-Patterns-

Students recognize similarities and generalize patterns; use patterns to create models and make predictions; describe the nature of patterns and relationships; and construct representations of mathematical relationships.

The learner will be able to:

• model patterns using objects such as counters, buttons, colored beads.
• recording in pictures and describing in words patterns in various settings.
• use a ten frame as a visual pattern for developing basic facts and part-part-whole relationships and to explore numerical patterns and pattern relationships.
• identify patterns and regularity in the environment and in actions and events. (symmetry in leaves, days of the week).
• explore repeating patterns, growing patterns, shrinking patterns, combination patterns.
• develop and use the strategy "look for a pattern".

Students describe the relationships among variables, predict what will happen to one variable as another variable is changed, analyze natural variation and sources of variability, and compare patterns of change.

The learner will be able to:

• searching for and exploring changes and variability: graph how the weather changes overtime.
• identify and describe predictable changes in a variety of settings: create a timeline of predictable changes in their school day.
• identifying, describing, modeling, and representing how one variable changes in relation to another: Buying more cans of pop increased the cost.
• exploring how the element of chance makes any set of data subject to variation: Put 30 chocolate chips in dough to make 10 cookies.  Discuss why each cookie does not have exactly three chips.
• explore different types of relationships and changes like constant, not constant, numerical and spatial patterns (growing and shrinking).
• use their knowledge of variability and change to make and defend their conjectures and predictions and to solve problems-such as make a book illustrating the growth of a plant.

Students develop spatial sense, use shape as an analytic and descriptive tool, identify characteristics and define shapes, identify properties and describe relationships among shapes.

The learner will be able to:

• exploring familiar shapes and identifying shapes in their environment.
• describe the attributes of familiar shapes, such as: a square has four equal sides with square corners.
• classify shapes by an attribute such as: has corners, one curved edge, no curved edge.
• construct three-dimensional shapes using marshmallows and tooth picks.
• exploring with tangram pieces to find possible arrangements of pieces as squares.
• drawing, tracing, or using models to illustrate concepts of parallel and perpendicular lines: use the edge of a book or paper to recognize straight lines or to show a line parallel or perpendicular to a table.
• describe the playground equipment in terms of the shape of the equipment.

Students identify location relative to other objects, and describe the effects of transformations (e.g., sliding, flipping, turning, enlarging, reducing) on an object.

The learner will be able to:

• giving position words to locate and describe objects like front, back, inside, outside, right, left, over, under, next to, between: place a cube on the right side of the desk.
• locating and describing objects in terms of their orientation: place a spot of red paint on the paper: fold it and fold again.  Where will the spots be?
• exploring what happens when an object is enlarged or reduced.
• describing situations that require direction, positions and orientation concepts: list the steps necessary to travel from your classroom to the media center.

Students compare attributes of two objects, or of one object with a standard (unit), and analyze situations to determine what measurement (s) should be made  and to what level of precision.

The learner will be able to:

• using non-standard objects like paper clips, cubes, straws, etc. to measure an object like a table.
• identifying the quantity to be measured in a given measuring task and selecting the most appropriate measuring instrument and units of measurement.
• estimating measurements for various objects in the environment.
• explore the relationship of one unit to another unit when measuring the same object.
• draw a map of the classroom together and compare it to the classroom.
• discover how many cups of milk are in 1 gallon.

Students collect and explore data, organize data into a useful form and develop skill in presenting and reading data displayed in different formats.

The learner will be able to:

• raising questions related to their interests and activities. (What are your favorite snacks, colors?)
• organizing and presenting data using different formats-such as: tallies, picture graphs, bar graphs.
• displaying information to illustrate both values and categories at the same time. (categories: boys, girls).
• identifying what data need to collected to answer a question or solve a problem, and suggesting strategies for collecting and presenting their data.  (Ask what is your favorite video game?  Record information and present data using tally marks).

Students examine data and describe characteristics of the distribution, relate data to the situation from which they arose, and use data to answer questions convincingly and persuasively.

The learner will be able to:

• describing and explaining data representations-a class-created graph representing different colors students are wearing.
• providing an appropriate title for a graph.
• exploring and identifying measure of center (mean, median).
• teacher writes a summary about the results of a survey.
• learning how different representations of the same set of data can communicate different information about data.
• encouraging invented pictures/representations for portraying data sets.
• generating questions and then collecting and interpreting data about topics relevant to them.

Students draw defensible inferences about unknown outcomes, make predictions, and identify the degree of confidence displayed in different formats.

The learner will be able to:

• using their data to develop descriptions and theories about their world: How much are we reading each week?
• designing and conducting surveys, experiments, and investigations: In what month do the most birthdays happen?
• explaining how they reach a decision, giving reasons based on their data.
• questioning each other about their conclusions.
• searching for patterns in data so they can identify trends and make predictions.
• solving data-analysis problems using an investigative approach which encourages: raising questions and brainstorming, understanding the problem, gathering and exploring data, describing, interpreting and analyzing data, making inferences and predictions, making and implementing decisions, and reflecting back.

Students experience counting and measuring activities to develop intuitive sense about numbers, develop understanding about properties of numbers, understand the need for and existence of different sets of numbers, and investigate properties of special numbers.

The learner will be able to:

• developing an understanding of whole numbers using: models that come in pairs (mittens, skip count by twos).
• reading, writing, and counting using objects to forms groups or subsets of a group given a number.
• investigating the base-ten numeration system using: ten frames and hundreds charts to recognize quantity of a number.
• developing strategies to learn basic facts: turn-around, counting on, and doubles.
• giving examples to illustrate the result of special numbers 0 and 1.
• applying their understanding to solve problem such as: If I had 20 candy bars, how many bars would 10 students get?

Students investigate relationship such as equality, inequality, inverses, factors and multiples, and represent and compare very large and very small numbers.

The learner will be able to:

• choose the smaller or greater number from a pair of cards.
• exploring, developing, and understanding the part-whole relationship of number: legs of a spiders: 4+4=8.
• developing strategies to classify numbers as even or odd by: using a hundreds chart for skip counting.
• solving problems that involve real-world applications where understanding of number relationships are demonstrated.

Students understand and use various types of operations (e.g., addition, subtraction, multiplication, division) to solve problems.

The learner will be able to:

• modeling operations with numbers using: dominos to find fact families.
• give a problem and ask how it should be solved.
• exploring properties of operations using: 3 green and 2 red cubes to demonstrate the commutative property.
• find which sign would complete this math sentence 2 3=5.

Students analyze problems to determine an appropriate process for solution and they are algebraic notations to model or represent problems.

The learner will be able to:

• constructing tables of input and output like: Guess my rule> 1, 3, 5, 7.
• demonstrating replacements for open sentences.
• working with a calculator to discover the rule of a problem.

Students develop and understanding of the notion of certainty and of probability as a measure of the degree of likelihood that can be assigned to a given event based on the knowledge available; and, they make critical judgments about claims that are made in probabilistic situations.

The learner will be able to:

• exploring and discussing everyday experiences and games which involve chance.
• exploring ways to model the probability of an event occurring.
• exploring counting problems and experiments which involve recording outcomes of events.
• conduct probability experiments which draw on their experiences and interests.

Students investigate practical situations such as scheduling routing sequencing, networking organizing and classifying; and analyze ideas like recurrence relations, induction and algorithm design.

The learner will be able to:

• exploring a variety of problems which involve counting and arranging objects.
• use diagrams to represent relationships.
• informally exploring situations which can be modeled using vertices connected by edges.
• exploring pattern activities which repeat a procedure over and over to develop a sequence.
• sequencing events/steps.
• looking for multiple solutions to a problem.

Students recognize that numbers are used in different ways such as counting, measuring, ordering, and estimating, understand and produce multiple representations of a number, and translate among equivalent representations.

The learner will be able to:

• relating sets of objects, oral names, and written symbols to show "how many".
• forming groups of ten by bundling groups of ten straws.
• exploring representations of a number.
• ordering: How are the clothing sizes indicated?  What does the order progression represent?
• estimate the numbers of items in a jar.
• working with real-life situations that involve numbers like: How much ribbon and wrapping paper are needed to wrap five birthday gifts given assorted boxes?