K-4 MATHEMATICS: Strand I: Patterns, Relationships and Functions – Standard 1: Patterns
| Elementary Benchmark | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | |||||
| 1. Recognize, describe, and extend numerical and geometric patterns. | Count, write, and order
numbers N.ME.00.05 Count orally to 100 by ones. Count to 30 by 2’s, 5’s and 10’s using grouped objects as needed. Explore number patterns: N.MR.00.10 Create, describe, and extend simple number patterns. Explore geometric patterns: G.GS.00.03 Create, describe, and extend simple geometric patterns. |
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Count, write, and order
numbers N.ME.01.01 Count to 110 by 1’s, 2’s, 5’s 2’s, 5’s, and 10’s,
starting from any number in the sequence; count to 500 by 100’s and 10’s;
use ordinals to identify position in a sequence. , e.g., 1st, 2nd,
3rd. Create and describe patterns involving geometric objects: G.SR.01.03 Create and describe patterns, such as repeating patterns, and growing patterns using number, shape, and size. G.SR.01.04 Distinguish between repeating and growing patterns. G.SR.01.05 Predict the next element in a simple repeating pattern. G.SR.01.06 Describe ways to get to the next element in simple repeating patterns. |
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Count, write, and order whole
numbers N.ME.02.01 Count to 1000 by 1’s, 10’s, and 100’s starting from any number in the sequence. N.ME.02.04 Count orally by 3’s and 4’s starting with 0, and by 2’s, 5’s, and 10’s starting from any number. |
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Count in steps, and
understand even and odd numbers N.ME.03.04 Count orally by 6’s, 7’s, 8’s, and 9’s starting with 0, making the connection between repeated addition and multiplication. N.ME.03.05 Know that even numbers end in 0, 2, 4, 6, or 8; name a whole number quantity that can be shared in two equal groups or grouped into pairs with no remainders; recognize even numbers as multiples of 2. Know that odd numbers end in 1, 3, 5, 7, or 9 and work with patterns involving even and odd numbers. |
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| 2. Represent and record patterns and relationships in a variety of ways including tables, charts, and pictures. | Create and describe patterns
involving geometric objects: G.SR.01.03 Create and describe patterns, such as repeating patterns, and growing patterns using number, shape, and size. |
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| 3. Use patterns to describe real-work phenomena. | ||||||||||
| 4. Explore various types of numeric and geometric patterns (repeating, growing, shrinking). | Create and describe patterns
involving geometric objects G.SR.01.03 Create and describe patterns, such as repeating patterns, and growing patterns using number, shape, and size. G.SR.01.05 Predict the next element in a simple repeating pattern. G.SR.01.06 Describe ways to get to the next element in simple repeating patterns. |
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| 5. Apply their experiences with patterns to help solve problems and explore new content. | Explore geometric patterns: G.GS.00.03 Create, describe, and extend simple geometric patterns. |
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Create and describe patterns
involving geometric objects G.SR.01..05 Predict the next element in a simple repeating pattern. |
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K-4 MATHEMATICS: Strand 1I: Patterns, Relationships, and Functions – Standard 2: Variability and Change
| Elementary Benchmark | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | |||||
| 1. Recognize change and variability when it occurs in a variety of settings. | ||||||||||
| 2. Recognize that change is often predictable, but variable, and that patterns emerge that help to describe the change. | ||||||||||
| 3. Explore change, and realize that changes are frequently interdependent. | ||||||||||
| 4. Use tables, charts, open sentences, and hands-on models to represent change and variability. | ||||||||||
| 5. Begin to describe and differentiate between types of relationships, especially repeating, growing, and shrinking patterns. | ||||||||||
| 6. Explore variability a nd change in a variety of contexts, investigations, and problems. |
K-4 MATHEMATICS: Strand II: Geometry and Measurement – Standard 1: Shape and Shape Relationships
| Elementary Benchmark | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | |||||
| 1. Recognize and name familiar shapes in one, two and three dimensions such as lines, rectangles and spheres and informally discuss the shape of a graph.. | Create, explore, and describe
shapes G.GS.00.01 Relate familiar three-dimensional objects inside and outside the classroom to their geometric name, e.g., ball/sphere, box/cube, soup can/cylinder, ice cream cone/cone, refrigerator/prism. |
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Create and describe shapes G.GS.01.01 Create common two-dimensional and three-dimensional shapes and describe their physical and geometric attributes, such as color and shape. |
M | Identify and describe shapes G.GS.02.01 Identify, describe, and compare familiar two-dimensional and three-dimensional shapes, such as triangles, rectangles, squares, circles, semi-circles, spheres, rectangular prisms. |
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of geometric objects G.GS.03.01 Identify points, line segments, lines and distance. G.GS.03.02 Identify perpendicular lines and parallel line s in familiar shapes and in the classroom. G.GS.03.03 Identify parallel faces of rectangular prisms, in familiar shapes and in the classroom. Name, and explore properties of shapes G.GS.03.04 Identify, describe, compare and classify two-dimensional shapes, e.g., parallelogram, trapezoid, circle, rectangle, square and rhombus, based on their component parts (angles, sides, vertices, line segment) and the number of sides and vertices. Explore and name three-dimensional solids G.GS.03.06 Identify, describe, build and classify familiar three-dimensional solids, e.g., cube, rectangular prism, sphere, pyramid, cone, based on their component parts (faces, surfaces, bases, edges, vertices). G.SR.03.07 Represent front, top, and side views of solids built with cubes. |
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Understand perpendicular,
parallel, and intersecting lines G.GS.04.01 Identify and draw perpendicular, parallel, and intersecting lines using a ruler and a tool or object with a square (90º) corner. Identify basic geometric shapes and their components, and solve problems G.GS.04.02 Identify basic geometric shapes, including isosceles, equilateral and right triangles, and use their properties to solve problems. G.SR.04.03 Identify and count the faces, edges, and vertices of basic three-dimensional geometric solids including cubes, rectangular prisms, and pyramids; describe the shape of their faces. Understand right angles MTE.04.10 Identify right angles and compare angles to right angles. |
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| 2. Describe the attributes of familiar shapes. | Create, explore, and describe
shapes G.GS.00.02 Identify, sort and classify objects by attribute and identify objects that do not belong in a particular group. |
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Create and describe shapes G.GS.01.01 Create common two-dimensional and three-dimensional shapes and describe their physical and geometric attributes, such as color and shape. |
M | Identify and describe shapes G.GS.02.01 Identify, describe, and compare familiar two-dimensional and three-dimensional shapes, such as triangles, rectangles, squares, circles, semi-circles, spheres, rectangular prisms. G.GS.02.04 Distinguish between curves and straight lines and between curved surfaces and flat surfaces. G.SR.02.05 Classify familiar plane and solid objects, e.g., square, rectangle, rhombus, cube, pyramid, prism, cone, cylinder, and sphere, by common attributes such as shape, size, color, roundness or number of corners and explain which attributes are being used for classification. |
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Name, and explore properties
of shapes G.GS.03.04 Identify, describe, compare and classify two-dimensional shapes, e.g., parallelogram, trapezoid, circle, rectangle, square and rhombus, based on their component parts (angles, sides, vertices, line segment) and the number of sides and vertices. G.SR.03.05 Compose and decmpose decompose triangles and rectangles to form other familiar two-dimensional shapes; e.g., form a rectangle using two congruent right triangles, or decompose a parallelogram into a rectangle and two right triangles. Explore and name three-dimensional solids G.GS.03.06 Identify, describe, build and classilfy familiar three-dimensional solids, e.g., cube, rectanglar rectangular prism, sphere, pyramid, cone, based on their component parts (faces, surfaces, bases, edges, vertices). |
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Identify basic geometric
shapes and their components, and solve problems. G.GS.04.02 Identify basic geometric shapes, including isosceles, equilateral and right triangles, and use their properties to solve problems. G.SR.04.03 Identify and count the faces, edges, and vertices of basic three-dimensional geometric solids including cubes, rectangular prisms, and pyramids; describe the shape of their faces. Understand right angles M.TE.04.10 Identify right angles and compare angles to right angles. |
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| 3. Compare, sort and classify familiar shapes. | Create, explore, and describe
shapes G.GS.00.01 Relate familiar three-dimensional objects inside and outside the classroom to their geometric name, e.g., ball/sphere, box/cube, soup can/cylinder, ice cream cone/cone, refrigerator/prism. G.GS.002.02 Identify, sort and classify objects by attribute and identify objects that do not belilong in a particular group. |
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Identify and describe shapes G.GS.02.01 Identify, describe, and compare familiar two-dimensional and three-dimensional shapes, such as triangles, rectangles, squares, circles, semi-circles, spheres, rectangular prisms. G.GS.02.02 Explore and predict the results of putting together and taking apart two-dimensional and three-dimensional shapes. G.SR.02.05 Classify familiar plane and solid objects, e.g., square, rectangle, rhombus, cube, pyramid, prism, cone, cylinder, and sphere, bu y common attributes such as shape, size, color, roundness or number of corners and explain which attributes are being used for classification. |
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Name, and explore properties
of shapes G.GS.03.04 Identify, describe, compare and classify two-dimensional shapes, e.g., parallelogram, trapezoid, circle, rectangle, square and rhombus, based on their component parts (angles, sides, vertices, line segment) and the number of sides and vertices. Explore and name three-dimensional solids G.GS.03.06 Identify, describe, build and classify familiar three-dimensional solids, e.g., cube, rectangular prism, sphere, pyramid, cone, based on their component parts (faces, surfaces, bases, edges, vertices). |
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Identify basic geometric
shapes and their components, and solve problems G.GS.04.02 Identify basic geometric shapes, including isosceles, equilateral and right triangles, and use their properties to solve problems. G.SR.04.03 Identify and count the faces, edges, and vertices of basic three-dimensional geometric solids including cubes, rectangular prisms, and pyramids; describe the shape of their faces. |
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| 4. Draw and build familiar shapes. | Explore geometric patterns G.GS.00.03 Create, describe, and extend simple geometric patterns. |
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Create and describe shapes G.GsS.01.01 Create common two-dimensional and three-dimensional shapes and describe their physical and geometric attributes, such as color and shape. |
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Name, and explore properties
of shapes G.SR.03.05 Compose and decompose triangles and rectangles to form other familiar two-dimensional shapes; e.g., form a rectangle using two congruent right triangles, or decompose a parallelogram into a rectangle and two right triangles. Explore and name three-dimensional solids G.GS.03.06 Identify, describe, build and classify familiar three-dimensional solids, e.g., cube, rectangular prism, sphere, pyramid, cone, based on their component parts (faces, surfaces, bases, edges, vertices). G.SR.03.07 Represent front, top, and side views of solids built with cubes. |
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Understand perpendicular,
parallel, and intersecting lines G.GS.04.01 Identify and draw perpendicular, parallel, and intersecting lines using a ruler and a tool or object with a square (90º) corner. |
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| 5. Explore ways to combine, dissect and transform shapes. | Create and describe shapes G.GS.01.01 Create common two-dimensional and three-dimensional shapes and describe their physical and geometric attributes, such as color and shape. |
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decompose triangles and rectangles to form other familiar two-dimensional
shapes; e.g., form a rectangle using two congruent right triangles, or
decompose a parallelogram into a rectangle and two right triangles. Explore and name three-dimensional solids. G.GS.03.06 Identify, describe, build and classify familiar three-dimensional solids, e.g., cube, rectangular prism, sphere, pyramid, cone, based on their component parts (faces, surfaces, bases, edges, vertices). |
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Recognize symmetry and
transformations G.TR.04.04 Recognize plane figures that have line symmetry. G.TR.04.05 Recognize rigid motion transformations (flips, slides, turns) of a two-dimensional object. |
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| 6. Recognize parallel and perpendicular line segments and figures that have similarity and/or congruence. | Recognize the basic elements
of geometric objects. G.GS.03.01 Identify points, line segments, lines and distance. G.GS.03.02 Identify perpendicular lines and parallel lines in familiar shapes and in the classroom. |
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Understand perpendicular,
parallel, and intersecting lines G.GS.04.01 Identify and draw perpendicular, parallel, and intersecting lines using a ruler and a tool or object with a square (90º) corner. Recognize symmetry and transformations G.TR.04.05 Recognize rigid motion transformations (flips, slides, turns) of a two-dimensional object. |
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| 7. Use shape, shape properties and shape relationships to describe the physical world and to solve problems. | Create, explore, and describe
shapes G.GS.00.01 Relate familiar three-dimensional objects inside and outside the classroom to their geometric name, e.g., ball/sphere, box/cube, soup can/cylinder, ice cream cone/cone, refrigerator/prism. |
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Identify and describe shapes G.GS.02.01 Identify, describe, and compare familiar two-dimensional and three-dimensional shapes, such as triangles, rectangles, squares, circles, semi-circles, spheres, rectangular prisms. Identify and describe shapes G.GS.02.02 Explore and predict the results of putting together and taking apart two-dimensional and three-dimensional shapes. G.GS.02.03 Draw rectangles and triangles, and compute perimeters by adding lengths of sides, recognizing the meaning of perimeter. G.SR.02.05 Classify familiar plane and solid objects, e.g., square, rectangle, rhombus, cube, pyramid, prism, cone, cylinder, and sphere, by common attributes such as shape, size, color, roundness or number of corners and explalin which attributes are being used for classification. |
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Recognize the basic elements
of geometric objects. G.GS.03.02 Identify perpendicular lines and parallel lines in familiar shapes and in the classroom. G.GS.03.03 Identify parallel faces of rectangular prisms, in familiar shapes and in the classroom. Name, and explore properties of shapes G.GS.03.04 Identify, describe, compare and classify two-dimensional shapes, e.g., parallelogram, trapezoid, circle, rectangle, square and rhombus, based on their component parts (angles, sides, vertices, line segment) and the number of sides and vertices. G.SR.03.05 Compose and decompose triangles and rectangles to form other familiar two-dimensional shapes; e.g., form a rectangle using two congruent right triangles, or decompose a parallelogram into a rectangle and two right triangles. Explore and name three-dimensional solids. G.GS.03.06 Identify, describe, build and classify familiar three-dimensional solids, e.g., cube, rectangular prism, sphere, pyramid, cone, based on their component parts (faces, surfaces, bases, edges, vertices). G.SR.03.07 Represent front, top, and side views of solids built with cubes. M.PS.03.13 Solve contextual problems about perimeters of rectangles and areas of rectangular regions. |
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Use perimeter and area
formulas MTE.04.06 Know and understand the formulas for perimeter and area of a square and a rectangle; calculate the perimeters and areas of these shapes and combinations of these shapes using the formulas. M.TE.04.07 Find one dimension of a rectangle given the other dimension and its perimeter or area. M.TE.04.08 Find the side of a square given its perimeter or area. M.TE.04.09 Solve contextual problems about perimeter and area of squares and rectangles in compound shapes. Problem Solving M.PS.04.11 Solve contextual problems about surface area. |
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K-4 MATHEMATICS: Strand II: Geometry and Measurement – Standard 2: Position
| Elementary Benchmark | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | |||||
| 1. Locate and describe objects in terms of their position, including front, back, inside, outside, right, left, over, under, next to, between and locations on the number line, on a coordinate graph and one a map. | Count, write, and order
numbers N.ME.01.05 Understand that a number to the right of another number on the number line is bigger and that a number to the left is smaller. G.LO.01.02 Describe relative position of objects on a plane and in space, using words such as above, below, behind, in front of. |
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Work with unit fractions N.ME.02.20 Place 0 and halves, e.g., ½ , 1-1/2, 2-1/2, on the number line; relate to a ruler. Use coordinate systems G.LO.02.07 Find and name locations using simple coordinate systems such as maps and first quadrant grids. |
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Understand simple fractions,
relation to the whole, and addition and subtraction of fractions N.ME.03.18 Place fractions with denominators of 2, 4, and 8 on the number line; relate the number line to a ruler,; compare and order up to three fractions with denominators 2, 4, and 8. |
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| 2. Locate and describe objects in terms of their orientation, direction and relative position, including up, down, front, back, N-S-E-W, flipped, turned, translated; recognize symmetrical objects and identify their lines of symmetry. | Create and describe shapes G.LO.01.02 Describe relative position of objects on a plane and in space, using words such as above, below, behind, in front of. |
M | Use coordinate systems G.LO.02.07 Find and name locations using simple coordinate systems such as maps and first quadrant grids. |
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transformations. G.TR.04.04 Recognize plane figures that have line symmetry. G.TR.04.05 Recognize rigid motion transformations (flips, slides, turns) of a two-dimensional object. |
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| 3. Explore what happens to the size, shape and position of an object after sliding, flipping, turning, enlarging, or reducing it. | Identify and describe shapes. G.TR.02.06 Recognize that shapes that have been slid, turned or flipped are the same shape, e.g., a square rotated 45º is still a square. |
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transformations. G.TR.04.04 Recognize plane figures that have line symmetry. G.TR.04.05 Recognize rigid motion transformations (flips, slides, turns) of a two-dimensional object. |
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| (Does not apply at the elementary grades.) | ||||||||||
| 5. Use concepts of position, direction and orientation to describe the physical world and to solve problems. | Create and describe shapes G.LO.01.02 Describe relative position of objects on a plane and in space, using words such as above, below, behind, in front of. |
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Recognize symmetry and
transformations G.TR.04.04 Recognize plane figures that have line symmetry. G.TR.04.05 Recognize rigid motion transformations (flips, slides, turns) of a two-dimensional object. |
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K-4 MATHEMATICS: Strand II: Geometry and Measurement – Standard 3: Measurement
| Elementary Benchmark | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | |||||
| 1. Compare attributes of objects; develop standard units of measurement; and select and use standard tools for measurement. | Explore concepts of time M.UN.00.01 Know and use the common words for the parts of the day (morning, afternoon, evening, night) and relative time (yesterday, today, tomorrow, last week, next year). M.TE.00.02 Identify tools that measure time (clocks measure hours and minutes; calendars measure days, weeks, and months). M.UN.00.03 Identify daily landmark times to the nearest hour (lunchtime is 12 o’clock, bedtime is 8 o’clock). Explore other measurement attributes M.UN.00.04 Compare two or more objects by length, weight and capacity, e.g., which is shorter, longer, taller? M.PS.00.05 Compare length and weight of objects by comparing to reference objects, and use terms such as shorter, longer, taller, lighter, heavier. |
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Estimate and measure length M.UN.01.01 Measure the lengths of objects in non-standard units (e.g., pencil lengths, shoe lengths) to the nearest whole unit. M.UN.01.02 Compare measured lengths using the words shorter, shortest, longer, longest, taller, tallest, etc. Tell time M.UN.01.03 Tell time on a twelve-hour clock face to the hour and half hour. Work with money M.Un.01.04 Identify the different denominations of coins and bills. M.UN.01.05 Match one coin or bill of one denomination to an equivalent set of coins/bills of other denominations, e.g., 1 quarter = 2 dimes and 1 nickel. M.UN.01.06 Tell the amount of money: in cents up to $1, in dollars up to $100. Use the symbols $ and ¢ M.PS.01.07 Add and subtract money in dollars only or in cents only. |
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Measure, add, and subtract
length M.UN.02.01 Measure lengths in meters, centimeters, inches, feet, and yards approximating to the nearest whole unit and using abbreviations: cm, m, in, ft, yd. Tell time and solve time problems M.UN.02.05 Using both A.M. and P.M., tell and write time from the clock face in 5 minute intervals, and from digital clocks to the minute; include reading time: 9:15 as nine-fifteen and 9:50 as nine-fifty. Interpret time both as minutes after the hour and minutes before the next hour, e.g., 8:50 as eight-fifty and ten to nine. Show times by drawing hands on clock face. M.UN.02.06 Use the concept of duration of time, e.g., determine what time it will be half an hour from 10:15. Record, add and subtract money M.UN.02.07 Read and write amounts of money using decimal notations, e.g., $1.15. M.PS.02.08 Add and subtract money in mixed units, e.g., $2.50 + 60 cents and $5.75 - $3, but not $2.50 + $3.10. Read thermometers M.UN.02.09 Read temperature using the scale on a thermometer in degrees Fahrenheit. |
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Measure and use units for
length, weight, temperature and time M.UN.03.01 Know and use common units of measurements in length, weight, and time. M.UN.03.02 Measure in mixed units within the same measurement system for length, weight and time: feet and inches, meters and centimeters, kilograms and grams, pounds and ounces, liters and milliliters, hours and minutes, minutes and seconds, years and months. M.UN.03.03 Understand relationships between sizes of standard units, e.g., feet and inches, meters and centimeters. M.UN.03.04 Know benchmark temperatures such as freezing (32º F, 0º C); boiling (212º F, 100º C); and compare temperatures to these, e.g., cooler, warmer. |
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Understand perpendicular,
parallel, and intersecting lines. G.GS.04.01 Identify and draw perpendicular, parallel, and intersecting lines using a ruler and a tool or object with a square (90º) corner. Measure using common tools and appropriate units M.UN.04.01 Measure using common tools and select appropriate units of measure. M.UN.04.03 Measure and compare integer temperatures in degrees. |
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| 2. Identify the attributes to be measured and select the appropriate unit of measurement for length, mass (weight), area, perimeter, capacity, time, temperature and money. | Explore other measurement
attributes M.UN.00.04 Compare two or more objects by length, weight and capacity, e.g., which is shorter, longer, taller? |
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Work with money M.UN.01.06 Tell the amount of money: in cents up to $1, in dollars up to $100. Use the symbols $ and ¢. |
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Tell time and solve time
problems M.UN.02.05 Using both A.M. and P.M., tell and write time from the clock face in 5 minute intervals, and from digital clocks to the minute; include reading time: 9:15 as nine-fifteen and 9:50 as nine-fifty. Interpret time both as minutes after the hour and minutes before the next hour, e.g., 8:50 as eight-fifty and ten to nine. Show times by drawing hands on clock face. M.UN.02.06 Use the concept of duration of time, e.g., determine what time it will be half an hour from 10:15. Record, add and subtract money M.UN.02.07 Read and write amounts of money using decimal notations, e.g., $1.15. |
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Measure and use units for
length, weight, temperature and time M.UN.03.01 Know and use common units of measurements in length, weight, and time. Understand meaning of area and perimeter and apply in problems M.UN.03.05 Know the definition of area and perimeter and calculate the perimeter of a square and rectangle given whole number side lengths. M.UN.03.06 Use square units in calculating area by covering the region and counting the number of square units. M.UN.03.07 Distinguish between units of length and area and choose a unit appropriate in the context. |
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Measure using common tools
and appropriate units M.UN.04.01 Measure using common tools and select appropriate units of measure. |
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| 3. Develop strategies for estimating measures and compare the estimates to the results of the measurement; decide if an estimate is "a good estimate." | Estimate and measure length M.UN.01.01 Measure the lengths of objects in non-standard units (e.g., pencil lengths, shoe lengths) to the nearest whole unit. M.UN.01.02 Compare measured lengths using the words shorter, shortest, longer, longest, taller, tallest, etc. |
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Measure, add, and subtract
length M.UN.02.01 Measure lengths in meters, centimeters, inches, feet, and yards approximating to the nearest whole unit and using abbreviations: cm, m, in, ft, yd. Understand the concept of area M.UN.02.03 Measure area using non-standard units to the nearest whole unit. |
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Understand meaning of area
and perimeter and apply in problems M.UN.03.08 Visualize and describe the relative sizes of one square inch and one square centimeter. Estimate perimeter and area M.TE.03.09 Estimate the perimeter of a square and rectangle in inches and centimeters; estimate the area of a square and rectangle in square inches and square centimeters. |
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Measure using common tools
and appropriate units M.PS.04.02 Give answers to a reasonable degree of precision in the context of a given problem. |
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| 4. Explain the meaning of measurements and recognize that the number of units it takes to measure an object is related to the size of the unit. | Estimate and measure length M.UN.01.01 Measure the lengths of objects in non-standard units (e.g., pencil lengths, shoe lengths) to the nearest whole unit. Tell time M.UN.01.03 Tell time on a twelve-hour clock face to the hour and half hour. |
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Measure, add, and subtract
length M.UN.02.01 Measure lengths in meters, centimeters, inches, feet, and yards approximating to the nearest whole unit and using abbreviations: cm, m, in, ft, yd. Understand the concept of area M.UN.02.03 Measure area using non-standard units to the nearest whole unit. M.TE.02.04 Find the area of a rectangle with whole number side lengths by covering with unit squares and counting, or by using a grid of unit squares; write the area as a product. |
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Measure using common tools
and appropriate units M.TE.04.04 Measure surface area of cubes and rectangular prisms by covering and counting area of the faces. Convert measurement units M.TE.04.05 Carry out the following conversions from one unit of measure to a larger or smaller unit of measure: meters to centimeters, kilograms to grams, liters to milliliters, hours to minutes, minutes to seconds, years to months, weeks to days, feet to inches, ounces to pounds (using numbers that involve only simple calculations.) |
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| 5. Explore scale drawings, models and maps and relate them to measurements of real objects. | ||||||||||
| 6. Apply measurement to describe the real world and to solve problems. | Measure, add and subtract
length M.PS.02.02 Compare lengths; add and subtract lengths (no conversion of units). Record, add and subtract money M.PS.02.08 Add and subtract money in mixed units, e.g., $2.50 + 60 cents and $5.75 - $3, but not $2.50 + $3.10. Solve measurement problems M.PS.02.10 Solve simple word problems involving length and money. |
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Solve measurement problems M.PS.03.10 Add and subtract lengths, weights and times using mixed units, within the same measurement system. M.PS.03.11 Add and subtract money in dollars and cents. M.PS.03.12 Solve applied problems involving money, length and time. M.PS.03.13 Solve contextual problems about perimeters of rectangles and areas of rectangular regions. |
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Use perimeter and area
formulas M.PS.04.09 Solve contextual problems about perimeter and area of squares and rectangles in compound shapes. Problem solving M.PS.04.11 Solve contextual problems about surface area. |
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K-4 MATHEMATICS: Strand III: Data Analysis and Statistics – Standard 1: Collection, Organization and Presentation of Data
| Elementary Benchmark | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | |||||
| 1. Collect and explore data through counting, measuring, and conducting surveys and experiments. | Use pictographs D.RE.01.01 Collect and organize data to use in pictographs. |
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for given data D.RE.04.01 Construct tables and bar graphs from given data. D.RE.04.02 Order a given set of data, find the median, and specify the range of values. |
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| 2. Organize data using concrete objects, pictures, tallies, tables, charts, diagrams, and graphs. | Use pictographs D.RE.01.01 Collect and organize data to use in pictographs D.RE.01.03 Make pictographs of given data, using both horizontal and vertical forms of graphs; scale should be in units of one and include symbolic representations, e.g., represents one child. |
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Create, interpret, and solve
problems involving pictographs D.RE.02.01 Make pictographs using a scale representation, using scales where symbols equal more than one. |
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Represent and solve problems
for given data D.RE.04.01 Construct tables and bar graphs from given data. D.RE.04.03 Solve problems using data presented in tables and bar graphs, e.g., compare data represented in two bar graphs; read bar graphs showing two data sets. |
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| 3. Present data using a variety of appropriate representations and explain the meaning of the data. | Use pictographs D.RE.01.03 Make pictographs of given data, using both horizontal and vertical forms of graphs; scale should be in units of one and include symbolic representations, e.g., represents one child. |
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for given data D.RE.04.03 Solve problems using data presented in tables and bar graphs, e.g., compare data represented in two bar graphs; read bar graphs showing two data sets. |
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| 4. Identify what data are needed to answer a particular question or solve a given problem, and design and implement strategies to obtain, organize and present those data. |
K-4 MATHEMATICS: Strand III: Data Analysis and Statistics – Standard 2: Description and Interpretation
| Elementary Benchmark | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | |||||
| 1. Read and explain data they have collected and organized themselves and progress to reading data from other sources. | Use pictographs D.RE.01.01 Collect and organize data to use in pictographs. D.RE.01.02 Read and interpret pictographs. D.RE.01.03 Make pictographs of given data, using both horizontal and vertical forms of graphs; scale should be in units of one and include symbolic representations, e.g., represents one child. |
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Create, interpret, and solve
problems involving pictographs D.RE.02.02 Read and interpret pictographs with scales, using scale factors of 2 and 3. |
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Use bar graphs D.RE.03.01 Read and interpret bar graphs, in both horizontal and vertical forms. D.RE.03.03 Solve problems using information in bar graphs, including comparison of bar graphs. |
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Represent and solve problems
for given data D.RE.04.03 Solve problems using data presented in tables and bar graphs, e.g., compare data represented in two bar graphs; read bar graphs showing two data sets. |
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| 2. Describe the shape of the data using informal language. | Use bar graphs D.RE.03.02 Read scales on the axes and identify the maximum, minimum, and range of values in a bar graph. |
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for given data D.RE.04.02 Order a given set of data, find the median, and specify the range of values. |
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| 3. Draw, explain and justify conclusions, such as trends based on data. | Create, interpret, and solve
problems involving pictographs D.RE.02.03 Solve problems using information in pictographs; include scales such as "each ■ represents 2 apples"; avoid partial cases. |
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Use bar graphs D.RE.03.03 Solve problems using information in bar graphs, including comparison of bar graphs. |
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for given data D.RE.04.03 Solve problems using data presented in tables and bar graphs, e.g., compare data represented in two bar graphs; read bar graphs showing two data sets. |
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| 4. Raise and answer questions about the source, collection, organization and presentation of data, as well as the conclusions drawn from the data; explore biases in the data. | Represent and solve problems
for given data D.RE.04.03 Solve problems using data presented in tables and bar graphs, e.g., compare data represented in two bar graphs; read bar graphs showing two data sets. |
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| 5. Formulate questions and problems and gather and interpret data to answer those questions. | Create, interpret, and solve
problems involving pictographs D.RE.02.03 Solve problems using information in pictographs; include scales such as "each ■ represents 2 apples"; avoid partial cases. |
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Represent and solve problems
for given data D.RE.04.01 Construct tables and bar graphs from given data. |
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K-4 MATHEMATICS: Strand III: Data Analysis and Statistics – Standard 3: Inference and Prediction
| Elementary Benchmark | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | |||||
| 1. Make and set hypotheses. | ||||||||||
| 2. Conduct surveys, samplings and experiments to solve problems and answer questions of interest to them. | ||||||||||
| 3. Formulate and communicate arguments and conclusions based on data and evaluate their arguments and those of others. | Represent and solve problems
for given data D.RE.04.03 Solve problems using data presented in tables and bar graphs, e.g., compare data represented in two bar graphs; read bar graphs showing two data sets. |
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| 4. Make and explain predictions based on data. | ||||||||||
| 5. Make predictions to answer questions and solve problems. |
K-4 MATHEMATICS: Strand IV: Number Sense and Numeration – Standard 1: Concepts and Properties of Numbers
| Elementary Benchmark | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | |||||
| 1. Develop an understanding of whole numbers and read, write and count using whole numbers; investigate basic concepts of fractions and decimals. | Count, write, and order
numbers N.ME.00.01 Count whole numbers and recognize how many objects are in sets to 30. N.ME.00.02 Use one-to-one correspondence to compare and order sets of objects to 30 using such phrases as "same number", "more than", or "less than."; use counting, matching, and graphing. N.ME.00.03 Compare and order numbers to 30 using phases such as "more than" or "less than." N.ME.00.04 Read and write numerals to 30 and connect them to the quantities they represent. |
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Count, write, and order
numbers N.ME.01.01 Count to 110 by 1’s, 2’s, 5’s, and 10’s, starting from any number in the sequence; count to 500 by 100’s and 10’s; use ordinals to identify position in a sequence, e.g., 1st, 2nd, 3rd. N.ME.01.02 Read, and write numbers to 110 and relate them to the quantities they represent. N.ME.01.03 Order numbers to 110; compare using the phrases: same as, more than, greater than, fewer than; use = symbol. Arrange small sets of numbers in increasing or decreasing order, e.g., write the following from smallest to largest: 21, 16, 35, 8. N.ME.01.04 Identify one more than, one less than, 10 more than, and 10 less than for any number up to 100. N.ME.01.05 Understand that a number to the right of another number on the number line is bigger and that a number to the left is smaller. N.ME.01.06 Count backward by 1’s, starting from any number between 1 and 100. Explore place value N.ME.01.07 Compose and decompose numbers to 30, including using bundles of tens and units, e.g., recognize 24 as 2 tens and 4 ones, 10 and 10 and 4, 20 and 4, and 24 ones. |
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Count, write, and order whole
numbers N.ME.02.01 Count to 1000 by 1’s, 10’s, and 100’s starting from any number in the sequence. N.ME.02.02 Read and write numbers to 1000 in numerals and words, and relate them to the quantities they represent. N.ME.02.03 Compare and order numbers to 1000; use the symbols > and <. N.ME.02.04 Count orally by 3’s and 4’s starting with 0, and by 2’s, 5’s, and 10’s starting from any number. Understand place value N.ME.02.05 Express numbers up to 1000 using place value, e.g., 137 is 1 hundred, 3 tens, and 7 ones; use concrete materials. Work with unit fractions N.ME.02.18 Recognize, name and represent commonly used unit fractions with denominators 12 or less; model ½, ⅓, and ¼ by folding strips. N.ME.02.19 Recognize, name, and write commonly used fractions: ½, ⅓, ⅔, ¼, 2/4, ¾. N.ME.02.20 Place 0 and halves, e.g., ½, 1-1/2, 2-1/2, on the number line; relate to a ruler. N.ME.02.21 For unit fractions from 1/12 to ½, understand the inverse relationship between the size of a unit fraction and the size of the denominator; compare unit fractions from 1/12 to ½. N.ME.02.22 Recognize that fractions such as 2/2, 3/3 and 4/4 are equal to the whole (one). |
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Understand and use number
notation and place value. N.ME.03.01 Read and write numbers to 10,000 in both numerals and words, and relate them to the quantities they represent, e.g., relate numeral or written word to a display of dots or objects. N.ME.03.02 Recognize and use expanded notation for numbers using place value to 10,000s place, e.g., 2,517 is 2 thousands, 5 hundreds, 1 ten, and 7 ones; 4 hundreds and 2 ones is 402; identify the place value of a digit in a number, e.g., in 3,241, 2 is in the hundreds place. N.ME.03.03 Compare and order numbers up to 10,000. Count in steps, and understand even and odd numbers. N.ME.03.04 Count orally by 6’s, 7’s, 8’s, and 9’s starting with 0, making the connection between repeated addition and multiplication. Understand simple fractions, relation to the whole, and addition and subtraction of fractions. N.ME.03.16 Understand that fractions may represent a portion of a whole unit that has been partitioned into parts of equal area of length; use the terms "numerator" and "denominator." N.ME.03.17 Recognize, name and use equivalent fractions with denominators 2, 4, and 8, using strips as area models. N.ME.03.18 Place fractions with denominators of 2, 4, and 8 on the number line; relate the number line to a ruler; compare and order up to three fractions with denominators 2, 4, and 8. |
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Understand and use number
notation and place value N.ME.04.01 Read and write numbers to 1,000,000; relate them to the quantities they represent, compare and order. N.ME.04.02 Compose and decompose numbers using place value to 1,000,000’s, e.g., 25,068 is 2 ten thousands, 5 thousands, 0 hundreds, 6 tens, and 8 ones. N.ME.04.03 Understand the magnitude of numbers up to 1,000,000; recognize the place value’s of numbers, and the relationship of each place value to the place to its right, e.g., 1,000 is 10 hundreds. Read, interpret and compare decimal fractions N.ME.04.15 Read and interpret decimals up to two decimal places; relate to money and place value decomposition. N.ME.04.16 Know that terminating decimals represent fractions whose denominators are 10, 10 x10, 10 x 10 x 10, etc., e.g., powers of 10. N.ME.04.17 Locate tenths and hundredths on a number line. N.ME.04.18 Read, write, interpret, and compare decimals up to two decimal places. N.ME.04.20 Understand fractions as parts of a set of objects. |
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| 2. Investiagte and develop an understanding of the base-10 place-value system. | Compose and decompose
numbers. N.ME.00.06 Understand the numbers 1 to 30 as having one, or two, or three groups of ten and some ones. Also count by tens with objects in ten-groups, to 100. |
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Count, write, and order
numbers N.ME.01.01 Count to 110 by 1’s, 2’s, 5’s, and 10’s, starting from any number in the sequence; count to 500 by 100’s and 10’s; use ordinals to identify position in a sequence, e.g., 1st, 2nd, 3rd. N.ME.01.02 Read and write numbers to 110 and relate them to the quantities they represent. N.ME.01.04 Identify one more than, one less than, 10 more than, and 10 less than for any number up to 100. N.ME.01.06 Count backward by 1’s, starting from any number between 1 and 100. Explore place value N.ME.01.07 Compose and decompose numbers to 30, including using bundles of tens and units, e.g., recognize 24 as 2 tens and 4 ones, 10 and 10 and 4, 20 and 4, and 24 ones. |
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Count, write, and order whole
numbers N.ME.02.02 Read and write numbers to 1000 in numerals and words, and relate them to the quantities they represent. N.ME.02.03 Compare and order numbers to 1000; use the symbols > and <. Understand place value N.ME.02.05 Express numbers up to 1000 using place value, e.g., 137 is 1 hundred, 3 tens, and 7 ones; use concrete materials. |
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Understand and use number
notation and place value N.ME.03.01 Read and write numbers to 10,000 in both numerals and words, and relate them to the quantities they represent, e.g., relate numeral or written word to a display of dots or objects. N.ME.03.02 Recognize and use expanded notation for numbers using place value to 10,000s place, e.g., 2,517 is 2 thousands, 5 hundreds, 1 ten, and 7 ones; 4 hundreds and 2 ones is 402; identify the place value of a digit in a number, e.g., in 3,241, 2 is in the hundreds place. Understand simple fractions, relation to the whole, and addition and subtraction of fractions. N.ME.03.16 Understand that fractions may represent a portion of a whole unit that has been partitioned into parts of equal area or length; use the terms "numerator" and "denominator." Understand simple decimal fractions in relation to money N.ME.03.21 Understand the meaning of $0.50 and $0.25 related to money, e.g., $1.00 shared by two people means $1.00 ÷ 2 = ½ dollar = $.50. |
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Read, interpret and compare
decimal fractions N.ME.04.15 Read and interpret decimals up to two decimal places; relate to money and place value decomposition. N.ME.04.17 Locate tenths and hundredths on a number line. N.ME.04.18 Read, write, interpret, and compare decimals up to two decimal places. N.MR.04.19 Write tenths and hundredths in decimal and fractions forms, and know the decimal equivalents for halves and fourths. |
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| 3. Develop an understanding of the properties of numbers (e.g., order) and of the properties of the special numbers 0 and 1. | Explore place value N.ME.01.07 Compose and decompose numbers to 30, including using bundles of tens and units, e.g., recognize 24 as 2 tens and 4 ones, 10 and 10 and 4, 20 and 4, and 24 ones. |
M | Understand place value N.ME.02.05 Express numbers up to 1000 using place value, e.g., 137 is 1 hundred, 3 tens, and 7 ones; use concrete materials. |
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notation and place value N.ME.03.02 Recognize and use expanded notation for numbers using place value to 10,000s place, e.g., 2,517 is 2 thousands, 5 hundreds, 1 ten, and 7 ones; 4 hundreds and 2 ones is 402; identify the place value of a digit in a number, e.g., in 3,241, 2 is in the hundreds place. |
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Understand and use number
notation and place value N.ME.04.02 Compose and decompose numbers using place value to 1,000,000’s, e.g., 25,068 is 2 ten thousands, 5 thousands, 0 hundreds, 6 tens, and 8 ones. N.ME.04.03 Understand the magnitude of numbers up to 1,000,000; recognize the place value’s of numbers, and the relationship of each place value to the place to its right, e.g., 1,000 is 10 hundreds. Multiply and divide whole numbers N.ME.04.09 Multiply two-digit numbers by 2, 3, 4, and 5, using the distributive property, e.g., 21 x 3 = (1 + 20) x 3 = (1 x 3) + (20 x 3) = 3 + 60 = 63. |
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| 4. Apply their understanding of number systems to model and solve problems. | Compose and decompose
numbers. N.MR.00.08 Describe and make drawings to represent situations/stories involving putting together and taking apart for totals up to 10; use finger and object counting. |
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Multiply and divide whole
numbers N.MR.03.14 Solve simple division problems involving remainders, viewing remainder as the "number left over" (less than the divisor), e.g., 4 children per group; we have 25 children; there are 6 groups with 1 child left over, interpret based on problem context. Problem solving with whole numbers N.MR.03.15 Given problems that use any one of the four operations with appropriate numbers, represent with objects, words, (including "product" and "quotient"), and mathematical statements; solve. |
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Add and subtract decimal
fractions N.MR.04.31 Use mathematical statements to represent problems that use addition and subtraction of decimals with up to two-digits; solve. Problem solving N.MR.04.37 Solve applied problems using the four basic arithmetic operations, for appropriate fractions, decimals, and whole numbers. |
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| 5. Develop strategies for estimating quantity and evaluate the reasonableness of their estimates. | Add and subtract whole
numbers N.FL.02.11 Estimate and calculate the sum of two numbers with three digits that do not require regrouping. |
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numbers N.FL.03.07 Estimate the sum and difference of two numbers with three digits (sums up to 1000), and judge reasonableness of estimates. |
M | Estimate N.FL.04.34 Estimate the answers to calculations involving addition, subtraction, or multiplication. N.FL.04.35 Know when approximation is appropriate and use it to check the reasonableness of answers; be familiar with common place-value errors in calculations. N.FL.04.36 Make appropriate estimations and calculations fluently with whole numbers using mental math strategies. |
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| 6. Select appropriate numbers and representations in order to solve problems. | Understand meaning of
multiplication and division N.MR.02.13 Understand multiplication as the result of counting the total number of objects in a set of equal groups, e.g., 3 X 5 gives the number of objects in 3 groups of 5 objects, or 3 X 5 = 5 + 5 + 5 = 15. N.MR.02.14 Represent multiplication using area and array models. N.MR.02.16 Given a simple situation involving groups of equal size or of sharing equally, represent with objects, words, and symbols; solve. |
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Problem solving with whole
numbers N.MR.03.15 Given problems that use any one of the four operations with appropriate numbers, represent with objects, words, (including "product" and "quotient"), and mathematical statements; solve. |
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numbers N.MR.04.30 Multiply fractions by whole numbers, using repeated addition and area or array models. Problem solving N.MR.04.37 Solve applied problems using the four basic arithmetic operations, for appropriate fractions, decimals, and whole numbers. |
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K-4 MATHEMATICS: Strand IV: Number Sense and Numeration – Standard 3: Number Relationships
| Elementary Benchmark | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | |||||
| 1. Compare and order numbers using "equal," "less than" or "greater than." | Count, write, and order
numbers N.ME.00.02 Use one-to-one correspondence to compare and order sets of objects to 30 using such phrases as "same number", "more than", or "less than"; use counting and matching. N.ME.00.03 Compare and order numbers to 30 using phrases such as "more than" or "less than." |
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Count, write, and order
numbers N.ME.01.03 Order numbers to 110; compare using the phrases: same as, more than, greater than, fewer than; use = symbol. Arrange small sets of numbers in increasing or decreasing order, e.g., write the following from smallest to largest: 21, 16, 35, 8. N.ME.01.04 Identify one more than, one less than, 10 more than, and 10 less than for any number up to 100. N.ME.01.05 Understand that a number to the right of another number on the number line is bigger and that a number to the left is smaller. |
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Count, write, and order whole
numbers N.ME.02.03 Compare and order numbers to 1000; use the symbols > and <. Work with unit fractions N.ME.02.20 Place 0 and halves, e.g., ½, 1-1/2, 2-1/2, on the number line; relate to a ruler. |
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Understand and use number
notation and place value N.ME.03.03 Compare and order numbers up to 10,000. Understand simple fractions, relation to the whole, and addition and subtraction of fractions. N.ME.03.17 Recognize, name and use equivalent fractions with denominators 2, 4, and 8, using strips as area models. N.ME.03.18 Place fractions with denominators of 2, 4, and 8 on the number line; relate the number line to a ruler; compare and order up to three fractions with denominators 2, 4, and 8. |
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Understand and use number
notation and place value N.ME.04.03 Understand the magnitude of numbers up to 1,000,000; recognize the place value’s of numbers, and the relationship of each place value to the place to its right, e.g., 1,000 is 10 hundreds. Read, interpret and compare decimal fractions N.ME.04.17 Locate tenths and hundredths on a number line. N.ME.04.18 Read, write, interpret, and compare decimals up to two decimal places. Understand fractions N.MR.04.23 Understand the relationships among halves, fourths and eights and among thirds, sixths and twelfths. N.MR.04.26 Compare and order up to three fractions with denominators 2, 4, and 8, and 3, 6, and 12, including improper fractions and mixed numbers. |
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| 2. Use part-whole relationships to explore numbers, develop number concepts and understand computation. | Explore place value N.ME.01.07 Compose and decompose numbers to 30, including using bundles of tens and units, e.g., recognize 24 as 2 tens and 4 ones, 10 and 10 and 4, 20 and 4, and 24 ones. Add and subtract whole numbers N.ME.01.08 List number facts (partners inside of numbers) for 2 through 10; e.g., 8 = 7 + 1 = 6 + 2 = 5 + 3 = 4 + 4; 10 = 8 + 2 = 2 + 8. |
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Understand place value N.ME.02.05 Express numbers up to 1000 using place value, e.g. 137 is 1 hundred, 3 tens, and 7 ones; use concrete materials. Understand meaning of multiplication and division N.MR.02.13 Understand multiplication as the result of counting the total number of objects in a set of equal groups, e.g., 3 X 5 gives the number of objects in 3 groups of 5 objects, or 3 X 5 = 5 + 5 + 5 = 15. Work with unit fractions N.ME.02.22 Recognize that fractions such as 2/2, 3/3 and 4/4 are equal to the whole (one). |
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Understand simple fractions,
relation to the whole, and addition and subtraction of fractions N.ME.03.16 Understand that fractions may represent a portion of a whole unit that has been partitioned into parts of equal area or length; use the terms "numerator" and "denominator." N.ME.03.17 Recognize, name and use equivalent fractions with denominators 2, 4, and 8, using strips as area models. N.ME.03.19 Understand that any fraction can be written as a sum of unit fractions, e.g. ¾ = ¼ + ¼ + ¼ |
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Use factors and multiples N.ME.04.04 Find all factors of a whole number up to 50, and list factor pairs. Understand fractions N.ME.04.20 Understand fractions as parts of a set of objects. N.MR.04.21 Explain why equivalent fractions are equal, using models such as fraction strips or the number line, for fractions with denominators of 12 or less, or equal to 100. N.MR.04.22 Locate and compare fractions on the number line, including improper fractions and mixed numbers with denominators of 12 or less. |
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| 3. Classify numbers as even or odd and explore concepts of factors and multiples. | Count in steps, and
understand even and odd numbers. N.ME.03.05 Know that even numbers end in 0, 2, 4, 6, or 8; name a whole number quantity that can be shared in two equal groups or grouped into pairs with no remainders; recognize even numbers as multiples of 2. Know that odd numbers end in 1, 3, 5, 7, or 9, and work with patterns involving even and odd numbers. |
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Use factors and multiples N.ME.04.04 Find all factors of a whole number up to 50, and list factor pairs. N.ME.04.05 List the first ten multiples of a given one-digit whole number; determine if a whole number is a multiple of a given one-digit whole number, and if a one-digit number is a factor of a given whole number. N.MR.04.06 Know that some numbers, including 2, 3, 5, 7 and 11 have exactly two factors (1 and the number itself) and are called prime numbers. N.MR.04.07 Solve problems about factors and multiples, e.g., since 100 = 4 x 25, and 200 = 2 x 100, then 200 = 2 x 4 x 25 = 8 x 25. |
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| 4. (Does not apply at the elementary grades.) | ||||||||||
| 5. Apply their understanding of number relationships in solving problems. | Problem solving with whole
numbers. N.MR.03.15 Given problems that use any one of the four operations with appropriate numbers, represent with objects, words, (including "product" and "quotient"), and mathematical statements; solve. |
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K-4 MATHEMATICS: Strand V: Numerical and Algebraic Operations and Analytical Thinking – Standard 1: Operations and their Properties
| Elementary Benchmark | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | |||||
| 1. Use manipulatives to model operations with numbers; develop their own methods of recording operations; and relate their models and recordings to standard symbolic expressions and algorithms. | Compose and decompose numbers N.MR.00.07 Compose and decompose numbers from 2 to 10, e.g., 5 = 4 + 1 = 2 + 3, with attention to the additive structure of number, e.g., 6 is 1 more than 5, 7 is one more than 6. N.MR.00.08 Describe and make drawings to represent situations/stories involving putting together and taking apart for totals up to 10; use finger and object counting. Add and subtract numbers N.MR.00.09 Record mathematical thinking by writing simple addition and subtraction sentences, e.g., 7 + 2 = 9, 10 - 8 = 2. |
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Add and subtract whole
numbers N.MR.01.10 Model addition and subtraction for numbers less than 20 for a given contextual situation using objects or pictures; explain in words; record using numbers and symbols; solve. |
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numbers N.MR.02.07 Find the distance between numbers on the number line, e.g., how far is 79 from 26? N.MR.02.09 Given a contextual situation that involves addition and subtraction for numbers up to two digits: model using objects or pictures, explain in words, record using numbers and symbols; solve. Understand meaning of multiplication and division N.MR.02.13 Understand multiplication as the result of counting the total number of objects in a set of equal groups, e.g., 3 X 5 gives the number of objects in 3 groups of 5 objects, or 3 X 5 = 5 + 5 + 5 = 15. N.MR.02.14 Represent multiplication using are and array models. N.MR.02.16 Given a simple situation involving groups of equal size or of sharing equally, represent with objects, words, and symbols; solve. |
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Multiply and divide whole
numbers N.MR.03.10 Recognize situations that can be solved using multiplication and division including finding "How many groups?" and "How many in a group?" and write mathematical statements for those situations. N.MR.03.14 Solve simple division problems involving remainders, viewing remainder as the "number left over" (less than the divisor), e.g., 4 children per group; we have 25 children; there are 6 groups with 1 child left over, interpret based on problem context. |
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Multiply fractions by whole
numbers N.MR.04.30 Multiply fractions by whole numbers, using repeated addition and area or array models. |
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| 2. Develop and apply the appropriate method of computation from among mental computation, estimation, paper-and-pencil or calculators; explain why they are choosing a method and how they know which operations to perform in a given situation. | Add and subtract whole
numbers N.FL.01.12 Know all the addition facts up to 10 + 10, and solve the related subtraction problems fluently. N.FL.01.14 Add three one-digit numbers. N.FL.01.15 Calculate mentally sums and differences involving a two-digit number and a one-digit number without regrouping; a two-digit number and a multiple of 10. N.FL.01.16 Compute sums and differences up to two-digit numbers using number facts and strategies, but no formal algorithm. |
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Add and subtract whole
numbers N.FL.02.06 Decompose 100 into addition pairs, e.g., 99 + 1, 98 + 2… N.FL.02.10 Add fluently two numbers up to two digits each, using strategies including formal algorithms; subtract fluently two numbers up to two digits each. N.FL.02.12 Calculate mentally sums and differences involving: three-digit numbers and ones; three-digit numbers and tens; three-digit numbers and hundreds. Understand meaning of multiplication and division N.FL.02.17 Develop strategies for fluently multiplying numbers up to 5 x 5. |
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Add and subtract whole
numbers N.FL.03.06 Add and subtract fluently two numbers; up to and including two-digit numbers with regrouping and up to four-digit numbers without regrouping. N.FL.03.07 Estimate the sum and difference of two numbers with three digits (sums up to 1000), and judge reasonableness of estimates. N.FL.03.08 Use mental strategies to fluently add and subtract two-digit numbers. Multiply and divide whole numbers N.FL.03.11 Find products fluently up to 10 x 10; find related quotients using multiplication and division relationships. N.FL.03.13 Mentally calculate simple products and quotients: up to a three-digit number by a one-digit number involving multiples of 10, e.g., 500 X 6 or 400 ÷ 8. |
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Add and subtract whole
numbers N.FL.04.08 Add and subtract whole numbers fluently. Multiply and divide whole numbers N.ME.04.09 Multiply two-digit numbers by 2, 3, 4, and 5, using the distributive property, e.g., 21 x 3 = (1 + 20) x 3 = (1 x 3) + (20 x 3) = 3 + 60 = 63. N.FL.04.10 Multiply fluently any whole number by a one-digit number, and a three-digit number by a two-digit number; for two-digit by one-digit multiplication, use distributive property to develop meaning for the algorithm. N.FL.04.11 Divide numbers up to four-digits by one-digit numbers and by 10. Add and subtract fractions N.MR.04.27 Add and subtract fractions less than 1 with denominators 12 or less and including 100, in cases where the denominators are equal or when one denominator is a multiple of the other; e.g., 1/12 + 5/12 = 6/12; 2/25 + 7/50 = 11/50. N.FL.04.28 Solve fraction problems involving sums and differences for fractions where one denominator is a multiple of the other (denominators 2 through 12, and 100). Add and subtract decimal fractions N.FL.04.32 Add and subtract decimals up to two decimal places. Multiply and divide decimal fractions N.FL.04.33 Multiply and divide decimals up to two decimal places by a one-digit whole number where the result is a terminating decimal, e.g. 0.42 ÷ 3 = 0.14, but not 5 + 3 = 1.6. Estimate N.FL.04.34 Estimate the answers to calculations involving addition, subtraction, or multiplication. N.FL.04.35 Know when approximation is appropriate and use it to check the reasonableness of answers; be familiar with common place-value errors in calculations. N.FL.04.36 Make appropriate estimations and calculations fluently with whole numbers using mental math strategies. |
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| 3. Explore properties of operations (e.g., commutative and distributive properties) and give examples of how they use those properties. | Explore place value N.ME.01.07 Compose and decompose numbers to 30, including using bundles of tens and units, e.g., recognize 24 as 2 tens and 4 ones, 10 and 10 and 4, 20 and 4, and 24 ones. Add and subtract whole numbers N.MR.01.11 Understand the inverse relationship between addition and subtraction, e.g., subtraction "undoes" addition: if 3 + 5 = 8, we know that 8 – 3 = 5 and 8 – 5 = 3; recognize that some problems involving combining, "taking away", or comparing can be solved by either operation. Add and subtract whole numbers N.FL.01.12 Know all the addition facts up to 10 + 10, and solve the related subtraction problems fluently. |
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Understand place value N.ME.02.05 Express numbers up to 1000 using place value, e.g., 137 is 1 hundred, 3 tens, and 7 ones; use concrete materials. Understand meaning of multiplication and division N.MR.02.15 Understand division (÷) as another way of expressing multiplication, using fact families within the 5 x 5 multiplication table; emphasize that division "undoes" multiplication, e.g. 2 x 3 = 6 can be rewritten as 6 ÷ 2 = 3 or 6 ÷ 3 = 2. |
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Understand and use number
notation and place value N.ME.03.02 Recognize and use expanded notation for numbers using place value to 10,000s place, e.g., 2,517 is 2 thousands, 5 hundreds, 1 ten and 7 ones; 4 hundreds and 2 ones if 402; identify the place value of a digit in a number, e.g., in 3,241, 2 is in the hundreds place. Multiply and divide whole numbers N.MR.03.09 Use multiplication and division fact families to understand the inverse relationship of these two operations, e.g., because 3 x 8 = 24, we know that 24 ÷ 8 = 3 or 24 ÷ 3 = 8; express a multiplication statement as an equivalent division statement. |
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Understand and use number
notation and place value N.ME.04.02 Compose and decompose numbers using place value to 1,000,000’s, e.g. 25,068 is 2 ten thousands, 5 thousands, 0 hundreds, 6 tens, and 8 ones. Multiply and divide whole numbers N.ME.04.09 Multiply two-digit numbers by 2, 3, 4 and 5, using the distributive property, e.g. 21x 3 = (1 + 20) x 3 = (1 x 3) + (20 x 3) = 3 + 60 = 63. N.FL.04.10 Multiply fluently any whole number by a one-digit number, and a three-digit number by a two-digit number; for two-digit by one-digit multiplication, use distributive property to develop meaning for the algorithm. N.MR.04.13 Use the relationship between multiplication and division to simplify computations and check results. Read, interpret and compare decimal fractions N.ME.04.16 Know that terminating decimals represent fractions whose denominators are 10, 10 x 10, 10 x 10 x 10, etc. e.g., powers of 10. |
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| 4. Apply operations efficiently and accurately in solving problems. | Problem solving with whole
numbers N.MR.03.15 Given problems that use any one of the four operations with appropriate numbers, represent with objects, words, (including "product" and "quotient"), and mathematical statements; solve. |
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numbers N.FL.04.14 Solve applied problems involving whole number multiplication and division. Add and subtract fractions N.FL.02.28 Solve fraction problems involving sums and differences for fractions where one denominator is a multiple of the other (denominators 2 through 12, and 100). Add and subtract decimal fractions N.MR.04.31 Use mathematical statements to represent problems that use addition and subtraction of decimals with up to two-digits; solve. Problem solving N.MR.04.37 Solve applied problems using the four basic arithmetic operations, for appropriate fractions, decimals, and whole numbers. |
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K-4 MATHEMATICS: Strand V: Numerical and Algebraic Operations and Analytical Thinking – Standard 2: Algebraic and Analytic Thinking
| Elementary Benchmark | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | |||||
| 1. Write and solve open sentences (e.g., + = 5) and write stories to fit the open sentence. | Compose and decompose numbers N.MR. 00.08 Describe and make drawings to represent situations/stories involving putting together and taking apart for totals up to 10; use finger and object counting. |
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Add and subtract whole
numbers N.MR.01.13 Apply knowledge of fact families to solve simple open sentences for addition and subtraction, such as: + 2 = 7 and 10 - = 6. |
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numbers N.MR.02.08 Find missing values in open sentences, e.g., 42 + = 57; use relationship between addition and subtraction. |
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numbers N.MR.03.10 Recognize situations that can be solved using multiplication and division including finding "How many groups?" and "How many in a group?" and write mathematical statements for those situations. N.MR.03.12 Find solutions to open sentences, such as 7 X = 42 or 12 ÷ = 4, using the inverse relationship between multiplication and division. |
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Multiply and divide whole
numbers N.FL.04.12 Find unknowns in equations such as a ÷ 10 = 25; 125 ÷ b = 25. |
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| 2. Explore algebraic concepts with manipulatives such as balance scales, tables of input and output, and pictorial representations of problems. | Add and subtract whole
numbers N.MR.01.10 Model addition and subtraction for numbers less than 20 for a given contextual situation using objects or pictures; explain in words, record using numbers and symbols; solve. |
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numbers N.MR.02.09 Given a contextual situation that involves addition and subtraction for numbers up to two digits; model using objects or pictures, explain in words, record using numbers and symbols; solve. Create, interpret, and solve problems involving pictographs D.RE.02.01 Make pictographs using a scale representation, using scales where symbols equal more than one. |
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| 3. Find replacements for the variable(s) in open sentences. | Add and subtract whole
numbers. N.MR.01.13 Apply knowledge of fact families to solve simple open sentences for addition and subtraction, such as: + 2 =7 and 10 - = 6. |
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numbers N.MR.02.08 Find missing values in open sentences, e.g., 42 + = 57; use relationship between addition and subtraction. |
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numbers N.MR.03.12 Find solutions to open sentences, such as 7 x = 42 or 12 ÷ = 4, using the inverse relationship between multiplication and division. |
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numbers N.FL.04.12 Find unknowns in equations such as a ÷ 10 = 25; 125 ÷ b = 25. N.MR.04.29 Solve for the unknown in equations such as: 1/8 + x = 5/8 or ¾ - y = 1/2 |
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| 4. Use analytic thinking to describe situations and solve problems. | ||||||||||
| 5. (Does not apply at the elementary grades.) |
K-4 MATHEMATICS: Strand VI: Probability and Discrete Mathematics – Standard 1: Probability
| Elementary Benchmark | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | |||||
| 1. Explain the difference between chance and certainty and give examples to illustrate their understanding. | ||||||||||
| 2. Compare events and describe them as "more likely" or "less likely" and use the language of fractions to describe simple probabilities. | ||||||||||
| 3. Conduct experiments with concrete objects to explore concepts and develop an intuitive understanding of how the conditions of the experiment can affect the outcome. | ||||||||||
| 4. Conduct experiments, record the outcomes, examine those outcomes to determine if they make sense and search for explanations of the outcomes. | ||||||||||
| 5. Conduct probability experiments and simulations to model and solve problems. |
K-4 MATHEMATICS: Strand VI: Probability and Discrete Mathematics – Standard 2: Discrete Mathematics
| Elementary Benchmark | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | |||||
| 1. Use manipulatives and diagrams to explore problems involving counting and arranging objects. | ||||||||||
| 2. Explore sets and set relationships by sorting and classifying objects. | Create, explore and describe
shapes G.GS.00.02 Identify, sort and classify objects by attribute and identify objects that do not belong in a particular group. |
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Count, write, and order
numbers N.MR.01.03 Order numbers to 110; compare using the phrases: same as, more than, greater than, fewer than; use = symbol. Arrange small sets of numbers in increasing or decreasing order, e.g., write the following from smallest to largest: 21, 16, 35, 8. Add and subtract whole numbers N.MR.01.09 Compare two or more sets in terms of the difference in number of elements. |
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| 3. Explore situations in which they model and trace paths using figures consisting of vertices connected by edges. | ||||||||||
| 4. Explore now-next patterns. | ||||||||||
| 5. Explore, develop and invent their own algorithms to accomplish a task or to solve numerical problems. | Add and subtract whole
numbers N.FL.01.16 Compute sums and differences up to two-digit numbers using number facts and strategies, but no formal algorithm. |
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| 6. Use discrete mathematics concepts as described above to model situations and solve problems; and look for whether or not there is a solution (existence problems), determine how many solutions there are (counting problems) and decide upon a best solution (optimization problems). |