# STRAND: Number and Operations Algebra Geometry Measurement Data Analysis and Probability STANDARD:

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1 how August/September Demonstrate an understanding of the place-value structure of the base-ten number system by; (a) counting with understanding and recognizing how many in sets of objects up to 50, (b) counting orally by 2s to 20 and by 5s and 10s to 100, (c) comparing and ordering numbers up to 100. Use ordinal numbers (e.g., what position?) and cardinal numbers (e.g., how many?) appropriately. Perform addition and subtraction with whole number combinations. Computational Fluency: (+ and -) All year. Recognize, reproduce, describe, extend, and create repeating patterns (e.g., color, shape, size, sound, movement, simple numbers) and translate from one representation to another (e.g.., red, red, blue, blue to step, step, clap, clap). Skip-count on a hundreds chart (e.g., by 2s up to 20 and 5s and 10s up to 100) to identify, describe, and predict number patterns. Describe direction, location, space, and shape (e.g., left, right, over, under, near, far, between). Develop an understanding of measurable properties (e.g., length, volume, weight, area, and time) using appropriate concepts and vocabulary that include; (a) time by estimating e.g., longer, shorter, minutes, hours, days, weeks. Use digital and analog (face) clocks to tell time to the half hour (year long). Gather data by interviewing, surveying, and making observations (year long). Represent data using objects, pictures, tables, and simple bar graphs (year long). Interpret what the graph or other representation shows (year long). Discuss the likelihood of events using terminology such as more likely, less likely, possible, or certain (year long). Observe, explore, and discuss whether some events occur more often than others (e.g., tossing two die and recording the sum after each toss to explore whether or not certain sums occur more frequently than others) (year long).

2 how October Demonstrate an understanding of the placevalue structure of the baseten number system by; (d reading, writing, modeling, and sequencing whole numbers up to 100 (including filling in missing numbers in a sequence), (e) counting orally backward from 100, and (f) connecting number words and numbers to the quantities they represent. Use a variety of models to demonstrate an understanding of addition and subtraction of whole numbers Use and explain estimation strategies to determine the reasonableness of answers involving addition and subtraction. Write number sentences that use concrete objects, pictorial, and verbal representations to express mathematical situations using invented and conventional symbols (e.g., +, -, =, ( ). Use materials to create representations of the surrounding environment (e.g., three-dimensional models, maps of the classroom). Create simple symmetrical shapes and pictures. Identify common geometric figures and classify them by common attributes by; (a) participating in discussions comparing, identifying, and analyzing attributes to develop the vocabulary needed to describe two- and three-dimensional geometric shapes and their attributes (e.g., sides, corners, edges, faces). (b) sorting two- and three-dimensional shapes into categories based on common attributes, (c) using the attributes of shapes to analyze ad identify examples and non-examples of geometric shapes, and (d) recognizing, naming, building, and drawing both polygonal (up to six sides) and curved shapes. Recognize and describe the symmetric characteristics of design (e.g., geometric designs made with pattern blocks). Participate in activities to develop mental visualization and spatial memory (e.g., quick image activities that require students to recall or reproduce a configuration of dots on a card or to determine the number of dots without counting). Predict the results of changing a shape s position or orientation by using rotation (i.e., turns), reflection (i.e., flips), and translations (i.e., slides). Organize data into appropriate categories by sorting based on shared properties.

3 how November Use strategies for wholenumber computation, with a focus on addition and subtraction (e.g., counting on or counting back, doubles, sums that make 10, direct modeling with pictures or objects, numerical reasoning based on number combinations and relationships). Decompose and recombine numbers using manipulatives (e.g., by breaking numbers apart and recombining) to create and construct equivalent representations for the same number e.g., 10 = or or ). Demonstrate a variety of methods to compute (e.g., objects, mental computation, paper and pencil, and estimation). Identify number patterns on the hundreds chart.

4 how December Given simple story problems, explain verbally how to select and use appropriate operations. Answer questions about how data can be gathered. Collect, organize, represent, and compare data by category on graphs and charts to answer simple questions (year long). Compare parts of the data (e.g., How many students in the class have lost only two teeth ) to make statements about the data as a whole (e.g., Most students in the class have lost only two teeth ) Participate in discussions about selecting an appropriate way to display the data. Make conclusions based on data (e.g., whether or not other groups would reach similar conclusions based on the same data. Determine whether or not the data gathered helps answer the specific question that was posed.

5 how January Develop an understanding of measurable properties (e.g., length, volume, weight, area, and time) using appropriate concepts and vocabulary that include; (b) length measuring and estimating (e.g., longer, shorter, meter, centimeter, inch, yard., (c) area by measuring and estimating (e.g. perimeter, rectangles, squares). Measure with multiple copies of units the same size (e.g., paper clips) Use repetition of a single unit to measure something larger than the unit (e.g., a yardstick/meter stick to measure a room).

6 how February Demonstrate an understanding of the placevalue structure of the baseten number system by; (g) grouping objects by 10s and 1s to explore place value (e.g., 24 equals two tens and four ones). Find the sum of three onedigit numbers to the sum of 15. Solve addition and subtraction problems with one- and two-digit numbers (e.g., = ). Understand and use the inverse relationship between addition and subtraction to solve problems and check solutions ( e.g., = 14 is related to 14 6 = 8). Represent equivalent forms of the same number through the use of physical models, diagrams, and number expressions to 20 (e.g., = 8, = 8). Demonstrate and describe the concept of equal (e.g. using objects, balance scales. Solve open number sentences that have variables representing numbers up to 10 (e.g. 10 = + 2).

7 how March Use concrete materials to investigate situations that relate to multiplication and division (e.g., equal grouping of objects, sharing equally). Describe qualitative change (e.g., a student growing taller, trees getting bigger, ice melting).

8 how April Describe situations that involve addition and subtraction of whole numbers including objects, pictures, and symbols (e.g., Robert has four apples, Maria has five more). Use combinations of shapes to make a new shape to demonstrate relationships between shapes (e.g., a hexagon can be made from six triangles)

9 how May Describe how to get from one location to another by visualizing the landmarks along the route. Visualize, describe, and record directions for navigating from one location to another to develop the vocabulary needed to describe direction, distance, location, and representation Create three dimensional shapes based on two dimensional representations. Identify structures from different views or match views of the same structure portrayed from different perspectives. Develop estimates and measure distances using nonstandard measurements. Develop an understanding of measurable properties (e.g., length, volume, weight, area, and time) using appropriate concepts and vocabulary that include; (e) volume by measuring, estimating, and weighing (e.g., full, empty). Develop an understanding of measurable properties (e.g., length, volume, weight, area, and time) using appropriate concepts and vocabulary that include; (d) weight by measuring estimating and weighing (e.g., heavy [-ier], light [-er]).

10 how Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Understand the meaning of operations and how they relate to one another. Compute fluently and make reasonable estimates. Understand patterns, relations, and functions. Represent and analyze mathematical situations and structures using algebraic symbols. Use mathematical models to represent and understand quantitative relationships. Analyze change in various contexts. Analyze characteristics and properties of two- and threedimensional geometric shapes and develop mathematical arguments about geometric relationships. Specify locations and describe spatial relationships using coordinate geometry and other representational systems. Apply transformations and use symmetry to analyze mathematical situations. Use visualization, spatial reasoning, and geometric modeling to solve problems. Understand measurable attributes of objects and the units, systems, and process of measurement. Apply appropriate techniques, tools, and formulas to determine measurements. Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them. Select and use appropriate statistical methods to analyze data. Develop and evaluate inferences and predictions that are based on data Understand and apply basic concepts of probability

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