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1.1 Understand and apply concepts and procedures from number sense. |
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Kindergarten |
Grade 1 |
Grade 2 |
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Number and Numeration |
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1.1.1 |
Understand the concept of number. · Count objects to at least 20 items using one-to-one correspondence. · Represent a number to at least 31 in different ways (e.g., numerals, pictures, physical models). [CU] · Show that the last count word names the quantity of the set (cardinality) (i.e., when counting fingers on a hand “one, two, three, four, five”, the “five” says how many fingers there are). [CU, MC] · Identify the base ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. [CU] · Explain how numbers are used and give examples. (e.g., to count, to order) |
Understand ways of representing whole numbers. · Represent a number to at least 100 in different ways (e.g., numerals, pictures, physical models) and translate from one representation to another. [CU, MC] · Group and regroup objects into 1's and 10's. [SP, RL, CU, MC] · Read, write, and recite, in any language, numbers to at least 100. [CU] · Count sets of objects less than 100 using a variety of grouping strategies. · Identify coins (penny, nickel, dime, quarter) and state their value. [CU] |
Understand place value in whole numbers. · Group and regroup objects into 1's, 10's, and 100's and explain relationships. [SP, RL,CU,MC] · Make combinations and name total value of coins. [SP, RL] · Determine the value of a digit based on its position in a number. · Read and write numbers to at least 1,000. [CU]
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1.1.2 |
Understand sequential relationships among whole numbers. · Tell what number comes before or after a given number. [CU] · Use comparative language (e.g., less than, more than, equal to) to compare numbers to at least 20. [CU] · Use a known quantity to at least 10 (benchmark) to compare sets (e.g., sets of counters). · Identify the ordinal position of objects at least through tenth, (e.g., first, second, …). [SP, RL, CU, MC]
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Understand sequential relationships among whole numbers. · Order three or more numbers to at least 100 from smallest to largest. [CU] · Use comparative language (e.g., less than, more than, equal to) to compare numbers to at least 100. [CU] · Skip count by 2, 5, and 10. · Count forwards and backwards, from a given number that is less than 100.
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Understand sequential relationships among whole numbers. · Order three or more numbers to at least 1,000 from smallest to largest. [CU] · Use comparative language (e.g., less than, more than, equal to) to compare numbers to at least 1,000. [CU]
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1.1 Understand and apply concepts and procedures from number sense. |
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Kindergarten |
Grade 1 |
Grade 2 |
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Number and Numeration |
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1.1.3 |
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1.1.4 |
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1.1 Understand and apply concepts and procedures from number sense. |
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Kindergarten |
Grade 1 |
Grade 2 |
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Computation |
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1.1.5 |
Understand the meaning of addition. · Express stories involving addition (e.g., join) with models, pictures, and symbols. [SP, RL, CU, MC] · Use addition in the classroom environment (e.g., boys and girls in attendance). [MC]
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Understand the meaning of subtraction. · Express stories involving subtraction (e.g., separate) with models, pictures, and symbols. [SP, RL, CU, MC] · Show relationships between addition and subtraction using physical models, diagrams, and acting out problems. [CU]
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Understand the meaning of addition and subtraction and how they relate to one another. · Show relationships between addition and subtraction using physical models, diagrams, and acting out problems. [CU] · Model real life situations involving addition and subtraction with part-part-whole (e.g. Peter has 11 cookies, 4 chocolate chip and the rest peanut butter. How many peanut butter cookies?) and compare (e.g., Peter has 11 cookies which is 4 more than Teresa. How many cookies does Teresa have?) using physical models, diagrams, and acting out problems. [SP, RL, CU, MC]
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1.1.6 |
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Understand and apply procedures for addition of whole numbers with fluency. · Use strategies (e.g., count on, count back, doubles) for addition facts to at least sums to 12. [SP, RL] · Recall addition facts through at least sums to 12. · Solve problems involving addition using and explaining procedures used. [SP, RL, CU]
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Understand and apply procedures for addition and subtraction of whole numbers with fluency. · Use strategies for addition and subtraction facts through at least 20. [SP, RL] · Recall addition and subtraction facts through at least 20. · Solve problems involving addition and subtraction with three digit numbers using and explaining procedures used. [SP, RL, CU]
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1.1 Understand and apply concepts and procedures from number sense. |
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Kindergarten |
Grade 1 |
Grade 2 |
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Computation |
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1.1.7 |
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Understand and apply strategies and appropriate tools for computing with whole numbers. · Use strategies and appropriate tools from among mental math, paper/pencil, manipulatives, or calculator to compute in a problem situation. [SP, RL] · Use counting strategies to combine whole numbers under 20. [SP, RL]
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Understand and apply strategies and appropriate tools for computing with whole numbers. · Use mental math strategies to compute (e.g., composing and decomposing numbers, friendly numbers, neighbors) through 100. [SP, RL] · Use calculator, manipulatives, or paper/pencil to solve problems. [SP, RL] · Explain methods to mentally group numbers efficiently. (e.g. when adding 52 and 59, add the 50’s together to get 100, then add eleven more.) [SP, RL, CU] |
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Estimation |
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1.1.8 |
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Understand and apply estimation strategies to determine the reasonableness of answers. · Use a known quantity (e.g., chunking) to make reasonable estimates. [SP, RL] · Use “friendly numbers” to make a reasonable estimate of a sum (e.g., 19 + 18 should be about 40, since 19 is about 20, 18 is about 20, and 20 + 20 is 40). [SP, RL] |
Understand and apply estimation strategies to predict computation results and to determine the reasonableness of answers. · Use estimation strategies (e.g., front-end estimation, clustering) to predict computation results and to determine the reasonableness of answers. [SP, RL]. · Justify reasonableness of an estimate in addition and subtraction. [CU] · Decide if a given estimate for a sum or difference is reasonable. [SP, RL] |
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1.2 Understand and apply concepts and procedures from measurement. |
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Kindergarten |
Grade 1 |
Grade 2 |
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Attributes, Units and Systems |
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1.2.1 |
Understand and apply appropriate terminology to compare attributes. · Use comparative vocabulary to describe objects (e.g., longer/shorter, heavier/lighter, nearer/further, thicker/thinner, shorter/taller). [CU] · Use terms to describe the duration of events (e.g., long time or short time). [CU] · Identify and sort objects based on an attribute (e.g., closed vs. open) [SP, RL, CU] |
Understand and apply attributes to describe and compare objects. · Order three or more objects according to an attribute (e.g., pencil lengths, students’ heights, and thickness of books). [SP, RL, CU] · Use physical models of measuring units to fill, cover, match, or make the desired comparison of the attribute with the unit. [SP, RL] · Read a clock with only the hour hand and use approximate language (e.g., almost 7, a little after 7). [CU]
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Understand and apply attributes to measure objects and time. · Identify attributes of an object that are measurable (e.g., time, length, distance around, capacity, area, or weight of objects). [CU, MC] · Compare lengths or distances where direct comparison is not possible (e.g., use a string, paper strip, or hand span to compare the height and width of a table). [SP, RL, MC] · Read a clock to tell time to the ˝ hour.
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1.2.2 |
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Understand the importance of appropriate and consistent units. · Select units appropriate to the object being measured (e.g., measure length of classroom with footprints, not beans) and explain why it was selected. [SP, RL] · Use a uniform unit to measure an object (e.g., cubes, paper strips). · Use a calendar as a record of time (e.g., yesterday, today, tomorrow, weeks, months, years, moon phases).
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Understand that unit size affects the outcome of the measurement. · Explain why more small paper clips than large are needed to measure the same length. [CU] · Select the most appropriate unit to measure the time of a given situation (e.g., Would you use minutes or hours to measure brushing your teeth, eating dinner, sleeping?). [SP, RL, MC]
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1.2 Understand and apply concepts and procedures from measurement. |
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Kindergarten |
Grade 1 |
Grade 2 |
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Attributes, Units and Systems |
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1.2.3 |
Understand that objects can be used as tools for nonstandard measurement. · Use nonstandard units to measure (e.g., paper strips, cubes, beans, hand widths). · Explain how to use a nonstandard unit to measure a given length (e.g., length of a table, width of a desk) [CU] |
Understand the need for and apply appropriate tools to measure. · Measure a variety of objects using appropriate nonstandard tools (e.g., arm length, hand width, lengths of rope) [SP, RL] · Explain the need for measurement. [CU] |
Understand the need for and apply appropriate tools to measure specific attributes. · Select a tool that can measure the given attribute (e.g., analogue clock: time, string: length, tiles: area, balance: weight, interlocking cubes: capacity). [SP, RL] · Demonstrate measurement procedure (e.g., start at a beginning point, place units end-to-end, not overlapping, and straight line). [CU] · Justify the use of one tool over another (e.g. the length of a hand is a better measurement tool for this situation than the length of a small cube.) [CU, SP, RL] |
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Procedures, Precision, and Estimation |
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1.2.4 |
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1.2 Understand and apply concepts and procedures from measurement. |
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Kindergarten |
Grade 1 |
Grade 2 |
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Attributes, Units and Systems |
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1.2.5 |
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1.2.6 |
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Understand how to estimate in measurement situations. · Estimate length, area, capacity, and weight using nonstandard units. [SP, RL] · Use important benchmarks (referents) (e.g., 5 or 10) to make initial and revised estimates. · Explain how a benchmark (referent) helps to make a reasonable estimate. [CU]
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1.3 Understand and apply concepts and procedures from geometric sense. |
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Kindergarten |
Grade 1 |
Grade 2 |
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Properties and Relationships |
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1.3.1 |
Know characteristics of familiar objects. · Describe familiar objects based on characteristics (e.g., big, small, like a box). [CU, MC] · Identify objects based on their characteristics. [MC]
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Know characteristics of 2-dimensional figures. · Describe 2-dimensional figures based on their characteristics. [CU, MC] · Draw 2-dimensional figures based on given characteristics. |
Understand characteristics of 2-dimensional geometric figures. · Sort and describe characteristics of 2-dimensional geometric figures (e.g., various polygons). [SP, RL, CU] · Draw a 2-dimensional shape that matches a set of characteristics (e.g., draw a four-sided shape that has all sides the same length) [SP, RL] |
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1.3.2 |
Know objects based on their attributes. · Identify and sort objects in their environment by characteristics (e.g., cans, balls, boxes, colors). [MC] · Compare objects using comparative language (e.g., bigger, taller, shorter, fatter). [CU]
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Understand how to sort and compare 2-dimensional figures using their characteristics. · Identify and sort 2-dimensional figures in their surroundings. [MC] · Compare 2-dimensional figures using comparative language (e.g., longer, wider). [CU] · Describe figures using accurate terminology (e.g., square, rectangle, triangle) |
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1.3 Understand and apply concepts and procedures from geometric sense. |
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Kindergarten |
Grade 1 |
Grade 2 |
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Locations and Transformations |
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1.3.3 |
Understand the relative position of objects in their environment. · Describe the location of objects relative to each other (e.g., in, out, over, under, behind, above, below, next to, etc.). [MC, CU] · Identify where a 3-dimensional object is located relative to a given object (e.g., where the eraser is relative to the desk) [CU] |
Understand the
location · Indicate if a number is above or below a benchmark number (e.g., greater than or less than 100). [CU] · Describe the location of a given number, between 1 and 100, on a number line. [CU] · Identify a point, up to 100, on a positive number line. [CU]
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Understand the
location · Indicate if a number is above or below a benchmark number (e.g., greater than or less than 1000). [CU] · Describe the location of a given number, between 1 and 1000, on a number line. [CU] · Identify a point, up to 1000, on a positive number line. [CU]
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1.3.4 |
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1.4 Understand and apply concepts and procedures from probability and statistics. |
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Kindergarten |
Grade 1 |
Grade 2 |
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Probability |
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1.4.1 |
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1.4.2 |
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1.4 Understand and apply concepts and procedures from probability and statistics. |
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Kindergarten |
Grade 1 |
Grade 2 |
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Statistics |
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1.4.3 |
Understand that data can be collected and organized. · Sort and classify data (e.g., sort by color or size). [SP, RL] · Use physical objects or pictures to build bar graphs. [CU] · Answer questions about graphs (e.g., How many cats? How many dogs?). [CU]
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Understand that data can be organized and displayed. · Display results of data collection by making student-invented and conventional displays. [CU] · Construct bar graphs with physical materials and record pictorially (e.g., shoes, cats, crops, egg rolls, tacos). [CU]
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Understand the components of a graph. · Identify title, horizontal and vertical axes, and key. · Construct a bar graph that includes a title, key, and single unit increment. [CU] · Name an appropriate title for a display of data. [CU]
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1.4.4 |
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Understand how a display provides information about a question. · Conduct a survey for a predetermined question and collect data using tallies, charts, lists, or pictures( e.g., who has animals at home, how many, what type). [SP, RL] · Identify a question that could be answered from a display. · Interpret results and draw conclusions from displays using comparative language (e.g. more, fewer). [CU, MC]
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1.4 Understand and apply concepts and procedures from probability and statistics. |
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Kindergarten |
Grade 1 |
Grade 2 |
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Statistics |
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1.4.5 |
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Understand how to read and interpret data from graphs. § Interpret a bar graph for comparative information (e.g., How many more than, less than?). [CU] · Read the labels from each axis of a graph. [CU |
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