocked and asked, “Hey, what happened to my pail of water?” He found out that one pail of sand, plus one pail of water, equals one pail of wet sand. So, questioning results in class was encouraged, so that math could be fun and creative and encourage problem solving.

Learn more about the math program and Choice Time 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

Children’s Creations of Islamic Designs

In my combined first and second grade, Arabic repeating mosaic designs that children made on graph paper were very popular. The whole class was first introduced to the process, and after that it was a popular Choice Time activity.

We began with ½” graph paper. In a block of four squares, a child would make a design with markers. Then, skipping one or more squares next to that, they would repeat the same square and design and continue across the page and making identical additional rows until the whole page was covered. When they felt the squares were complete, they would make some lines or designs in the blank squares connecting the decorated ones. Again, these lines and designs were identical. Sometimes a child might outline the four squares and repeat that square with the spaces across the page and continue the rows until the page was covered. Then they would go back and put one design in every square, returning to add additional identical designs in every square, and then connecting all the squares.

After being first introduced to the whole class, the youngest children had some difficulty carrying out their repetitive pattern but didn’t realize it. They just didn’t choose to make any more after that first one in the fall but were apt to design some later in the year. I’ve often thought how amazing children are when they choose to do the things they are capable of and just neglect to participate if it’s beyond them with no apparent discomfort. They just get involved in something else.

Graph paper was always available for future designs, and as time went on designs became more and more complex. Some would use 1” graph paper or ¼” graph paper, began their design with six squares or a rectangle, or just became far more elaborate with each additional design created. It was a very popular activity  because each child could participate at her own level.

The designs involved the concepts of patterning, symmetry, transformations, and geometric shapes.

See an illustration of the Islamic Designs and read about the math program 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

Patterning in First and Second Grade

In my combined first and second grade, patterning was a popular activity in the math center during Choice Time.

When using geoboards, most often symmetry was the choice of design, while sometimes repeating designs or making pictures were created. Initially, young children might have put as many elastics on as possible, and we might guess how many were used. But, as they observed others, their choices became more elaborate.

When a child presented a pattern on a pegboard during evaluation time, children were asked to tell what the pattern was. They might see, for example, if the pattern was red, blue, green, yellow, red, blue, green, yellow, red, blue, in the first row, then the second row would start with green and yellow. After looking at the horizontal pattern, we would look at the vertical one and see it’s now red, green, red, green, etc. with each successive row containing just two alternate colors. Then, we’d look at the patterns diagonally noticing red, yellow, green, blue, etc. Since this equipment involved colors, numbers could substitute, so 1 was red, 2 was blue, 3 was green, and 4 was yellow, exposing them to the patterning of number. After seeing the patterns with colors, the board might be hidden, and asked if we went vertically, what would the numbers be? And then show them.

Of course, the youngest children might present a pegboard with no recognizable pattern. They might be asked if there were more red or blue pegs. Let’s count and see. Or, if they were ready for something more complex, are there more red and blue pegs than green and yellow? Again, counting to see. This equipment, as with all equipment and activities that were provided in the class, accommodated different abilities and yet was shared with all. The youngest children received as much attention for their efforts as the older ones. However, the youngest children were always exposed to higher achievements that they, too, could participate in when they were ready. By making the simplest offerings more complex, it still could appeal to the brightest. Hopefully, everyone had a chance to feel good about their projects.

So, patterning was a big part of our program. It is important because math is a patterning of number and a study of patterns. So many problems can be solved if patterning is well understood plus it contributes to their study of geometry.

Read more about the math center and patterning 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

Parquetry Blocks Activity Cards

In my combined first and second grade classroom, besides using parquetry blocks to create original designs,  nine activity cards were used that were made in cardboard, 4 ½” x 14”. The first card was simple with each progressing card more complicated than the previous one. The purpose was to see if the pattern could be continued. A child could place the appropriate parquetry blocks on the card and then continue on or just create the pattern.

For each card, the Parquetry Blocks go in a row from the left of a card to the right:

The following sequence of cards was made in color.

1. Two alternating shapes and colors

2. Three alternating shapes and colors

3. Two alternating shapes and colors, position rotated 1800

4. One shape, three colors, three positions

5. One shape, three colors, four positions

6. Two shapes, three colors, four positions

7. A tessellation

8. Several pieces of one color blending to make one shape with edges distinctive

9. Several pieces of one color blending to make one shape with edges indistinct

Either using the design cards or creating their own designs offered opportunities for becoming aware of transformations, spatial relationships, logical thinking, and problem solving.

See more about the math program with games and activities in my book, Early Childhood Programs: Opportunities for Academic, Cognitive, and Personal Success.  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

   Teaching Young Children © Peggy Broadbent 2011 - All Rights Reserved