1.1 Understand and apply concepts and procedures from number sense.

Kindergarten

Grade 1

Grade 2

Number and Numeration

1.1.1

Understand the concept of number.

·          Count objects to at least 20 items using one-to-one correspondence.

·          Represent a number to at least 31 in different ways (e.g., numerals, pictures, physical models). [CU]

·          Show that the last count word names the quantity of the set (cardinality) (i.e., when counting fingers on a hand “one, two, three, four, five”, the “five” says how many fingers there are). [CU, MC]

·          Identify the base ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. [CU]

·          Explain how numbers are used and give examples. (e.g.,  to count, to order)

Understand ways of representing whole numbers.

·          Represent a number to at least 100 in different ways (e.g., numerals, pictures, physical models) and translate from one representation to another. [CU, MC]

·          Group and regroup objects into 1's and 10's. [SP, RL, CU, MC]

·          Read, write, and recite, in any language, numbers to at least 100. [CU]

·          Count sets of objects less than 100 using a variety of grouping strategies.

·          Identify coins (penny, nickel, dime, quarter) and state their value. [CU]

Understand place value in whole numbers.

·          Group and regroup objects into 1's, 10's, and 100's and explain relationships. [SP, RL,CU,MC]

·          Make combinations and name total value of coins. [SP, RL]

·          Determine the value of a digit based on its position in a number.

·          Read and write numbers to at least 1,000. [CU]

1.1.2

Understand sequential relationships among whole numbers.

·          Tell what number comes before or after a given number. [CU]

·          Use comparative language (e.g., less than, more than, equal to) to compare numbers to at least 20. [CU]

·          Use a known quantity to at least 10 (benchmark) to compare sets (e.g., sets of counters).

·          Identify the ordinal position of objects at least through tenth, (e.g., first, second, …). [SP, RL, CU, MC]

Understand sequential relationships among whole numbers.

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

·          Use comparative language (e.g., less than, more than, equal to) to compare numbers to at least 100. [CU]

·          Skip count by 2, 5, and 10.

·          Count forwards and backwards, from a given number that is less than 100.

Understand sequential relationships among whole numbers.

·          Order three or more numbers to at least 1,000 from smallest to largest. [CU]

·          Use comparative language (e.g., less than, more than, equal to) to compare numbers to at least 1,000. [CU]

1.1 Understand and apply concepts and procedures from number sense.

Kindergarten

Grade 1

Grade 2

Number and Numeration

1.1.3

1.1.4

1.1 Understand and apply concepts and procedures from number sense.

Kindergarten

Grade 1

Grade 2

Computation

1.1.5

Understand the meaning of addition.

·          Express stories involving addition (e.g., join) with models, pictures, and symbols. [SP, RL, CU, MC]

·          Use addition in the classroom environment (e.g., boys and girls in attendance). [MC]

Understand the meaning of subtraction.

·          Express stories involving subtraction (e.g., separate) with models, pictures, and symbols. [SP, RL, CU, MC]

·          Show relationships between addition and subtraction using physical models, diagrams, and acting out problems. [CU]

Understand the meaning of addition and subtraction and how they relate to one another.

·          Show relationships between addition and subtraction using physical models, diagrams, and acting out problems. [CU]

·          Model real life situations involving addition and subtraction with part-part-whole (e.g. Peter has 11 cookies, 4 chocolate chip and the rest peanut butter. How many peanut butter cookies?) and compare (e.g., Peter has 11 cookies which is 4 more than Teresa. How many cookies does Teresa have?) using physical models, diagrams, and acting out problems. [SP, RL, CU, MC]

1.1.6

Understand and apply procedures for addition of whole numbers with fluency.

·          Use strategies (e.g., count on, count back, doubles) for addition facts to at least sums to 12. [SP, RL]

·          Recall addition facts through at least sums to 12.

·          Solve problems involving addition using and explaining procedures used. [SP, RL, CU]

Understand and apply procedures for addition and subtraction of whole numbers with fluency.

·          Use strategies for addition and subtraction facts through at least 20. [SP, RL]

·          Recall addition and subtraction facts through at least 20.

·          Solve problems involving addition and subtraction with three digit numbers using and explaining procedures used. [SP, RL, CU]

1.1 Understand and apply concepts and procedures from number sense.

Kindergarten

Grade 1

Grade 2

Computation

1.1.7

Understand and apply strategies and appropriate tools for computing with whole numbers.

·          Use strategies and appropriate tools from among mental math, paper/pencil, manipulatives, or calculator to compute in a problem situation. [SP, RL]

·          Use counting strategies to combine whole numbers under 20. [SP, RL]

Understand and apply strategies and appropriate tools for computing with whole numbers.

·          Use mental math strategies to compute (e.g., composing and decomposing numbers, friendly numbers, neighbors) through 100. [SP, RL]

·          Use calculator, manipulatives, or paper/pencil to solve problems. [SP, RL]

·          Explain methods to mentally group numbers efficiently. (e.g. when adding 52 and 59, add the 50’s together to get 100, then add eleven more.) [SP, RL, CU]

Estimation

1.1.8

Understand and apply estimation strategies to determine the reasonableness of answers.

·          Use a known quantity (e.g., chunking) to make reasonable estimates. [SP, RL]

·          Use “friendly numbers” to make a reasonable estimate of a sum (e.g., 19 + 18 should be about 40, since 19 is about 20, 18 is about 20, and 20 + 20 is 40). [SP, RL]

Understand and apply estimation strategies to predict computation results and to determine the reasonableness of answers.

·          Use estimation strategies (e.g., front-end estimation, clustering) to predict computation results and to determine the reasonableness of answers. [SP, RL].

·          Justify reasonableness of an estimate in addition and subtraction. [CU]

·          Decide if a given estimate for a sum or difference is reasonable. [SP, RL]

1.2 Understand and apply concepts and procedures from measurement.

Kindergarten

Grade 1

Grade 2

Attributes, Units and Systems

1.2.1

Understand and apply appropriate terminology to compare attributes.

·          Use comparative vocabulary to describe objects (e.g., longer/shorter, heavier/lighter, nearer/further, thicker/thinner, shorter/taller). [CU]

·          Use terms to describe the duration of events (e.g., long time or short time). [CU]

·          Identify and sort objects based on an attribute (e.g., closed vs. open) [SP, RL, CU]

Understand and apply attributes to describe and compare objects.

·          Order three or more objects according to an attribute (e.g., pencil lengths, students’ heights, and thickness of books). [SP, RL, CU]

·          Use physical models of measuring units to fill, cover, match, or make the desired comparison of the attribute with the unit. [SP, RL]

·          Read a clock with only the hour hand and use approximate language (e.g., almost 7, a little after 7). [CU]

Understand and apply attributes to measure objects and time.

·          Identify attributes of an object that are measurable (e.g., time, length, distance around, capacity, area, or weight of objects). [CU, MC]

·          Compare lengths or distances where direct comparison is not possible (e.g., use a string, paper strip, or hand span to compare the height and width of a table). [SP, RL, MC]

·          Read a clock to tell time to the ½ hour.

1.2.2

Understand the importance of appropriate and consistent units.

·          Select units appropriate to the object being measured (e.g., measure length of classroom with footprints, not beans) and explain why it was selected. [SP, RL]

·          Use a uniform unit to measure an object (e.g., cubes, paper strips).

·          Use a calendar as a record of time (e.g., yesterday, today, tomorrow, weeks, months, years, moon phases).

Understand that unit size affects the outcome of the measurement.

·          Explain why more small paper clips than large are needed to measure the same length. [CU]

·          Select the most appropriate unit to measure the time of a given situation (e.g., Would you use minutes or hours to measure brushing your teeth, eating dinner, sleeping?). [SP, RL, MC]

1.2 Understand and apply concepts and procedures from measurement.

Kindergarten

Grade 1

Grade 2

Attributes, Units and Systems

1.2.3

Understand that objects can be used as tools for nonstandard measurement.

·          Use nonstandard units to measure (e.g., paper strips, cubes, beans, hand widths).

·          Explain how to use a nonstandard unit to measure a given length (e.g., length of a table, width of a desk) [CU]

Understand the need for and apply appropriate tools to measure.

·          Measure a variety of objects using appropriate nonstandard tools (e.g., arm length, hand width, lengths of rope) [SP, RL]

·          Explain the need for measurement. [CU]

Understand the need for and apply appropriate tools to measure specific attributes.

·          Select a tool that can measure the given attribute (e.g., analogue clock: time, string: length, tiles: area, balance: weight, interlocking cubes: capacity). [SP, RL]

·          Demonstrate measurement procedure (e.g., start at a beginning point, place units end-to-end, not overlapping, and straight line). [CU]

·          Justify the use of one tool over another (e.g. the length of a hand is a better measurement tool for this situation than the length of a small cube.) [CU, SP, RL]

Procedures, Precision, and Estimation

1.2.4

1.2 Understand and apply concepts and procedures from measurement.

Kindergarten

Grade 1

Grade 2

Attributes, Units and Systems

1.2.5

1.2.6

Understand how to estimate in measurement situations.

·          Estimate length, area, capacity, and weight using nonstandard units. [SP, RL]

·          Use important benchmarks (referents) (e.g., 5 or 10) to make initial and revised estimates.

·          Explain how a benchmark (referent) helps to make a reasonable estimate. [CU]

1.3 Understand and apply concepts and procedures from geometric sense.

Kindergarten

Grade 1

Grade 2

Properties and Relationships

1.3.1

Know characteristics of familiar objects.

·          Describe familiar objects based on characteristics (e.g., big, small, like a box). [CU, MC]

·          Identify objects based on their characteristics. [MC]

Know characteristics of 2-dimensional figures.

·          Describe 2-dimensional figures based on their characteristics. [CU, MC]

·          Draw 2-dimensional figures based on given characteristics.

Understand characteristics of 2-dimensional geometric figures.

·          Sort and describe characteristics of 2-dimensional geometric figures (e.g., various polygons). [SP, RL, CU]

·          Draw a 2-dimensional shape that matches a set of characteristics (e.g., draw a four-sided shape that has all sides the same length) [SP, RL]

1.3.2

Know objects based on their attributes.

·          Identify and sort objects in their environment by characteristics (e.g., cans, balls, boxes, colors). [MC]

·          Compare objects using comparative language (e.g., bigger, taller, shorter, fatter). [CU]

Understand how to sort and compare 2-dimensional figures using their characteristics.

·        Identify and sort 2-dimensional figures in their surroundings. [MC]

·          Compare 2-dimensional figures using comparative language (e.g., longer, wider). [CU]

·          Describe figures using accurate terminology (e.g., square, rectangle, triangle)

1.3 Understand and apply concepts and procedures from geometric sense.

Kindergarten

Grade 1

Grade 2

Locations and Transformations

1.3.3

Understand the relative position of objects in their environment.

·          Describe the location of objects relative to each other (e.g., in, out, over, under, behind, above, below, next to, etc.). [MC, CU]

·          Identify where a 3-dimensional object is located relative to a given object (e.g., where the eraser is relative to the desk) [CU]

Understand the locations of numbers on a positive number line.

·          Indicate if a number is above or below a benchmark number (e.g., greater than or less than 100). [CU]

·          Describe the location of a given number, between 1 and 100, on a number line. [CU]

·          Identify a point, up to 100, on a positive number line. [CU]

Understand the locations of numbers on a positive number line.

·          Indicate if a number is above or below a benchmark number (e.g., greater than or less than 1000). [CU]

·          Describe the location of a given number, between 1 and 1000, on a number line. [CU]

·          Identify a point, up to 1000, on a positive number line. [CU]

1.3.4

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

Kindergarten

Grade 1

Grade 2

Probability

1.4.1

1.4.2

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

Kindergarten

Grade 1

Grade 2

Statistics

1.4.3

Understand that data can be collected and organized.

·          Sort and classify data (e.g., sort by color or size). [SP, RL]

·          Use physical objects or pictures to build bar graphs. [CU]

·          Answer questions about graphs (e.g., How many cats? How many dogs?). [CU]

Understand that data can be organized and displayed.

·          Display results of data collection by making student-invented and conventional displays. [CU]

·           Construct bar graphs with physical materials and record pictorially (e.g., shoes, cats, crops, egg rolls, tacos). [CU]

Understand the components of a graph.

·          Identify title, horizontal and vertical axes, and key.

·          Construct a bar graph that includes a title, key, and single unit increment. [CU]

·         Name an appropriate title for a display of data. [CU]

1.4.4

Understand how a display provides information about a question.

·          Conduct a survey for a predetermined question and collect data using tallies, charts, lists, or pictures( e.g., who has animals at home, how many, what type). [SP, RL]

·          Identify a question that could be answered from a display.

·          Interpret results and draw conclusions from displays using comparative language (e.g. more, fewer). [CU, MC]

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

Kindergarten

Grade 1

Grade 2

Statistics

1.4.5

Understand how to read and interpret data from graphs.

§          Interpret a bar graph for comparative information (e.g., How many more than, less than?). [CU]

·        Read the labels from each axis of a graph. [CU

1.5 Understand and apply concepts and procedures from algebraic sense.

Kindergarten

Grade 1

Grade 2

Patterns, functions and other relations

1.5.1

Know how to recognize patterns.

·          Identify and extend patterns. (e.g., ABAB, green-green-blue, counting). [CU]

·          Explain why a group is sorted together. (e.g. letters with curves, flags with red in them) [CU]

·          Create an AB pattern

Understand the concept of patterns.

·          Create and describe a variety of repeating patterns using sounds, objects, and symbols. [CU]

·          Describe and extend a repeating pattern (e.g., ABAC, ABAC; snap, clap, snap, stomp). [CU]

·          Identify the unit in a repeating pattern (e.g., in A-A-B-A-A-B the unit is A-A-B). [SP, RL]

·          Identify and describe numerical patterns in the 100’s chart. [CU]

Understand how patterns are generated.

·          Translate a pattern from one representation to another (e.g., snap-clap-stomp translates to ABC). [CU]

·          Identify, extend, create, and explain patterns of addition and subtraction represented in charts and tables. [CU, MC]

·          Describe a pattern based on odd and even numbers. [SP, RL]

1.5.2

1.5 Understand and apply concepts and procedures from algebraic sense.

Kindergarten

Grade 1

Grade 2

Symbols and representations

1.5.3

Understand the concepts of equality and inequality.

·          Use physical objects to model language (e.g., same, different, equal, not equal, more, less). [CU]

·          Model/act out story problems to solve whole number equations and inequalities (e.g., there are three kids and 2 have 3 crayons, one has two crayons. How can you make it so all kids have the same numbers?). [SP, RL, CU, MC]

Understand the meaning of symbols and labels used to represent situations.

·          Demonstrate equality by recording number sentences with balance using the “=” symbol (e.g., 9 = 4 + 5, 4 + 5 = 2 + 7, 9 = 9). [CU]

·          Complete open sentences showing equalities (e.g. 5 = ____).

·          Explain, using pictures or words, the meaning of equality. [CU]

·          Give an example of equality in real life (e.g., .On the first turn Juan scored 4 points; on the second turn he scored 5 points. On the first turn Ivana scored 2 points; on the second turn she scored 7 points.  After two turns, they are tied with the same number of points.). [MC]

Understand the meaning of symbols and labels used to represent situations.

·          Explain and use the symbols < and > to express relationships. [CU].

·          Use number sentences with symbols and labels to represent real-world problems involving addition and subtraction. [SP, RL, MC]

·          Give an example of inequality in real life (e.g., .On the first turn Juan scored 6 points; on the second turn he scored 8 points. On the first turn Ivana scored 9 points; on the second turn she scored 7 points.  After two turns, Juan’s points are less than Ivana’s points.). [MC]

1.5.4

1.5 Understand and apply concepts and procedures from algebraic sense.

Kindergarten

Grade 1

Grade 2

Evaluating and solving

1.5.5

Understand and apply the procedures for evaluating and solving for the unknown using addition and subtraction.

·          Solve equations with an “unknown” (e.g., 6 + £ = 11). [SP, RL]

·          Evaluate an expression for a given value for the unknown {e.g., evaluate 5 + £, when £ = 6). [SP, RL]

·          Justify the selection of a particular value for an unknown quantity in a real world situation (e.g. Two girls had ten cookies. If Kwame had six, how many did Ellie have? Explain.). [SP, RL, CU, MC]

1.5.6

2.1 Investigate Situations

Kindergarten

Problem Solving example: A classroom needs a play ground ball for each student in the class. The class has fewer playground balls than are needed.

Grade 1

Problem Solving example: A classroom is presenting a play and everyone has invited 2 guests. Enough chairs are needed to seat all the guests. There are some chairs in the classroom.

Grade 2

Problem Solving example: A classroom is planning an all-day skating party on Thursday and each student must pay for admission ($2), a box lunch ($3), and skate rental ($2). The teacher needs a total amount to reserve the rink.

2.1.1

Understand how to investigate a familiar situation.

·          State information presented in teacher-lead discussion to determine if there is a problem that needs an answer. (e.g., A classroom activity requires a playground ball for each student. There are some balls available in the classroom.)

Understand how to investigate a familiar situation.

·     State information presented in a teacher-lead discussion to determine if there is a problem (e.g., A classroom is having a play and each student invited two guests. Chairs are needed for the guests. There are some chairs available in the classroom.

·     State information presented in a teacher-lead activity (e.g., If there are 12 wheels in a group, how many bicycles and tricycles are there?) are with a certain amount of wheels.

Understand how to investigate a familiar situation.

State or record information presented in situation (e.g. The classroom is planning a skating party on Thursday and each student must pay for admission, lunch, and skates. The teacher needs to know the total cost in order to research the rink.)

·          Investigate a problem involving combinations of coins and explain verbally or in writing understanding of  information presented .[1.1.1]

2.2 Define Problems

Kindergarten

Problem Solving example: A classroom needs a play ground ball for each student in the class. The class has fewer playground balls than are needed.

Grade 1

Problem Solving example: A classroom is presenting a play and everyone has invited 2 guests. Enough chairs are needed to seat all the guests. There are some chairs in the classroom.

Grade 2

Problem Solving example: A classroom is planning an all-day skating party on Thursday and each student must pay for admission ($2), a box lunch ($3), and skate rental ($2). The teacher needs a total amount to reserve the rink.

2.2.1

Understand how to define a problem with teacher guidance. 

·           State the problem in own words (e.g., Are there enough playground balls? If not, how do we get enough for the class?).

·           Generate questions that would need to be answered in order to solve the problem (e.g., How many balls are in the classroom? How many more do we need?)

·           Identify known and unknown information with teacher guidance. (e.g., known: the number of students in the class, and the number of balls needed. unknown: the number of additional playground balls needed).  [1.1.5]

·           State the problem in words (e.g., Analyze attributes of objects to determine how to sort them.[1.2.1]

Understand how  to define a problem with teacher guidance.

·          State the problem is own words (e.g., Are there enough chairs for the guests? If not, how many more chairs do we need?)

·          Generate questions that would need to be answered in order to solve the problem (e.g., How many guests are attending?  How many more chairs do we need? )

·          Identify known and unknown information with teacher guidance (e.g. known: number of students, number of guests invited, number of chairs in classroom; unknown: number of guests attending, number of chairs needed). [1.1.5]

·          State the problem in own words (e.g., how many crayons will each student get when the bag is divided fairly?

·          Generate questions that would need to be answered to solve the problem (e.g., How many crayons are in the bag? How many students are in class?

·          Identify the known and unknown information.

Understand how to define a problem.

·           Explain the problem, verbally or in writing, in own words (e.g. How much will the skating party cost?)

·           Generate questions that would need to be answered in order to solve problem [e.g., What is the cost of a ticket and skate rental for the skating rink? What is the cost of food? What is the cost for each student? What will a skating party cost? ] [1.4.4]

·           Identify known and unknown information (e.g., known: the cost of admission, skates, lunch, and the number of students going; unknown: cost for each student and total cost)

·           Identify extraneous information (e.g., the party is planned for Thursday).

·        State the problem in own words (e.g. what is the pattern in this string of numbers?)

·        Generate questions that would need to be answered to solve the problem (e.g., does each number get bigger or smaller? By how much?)

·        Identify the known and unknown information.

2.3 Construct Solutions

Kindergarten

Problem Solving example: A classroom needs a play ground ball for each student in the class. The class has fewer playground balls than are needed.

Grade 1

Problem Solving example: A classroom is presenting a play and everyone has invited 2 guests. Enough chairs are needed to seat all the guests. There are some chairs in the classroom.

Grade 2

Problem Solving example: A classroom is planning an all-day skating party on Thursday and each student must pay for admission ($2), a box lunch ($3), and skate rental ($2). The teacher needs a total amount to reserve the rink.

2.3.1

Understand how to create a plan, with teacher guidance, to solve a problem.

·           Gather and organize categorical data (e.g., In a teacher lead activity, create a 2 column chart – one column for student names and tally marks in the other to represent which students are assigned a ball). [1.4.3]

·           Use pictures, objects, physical models, tallies, or people to find solutions.

Understand how to create a plan, with teacher guidance, to solve a problem.

·     Gather and organize categorical data (e.g. In a teacher guided activity, create a 2-column chart – one column for student names and the other to record the number of guests attending the play). [1.4.3]

·     Determine what strategy will be used to reach a solution (e.g., counting, skip counting, objects, or physical models).

Understand how to create a plan to solve a problem.

·           Gather and organize relevant information (e.g., create a 4 column chart with student names in one column and the other three for costs related to the party: admission, skates, lunch; draw a seating chart and write in costs by each student).

·           Determine what strategy will be used to reach a solution (skip counting by 2s and 3s, calculator, physical models) lists, tables for times [in whole seconds] of a relay race to find the order of finish). [1.1.2]

2.3.2

Apply effective strategies, based in the content strands of number sense, measurement, geometric sense, and statistics, with teacher guidance, to find a solution.

·       Use appropriate tools to find a solution (e.g., draw pictures, use chart to count how many empty spaces there are for the playground balls) [1.1.1, 1.1.5].

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

Apply effective strategies, based in the content strands of number sense, measurement, geometric sense, and statistics. with teacher guidance, to find a solution.

·     Use strategies (use chart to count, skip count, or cluster; use physical models) [1.1.1, 1.1.5]

·     Use appropriate tools from among mental math, paper/pencil, manipulatives, or calculator (e.g., ( to determine the total number of guests attending and the total number of chairs needed for the class play) [1.1.7].)

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

Apply effective strategies, based in the content strands of number sense, measurement, geometric sense, and statistics to find a solution.

·          Use estimation strategies (e.g., front-end estimation, clustering) to predict computation results. [1.1.8]

·          Use appropriate tools from among mental math, paper/pencil, manipulative, or calculator (e.g., to determine the total cost of the skating party). [1.1.7]

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

·          Determine if items will fit through a door. (e.g., seeing if a pencil will fit through requires only testing it, while a bookcase or teacher’s desk will require a different strategy). [1.2.6]

3.1 Analyze Information

Kindergarten

Problem Solving example: A classroom needs a play ground ball for each student in the class. The class has fewer playground balls than are needed.

Grade 1

Problem Solving example: A classroom is presenting a play and everyone has invited 2 guests. Enough chairs are needed to seat all the guests. There are some chairs in the classroom.

Grade 2

Problem Solving example: A classroom is planning an all-day skating party on Thursday and each student must pay for admission ($2), a box lunch ($3), and skate rental ($2). The teacher needs a total amount to reserve the rink.

3.1.1

Understand how to analyze information presented in familiar situations, with teacher guidance.

·    Restate understanding of the situation (e.g., each student requires a playground ball. There are not enough in the classroom).

·    Compare positions of students in a line using ordinal numbers (e.g. 1^st, 2^nd).[1.1.2]

·    Using a calendar, show how many days in a month have passed. [1.1.1]

Understand how to analyze information presented in familiar situations.

.

·     Restate understanding of the situation (e.g. each guest attending the play will require a chair. There are not enough in the classroom).

·     Interpret results and draw conclusions from displays using comparative language (e. g., more, fewer). [1.4.4]

·     Determine how many students are in class, knowing how many are absent. [1.1.5]

Understand how to analyze information presented in familiar situations.

Explain understanding of a situation, verbally or in writing (e.g., there are costs for admission, skates, lunch for the party, and we need to know what it will cost for all of us so our teacher can reserve the rink.)

·          Estimate how much money will be collected for a local charity based on collection data at a given point.

·          Determine how much paper will be needed  to cover the bulletin board given the paper size.

3.2 Make Predictions, Inferences, and Conjectures

Kindergarten

Problem Solving example: A classroom needs a play ground ball for each student in the class. The class has fewer playground balls than are needed.

Grade 1

Problem Solving example: a classroom is presenting a play and everyone has invited 2 guests. Enough chairs are needed to seat all the guests. There are some chairs in the classroom.

Grade 2

Problem Solving example: A classroom is planning an all-day skating party on Thursday and each student must pay for admission ($2), a box lunch ($3), and skate rental ($2). The teacher needs a total amount to reserve the rink.

3.2.1

Understand how to make a reasonable prediction based on the information given in a familiar situation.

·    Predict a numerical solution for a problem (e.g., guess how many more playground balls are needed).

Understand how to make a reasonable prediction based on prior knowledge and the information given in a familiar situation.

·    Predict a numerical solution for a problem (e.g., predict how many more chairs will be  needed).

Understand how to make a reasonable prediction based on prior knowledge and the information given in a familiar situation.

·    Predict a numerical solution for a problem (e.g., predict how much it will cost for the class to attend the skating party).

3.2.2

Understand how to make a reasonable inference based on prior knowledge and the information given in a familiar situation.

·     Make an inference based on information provided (e.g. the boys in class did a better job convincing their guests to attend because there are more guests coming for the boys than the girls).

Understand how to make a reasonable inference based on prior knowledge and the information given in a familiar situation.

·    Make an inference based on information provided (e.g., when you skate at the rink with a big group it costs less for each person than when you go with a friend.)

3.2.3

Analyze procedures used to solve problems in familiar situations.

·          Justify the importance of counting in a situation rather than making a guess at a number of items for a specific purpose. (e.g., counting the number of chairs needed for the play rather than guessing).

Analyze procedures used to solve problems in familiar situations.

·          Justify the use of a chart, or table to collect and organize information used to solve a problem (e.g., the 2 or 4 column chart helped to keep track of the information).

·          Justify the use of one tool over another (e.g., the length of a hand is a better measurement tool for this situation than the length of a small cube.) [1.2.3]

·        Analyze a pattern based on odd and even numbers. (e.g., does it match a skip counting by 2 procedure) [1.5.1]

3.3 Draw Conclusions and Verify results

Kindergarten

Problem Solving example: A classroom needs a play ground ball for each student in the class. The class has fewer playground balls than are needed.

Grade 1

Problem Solving example: A classroom is presenting a play and everyone has invited 2 guests. Enough chairs are needed to seat all the guests. There are some chairs in the classroom.

Grade 2

Problem Solving example: A classroom is planning an all-day skating party on Thursday and each student must pay for admission ($2), a box lunch ($3), and skate rental ($2). The teacher needs a total amount to reserve the rink.

3.3.1

Understand how to justify results using evidence.

·    Use tools (e.g., tally marks, physical models, words) to check for reasonableness of an answer (e.g., line up students, pass out the playground balls to students to see how many students do not receive one).

·     Check reasonableness of an estimation by acting it out, using pictures, or physical models (e.g., If there are 10 crayons, how many crayons do you think each child will get? Pass out crayons.)

Understand how to justify results using evidence.

·     Check reasonableness of results by using pictures, physical models, or acting it out (e.g., students raise one hand for one guest attending and two hands if two guests are attending).

·     Draw conclusions from displays using comparative language (e.g., more students have two guests coming, or fewer students have only one guest coming). Provide examples from displays to support conclusions. [1.4.4]

·     Check reasonableness of results in measurement by comparing the object measured to a second measured object.

Understand how to justify results using evidence.

o       Check for reasonableness of results by using a calculator for repeated addition to determine the total cost of the skating party.

o       Interpret results and draw conclusions from displays using comparative language (e.g., greater than, less than). Provide data to justify conclusions.

·          Justify the selection of a particular value for an unknown quantity in a real world situation (e.g., Two girls had ten cookies.  If Kwame had six, how many did Ellie have?  Explain.  [1.5.5]

3.3.2

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

·     Explain why a strategy or tool was used in solving a problem (e.g. why a two-column chart was helpful to gather the information needed about the number of guests attending the play)

·     Select units appropriate to the object being measured (e.g., measure length of classroom with footprints, not beans) and explain why it was selected. [1.2.2]

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

·        Explain why a strategy or tool used in solving a problem (e.g., Why a seating chart was helpful to help determine total cost of skating).

·        Select the most appropriate unit to measure the time of a given situation (e.g., Would you use minutes or hours to measure brushing your teeth, eating dinner, sleeping?). [1.2.2] and explain why it was selected.

4.1 Gather Information

Kindergarten

Grade 1

Grade 2

4.1.1

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

[dh1] 

Determine what information is needed how to collect it for a given purpose (e.g. To help explain something, to find out if something is needed) and who the information is for (e.g. for the classroom, for the adults at home, for the librarian).

·           Develop and follow a plan to gather data about an event (e.g., how many students will attend the Saturday Movie Afternoon at school?)

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

·          Determine what information is needed how to collect it for a given purpose (e.g. To help explain something, to find out if something is needed) and who the information is for (e.g. for the classroom, for the adults at home, for the cafeteria, for the principal).

·          Develop and follow a plan to gather information about supplies needed for a project (e.g., how many pieces of paper will be needed to create a pattern design for each of the kindergarten windows?).

4.1.2

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

·          Using a model, follow simple written directions for creating an art project (e.g., requiring cutting and folding geometric shapes).

·          Generate questions that could be answered using informational text (e.g. TV ads, books, menus, cereal boxes).

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

·    After reading an informational text (e.g., health article) in class, decide what information would be important to learn about the students in the second grade (e.g., how many students eat a nutritious breakfast). Determine what questions to ask in a survey. Graph the results.

4.2 Organize, Represent, and Share Information

Kindergarten

Problem Solving example: A classroom needs a play ground ball for each student in the class. The class has fewer playground balls than are needed.

Grade 1

Problem Solving example: A classroom is presenting a play and everyone has invited 2 guests. Enough chairs are needed to seat all the guests. There are some chairs in the classroom.

Grade 2

Problem Solving example: A classroom is planning an all-day skating party on Thursday and each student must pay for admission ($2), a box lunch ($3), and skate rental ($2). The teacher needs a total amount to reserve the rink.

4.2.1

Understand how to organize information, with teacher guidance, to communicate to a given audience.

·          Use a 2 column chart, with teacher guidance, to organize data (e.g. one column for student names and tally marks in the other to represent which students are assigned a ball) for the classroom.

·          Use physical objects or pictures to build bar graphs to answer a question generated by the class (e.g., How many of each kind of pet do we own?)

Understand how to organize information, with teacher guidance, to communicate  to a given audience.

Organize and display data on a chart to communicate solution for the given audience (e.g., use a 2- or 3 column chart to display the number of guests per student attending a class play and if there is a chair for each guest, how many will be needed to inform the custodian). 

·    Display results of data collection by making student-invented and conventional displays (e.g., hair color, eye color, teeth missing).

Understand how to organize information to communicate to a given audience.

·        Organize and display data on a chart to communicate solution to a specific audience (e.g., use a chart to display individual costs and total cost for the skating party for parents and PTA).

·          Construct a bar graph with a title, key, and single unit increment to display survey results (e.g., the number of brothers and sisters of students in the class).

4.2.2

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

·          Explain or represent ideas using mathematical language from:

·Number sense (e.g., numbers 1 to 10 [1.1.1])

·Measurement (e.g. compare objects to describe relative size [1.2.1])

·Geometric sense (e.g. name objects based on their characteristics – I have 4 equal sides, what am I? [1.3.1])

·Algebraic sense (e.g. create a pattern such as AB).

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

·     Explain or represent ideas using mathematical language from:

Number sense (e.g., numbers to at least 100 [1.1.1])

Measurement (e.g., order 3 or more objects according to an attribute and identify the chosen attribute [1.2.1])

Geometric Sense (e.g., name and describe 2-D figures based on their characteristics. [1.3.1])

Statistics (e.g., construct bar graphs with physical materials [1.4.3])

Algebraic Sense (e.g., explain the meaning of equality [1.5.3])

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

·         Explain or represent ideas using mathematical language from:

          Number Sense (e.g. numbers to

           At least 1000 [1.1.1])

·          Measurement (e.g. identify attributes of an object that are measurable : time, length, distance around, capacity, area or weight of objects [1.2.1]),

·          Geometric Sense (e.g., describe characteristics of 2-D geometric figures -  various polygons [1.3.1]),

·          Statistics (e.g., construct bar graph using a single increment scale [1.4.3])

·          Algebraic Sense (e.g., explain and use the symbols < and > to express relationships. [1.5.3])