Number and Operations Grade 2 K-12 Enduring Understanding 1 ...

Geometry and Measurement Strand Grade 2Mathematics Enduring Understanding 2: Spatial relationships can be described using coordinate geometry and other representationalsystems.Essential Standard Grade Band K-2:Describe, name, and interpret relative positions, directions, and distances in spacePerformance Indicators Assessment Samples – SOL/Blooms VocabularyAll students will:Knowledge/Comprehension Level:left• Give students a map of the school. Have the students draw theshortest route for the principal to go to the classroom.right• Understand that directionand distance can be used innavigating space.Application/Analysis Level:• “Tanya the Turtle” (Investigations in Number, Data, and Space, “HowLong, How Far?”)Tanya the Turtle is hungry and tired. She wants to have a snackbefore going back to her lily pad. She knows where two flies arein the pond. Using the grid below, list the moves Tanya mustmake to get the two flies and then go back to her lily pad for arest.northsoutheastwestSystemsDiscipline Level Concept: Relationships

Geometry and Measurement Strand Grade 2Mathematics Enduring Understanding 2: Spatial relationships can be described using coordinate geometry and other representationalsystems.Synthesis/Evaluation Level:• “Andy the Ant” (Investigations in Number, Data, and Space, “HowLong, How Far?”)Supporting Skills and Processes: Using directional vocabulary and working with gridsSystemsDiscipline Level Concept: Relationships

Geometry and Measurement Strand Grade 2Mathematics Enduring Understanding 3: Attributes of objects can be measured using processes and quantified units, and usingappropriate techniques, tools, and formulas.Essential Standard Grade Band K-2:Understanding attributes of measurement by directly comparing objects, and selecting an appropriate unit and toolsPerformance Indicators Assessment Samples – SOL/Blooms VocabularyAll students will:cent symbolKnowledge/Comprehension Level:• Ask the student to write $3.49. Look for the correct use of the dollardollar symbolsign/decimal.decimal point• Understand that objectscan be ordered bymeasurable attributes,including length,weight/mass, volume,value, time andtemperature.• Understand that thereare tools that measurespecific attributes.• Measure using nonstandardand standardunits length, liquidvolume, weight,temperature, and time(to the nearest 5minutes).• Select an appropriateunit and tool for theattribute beingmeasured.• Count or compare acollection of coinswhose total value is$2.00 or less, using thecorrect symbols.Application/Analysis Level:• Calendar Interpretation:Use the calendar to answer the questions:Five days after March 16 is what day?Three days before March 25 is what day?What will be the date one week from March 30?greater thanless thanequal toinchcentimeterdistancesurfacesquare unitsvolumeweightmasspoundkilogramquarter houranalog clockdigital clockliquid volumecupscent symbolSystemsDiscipline Level Concept: Quantifying Representation

Geometry and Measurement Strand Grade 2Mathematics Enduring Understanding 3: Attributes of objects can be measured using processes and quantified units, and usingappropriate techniques, tools, and formulas.Synthesis/Evaluation Leveldollar symbolArea and PerimeterEach small square on the gird provided is one square unit.decimal pointgreater than• Create a design that meets these criteria:o (1) covers 12 square unitsless thano (2) the distance around the figure is 16 unitsequal toinchcentimeterdistancesurfacesquare unitvolumeweightmasspoundkilogramquarter houranalog clockdigital clockliquid volumepintquartgallonliterequivalentmonthSystemsDiscipline Level Concept: Quantifying Representation

Geometry and Measurement Strand Grade 2Mathematics Enduring Understanding 11: Analyze characteristics and properties of 2- and 3-dimensional geometric shapes and developmathematical arguments about geometric relationshipsCommunicationDiscipline Level Concept: Reasoning and Justification

Geometry and Measurement Strand Grade 2Mathematics Enduring Understanding 11: Analyze characteristics and properties of 2- and 3-dimensional geometric shapes and developmathematical arguments about geometric relationshipsSOL: 2.16 The student will identify, describe, compare, and contrast plane and solid geometric figures (circle/sphere, square/cube, andrectangle/rectangular prism).CommunicationDiscipline Level Concept: Reasoning and Justification

Geometry and Measurement Strand Grade 2Mathematics Enduring Understanding 12: Transformations, symmetry, and spatial reasoning can be used to analyze and modelmathematical situations.Essential Standard Grade Band K-2:Develop an understanding of transformations and symmetry with shapesPerformance Indicators Assessment Samples – SOL/Blooms VocabularyAll students will:Knowledge/Comprehension Level:• Recognize, name, build, • Draw the lines of symmetry for each shape or letter.draw, compare, and sort2D and 3D shapes.line of symmetryverticalhorizontalApplication/Analysis Level:• Look at the cutout in the drawingdiagonal• Draw a picture of what the paper will look like when it is unfolded.CommunicationDiscipline Level Concept: Reasoning and Justification

Data Analysis and Probability Grade 2Mathematics Enduring Understanding 5: Mathematical models are used to predict and make inferences about data.Essential Standard Grade Band K-2: Discuss events related to student experiences by conducting surveys and reading graphs of studentinformationPerformance Indicators Assessment Samples – SOL/Blooms VocabularyAll students will:Knowledge/Comprehension levelShow students a weather graphs for the months of February, April, May, more! Understand that they can August, and December. Ask questions about the number of sunny daysgather data aboutthemselves and theirsurrounding in order toanswer questions.comparing one month to another.lessfewer! Understand that the datagathered and analyzedfrom observations andsurveys can have animpact on our everydaylives.greater thanless thanequal to! Understand and constructpicture graphs, objectgraphs, and bar graphs torepresent data and answerquestions.picture graphsbar graphsdata! Understand thatinterpretation of the datacould lead to additionalquestions to becompareinvestigated.Application /Analysis levelStudents will collect temperature data for a month, and then display the datain a graph.Synthesis/Analysis levelStudents will make an observation about their data, and write a letter to nextyear’s second graders informing them what clothing they should haveProperties and ModelsDiscipline Level Concept: Models

Data Analysis and Probability Grade 2Mathematics Enduring Understanding 5: Mathematical models are used to predict and make inferences about data.prepared for that month.Supporting SOL2.23 The student will read, construct, and interpret a simple picture and bar graph.Properties and ModelsDiscipline Level Concept: Models

Data Analysis and Probability Strand Grade 2Mathematics Enduring Understanding 6: Data can be collected, organized, and displayed in purposeful ways.Essential Standard Grade Band K-2: Pose questions, gather, and use various methods to represent data about themselves and theirsurroundingsPerformance Indicators Assessment Samples – SOL/Blooms VocabularyAll students will:Use the following activity for the assessments:• Vary, Vary Interesting Things (Exploring Statistics in the graph! Understand and construct picture Elementary Grades, Dale Seymour)graphs, object graphs, and bargraphs to represent data andanswer questions.Fill bundles or containers with a wide variety of materials, suchas wallpaper samples, buttons, fabric swatches, alphabet letters,attribute blocks, catalog pictures of tools, jewelry, or hats (onebundle per group of 3 or 4 students).constructcollectIt is always interesting to see how other people organize things.You will be working in small groups and analyzing materials ina bag or bundle.Knowledge/Comprehension level1. What is in your bag (or bundle)?2. How can these materials be sorted?3. Choose one sorting factor (attribute) to sort your bundle.organizedisplaybar graphpicture graphdataApplication /Analysis level1. Using the attribute chosen, organize the objects in yourbundle2. Use the objects in your sort to create a physical graphattributesortProperties and ModelsDiscipline Level Concept: Analysis and Evaluation

Data Analysis and Probability Strand Grade 2Mathematics Enduring Understanding 6: Data can be collected, organized, and displayed in purposeful ways.Synthesis/Evaluation level:• Ages of Students graph (Navigating through Data K-2,NCTM)Use the following graph about students to answer thequestions:1. What is the title of the graph?2. What are the possible ages?3. How many more people are 7 years old than the peoplewho are 6 years old?4. Are more people older or younger than 7?SOL2.17 The student will use data from experiments to construct picture graphs, pictographs, and bar graphs.2.18 The student will use data from experiments to predict outcomes when the experiment is repeated.2.19 The student will analyze data displayed in picture graphs, pictographs, and bar graphs.Properties and ModelsDiscipline Level Concept: Analysis and Evaluation

Patterns and Algebra Grade 2Mathematics Enduring Understanding 4: Situations and structures can be represented, modeled and analyzed using algebraicsymbols.Supporting SOL:SOL 2.9 The student will recognize and describe the related facts that represent and describe the inverse relationship between addition and subtraction.Properties and ModelsDiscipline Level Concept: Models

Patterns and Algebra Grade 2Mathematics Enduring Understanding 10: Change, in various contexts, both quantitative and qualitative, can be identified andanalyzed.Essential Standard Grade Band K-2: Describe change both quantitatively and qualitativelyPerformance Indicators Assessment Samples – SOL/Blooms VocabularyAll students will:Knowledge/Comprehension Level:• Continue the pattern 32, 34, 36 ,___, ____,____• Identify, describe,Patternextend, and createApplication/Analysis Level:repeating and growingSkip counting• Extend the pattern 60, 50, 40, _____, ____,____numeric patterns andsequential patterns toCalculatorSynthesis/Evaluation Level:build foundations for • Say, “If you walked by a classroom and heard the children say 6, 9, 12,understandingOddwhat do you think you would hear next?”multiples and factors.Even• Describe patterns inskip counting and usethose patterns topredict the nextnumber or numbers inthe skip countingsequence (forward andbackward).• Understand thatcollections of objectscan be grouped andskip counting can beused to count thecollection.SOL:2.4 The student willa) count forward by twos, fives, and tens to 100, starting at various multiples of 2, 5, or 10;b) count backward by tens from 100; andc) recognize even and odd numbers.Change and InteractionsDiscipline Level Concept: Cause and Effect