1.1 Understand and apply concepts and procedures from number sense.

Grade 3

Grade 4

Grade 5

Number and Numeration

1.1.1

Understand the concept of whole numbers. W

·          Represent a number to at least 100,000 in different ways (e.g., words, numerals, pictures, physical models). [CU]

·          Translate from one representation of a whole number to another in standard, expanded, and word forms. [SP, RL, CU, MC]

·          Generate equivalent representations for a given number by decomposing and composing. [SP, RL]

·          Explain the difference between the natural numbers and the whole numbers

·          Explain what makes a number odd or even.

Understand the concept of decimals (money) and fraction. W

·          Interpret fractions as parts of a whole object, number, or set (e.g., ½ of a medium pizza and ½ of a large pizza are not equal amounts).

·          Symbolically represent parts of a whole or parts of a set with common denominators. [CU]

·          Explain how fractions (denominators of 2, 3, 4, 6, and 8) represent information across the curriculum (e.g., interpreting circle graphs, fraction of states that border an ocean). [CU, MC, SP, RL]

·           Represent decimals (money) in multiple ways (e.g., symbols, physical models)

Understand the concepts of fractions and decimals. W

·          Demonstrate understanding of the concepts and symbolic representations of mixed numbers and improper fractions and decimals

·          Create a model when given a symbolic representation or write the fraction when given a model (e.g., number line). [CU]

·          Explain the value of a given digit in a decimal to at least the thousandths place. [CU]

·          Explain how the value of a fraction changes in relationship to the size of the whole (e.g., half a pizza vs. half a cookie). [CU]

·          Use factors and multiples to rename equivalent fractions. [SP, RL]

·          Read and write decimals to at least the thousandth place. [CU]

1.1.2

Understand the relative values of whole numbers. W

·          Compare whole number values to at least 100,000 using the symbols for "greater than", "less than", and “equal to".

·          Order three or more numbers to at least 100,000 from smallest to largest. [CU]

·          Compare combined quantities (e.g. 50 + 3 is greater than 40 + 9) [SP, RL]

Understand the relative values of fractions and decimals (money). W

·          Model and describe equivalent fractions (e.g., paper folding, geoboards, parallel number lines). [CU]

·          Use a number line to approximate and label halves, thirds, and fourths in relationship to whole units. [CU, MC]

·          Order fractions with like denominators.. [CU, MC]

·          Demonstrate and explain equivalent relationships between decimals and fractions (e.g., $.50 is equal to ½ a dollar and 50/100 of a dollar) using models. [CU, MC]

Understand the relative values of non-negative fractions or decimals. W

·          Demonstrate understanding of the relative values of non-negative fractions (denominators of 2, 3, 4, 5, 6, or 10) or decimals.

·          Compare, order, or illustrate whole numbers, decimals, and fractions using concrete models (e.g., number line or shaded grid) or implementing strategies (e.g., like denominators, benchmarks, conversions). [SP, RL, CU, MC]

·          Determine equivalence among fractions. [SP, RL]

·          Explain the relative values of non-negative fractions or decimals. [CU]

1.1 Understand and apply concepts and procedures from number sense.

Grade 3

Grade 4

Grade 5

Number and Numeration

1.1.3

Understand and apply the commutative and identity properties of addition on whole numbers. W

·          Explain how the commutative property works with addition and not subtraction, using words, numbers, or physical models. [CU]

·          Describe how the identity property works with addition. [CU]

·          Evaluate addition equations as true or false and explain based on the commutative and identity properties for addition. (e.g., 14 + (0 + 38) = 38 + (14 + 0))

Understand and apply the associative property of addition, and commutative, associative, identity, and zero properties of multiplication on whole numbers. W

·          Describe how the commutative property works with multiplication and not division using words, numbers, or physical models. [CU]

·          Describe how the identity property for addition is different from the identity property for multiplication using words, numbers, or physical models.  [CU]

·          Evaluate equations as true or false and explain based on any of the properties for multiplication

(e.g., 4 x (5 x 6) = (4 x 5) x 6). [SP, RL]

·          Evaluate equations as true or false and explain based on any of the properties

(e.g., 14 + (62 + 38) = (14 + 62) + 38). [SP, RL]

Understand and apply concepts of divisibility. W

·        Apply the concepts of odd and even numbers to check for divisibility, finding factors and multiples.

·          Illustrate prime or composite numbers by creating a physical model (e.g., arrays, area models). [CU]

·          Identify the prime numbers between 1 and 100

·          Explain why a whole number between 1 and 100 is prime or composite. [CU]

·          Explain a method to find the least common multiple (LCM) and greatest common factor (GCF) of two numbers.

·          Solve problems related to primes, factors, multiples, and composites in a variety of situations (e.g., find a mystery number, find unit pricing, increase or decrease a recipe, find the portions for a group) .[SP, RL, MC]

1.1.4

1.1 Understand and apply concepts and procedures from number sense.

Grade 3

Grade 4

Grade 5

Computation

1.1.5

Understand the meaning of multiplication and division on whole numbers. W

·          Illustrate multiplication and division using models and diagrams. [CU]

·          Illustrate and explain the inverse relationship between multiplication and division using physical diagrams, words, and symbols (e.g., arrays, fact families). [CU]

·          Describe and compare strategies to solve problems involving multiplication and division (e.g., alternative algorithms different strategies, decomposition, properties of multiplication). [CU]

Understand the meaning of addition and subtraction on like-denominator fractions. W

·          Represent addition and subtraction of decimals through hundredths using models (e.g., with money). [CU]

·          Represent addition and subtraction of fractions with like denominators using models (e.g., fraction circles, number lines, geoboards). [CU]

·          Explain the meaning of addition and subtraction of like denominator fractions. [CU]

Understand the meaning of addition and subtraction on non-negative decimals and fractions. W

·          Demonstrate understanding of the meaning of addition and subtraction of non-negative decimals and fractions.(e.g., fractions with denominators of 2, 4, 8 or 2, 3, 6, 12 or 5, 10 – highest LCM of 12).

·          Explain the meaning of adding and subtracting fractions and decimals using words, symbols, or other models. [CU]

·          Create a problem situation involving addition or subtraction of non-negative decimals or fractions. [SP, RL, CU, MC]

1.1.6

Apply procedures of addition and subtraction on whole numbers with fluency. W

·          Describe and compare strategies to solve three-digit addition and subtraction problems (e.g., child developed algorithms, decomposition). [SP, RL, CU, MC]

·          Use joining, separating, adding-on, and finding the difference to solve problems.

·          Write and solve multi-step problem situations that involve addition and subtraction. [SP, RL, CU, MC]

Apply procedures of multiplication and division on whole numbers with fluency. W

·          Use a variety of strategies to mentally access multiplication and division facts through 12's. [SP, RL]

·          Recall multiplication and division facts through 12’s.

·          Record, share, and evaluate algorithms used in computational situations. [CU]

·          Write and solve problem situations with whole numbers using a combination of any two operations. [SP, RL, CU, MC]

·          Interpret remainders of a division problem in a given situation. [SP, RL, MC]

Apply procedures of addition and subtraction on non-negative decimals and like-denominator fractions. W

·          Fractions with denominators of: 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 16, 20, and 100)

·          Explain a strategy for adding fractions. [CU]

·          Write and solve problem situations to find sums or differences of decimals or like-denominator fractions. [SP, RL, CU, MC]

1.1 Understand and apply concepts and procedures from number sense.

Grade 3

Grade 4

Grade 5

Computation

1.1.7

Understand and apply strategies and tools as appropriate to tasks involving addition and subtraction on whole numbers.

·          Use appropriate strategies and tools from among mental computation, estimation, calculators, and paper and pencil to compute in a problem situation. [SP, RL]

·          Defend situations in which estimation is sufficient (e.g., grocery shopping or party supplies). [CU]

·          Use mental arithmetic, pencil and paper, or calculator as appropriate to the task involving addition and subtraction of whole numbers.

Understand and apply strategies and tools as appropriate to tasks involving multiplication and division on whole numbers.

·          Select and justify appropriate strategies and tools from among mental computation, estimation, calculators, and paper and pencil to compute in a problem situation. [SP, RL]

§          Use estimation strategies appropriately when the exact answer is not necessary. [SP, RL]

§          Identify and justify situations when estimation is not appropriate. [SP, RL, CU, MC]

§          Use mathematical tools as appropriate to the task involving multiplication and division of whole numbers

Understand and apply strategies and tools as appropriate to tasks involving addition and subtraction of non-negative, like denominator fractions or decimals.

·          Select and justify strategies and appropriate tools from among mental computation, estimation, calculators, manipulatives, and paper and pencil to compute a problem situation. [SP, RL]

·          Use mental arithmetic to add and subtract non-negative decimals and like-denominator fractions.

Estimation

1.1.8

Understand and apply estimation strategies to determine the reasonableness of answers in situations involving addition and subtraction on whole numbers. W

·          Identify when an approximation is appropriate;

·          Use estimation to determine the reasonableness of answers in situations

·          Describe and justify reasonableness of an estimate in computation. [SP, RL, CU]

·          Use a variety of estimation strategies (e.g., multiples of 10 and 100, rounding, front-end estimation, compatible numbers, clustering). [SP, RL]

·          Describe and justify whether an approximation is or is not appropriate. [SP, RL, CU]

Understand and apply estimation strategies to determine the reasonableness of answers in situations involving multiplication and division on whole numbers. W

·          Identify when an approximation is appropriate

·          Use estimation to determine the reasonableness of answers in situations.

·          Use a variety of strategies to approximate sums, differences, products, and quotients. [SP, RL]

·          Make and explain an appropriate adjustment when an estimate and a solution don't agree. [SP, RL, CU]

Understand and apply estimation strategies to determine the reasonableness of answers in situations involving addition and subtraction on non-negative decimals and like-denominator fractions. W

·          Identify when an approximation is appropriate;

·          Use estimation to determine the reasonableness of answers in situations

·          Use estimation strategies prior to computation of addition and subtraction of decimals and like-denominator fractions to determine reasonableness of answers. [SP, RL]

·          Identify reasonableness of estimated answers for a given situation. [SP, RL]

·          Articulate various strategies used during estimation. [CU]

1.2 Understand and apply concepts and procedures from measurement.

Grade 3

Grade 4

Grade 5

Attributes, Units and Systems

1.2.1

Understand how different attributes (of length, perimeter,  time, money value, weight/mass, and temperature) are used to describe objects. W

·          Describe the different measures (hour, minutes, and seconds) of time displayed on a clock. [CU]

·          Given an object, name the attributes that can be measured. [CU, MC]

·          Identify temperature on thermometers with different scales (e.g., increments of 1, 2, 5, or 10 degrees).

·          Use measurements of length, perimeter, time, money, weight, and temperature to describe and compare objects. [CU]

Understand the concept of area. W

·          Demonstrate and explain that area is covering a shape and perimeter is enclosing a shape. [CU, MC]

·          Describe situations where area is the needed measurable attribute (e.g., buying carpet to cover a floor, painting a wall, describing the amount of floor space in a room).  [CU, MC]

·          Compare areas of different shapes and sizes. [SP, RL]

·          Use measurements of area to describe and compare objects. [CU]

Understand the concept of angle measurement. W

·          Describe and compare angles in a variety of objects. [CU, MC]

·          Identify angles in the environment. [MC]

·          Classify angles as right, acute or obtuse. [CU]

·          Identify types of angles in polygons (e.g., right, acute, obtuse). [MC]

·          Explain and provide examples of how angles are formed.

1.2.2

Understand the differences between non-standard and standard units of measurement for length and weight/mass in either U.S. or metric systems. W

·          Given an attribute of length or weight/mass, identify an appropriate unit of measurement.

·          Measure the length or weight/mass of objects and compare measurements using standard units.

·          Explain when standard units of measurement are more appropriate than nonstandard units.

·          Identify when two measurements are not necessarily equal (e.g., 1 pace long can represent). [CU, MC]).

Understand the differences between length units and area (square) units in U.S. or metric systems. W

·          Measure perimeter and area for regular and irregular shapes (e.g., use tiles, inches, or grid paper to find perimeter or area of mats, CDs, or skateboards). [SP, RL, MC]

·          Compare and describe area measurements made using different units (e.g., square inches vs. square centimeters). [SP, RL]

·          Describe how the unit chosen to measure linear dimensions can determine the unit used to measure area (e.g., measuring perimeter in cm produces an area in square cm) [CU].

Understand degrees (30°, 45°, 60°, and 90°) as units of measurement for angles. W

·          Demonstrate understanding of the concept of degrees in angles as units of measurement - specifically 30°, 45°, 60°, 90°, and 180° angle measurements and their relation to right angle.

·          Measure angles to the nearest 5 degrees using a protractor, angle ruler, or other appropriate tool. [SP, RL]

·          Measure angles in assorted polygons and determine the total number of degrees in the polygon. [SP, RL]

·          Describe relationships between angle measures (e.g., two 30° angles have the same total measure as one 60° angle) [CU]

·          Explain how degrees are used as measures of angles (e.g., a circle can be divided into 360°).

1.2 Understand and apply concepts and procedures from measurement.

Grade 3

Grade 4

Grade 5

Attributes, Units and Systems

1.2.3

Understand how measurement units of length (U.S.) and capacity (U.S.) are organized into systems.

·          Describe the various units of measurement for length and capacity and explain how they are organized.

·          Explain the benefits and appropriate uses of standard units of measurement for length and capacity using  our customary (U.S.) system. [CU]

Understand how measurement units of time and weight (U.S.), are organized into systems. W

·          Demonstrate understanding of how units of measurement are organized into time and weight in U.S. systems.

·          Know and correctly label the basic units of measurement for time and weight measure in the metric and customary system. [CU]

·          Explain the benefits and appropriate uses of standard units of measurement for area using both customary and metric systems.

Understand how measurement units of capacity, weight, and length are organized in the metric system. W

·          Demonstrate understanding of how units of measurement are organized into capacity, weight and length in the metric systems.

·          Explain and give examples of the metric system standard units for capacity, weight, and length..

Procedures, Precision, and Estimation

1.2.4

Understand and apply systematic procedures to measure length, perimeter, time, weight, money value, and temperature. W

·          Use systematic procedures to measure length, perimeter, time, weight, money value, and temperature to describe and compare objects.

·   Identify attribute to measure

·   Select and use appropriate units

·   Select and use tools that match the unit

·   Count, or compute, and label measures

·          Determine the attribute to be measured.

·          Explain and use a method for making change with coins. [CU].

Understand and apply systematic procedures to determine the area of figures composed of rectangles. W

·          Use systematic procedures to measure, describe and compare the areas of figures composed of rectangles..

·   Identify attribute to measure

·   Select and use appropriate units

·   Select and use tools that match the unit

·   Count, or compute, and label area measures

·          Explain and use a method for measuring the area of an irregular shape (e.g., Describe an irregular shape in terms of the composition of regular figures). [CU]

Understand and apply systematic procedures to determine the areas of rectangles and right triangles. W

·          Use systematic procedures to measure, describe and compare the areas of rectangles (including squares) and right triangles.

·   Identify attribute to measure

·   Select and use appropriate units

·   Select and use tools that match the unit

·   Count, or compute, and label measures

·          Determine the appropriate unit to measure the area of objects (e.g., square cm, sq. feet, and sq. miles). [SP, RL]

·          Use measurements of area to describe and compare rectangles

·          Select an appropriate tool according to the unit chosen. [MC]

·          Compare the object being measured with the units on the tool being used and record and label the units. [SP, RL, CU]

·          Explain and use a method for measuring the area of a rectangle. [CU]

1.2 Understand and apply concepts and procedures from measurement.

Grade 3

Grade 4

Grade 5

Procedures, Precision, and Estimation

1.2.5

Understand and apply formulas to measure perimeter of rectangles. W

·          Demonstrate understanding of or use formulas to find the perimeter of any rectangle.

·          Explain how to find the perimeter of any rectangle using a rule

·          Explain why linear units are used for perimeter. [CU]

·          Explain how to use a formula to find the perimeter of a rectangle. [CU]

·          Find and compare all possible rectangles with whole number dimensions and a whole number perimeter. (e.g. Find all possible rectangles with a perimeter of 28 and whole number measures as lengths of sides). [SP, RL, CU]

Understand and apply formulas to measure area of rectangles and right triangles. W

·          Demonstrate understanding of or use formulas to find the area of any rectangle or right triangle

·          Explain how to find the area of any rectangle using a rule

·          Explain why square units are used for area. [CU]

·          Explain and use formulas to find the area of a rectangle. [CU]

·          Explain and use a formula to find the area of a right triangle. [CU]

·          Find and compare all possible rectangles or right triangles with whole number dimensions with a given area (e.g., a rectangle with an area of 24 square feet could be 1’x24’, 2’x12’,3’x8’, or 4’x6’). [SP, RL, CU]

·           

1.2.6

Understand and apply strategies to obtain reasonable estimates of linear, time, weight, and temperature measurements. W

·          Identify situations in which estimated measurements are sufficient; estimate length, perimeter, time, money, weight or temperature.

·          Estimate a measurement using standard or nonstandard units (e.g., paper clips, inches, minutes, or foot lengths). [SP, RL]

·          Use referents to standard units (e.g., width of pinkie finger is similar to a centimeter). [MC]

Understand and apply strategies to obtain reasonable estimates of area measurements for irregular figures. W

·          Identify situation in which estimate measurements are sufficient; estimate areas of irregular figures.

·          Compare areas of irregular shapes with different perimeters {e.g., leafs, ponds) [SP, RL, MC]

·          Apply a process that can be used to find a reasonable estimate of the area measurement of an irregular shape (e.g., use tiles or pieces of paper to measure leafs, ponds) [SP, RL, CU]

·          Describe a procedure to estimate the area of an irregularly shaped room. [SP, RL, CU

Understand and apply strategies to obtain reasonable estimates of angles, and area measurements for rectangles and triangles. W

·          Identify situation in which estimated measurements are sufficient; estimate measures of angles  and areas in rectangles and triangles

·          Estimate a measurement using standard or nonstandard units (e.g., tiles, square feet, note cards). [SP, RL]

·          Use estimation to justify reasonableness of a measurement (e.g., estimate the area of the classroom by using carpet squares). [SP, RL]

·          Determine whether an angle is closest to 30° 45°,60°, 90°

1.3 Understand and apply concepts and procedures from geometric sense.

Grade 3

Grade 4

Grade 5

Properties and Relationships

1.3.1

Understand the concept of congruence. W

·          Identify, describe and compare congruent 2-dimensional geometric figures. [SP, RL, CU, MC]

·          Given a variety of figures, determine which figures are congruent. [MC]

·          Draw a shape that is congruent to a given2-dimensional shape. [CU]

·          Explain congruence and use an example to demonstrate it.

Understand and illustrate concepts of parallel and perpendicular lines and line symmetry in 2-dimensional shapes and  figures. W

·          Identify symmetrical 2-dimensional figures and shapes (e.g., quilt blocks, textiles) [CU]

·          Complete a picture or design over a line of symmetry.

·          Identify and draw a line of symmetry (e.g., folding or using a mirror). [CU]

·          Identify parallel and perpendicular lines in 2-dimensional figures and shapes and in the environment. [SP, RL, CU, MC]

·          Describe attributes of 2-dimensional geometric figures using appropriate vocabulary (e.g., parallel, perpendicular, symmetric). [CU, MC]

·          Explain parallel and perpendicular and give examples to demonstrate them.

Understand characteristics of angles, polygons and circles . W

·          Explain the difference between a regular and irregular polygon. [CU]

·          Identify, sort, classify, or explain the properties of angles, polygons, or circles based on attributes (e.g., triangles (right, equilateral, isosceles, or scalene), angles (acute, right, obtuse, or straight), circles (diameter, radius, and circumference), or quadrilaterals (squares, rectangles, parallelograms, or trapezoids)). [SR, CU]

·          Construct a geometric shape and shape using geometric properties. [SR, MC]

1.3.2

Understand and apply attributes and properties of polygons. W

·          Use attributes and properties to identify, name, draw, compare, and/or sort 2-dimensional shapes and figures.

·          Draw 2-dimensional figures given particular attributes (e.g., triangle, rectangle with all sides the same length)

·          Identify, name and describe the attributes and properties of polygons. [CU]

·          Given two polygons, explain how they are alike and different in terms of their attributes and properties (e.g., using a Venn diagram). [CU]

·          Give oral directions so that someone else can duplicate a design involving polygons (e.g., to a friend who can’t see the design). [CU]

Apply understanding of congruence to 2-dimensional shapes and figures. W

·          Identify, describe, and compare attributes of congruent figures in multiple orientations. [CU, SP, RL]

·          Build and draw congruent figures. [CU]

·          Identify, name, compare and sort congruent 2-dimensional figures and shapes in multiple orientations. [SP, RL]

Apply understanding of the properties of parallel and perpendicular and line symmetry to 2-dimensional shapes and figures. W

·          Identify, name, compare and sort parallel and perpendicular lines in 2-dimensional figures. [SP, RL, CU]

·          Draw and label a design that includes a given set of attributes. [CU]

·         Compare shapes using symmetry. [CU]

·          Determine whether lines are parallel or perpendicular to a part of a given shape.

1.3 Understand and apply concepts and procedures from geometric sense.

Grade 3

Grade 4

Grade 5

Locations and Transformations

1.3.3

Understand relative locations, including intervals, of numbers on a positive number line. W

·          Given directions for movement on a positive number line, identify the point of final destination using real-world examples (e.g., travel back and forth on a street, temperature variation at different times of the day, dance steps from diverse cultures). [SP, RL, MC]

·          Identify the interval on a given number line (e.g., describe the scale on a graph). [CU]

·          Describe the relative locations of points on a number line with positive coordinates. [CU]

Apply understanding of the location of points on a coordinate grid in the first quadrant. W

·          Describe the location in the first quadrant on a coordinate grid in terms of horizontal and vertical position (e.g., to the right and up, longitude and latitude). [CU, MC]

·          Plot a given set of ordered pairs in the first quadrant of a coordinate grid. [CU]

·          Give directions from one location to another using ordered pairs in the first quadrant of a coordinate grid (e.g., given a state map, specify location of landmarks). [CU, MC]

Apply understanding of the location of non-negative rational numbers on a positive number line. W

·          Use a number line to order fractions or decimals from least to greatest (e.g., not limited to a number line marked from 0 to 1). [SP, RL]

·          Explain what the relative position of numbers on a positive number line means (e.g., to the right means greater than) [CU]

·          Identify the appropriate values of points on an incomplete number line involving fractional or decimal increments (e.g., using a ruler, reading a fuel gauge). [CU]

1.3.4

Understand and apply single transformations using a translation (slide) or reflection (flip). W

·          Simulate translations and reflections using objects (e.g., pattern blocks, geo-blocks). [MC]

·          Record results of a translation or a reflection (e.g., given a polygon on a grid, translate or reflect it, and list the new ordered pairs of the vertices). [CU]

·          Identify and draw a single translation (slide) or a single reflection (flip). [CU]

Apply understanding of translations (slides) or reflections (flips) to congruent figures. W

·          Identify a specific transformation as a translation (slide) or reflection (flip). [CU]

·          Given a shape on a grid, perform and draw at least one transformation (i.e., translation or reflection). [SP, RL]

·          Draw, using a transformation, congruent figures and shapes in multiple orientations. [SP, RL]

·          Explain a series of transformations in art, architecture, or nature. [CU, MC]

·          Record results of a translation or reflection (e.g., plot a set of ordered pairs on a grid that are vertices of a polygon, translate or reflect it, and list the new ordered pairs). [CU, MC]

1.4 Understand and apply concepts and procedures from probability and statistics.

Grade 3

Grade 4

Grade 5

Probability

1.4.1

Understand when events are certain or impossible, and more likely, less likely, or equally likely. W

·          Identify the likelihood of events and use the vocabulary of probability (e.g., weather, if homework will be assigned, simple games). [CU, MC]

·          Place events in order of likelihood of occurrence (e.g., use a number line marked from 0 to 1). [SP, RL, MC]

Understand the likelihood (chance) of events occurring. W

·          Predict and test how likely it is that a certain outcome will occur (e.g., regions of a spinner, flip of a coin, toss of dice). [SP, RL]

·          Represent the probability of a single event on a scale of 0 to 1. [MC]

·          Given a fair game, create an advantage for one of the players (e.g., if the game selecting marbles include more marbles of one color than the other). [SP, RL]

·          Explain the likelihood of single event. [CU]

·          Determine if a game for two people is fair. [SP, RL]

1.4.2

1.4 Understand and apply concepts and procedures from probability and statistics.

Grade 3

Grade 4

Grade 5

Statistics

1.4.3

Understand data collection and display methods to obtain desired information. W

·          Understand how to ask questions to get needed data.

·          Interpret graphs for comparative information (e.g., find the difference in selected data). [SP, RL, CU, MC]

·          Pose questions and gather data.

·          Make a survey and collect data (e.g., use tally marks, make a table). [CU]

Understand and apply data collection methods to obtain the desired information. W

·          Identify appropriate questions and populations to obtain the desired kind of information.

·          Formulate questions for surveys and collect data. [SP, RL, CU]

·          For a given question decide whether to conduct a survey, use observations or measure. [SP, RL]

·          Make a plan to answer a question including how to record and organize data. [SP, RL, CU, MC]

·          Identify appropriate questions and populations to ask in order to obtain the desired information. [SP, RL, CU]

Understand how different collection methods or different questions can affect the results. W

·          Identify how different collection methods for a question affect the data collected; identify how different questions affect the data collected.

·          Ask the same question using different data collection methods that result in other points of view being supported. [SP, RL]

·          With a given question, explain how different data collection methods affect the nature of the data set (e.g., phone survey, internet search, person-to-person survey). [CU, MC].

1.4.4

                Understand and apply mode to describe a set of data. W

·          Create and solve a problem situation where mode is meaningful for a set of data. [SP, RL, CU, MC]

·          Explain how to find the mode to describe a set of data. [CU]

Understand and apply median and range to describe a set of data. W

·          Find and use median and mode to describe a set of data.

·          Use a variety of strategies to determine median and range from a set of data (e.g., use a graph, pictures or objects). [SP, RL]

·          Calculate the range of a data set. [SP, RL]

·          Compare the mode and median from a set of data and determine which measure better describes the average. [SP, RL]

Understand and apply the mean of a set of data. W

·          Understand and find mean using objects and pictures; use median and mode to describe a set of data.

·          Find the mean from a given set of data using objects, pictures, or formulas.

·          Given a problem situation, determine and defend whether mean, median, or mode is the most appropriate measure of average. [SP, RL, CU, MC]

·          Explain how to find the mean of a set of data and explain the significance of the mean. [CU]

1.4 Understand and apply concepts and procedures from probability and statistics.

Grade 3

Grade 4

Grade 5

Statistics

1.4.5

Understand representations of data from tables, charts, and bar graphs W

·       Pose questions that can be answered from a given graph. [CU, MC]

·       Interpret bar graphs for comparative information. [CU]

·       Make inferences based on the data or determine if the data can support inferences made. [CU, MC]

·       Read and report on data from tables, charts, and bar graphs. [CU]

·       Explain how types of graphs or the graph construction can support different points of view. (e.g. starting the axis numbers at 50 rather than 0.) [CU, SP, RL]

·       Create bar graphs including labels for title, both axes, scale units (e.g., 2’s, 5’s, 10’s), and key if needed. [SP, RL, CU, MC]

Understand representations of data from line plots and pictographs. W

·          Read data from line plots and pictographs.

·          Describe a trend from a given line plot. [CU, MC]

·          Interpret a pictograph where scale is different from one.

·          Using a set of data create two different graphic displays. [CU, MC]

·          Read and interpret data from line plots and pictographs. [SP, RL, CU]

Apply strategies to organize, display, and interpret data. W

·        Read and interpret data from text, bar and circle graphs and determine when using each of these is appropriate.

·        Identify and use data from text passages, histograms, stem-and-leaf plots, circle graphs

·          Use histograms, pictographs, and stem-and-leaf plots to display data. [CU, MC]

·          Construct assorted graphs that include labels, appropriate scale, and key. [CU]

·        Read and describe data from circle graphs. [CU]

·        Interpret skew, clusters and gaps in given one-variable data displays.

1.4.6

1.5 Understand and apply concepts and procedures from algebraic sense.

Grade 3

Grade 4

Grade 5

Patterns, functions and other relations

1.5.1

Understand patterns of objects, including number patterns with a single addition or subtraction operation. W

·          Recognize and extend patterns of numbers, figures, and objects using addition and subtraction based on a single arithmetic operation between the terms.

·          Identify, extend, and describe numerical patterns (e.g., skip counting, 100 chart, multiplication table). [CU]

·          Describe the pattern in a number sequence (e.g., Guess My Rule, Function Machine). [CU]

·          Identify the rule for a pattern based on a single operation (e.g., add 3). [SP, RL]

·          Extend patterns of numbers or shapes, using addition and subtraction based on a single arithmetic operation between the terms. [SP, RL]

Understand patterns of objects, including number patterns, using addition, subtraction, or multiplication based on a single arithmetic operation. W

·          Extend or create patterns of numbers, shapes, or objects using addition, subtraction, or multiplication based on a single operation between terms.

·          Extend and represent patterns using words, tables, numbers, and pictures. [SP, RL]

·          Create a number pattern and explain what makes it a pattern. [CU]

·          Describe the rules for a pattern based on one operation (e.g., add 4, multiply by 2). [CU]

Understand patterns of objects, including relationships between two sets of numbers, based on a single arithmetic operation. W

·          Extend or create patterns of numbers, shapes, or objects based on a single arithmetic operation between the terms.

·          Determine the operation that changes the elements of one set of numbers into the elements of another set of numbers. (e.g., if one set is 1,2,3,… and another set is 5,10, 15, … a rule would be to multiply each number in the first set by 5 to get the corresponding number in the second set).[SP, RL]

·          Explain why a given rule fits a pattern based on a single arithmetic operation in the rule. [SP, RL, CU]

1.5.2

Understand a pattern to develop a rule describing the pattern, which may include a single arithmetic operation. W

·          Use the rule for a pattern (which may include a single arithmetic operation) to extend or fill in parts of a pattern. [SP, RL]

·          Solve a problem that uses a pattern with a single operation. [SP, RL, CU]

·          Model growing patterns using objects and pictures (e.g., a stair step sequence, or a “growing” L shape in which a unit is added to each leg to show 3, 5, 7, 9, . . .) [SP, RL]

Analyze a pattern to develop a rule describing the pattern, including combinations of two arithmetic operations. W

·          Use the rule for a pattern (which may include a combination of two arithmetic operations) to extend a pattern. [SP, RL]

·          Solve a problem that uses a pattern of alternating operations (e.g., A frog climbed up 3 feet each day and then slipped down 1 foot each night.  How long did it take the frog to reach the top of the building that is 15 feet high?) [SP, RL]

1.5 Understand and apply concepts and procedures from algebraic sense.

Grade 3

Grade 4

Grade 5

Symbols and representations

1.5.3

Apply understanding of the concept of mathematical equality. W

·          Write an equation or expression for a given situation. (e.g., There are 23 children in a class. If 15 are present, how many are absent?). [SP, RL, CU]

·          Given an expression or equation using =, identify or write a situation that represents it. [SP, RL, CU, MC]

·          Explain equality and the use of “=” in equations. [CU]

Apply understanding of the concept of mathematical inequality. W

·          Understand inequality and use “=,>, and <” in equations and inequalities.

·          Compare multiplication or division number sentences using the symbols >, <, and = (e.g., 5 x 3 > 3 x 2).

·          Select operational and relational symbols to make a multiplication or division number sentence true

(e.g., 4 _ 3 = 12; 5 x 12 _ 64).

·          Explain inequality and the use of “>” or “<” in inequalities. [CU]

·          Given an expression or equation using < or >, identify or write a situation that represents it. [SP, RL, CU, MC]

Understand and apply the concept of mathematical inequality. W

·          Express relationships between quantities using “=, ≠,   <, or >”.

·          Express relationships between quantities using “ £, or ³”.

·          Given an expression or equation using ≠, £, or ³, identify or write a situation that represents it. [SP, RL, CU, MC]

·          Given a real-world situation, use =, ≠, £, or ³ to describe quantities. [SP, RL, CU, MC]

·          Explain inequality and the use of “≠”, “£”, or “³”. [CU]

1.5.4

Understand and apply operational and relational symbols and notations to write equations involving addition and subtraction. W

·          Write and explain mathematical statements (e.g., 7 + £ = 8 or £ +8 = 10). [CU]

·          Identify and use appropriate symbols and notations in reading and writing expressions and equations involving addition and subtraction.

·          Given an equation involving addition or subtraction, write a situation that represents it. [SP, RL, CU, MC]

Understand and apply operational and relational symbols and notations to write expressions and equations involving multiplication and division. W

·          Identify and use appropriate symbols and notations in reading and writing expressions and equations.

·          Given an equation involving multiplication or division, write a situation that represents it. [SP, RL, CU, MC]

·          Given a situation involving multiplication or division, write an equation that represents it. [SP, RL, CU, MC]

Understand how to represent situations involving one operation or two alternating arithmetic operations. W

·          Translate a situation involving one arithmetic operation into algebraic form using equations, tables, and graphs. [SP, RL, CU]

·          Translate a situation involving two alternating arithmetic operations into algebraic form using equations, tables, and graphs (e.g., a snail crawls up 3 feet each day and slides back 2 feet each night). [SP, RL, CU]

·          Identify or describe a situation involving one arithmetic operation that may be modeled by a graph. [SP, RL, CU]

·          Identify or describe a situation involving two alternating arithmetic operations that may be modeled by a graph (e.g., a snail crawls up 3 feet each day and slides back 2 feet each night). [SP, RL, CU]

1.5 Understand and apply concepts and procedures from algebraic sense.

Grade 3

Grade 4

Grade 5

Evaluating and solving

1.5.5

Understand and apply a variety of strategies to evaluate expressions with addition, subtraction, or multiplication. W

·          Substitute a numeric value for a symbol in expressions or equations (e.g., if X = 7, find £ x 3; If w= 12 and I= 36, what is w x I?). [SP, RL]

Understand and apply a variety of strategies to evaluate expressions with division. W

·          Evaluate expressions with multiplication using manipulatives, pictures, and symbols. [SP, RL, CU]

·          Substitute a symbol for a numeric value in an expression or in equations (e.g., X = 4, find 20 ¸ X; If H= 12 and t= 36, what is t ¸ H?). [SP, RL]

1.5.6

Understand and apply strategies to solve equations that have addition or subtraction. W

·          Solve problems involving equality (e.g., 5 + 3 = £ + 2). [SP, RL]

·          Solve equations with addition and subtraction using manipulatives, pictures, and symbols. [SP, RL, CU]

·          Describe a strategy used to solve an equation with addition or subtraction. [CU]

Understand and apply strategies to solve equations that have multiplication. W

·          Solve missing factor equations (e.g., £ ´ 3 = 12). [SP, RL]

·          Describe and compare strategies used to solve an equation with multiplication. [SP, RL, CU]

Apply strategies to solve equations that have division. W

·          Solve for a missing value in an equation involving division (e.g., 12 ¸ £ = 3). [SP, RL]

·          Describe and compare strategies used to solve an equation with multiplication or division. [SP, RL, CU]

2.1 Investigate Situations

Grade 3

Miguel’s class has set a goal to increase nightly reading to at least 30 minutes. He is taking a survey of his class to determine about how many minutes they read each night to see if they have met the goal. Miguel likes to read books by Matt Christopher.

Grade 4

Jamal and his sister, Aleesha, want to buy a pet. Their mother said she will help by paying for the ongoing cost of food  if they can save the money to buy the pet and all the needed equipment, bedding, and food to get started. They have $17.83 saved already and most of that money is in quarters. They are reading pet store ads. to see what the costs would be if they bought a mouse, a hamster, or a guinea pig.

Grade 5

Mrs. Allen’s class won a pizza party sponsored by the PTA for best school attendance. There are 30 students in the class. 10 pizzas arrived but they were cut in three different ways. Three pizzas were cut in eighths, three were cut in fourths, and four were cut in halves. Mrs. Allen wouldn’t let the students start eating until she was sure everyone received equal shares.

2.1.1

Apply strategies and approaches to investigate situations.

·       Use strategies/approaches to examine the situation and determine if there is a problem to solve (e.g., ask questions, or  paraphrase information provided: Miguel is taking a survey to determine about how many minutes students read on school nights. The class goal is at least 30 minutes/night).

·          Use strategies/approaches (e.g., draw pictures, use physical models) to find and compare all possible rectangles with whole number dimensions and a whole number perimeter. (e.g., Find all possible rectangles with a perimeter of 28 and whole number measures as lengths of sides). [1.2.5]

Apply strategies and approaches to investigate situations.

·       Use strategies/approaches to examine the situation and determine if there is a problem to solve: (e.g., ask questions, make lists, or paraphrase information provided in ads: two kids want to buy a pet. They have some money but they need to find out if they can afford a mouse, hamster, or guinea pig and the equipment and food for it.)

·          Use strategies/approaches (e.g., draw pictures, use physical models) to compare and describe area measurements made using different units (e.g., square inches vs. square centimeters). [1.2.2]

Apply strategies and approaches to investigate situations.

·          Use strategies/approaches to examine the situation and determine if there is a problem to solve: (e.g., draw pictures, ask questions, or paraphrase information provided: 30 students in a class have ten pizzas to divide fairly. Three are sliced in eighths, three are sliced in fourths and 4 are sliced in halves.)

·          Given a fair game, use strategies and approaches to create an advantage for one of the players (e.g., if the game involves drawing a marble from a bag of marbles and the favorable outcomes are red marbles or black marbles, add more of one color to the bag.) [1.4.1]

2.2 Define Problems

Grade 3

Miguel’s class has set a goal to increase nightly reading to at least 30 minutes. He is taking a survey of his class to determine about how many minutes students read each night during the school week to see if they have met the goal. Miguel likes to books by Matt Christopher.

Grade 4

Jamal and his sister, Aleesha, want to buy a pet. Their mother said she will help by paying for the ongoing cost of food  if they can save the money to buy the pet and all the needed equipment and food to get started. They have $18.73 saved already and most of that money is in quarters. They are reading pet store ads. to see what the costs would be if they bought a mouse, a hamster, or a guinea pig.

Grade 5

Mrs. Allen’s class won a pizza party sponsored by the PTA for best school attendance. There are 26 students in the class. 10 pizzas arrived but they were cut in three different ways. Three pizzas were cut in eighths, three were cut in fourths, and four were cut in halves. Mrs. Allen wouldn’t let the students start eating until she was sure everyone received equal shares.

2.2.1

Analyze a situation to define the problem.

·       Using information from investigation, determine the problem (e.g., has the class met its reading goal?)

·       Generate questions that would need to be answered in order to solve the problem (e.g., About how many minutes did each person read? Can we estimate or do we need an exact number? What is the difference between the goal and the minutes read?)

·       Identify known and unknown information (e.g., known: who the students are, the class goal; unknown: the number of minutes each student read, if the class reached the goal).

·       Identify information that is needed and not needed to solve the problem (e.g., needed: the class goal; not needed: Miguel likes Matt Christopher books).

·       Create (and solve) a problem situation where mode is meaningful for a set of data. [1.4.4]

·       Given an equation involving addition or subtraction, write a situation that represents it. [1.5.4]

Analyze a situation to define the problem.

·       Using information from investigation, determine the problem (e.g., Do Jamal and Aleesha have enough money?)

·       Generate questions that would need to be answered in order to solve the problem (e.g., How much will each animal cost? How much is equipment and food for each animal?

·       Identify known and unknown information (e.g., known: How much money Jamal and Aleesha have; unknown: all the costs for each animal.)

·       Identify information that is needed or not needed (e.g., needed: all costs related to purchasing the animals, the amount that the kids have saved; not needed: that the money is in quarters).

·           Write (and solve) multi-step problem situations that involve multiplication and division. [1.1.6]

·           Create (and solve) a problem situation where median is meaningful for a set of data. [1.4.4]

Analyze a situation to define the problem. Using information from investigating the situation, determine the problem (e.g., How can ten pizzas be fairly divided among 26 students?

·          Generate questions that would need to be answered in order to solve the problem (e.g., How should the pizzas be sliced? Can we use the slices that have already been made? How many pieces is each student’s fair share?)

·          Identify known and unknown information: (known: number of students, number of pizzas to share; unknown: size of each slice, number of equal slices, number of pieces/student)

·          Identify information that is needed or not needed (e.g., needed:  number of students,  number of pizzas, how pieces have already been cut; not needed: reason for the pizza party).

·          Given a problem situation, determine and defend whether mean, median, or mode is the most appropriate measure of average. [1.4.4]

·          Given an equation involving one or two alternating arithmetic operations, write a situation that represents it. [1.5.4]

2.3 Construct Solutions

Grade 3

Miguel’s class has set a goal to increase nightly reading to at least 30 minutes. He is taking a survey of his class to determine about how many minutes students read each night during the school week to see if they have met the goal. Miguel likes to books by Matt Christopher.

Grade 4

Jamal and his sister, Aleesha, want to buy a pet. Their mother said she will help by paying for the ongoing cost of food  if they can save the money to buy the pet and all the needed equipment and food to get started. They have $18.73 saved already and most of that money is in quarters. They are reading pet store ads. to see what the costs would be if they bought a mouse, a hamster, or a guinea pig.

Grade 5

Mrs. Allen’s class won a pizza party sponsored by the PTA for best school attendance. There are 26 students in the class. 10 pizzas arrived but they were cut in three different ways. Three pizzas were cut in eighths, three were cut in fourths, and four were cut in halves. Mrs. Allen wouldn’t let the students start eating until she was sure everyone received equal shares.

2.3.1

Apply planning process to create a plan to solve a problem.

·       Gather and organize data and information (e.g. create a survey to find out about how many minutes students are watching TV. Organize data on a 2-column chart).

·       Determine what strategy will be used to solve the problem (e.g. estimate from data gathered using compatible numbers).

Apply planning process to create plan to solve a problem.

·           Gather and organize data (e.g. determine how to break information into categories (e.g. cost of animal, cost of cage, cost of food, cost of bedding, cost of equipment in order to create a table).

·           Determine what tools should be used   to construct a solution (e.g., calculators,, paper and pencil, calculator, mental math physical models such as play money).

Apply planning process to create plan to solve a problem.

·        Gather and organize the necessary information or data from the problem (e.g.,, draw pictures, create a chart or table or use models to organize information.)

·        Determine what tools should be used to construct a solution (e.g. paper and pencil, pictures, physical models).

2.3.2

Apply effective strategies and appropriate concepts and procedures from number sense, measurement, geometric sense, and statistics to construct a solution.

·    Use strategies to solve problems (e.g., use compatible number estimation. If one student reads 45 minutes and another student reads 18 minutes, that is about 60 minutes.

·    Use appropriate tools to estimate solution (e.g. mental math or paper/pencil).

·    Recognize when an approach is unproductive and try a new approach.

Apply effective  strategies and appropriate concepts and procedures from number sense, measurement, geometric sense, and statistics to construct a solution.

·          Use strategies to solve problems (e.g., column addition, play $ to determine costs, and subtraction to determine how much money is needed if they don’t have enough.)

·          Use appropriate tools to solve problems (e.g. paper and pencil, calculator, or physical models – play money)

·          Recognize when an approach is unproductive and try a new approach.

·           

Apply effective strategies and appropriate concepts and procedures from number sense, measurement, geometric sense, and statistics to construct a solution.

·        Use strategies to solve problems (e.g., draw pictures, use physical).

·        Use appropriate tools to solve problems (e.g., paper and pencil, mental math)

·         Recognize when an approach is unproductive and try a new approach.

·          Solve problems related to primes, factors, multiples, and composites in a variety of situations (e.g., find a mystery number, find unit pricing). [1.1.3]

·          Determine the operation that changes the elements of one set of numbers into the elements of another set of numbers (e.g., if one set is 1,2,3, and another set is 5, 10, 15, a rule would be to multiply each number in the first set by 5 to get the second set). [1.5.1]

3.1 Analyze Information

Grade 3

Miguel’s class has set a goal to increase nightly reading to at least 30 minutes. He is taking a survey of his class to determine about how many minutes students read each night during the school week to see if they have met the goal. Miguel likes to books by Matt Christopher.

Grade 4

Jamal and his sister, Aleesha, want to buy a pet. Their mother said she will help by paying for the ongoing cost of food  if they can save the money to buy the pet and all the needed equipment and food to get started. They have $18.73 saved already and most of that money is in quarters. They are reading pet store ads. to see what the costs would be if they bought a mouse, a hamster, or a guinea pig.

Grade 5

Mrs. Allen’s class won a pizza party sponsored by the PTA for best school attendance. There are 26 students in the class. 10 pizzas arrived but they were cut in three different ways. Three pizzas were cut in eighths, three were cut in fourths, and four were cut in halves. Mrs. Allen wouldn’t let the students start eating until she was sure everyone received equal shares.

3.1.1

Analyze information presented in familiar situations.

·       Break down situation in order to explain or paraphrase it (e.g., survey is conducted to determine about how many minutes per night students are reading in order to estimate whether the class has met 30 min./night goal).

·       Compare combined quantities (e.g., 50 +3 is greater than 40=9) [1.1.2]

Analyze information presented in familiar situations.

·          Break down situation in order to explain or paraphrase it (e.g., each animal has costs related to cage, bedding, food, which must be calculated in order to see if the kids have enough money to buy an animal.)

·          For a given question, determine which data collection method is most appropriate.[1.4.3]

·          Compare the mode and median from a set of data and determine which measure better describes the average. [1.4.4]

Analyze  information in familiar situations.

·          Break down situation in order to explain or paraphrase it (e.g., 26 students need to share 10 pizzas equally. The pizzas are already sliced, but not evenly.  Using eighths, determine how the pizza can be cut and shared equally).

·          Compare, order, or illustrate whole numbers, decimals, and fractions using concrete models (e.g., number line, shaded grid) or implementing strategies (e.g., like denominators, benchmarks, conversions). [1.1.2]

·          Determine if a game for two people is fair. [1.4.1]

·          Given a problem situation, determine and defend whether mean, median, or mode is the most appropriate measure of average. [1.4.4]

3.2 Make Predictions, Inferences, and Conjectures

Grade 3

Miguel’s class has set a goal to increase nightly reading to at least 30 minutes. He is taking a survey of his class to determine about how many minutes students read each night during the school week to see if they have met the goal. Miguel likes to books by Matt Christopher.

Grade 4

Jamal and his sister, Aleesha, want to buy a pet. Their mother said she will help by paying for the ongoing cost of food  if they can save the money to buy the pet and all the needed equipment and food to get started. They have $18.73 saved already and most of that money is in quarters. They are reading pet store ads. to see what the costs would be if they bought a mouse, a hamster, or a guinea pig.

Grade 5

 Mrs. Allen’s class won a pizza party sponsored by the PTA for best school attendance. There are 26 students in the class. 10 pizzas arrived but they were cut in three different ways. Three pizzas were cut in eighths, three were cut in fourths, and four were cut in halves. Mrs. Allen wouldn’t let the students start eating until she was sure everyone received equal shares.

3.2.1

Apply prediction skills.

·          Make a reasonable prediction based on prior know ledge and investigation of situation (e.g., After collecting survey data and before estimation, predict whether the class will meet its goal)

·           Defend prediction with evidence from the situation.

·          Given a pattern, predict the next numbers in the pattern

Apply prediction skills

·          Make a reasonable prediction based on prior know ledge and investigation of situation (e.g., After reading the pet store ads, predict whether the kids will be able to buy a pet).

·          Defend prediction with evidence from the situation.

·          Predict whether events will be more likely, less likely, or equally likely (e.g., Is it more likely we will have rain or snow, which is less likely – rain or snow?)

Apply prediction skills.

·          Make a reasonable prediction based on prior know ledge and investigation of situation (e.g., Using mental math, predict how many pieces will each student will receive.)

·          Defend prediction with evidence from the situation.

·          Predict and test how likely it is that a certain outcome will occur ( e.g., regions of a spinner, flip of a coin, toss of dice). [1.4.1]

3.2.2

Apply inference skills to make  conjectures, supported by examples.

·          Make inferences (conjectures) using information from the situation to support the inference (e.g., the class probably did not make the reading goal because the community softball league has started up and most kids are involved in the evenings).

·          Interpret graphs for comparative information (e.g., find the difference in selected data and infer the reason for it). [1.4.3]

Apply inference skills to make   conjectures, supported by examples

·          Make inferences (conjectures) using information from the situation to support the inference (e.g., guinea pig equipment/food is more expensive because the animal is larger and requires a bigger cage and pellets ).

·          Make inferences based on a set of data and support with evidence. [1.4.5]

·          Judge the appropriateness of inferences made from a set of data and support the judgment. [1.4.5]

Apply inference skills to make  conjectures, supported by examples.

·           

·          Analyze the distribution of data (e.g., given unlabeled graphs and data sets, match the appropriate date to a graph) [1.4.5]

·          Make inferences based on a set of data and support with evidence. [1.4.5]

·          Judge the appropriateness of inferences made from a set of data and support the judgment. [1.4.5]

3.2 Make Predictions, Inferences, and Conjectures

Grade 3

Miguel’s class has set a goal to increase nightly reading to at least 30 minutes. He is taking a survey of his class to determine about how many minutes students read each night during the school week to see if they have met the goal. Miguel likes to books by Matt Christopher.

Grade 4

Jamal and his sister, Aleesha, want to buy a pet. Their mother said she will help by paying for the ongoing cost of food  if they can save the money to buy the pet and all the needed equipment and food to get started. They have $18.73 saved already and most of that money is in quarters. They are reading pet store ads. to see what the costs would be if they bought a mouse, a hamster, or a guinea pig.

Grade 5

 Mrs. Allen’s class won a pizza party sponsored by the PTA for best school attendance. There are 26 students in the class. 10 pizzas arrived but they were cut in three different ways. Three pizzas were cut in eighths, three were cut in fourths, and four were cut in halves. Mrs. Allen wouldn’t let the students start eating until she was sure everyone received equal shares.

3.2.3

Analyze procedures used to solve problems in familiar situations.

·          Describe and compare estimation strategies used (e.g., front end estimation vs. using compatible numbers).[1.1.8]

·          Describe and compare strategies to solve three-digit addition and subtraction problems (e.g., child-developed algorithms, decomposition). [1.1.6]

·          Explain how types of graphs or the graph construction can support different points of view (e.g., starting the axis numbers at 50 rather than 0). [1.4.5]

Analyze procedures used to solve

problems in familiar situations.

·          Describe and compare data organization methods (e.g. charts used for organizing costs for each animal). [1.4.3]

·          Describe and compare strategies used for estimation. 1.1.8]

Analyze procedures used to solve problems in familiar situations.

·          Describe and compare strategies and tools used (e.g. drawing pizzas vs. paper and pencil calculations).

·          Ask the same question using different data collection methods that result in other points of view being supported. [1.4.3]

3.3 Draw Conclusions and Verify results

Grade 3

Miguel’s class has set a goal to increase nightly reading to at least 30 minutes. He is taking a survey of his class to determine about how many minutes students read each night during the school week to see if they have met the goal. Miguel likes to books by Matt Christopher.

Grade 4

Jamal and his sister, Aleesha, want to buy a pet. Their mother said she will help by paying for the ongoing cost of food  if they can save the money to buy the pet and all the needed equipment and food to get started. They have $18.73 saved already and most of that money is in quarters. They are reading pet store ads. to see what the costs would be if they bought a mouse, a hamster, or a guinea pig.

Grade 5

Mrs. Allen’s class won a pizza party sponsored by the PTA for best school attendance. There are 26 students in the class. 10 pizzas arrived but they were cut in three different ways. Three pizzas were cut in eighths, three were cut in fourths, and four were cut in halves. Mrs. Allen wouldn’t let the students start eating until she was sure everyone received equal shares.

3.3.1

Understand how to justify results using evidence.

·          Check for reasonableness of results by using a different strategy or tool to solve the problem (e.g., use front end estimation to determine about how many minutes students were reading/night).

·          Justify whether estimation is appropriate for the situation.

·          Identify when two measurements are not necessarily equal (e.g., there are different people are dong the pacing). [1.2.2]

·          Use estimation to justify reasonableness of a measurement (e.g., estimate length of a classroom by pacing it off, select temperature of an ice rink from a range of degrees). [1.2.6]

Understand how to justify results using evidence.

·          Check for reasonableness of results by using a different strategy or tool to solve the problem (e.g., use front end estimation to determine about how many minutes students were reading/night).

·          Provide examples to support results

·          Justify whether estimation is appropriate for a situation. [1.1.8]

·          Use estimation strategies prior to computation of multiplication and division of whole numbers to determine reasonableness of answers. [1.1.8]

Understand how to justify results using evidence.

·          Check for reasonableness of results by using a different strategy or tool to solve the problem (e.g., compare the results from students who used physical models vs. those who used computation).

·          Provide examples to support results

·          Justify whether an estimate is appropriate or not.[1.1.8]

·          Use estimation strategies prior to computation of addition and subtraction of decimals and like-denominator fractions to determine reasonableness of answers. [1.1.8]

·          Use estimation to justify reasonableness of a measurement (e.g., estimate the area of a classroom by counting carpet squares). [1.2.6]

3.3.2

Understand how to validate thinking about numerical, measurement, geometric, or statistical ideas by using models, known facts, patterns, or relationships.

·          Explain how comparisons can be used to draw a conclusion (e.g., the class won’t have met the reading goal because fewer students read less than more this month).

·          Identify, describe, and compare congruent 2-D geometric figures. [1.3.1]

Understand how to validate thinking about numerical, measurement, geometric, or statistical ideas by using models, known facts, patterns, or relationships.

·           Explain the meaning of a decimal using physical models [1.1.5]

·          Explain what the relative position of numbers on a positive number line means (e.g., to the right means greater than).  [1.3.3]

Understand how to validate thinking about numerical, measurement, geometric, or statistical ideas by using models, known facts, patterns, or relationships.

·          Explain how the value of a fraction changes in relationship to the size of the whole (e.g., half a pizza vs. half a cookie). [1.1.1]

·          Create 3-D shapes from 2-D figures (e.g., cylinder from two circles and a rectangle) and explain the relationship. [1.3.2]

4.1 Gather Information

Grade 3

Grade 4

Grade 5

4.1.1

Understand how to follow a simple plan for collecting information for a given purpose.

·          Determine how to collect information for a specific purpose or audience (e.g. to convince a parent or other adult, to demonstrate a need for change, to provide information).

·          Develop and follow a plan based on the kind of information needed, the purpose, and the audience. (e.g., survey, gather data from a chart or graph, read in a text to gather information).

Understand how to develop and follow a simple plan for collecting information for a given purpose.

·           Determine how to collect information for a specific purpose or audience (e.g. to convince a parent or other adult, to demonstrate a need for change, to provide information).

·           Develop and follow a plan based on the kind of information needed, the purpose, and the audience . (e.g., survey, gather data from a chart or graph, read in a text to gather information)..

Understand how to develop and follow a simple plan for collecting information for a given purpose.

·           Determine how to collect information for a specific purpose or audience (e.g. to convince a parent or other adult, to demonstrate a need for change, to provide information).

·        Develop and follow a plan based on the kind of information needed, the purpose, and the audience . (e.g., survey, gather data from a chart or graph, read in a text to gather information)..

·          Ask the same question using different data collection methods that result in other points of view being supported. [1.4.3]

·          With a given question, explain how different data collection methods affect the nature of the data set (e.g., phone survey, person-to-person survey, internet search) [1.4.3]

4.1.2

Understand how to extract information for a given purpose from one or two different sources using reading, listening, and observation.

·          Read directions for movement on a positive number line, identify the point of final destination using real –world examples (e.g., travel back and forth on a street, temperature variations during the day).[1.3.3]

·          Read and report on data from tables, charts, and bar graphs. [1.4.5]

Understand how to extract information for a given purpose from one or two different sources using reading, listening, and observation.

·          Listen and observe to simulate translations and reflections using objects (e.g. pattern blocks, geo-blocks) [1.3.4]

·          Read and follow directions using a coordinate grid (e.g. on a city street map). [1.3.3]

Understand how to extract information for a given purpose, from one or two different sources using reading, listening, and observation.

·          After reading a text, generate questions and develop a survey (e.g., to determine how many students agree or disagree with the author).

·          Identify and use data from text passages, histograms, stem-and-leaf plots, and circle graphs. [1.4.5]

4.2 Organize, Represent, and Share Information

Grade 3

Miguel’s class has set a goal to increase nightly reading to at least 30 minutes. He is taking a survey of his class to determine about how many minutes students read each night during the school week to see if they have met the goal. Miguel likes to books by Matt Christopher.

Grade 4

Jamal and his sister, Aleesha, want to buy a pet. Their mother said she will help by paying for the ongoing cost of food  if they can save the money to buy the pet and all the needed equipment and food to get started. They have $18.73 saved already and most of that money is in quarters. They are reading pet store ads. to see what the costs would be if they bought a mouse, a hamster, or a guinea pig.

Grade 5

Mrs. Allen’s class won a pizza party sponsored by the PTA for best school attendance. There are 26 students in the class. 10 pizzas arrived but they were cut in three different ways. Three pizzas were cut in eighths, three were cut in fourths, and four were cut in halves. Mrs. Allen wouldn’t let the students start eating until she was sure everyone received equal shares.

4.2.1

Understand how to organize information for a given purpose.

·          From survey results, create a display to represent information (e.g., the approximate number of minutes read and whether or not the goal was met.)

·          Create bar graphs including labels for title, both axes, scale units (e.g., 2’s, 5’s, 10’s), and key if needed. [1.4.2]

·          Create and solve a problem situation where mode is meaningful for a set of data. [1.4.4] Display information to be shared.

Understand how to organize information for a given purpose.

·          Organize information on a chart and create a summary of the results to inform a specific audience (e.g. chart all related costs for the purchase of each pet. Write up a summary explaining the results and the kids possible decisions based on the results.)

·          Construct assorted line and pictographs that include labels, a scale that is not one, and a key. [1.4.5]

·          Create a chart or display to represent equivalent fractions. [1.1.2]

Understand how to organize information for a given purpose.

·          Determine what is the best method for organizing and representing information for a specific purpose (e.g., a physical model or a calculation to inform the teacher how many pieces of pizza each student should receive).

·          .Record results of a translation or reflection (e.g., plot a set of ordered pairs on a grid that are vertices of a polygon, translate or reflect it, and list the new ordered pairs).  [1.3.4]

·          Represent and interpret all possible outcomes of experiments (e.g., an organized list, a table, a tree diagram, or a sample space). [1.4.2]

·          Construct assorted graphs including histograms, pictographs, and stem-and leaf-plots that include labels, appropriate scale, and key. [1.4.5]

4.2 Organize, Represent, and Share Information

Grade 3

Miguel’s class has set a goal to increase nightly reading to at least 30 minutes. He is taking a survey of his class to determine about how many minutes students read each night during the school week to see if they have met the goal. Miguel likes to books by Matt Christopher.

Grade 4

Jamal and his sister, Aleesha, want to buy a pet. Their mother said she will help by paying for the ongoing cost of food  if they can save the money to buy the pet and all the needed equipment and food to get started. They have $18.73 saved already and most of that money is in quarters. They are reading pet store ads. to see what the costs would be if they bought a mouse, a hamster, or a guinea pig.

Grade 5

Mrs. Allen’s class won a pizza party sponsored by the PTA for best school attendance. There are 26 students in the class. 10 pizzas arrived but they were cut in three different ways. Three pizzas were cut in eighths, three were cut in fourths, and four were cut in halves. Mrs. Allen wouldn’t let the students start eating until she was sure everyone received equal shares.

4.2.2

Understand how to communicate or represent ideas using mathematical language or notation.

·          Explain or represent ideas using mathematical language or notation;

·          Translate from one representation of a whole number to another in standard, expanded, and word forms. [1.1.1]

·          Name attributes of an object that can be measured. [1.2.4]

·          Identify, describe and compare congruent 2-D geometric shapes [1.3.1]

·          Make a survey and collect data (e.g., use tally marks, make a table)[1.4.3]

·          Identify and use appropriate symbols and notation in reading and writing simple expressions and equations involving addition and subtraction. [1.5.4]

Understand how to communicate or represent ideas using mathematical language or notation.

·          Explain or represent ideas using mathematical language or notation:

·          Symbolically represent parts of a whole or parts of a set with common denominators. [1.1.1]

·          Use measurements of area to describe and compare objects. [1.2.1]

·          Describe the location in the first quadrant on a coordinate grid in terms of horizontal and vertical position (e.g., to the right and up, longitude and latitude).1.3.3]

·          Describe a trend from a given line plot. [1.4.5]

·          Describe the rule for a pattern with a single arithmetic operation in the rule. [1.5.2]

Understand how to communicate or represent ideas using mathematical language or notation.

·          Explain or represent ideas using mathematical language orientations.

·          Explain the value of a given digit in a decimal to at least the thousandths place. [1.1.1]

·          Describe a procedure for measuring an

·          Describe relationships between angle measures (e.g., two 30° angles have the same total measure as one 60° angle). [1.2.2]

·          Draw and label a design that includes a given set of attributes. [1.3.2]

·          Explain how to find the mean of a set of data and explain the significance of the mean. [1.4.4]

·          Given an expression or equation, identify or write a situation that represents it. [1.5.3]