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NumbersGeometry, Shapes, & SpaceMeasurementPatterns & ReasoningStatistics & Probability3 years oldDuring their third year, many children can tell their age and hold up that many fingers to demonstrate.During the third, fourth and fifth years, children physically explore and gain understanding of the directional words “up,” “down,” ?“front,” ?“back,” ?“over,” ?“under,” “above,” ?“on,” ?“beside,” ?“next to,” ?“in front,” ?“behind,” ?“inside,” ?“outside,” ?“between,” ?“left,” ?“right,” etc.During the third and fourth years, many children figure out how to compare two different objects. They might take two pencils and put them side by side and then tell you which is longer.During the third year, some children figure out how to follow a simple sequence of familiar events. For example, they can describe the steps they follow in taking a bath. “First we plug the drain, then we run the water, and finally we take the bath.”Between the ages of three and five, children can begin to organize items into different categories and compare the results to answer a question, such as which group has more. For example, children might put all the brown socks in one pile, all the white socks in another, and all the black socks in a third pile.4 years oldDuring the fourth year, many can count up to five items, some can count up to 10, and a few can count to 20.Many four-year-olds can tell what number comes after a given number in a sequence up to 10. For example, if asked ?“What comes after 1-2-3-4-5-6?” ?many can answer ?“7,” ?and so forth.Given two numbers between one and 10, many five-year-olds can tell which of the two is larger.During the fourth year, many children can recognize and name shapes with different sizes and orientations (for example, circles, squares, rectangles, and triangles).Many four-year-olds will naturally make shapes that show symmetry without necessarily understanding the concept. For example, they might make a structure with blocks where one side of the structure is identical to the other because it appeals to them.During their fourth year, many children will be able to compare objects using words such as ?“bigger” ?and ?“smaller,” ?“longer” ?and ?“shorter,” ?“heavier” ?and ?“lighter,” ?and ?“faster” ?and “slower.” Some children may figure out how to measure an object (like a book) by using a number of identical smaller objects, such as paper clips lined up end to endDuring the fourth year, many children can follow, and make their own, simple patterns that repeat. For example, if shown a color pattern like red-blue, red-blue, children will know that another red-blue comes next. Children may also be able to follow and make their own sound patterns, such as clap-stomp-clap-stomp.By the fourth year, most children can place a small group of objects in order from biggest to smallest and talk about what they are doing using the words ?“big,” “bigger,” ?and ?“biggest.”During the fourth year, many children figure out that some things can only be answered or understood after they test it themselves. For example, if a child is told that the cloth ball just picked up won’t really bounce, the child is most likely to try bouncing it several times to see if this is true.5 years oldBy the fifth year, they can accurately use the words in a sentence.By the fifth year, most children will be able to look at different-sized containers of the same shape and tell which holds more or less.Four- and five-year-olds can sort a group of items by one or more characteristics. Given a bag of socks, children can sort them by color, or by size. They are able to explain how they sorted the objects.By age five, many can look at the size of the piles they made to answer the question: Which color sock is most common in our family? When guided by an adult, many five-year-olds can understand simple graphs and use the information to answer questions.Home Activities for Math Skills Development: PreschoolersLANGUAGE:Adults should surround children with language and incorporate simple math vocabulary in everyday conversations. At this age, math vocabulary can mean: ? The names of shapes: circle, square, oval, rectangle, etc.? Numbers: start with simple numbers, such as 0-10? Words that show spatial relationships: under, on, above, below, in front of, etc.? Directional words: straight, left, right, high, low, near, far, etc.? Comparative words: more than, less than, taller, bigger, fewer, smallest, etc.? Descriptive words: light/heavy; empty/full; hot/cold; etc.? Time: before, after, then, etc.? Other math words: pair, group/set, names of coins, words to describe measurements, etc. ◆ Sing songs about numbers, such as “One, Two, Buckle My Shoe” or “Five Monkeys Jumping on the Bed.” ◆ Use simple language that emphasizes time, such as “After dinner, we will read a book, then go to bed.” Not only will this help young children develop a sense of time, but knowing what will happen next eases transition times for them. OBSERVATIONS: Point out objects in the environment to your preschooler. Say, “Look at the cars!” or “Can you smell the flowers?” As children get older, point out written words and numbers as well. For example, say, “That signs has a three and a five together, which stands for ‘35’.” READING: Children learn vocabulary when adults read to them. Classics such as The Three Little Pigs, The Three Billy Goats Gruff, Little Red Riding Hood, and Goldilocks and the Three Bears all emphasize comparative language. Ask your children to make predictions before reading a story by saying, “What do you think this book will be about?” COUNTING:In addition to teaching children how to rote count, show them how to count objects. Set out items, such as toys, and have them touch each one as they count. Begin with small sets of two or three objects. Increase the number of objects as they become more skilled at counting. Also, let them see you counting; when putting dishes away after dinner, count the number of clean forks out loud. Ask, “How many carrots do you think are on your plate?” See if they’ll count to find out! TRY THESE ACTIVITIES DURING PLAYTIME:MATCHING & COMPARING: When folding laundry, have your toddler or preschooler try to match the socks. Then ask, “Which socks are (mommy’s/daddy’s/yours)?” When playing with blocks, choose one and have your child try to find another block that looks just like it. Let children hear you compare objects, for example say, “This tree is taller than that one.” SERIATION/ORDERING: Say to your preschooler, “Can you help me put your (stuffed animals/blocks) in order from smallest to largest?” Start with one object, then ask, “Which one is the next largest?” Online seriation activity: Visit 9.692.html to put animals in order from smallest to largest SEQUENCING: Make a simple pattern with two or three blocks and challenge your preschooler to match the sequence. Use stringing beads to create repeating sequences (patterns). See if they can copy what you have done. Online patterning activity: Visit 9.693.html to put birds in a pattern with your child. CLASSIFYING & SORTING OBJECTS: Encourage preschoolers to sort objects by one attribute. Say, “Can you put all of the yellow cars in a pile?” Have your preschooler help you clean up after playing with toys. Say, “Let’s put all of the blocks in the box.” Online sorting activity: Visit deepblue/sortingfish.html to sort big/ little fish. MEASURING: Let children help you prepare snacks or meals. Though they will not understand the concept of what a “teaspoon” is, if they have experiences with different measuring tools, they will likely grasp that a “teaspoon” of sugar is a “little sugar” whereas a “cup” of sugar is lot. Play games with measuring. Say, “How many blocks long is your foot? Let’s see!” Use the objects to measure their feet, then say, “Your foot is (two) blocks long!” FREE PLAY: Provide a variety of materials for them to explore. For example, when in the bathtub, give them toys that allow them to pour (bucket/cup), squeeze (sponges/droppers), etc. This is how they will test cause and effect relationships and form other mathematical ideas! ................
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