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# Child Development Tracker: Mathematics From Age 4 to 5 (page 4)

— PBS Parents
Updated on Jul 9, 2010

### Measurement

• During the first half of this year, some four-year-olds will still be discovering attributes of objects by filling a container with solids or liquids (e.g., ice cubes or water). These children will also figure out that different sized containers will hold more or less.
• During the first part of this year, the average child will recognize, informally discuss, and develop language to describe attributes such as "big" or "small" (height/area/volume), "long" and "tall" or "short" (length/height), "heavy" or "light" (weight), and "fast" or "slow" (speed).
• Throughout this year, some children will still be learning the concepts of "same" and "different," as well as how to describe the ways in which items are the same or different. Also during the first half of this year, some children compare a single attribute of several objects (e.g., The child says, "She has a bigger piece of cake than I do."). The average child makes such comparisons during the second half of this year. During the first half of this year, some children can order objects from smallest to largest (e.g., lines up from shortest to tallest, nests cups, etc.) and describe relationships among objects (e.g., "big," "bigger," "biggest"). The average child develops these skills during the second half of this year.
• Throughout the year, some children may still be developing their sense of time through their participation in daily activities (e.g., knows the basic sequence of the day). By the end of this year, children should understand daily time concepts like "morning," "afternoon," "night," "earlier," "later," and "soon." Children should also be able to identify basic concepts associated with night/day and seasons, but may still confuse "yesterday," "today," and "tomorrow." During the first half of this year, some children can recite the days of the week and seasons, but cannot tell time. Some children this age also recognize that a specific time is associated with certain events (e.g., favorite TV show comes on at 4:00). The average child understands these things during the second half of this year. Finally, during the second half of this year, some children will have developed a strong sense of time and will know when events close to them take place. They will know the days of the week, the months, and the seasons, but will still be learning how to tell time.
• During the first half of this year, some children may solve a problem by comparing lengths directly (e.g. placing two sticks side by side to see which is longer). The average child does this during the second half of this year.
• During the first half of this year, some children may compare the areas of two objects by placing one object on another. The average child does this during the second half of this year.
• Throughout this year, some four-year-olds will make informal comparisons and estimates (e.g., says, "I'm as tall as the yellow bookshelf.").

### Patterns, Reasoning, and Algebra

• During the first half of the year, some children will understand a sequence of events when it is clearly explained (e.g., parent says, "First we plug the drain, then we run the water, and finally we take the bath."). The average child shows such understanding during the second half of this year. In addition, children during the second half of this year recognize regularities in a variety of contexts (e.g., events, designs, shapes, sets of numbers).
• Throughout this year, some children can identify the "core" of simple repeating patterns (i.e., the basic sequence or building block that is repeated) and extend the pattern by replicating the core (e.g., for the pattern "red/blue/red/blue/red/blue," the child will add "red/blue"). Children show varying levels of progress with this skill through age six. This development is also true for when children imitate pattern sounds and physical movements (e.g., clap, stomp, clap, stomp...).
• During the second half of this year, a few four-year-olds will discover the concepts of "even" numbers (i.e., a number of items that can be shared fairly between two people), and "odd" numbers (i.e., sharing between two people results in a leftover item).
• During the second half of this year, a very small number of four-year-olds may be able to use letters to represent the "core" of a repeating pattern (i.e., the basic sequence or building block that is repeated) of up to "three" elements (e.g., "ABC" for "123123123...").
• Throughout this year, a few four-year-olds may begin to summarize with natural language the ideas of "additive identity" (e.g., says, "You did not add anything, so it is still the same"), "subtractive identity" (e.g., says, "You did not take anything away, so it is still the same"), and "subtractive negation" (e.g., says, "You took it all; there is nothing left."). During the second half of this year, a small number of children may also summarize "additive commutativity" (e.g., says, "You can add numbers in any order.").
• During the first half of the year, the average four-year-old will be able to use deductive reasoning (using what we know to logically reason out a conclusion about what we do not know) to solve everyday problems (e.g., figures out which child is missing by looking at children who are present).
• During the first half of this year, some children will move beyond using arbitrary rules (e.g., creating a category for "because I like it") to complete an adult-imposed classification task. Instead, these children can stick with one feature (e.g., color, shape, size) in sorting objects into a class. The average child can stick with one feature when classifying during the second half of this year. Throughout this year, a small number of children will be able to sort and classify on the basis of one or more characteristics (e.g., color, size, etc.), and can articulate why items are grouped together.
• During the first half of this year, some children will be able to reason "transitively" (e.g., if Abby is older than Betsy, and Betsy is older than Charlene, then Abby is also older than Charlene). The average child can reason this way during the second half of this year. A small number of children throughout the year will also be able to sequence events chronologically.

### Statistics and Probability

• During this year, some children will recognize that some questions, issues, or areas of disagreement are "empirical questions" that cannot be answered without first collecting data. Also, children will be able to collect relevant data for addressing a question or making a decision of personal importance.
• Throughout this year, children will learn to organize and describe data (e.g., by constructing real or picture graphs) to address a question (e.g., What eye color is most common in the family?) or make a decision of personal importance (e.g., Which ice cream shop has the most flavors?).
• Children will develop skills to read and interpret real graphs or picture graphs that summarize information needed to address a question, make a prediction, communicate to others, or make a decision of personal importance.
• Children will begin to understand that some events are more likely to occur than others (e.g., snow is more likely in winter than in summer). They will also begin to understand and use the language of probability (e.g., "certain" or "sure," "uncertain" or "unsure," "likely" or "probable," "unlikely" or "improbable," "maybe" or "possible," and "impossible").

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