Picking Up Patterns
The ability to reproduce and create patterns is an early math skill that we adults can encourage in young children. Patterns occur throughout mathematics, right from the simplest of concepts to the most complex. Helping children learn to look for patterns will help them gain a deeper understanding of math. Because young children learn best by touching and seeing, the first patterning experiences we give them at school are with objects rather than with numbers.
Children between 3 and 5 begin to be able to reproduce a pattern created by someone else. For example, if an adult uses blocks to create the pattern of “rectangle, square, rectangle, square, and so on, the child should work toward being able to look at that pattern and use his/her own blocks to make the same pattern.
Almost any set of objects around the house can create a simple alternating patter (ABAB):
- Spoon, fork, spoon, fork, etc.
- Blue napkin, red napkin, blue napkin, red napkin, etc.
- Nut, bolt, nut, bolt, etc.
- Crayon, marker, crayon, marker, etc.
After children perceive and create this simple patterning, adults can offer more complicated patterns such as nut, nut, bolt, nut, nut, bolt, etc. (AABAAB) or nut, nut, bolt, bolt, bolt, nut, nut, bolt, bolt, bolt, etc. (AABBBAABBB).
Encourage children to create their own patterns with objects. Ask them to predict which object would come next in one of your patterns. Invite them to sketch their patterns.
Finding patterns in the world around them and creating patterns themselves will help children see patterns in more complex mathematics later on.
Math Moments
In every classroom, at any time during the day, the potential for a “math moment” exists. The room is one big learning center where strands of mathematical discovery are continually being woven. Children learn to make sense of their world through everyday experiences.
To stimulate a math moment, teachers use a variety of materials and ideas to create an environment in which children explore math concepts. In the math centre are board games, puzzles, matching and guessing games, dominoes, cards, pattern blocks and collections of objects that give children opportunities to recognize numbers and build math skills.
But math moments do not occur only in the math centre. Look around our room… In the block centre, children construct houses, towers, parking garages, bedrooms, etc. (by sorting and organizing) and use words like long, short, and tall. When a child brings a birthday treat, s/he passes out one napkin per child and the same number of treats for each person. We take attendance and keep track of how many days we’ve been in school. When the class votes on what stories to read or for some other decision, children compare quantities. When we clean up the room we sort toys and writing materials into appropriate tubs and containers – felts with felts, crayons with crayons, animals with animals, cars with cars, etc.
Parents can accept the challenge to find math moments at home and about town. With your child, identify numbers and shapes in your junk mail. As you cook or run errands together, you can make comments or ask questions that encourage meaningful math understandings. For instance, “We need a bottle of juice for each person in the family and your friend Sally, too. How many shall I get?” When shopping ask your child to find products that are sold in groups of 5 or 10 or 100… or see how many places you can find the number 3 or 5 or 7… Children love to be consulted on such issues! Just keep it all in fun!
Sorting Stuff
Children learn many math skills long before they are ready for the “basics” of addition and subtraction. One of these skills is the ability to sort objects.
When they sort, children group things that belong together in some way. Children often sort by colour – red blocks in one group, blue blocks in another – or by shape – triangle blocks here, rectangle blocks there.
When children’s rooms are organized, their toys become natural objects to sort. At cleanup time, alphabet blocks go into one container, coloured blocks go into another, farm animal figures go in one tub and toy cars into a box.
In helping with the laundry, children can sort clothes into piles of shirts, shorts, pants, underwear and socks. After dishes are done, children can put away knives, forks and spoons. In helping to put away groceries, children can separate boxes from cans or bathroom items from kitchen items. By lending a hand in sorting things into the appropriate recycling containers, children also develop earth-friendly habits.
Early in a child’s explorations of sorting activities, adults play a useful role by providing words for what the child is doing (“I see you are putting all the square blocks together”). We also can help extend the sorting (Let’s see if we can find all the rectangle blocks”). In time, the child begins to use these words and expand his or her understanding of the mathematical world.
Dice, Cards and Math
Dice and playing cards are inexpensive, fun to work with and suitable for a variety of math activities. They help children learn one-to-one correspondence (pointing to objects while counting), comparison of numbers (more/less/same) and other math skills.
Dice can be used in very simple ways, such as by players rolling a single die and advancing on a game board. Such games often can be purchased second hand or created by families at home.
A piece of cardboard or poster board can serve as a game board. A child can select a starting and ending place for the game. For example, for a game called “Going to the Park”, HOME could be the starting place and PARK could be the destination. Your child could draw, alone or with help, boxes on streets leading from home to the park. Use dice or numbered cards to determine how many spaces to advance. Make up your own object and rules! A game of this kind promotes problem solving, number recognition and counting skills. Or, play commercial games with your children – look at the box to find out if the game is appropriate for your child’s age group.
For older children, more advanced games can involve rolling two or more dice and adding (or subtracting) the numbers shown. Dice also can be used to help children look for number patterns and factors by finding all the ways to make a certain number on a pair of dice. Let your children make up their own dice games!
Dice do not need to be six sided. Game and hobby stores sell dice with 4, 8, 10, 12, 20 and even 100 sides! For dice and card game ideas that build math skills, look for “Box Cars and One Eyed Jacks”. There is a complete set of these books and they are a wonderful resource.
Playing card games, too, offer many possibilities for math skill development. Children can play “War” or other games that involve a comparison between two or more numbers. They can count decks to determine how many cards are red, how many are hearts, how many are face cards, how many are less than 7, and so on. Such games and others like “Rummy” or “Go Fish” teach children about grouping and sorting. For other card game ideas, check the library for books on the subject…
Families can also create their own card games. If your family invents a game that is fun, we’d love to hear about it!
Let the Games Begin!
Children learn best when activities are meaningful to them. Experts in the early development of mathematical concepts tell us that children develop mathematical understanding in situations in which number and quantity are relevant and important to them.
Games provide this opportunity. Playing games is a wonderful way for children to share time with family members, to have fun, and to learn. Kids love to play games with their favorite grown-ups.
In simple card games such as “Go Fish”, “Concentration” or “Crazy Eight’s”, children learn many different things. They identify numerals, match numerals or objects and practice memory skills. They also develop fine motor coordination by picking up and handling the cards.
Playing dominoes or games with dice, children learn to count the dots and relate those dots to the number they represent. Moving game pieces the right number of spaces on a board adds the concept of one-to-one correspondence (being able to point to an object as it is counted), and constantly comparing the rolled numbers helps develop number sense.
The games we choose should be appropriate for the age of the child. With commercial games, look for the age recommendations on the game box. Remember that noncompetitive games are best – young children hate to lose.
As we play games with children, we can extend their mathematical thinking by asking simple questions: “How many matches did you get? Do you have more red cards or black? Would you like to deal us 6 cards?” Continued opportunities to play games and talk and think about number concepts help children develop their own math understandings.
***Borrowed from Tracy Fulton, New Westminister School District***