Mathematical Practices (MP)



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Grade 2 —Mathematics

Mathematical Practices (MP)

MP 1. Make sense of problems and persevere in solving them.

MP 2. Reason abstractly and quantitatively.

MP 3. Construct viable arguments and critique the reasoning of others.

MP 4. Model with mathematics.

MP 5. Use appropriate tools strategically.

MP 6. Attend to precision.

MP 7. Look for and make use of structure.

MP 8. Look for and express regularity in repeated reasoning.

Standards

Skills

Suggested sample teacher activities/materials

Assessment

Notes

Operations and Algebraic Thinking (OA)

Represent and solve problems involving addition and subtraction

2.OA.1 (DOK 1, 2)

Use strategies to add and subtract within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.



Identify the unknown in an addition or subtraction word problem
Determine operation needed to solve addition and subtraction problems in situations including add to, take from, put together, take apart, and compare
Use drawings or equations to represent one-and two-step word problems

Add and subtract within 100 to solve one-step word problems with unknowns in all positions


Write an addition and subtraction equation with a symbol for the unknown

Saxon L. 22

Saxon L. 22

Saxon L. 10-1
Saxon L. 22 (extension)

Saxon L. 22 (extension)







Some but not all word problems must include standard units of length.

Add and subtract within 20

2.OA.2 (DOK 1)

Use mental strategies to fluently add and subtract within 20.



Know mental strategies for addition and subtraction
Know from memory all sums of two, one-digit numbers
Apply mental strategies to add and subtract fluently within 20
Fluently add and subtract within 20

Saxon L. 5

Saxon L. 5

Saxon L. 5

Saxon L. 5









Work with equal groups of objects to gain foundations for multiplication

2.OA.3 (DOK 1)

Determine whether a group of objects up to 20 is odd or even.

Write an equation to represent an even number using two equal addends or groups of 2.


Recognize that in groups of even numbers objects will pair up evenly
Determine whether a group of objects is odd or even, using a variety of strategies
Generalize the fact that all even numbers can be formed from the addition of 2 equal addends

Counts a group of objects up to 20 by 2s.


Write an equation to express a given even number as a sum of two equal addends

Saxon L. 13

Number kids, calendar, meeting board, temperature


Meeting board, fact families

Saxon L. 13

Fact families, meeting board





Strategies may include pairing objects or counting by 2s.

2.OA.4 (DOK 1, 2)

Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns.

Write an equation to express the total as a sum of equal addends.


Write an equation with repeated equal addends from an array
Generalize the fact that arrays can be written as repeated addition problems
Solve repeated addition problems to find the number of objects using rectangular arrays

Saxon L. 121

Saxon L. 121


Augment L. 121






Example: 4+4+4=12 or

3+3+3+3=12


****

****


****

Number and Operations in Base Ten (NBT)

Understand place value

2.NBT.1

Demonstrate understanding that the three digits of a three-digit number represent amounts of hundreds, tens, and ones, including:




  1. 100 can be thought of as a bundle of ten tens—called a “hundred”.

  2. Multiples of 100 represent a number of hundreds, 0 tens, and 0 ones.




Explain the value of each digit in a 3-digit number
Identify a bundle of 10 tens as a “hundred”
Represent a three-digit number with hundreds, tens and ones

Saxon L. 74

Augment 74; CD- manipulatives, Tier II act.

Saxon L. 74





Example: 706 represents 7 hundreds, 0 tens, and 6 ones.

2.NBT.2

Count forward and backward from any given number with 100.


Skip-count by 5s, 10s, and 100s.














2.NBT.3 (DOK 1)

Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.



Know what expanded form means
Recognize that the digits in each place represent amounts of thousands, hundreds, tens or ones
Read numbers to 1000 using base ten numerals
Read numbers to 1000 using number names
Read numbers to 1000 using expanded form
Write numbers to 1000 using base ten numerals
Write numbers to 1000 using number names

Write numbers to 1000 using expanded form


Decompose numbers less than or equal to 10 into pairs in more than one way
Record decomposition of a number within 10 by a drawing or written equation

Saxon L. 84
L. 83 Augment to 1000

Saxon L. 84

SuperTeacher wksts, rearranging digits, 3-digit number match, writing and reading #s to 999
Saxon L. 84

Saxon L. 84


SuperTeacher Wkst, writing and reading #s to 999

Saxon L. 4 (to 100)

Tier II math games (match, concentration, show toss, pairing socks, mittens, etc.)

Saxon L. 61








2.NBT.4 (DOK 1)

Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, recording the results of comparison with the symbols >,=, and <.



Know the value of each digit represented in a three-digit number
Know what <, > and = symbols each represent
Compare two three-digit numbers based on place value of each digit
Use >, = and < symbols to record the results of comparisons

Saxon L. 76

Saxon L. 81

Saxon L. 81

Saxon L. 81









Use place value understanding and properties of operations to add and subtract

2.NBT.5 (DOK 1)

Use strategies based on place value, properties of operations, and/or the relationship between addition and subtraction to fluently add and subtract within 100.



Know strategies for adding and subtracting based on place value
Know strategies for adding and subtracting based on properties of operations

Know strategies for adding and subtracting based on the relationship between addition and subtraction


Fluently add and subtract within 100
Choose a strategy (place value, properties of operations and/or the relationship between addition and subtraction) to fluently add and subtract within 100

Saxon L. 61

Saxon L. 29

Saxon L. 29

Saxon L. 5


Saxon L. 53







2.NBT.6 (DOK 1)

Use strategies based on place value and properties of operations to add up to four two-digit numbers.

Know strategies for adding two-digit numbers based on place value and properties of operations
Use strategies to add up to four two-digit numbers

L. 53, L. 54 augment to include properties of operations
L. 68 augment to include 4 2-digit numbers







2.NBT.7 (DOK 1, 2)

Demonstrate understanding of place value within 1000 when adding or subtracting three-digit numbers.


Use concrete models or drawings and strategies based on place value, properties of operation, and/or the relationship between addition and subtraction to add and subtract within 1000.
Use a written method to explain the strategy.

Understand place value within 1000
Decompose any number within 1000 into hundreds, tens, and ones
Choose an appropriate strategy for solving an addition or subtraction problem within 1000
Relate the chosen strategy (using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction) to a written method (equation) and explain the thinking used
Use composition and decomposition of hundreds and tens when necessary to add and subtract within 1000

Saxon L. 38
SuperTeacher wksts *expand form
Saxon L. 53

Saxon L. 53

Saxon L. 61








2.NBT.8 (DOK 1)

Mentally add or subtract 10 to 100 to or from a given number between 100 and 900.



Know place value within 1000

Apply knowledge of place value to mentally add or subtract 10 or 100 to/from a given number 100-900



Saxon L. 38
Saxon L. 74 (Extension)







Measurement and Data (MD)

Measure and estimate lengths in standard units

2.MD.1 (DOK 1)

Select and use appropriate tools to measure the length of an object.



Identify tools that can be used to measure length
Determine which tool is most appropriate to use to measure the length of an object
Measure the length of objects, using appropriate tools

Saxon L. 43

Saxon L. 43


Saxon L. 55-2






Tools may include rulers, yardsticks, meter sticks, and measuring tapes.

2.MD.2 (DOK 1, 2)

Measure the length of an object using different standard units of measurement.


Describe how the two measurements relate to the size of the units chosen.

Know how to measure the length of objects with different units
Compare measurements of an object taken with two different units
Describe why the measurements of an object taken with two different units are different
Explain the length of an object in relation to the size of the units used to measure it

Saxon L. 55-2

Saxon L. 55-2

Saxon L. 55-2

Saxon L. 55-2






Different standard units of measurement may include inches and feet, inches and centimeters, feet and yards, yards and meters, etc.

2.MD.3 (DOK 1)

Estimate lengths using units of inches, feet, centimeters, and meters.




Know strategies for estimating length
Recognize the size of inches, feet, centimeters, and meters
Determine if an estimate is reasonable
Estimate lengths in units of inches, feet, centimeters, and meters

Saxon L. 102 (Extension)

Saxon L. 99 (in/ft); L. 102 (cm/m)


Saxon L. 102 (Extension)
Saxon L. 102







2.MD.4 (DOK 1)

Measure to determine how much longer one object is than another, expressing the difference with a standard unit of measurement.




Name standard length units
Compare lengths of two objects

Determine how much longer one object is than another in standard

length units


Saxon L. 99
Saxon L. 99

Saxon L. 99









Relate addition and subtraction to length

2.MD.6 (DOK 1)

Represent whole numbers as a number line diagram with equally spaced points.

Represent whole-number sums and differences within 100 on a number line diagram.


Represent whole numbers from 0 on a number line with equally spaced points
Explain length as the distance between zero and another mark on the number line diagram
Use a number line to represent the solution of whole-number sums and differences related to length within 100

Saxon L. 56

Saxon L. 56


Saxon L. 56 (Extension)






Students must demonstrate appropriate spatial representation.
Example:

2 would be placed closer to 0 than to 10



Work with time and money

2.MD.7 (DOK 1)

Tell and write time to the nearest five minutes (including quarter after and quarter to) with using a.m. and p.m. using analog and digital clocks.



Look for and make use of structure
Tell time using analog clocks to the nearest 5 minutes
Tell time using digital clocks to the nearest 5 minutes

Write time using analog clocks and digital clocks


Identify the hour and minute hand on an analog clock
Identify and label when a.m. and p.m. occur
Determine what time is represented by the combination of the number on the clock face and the position of the hands

Saxon L. 78
Saxon L. 12 (Analog);

L. 3 (digital


Saxon L. 3

Saxon L. 6

Saxon L. 3

Saxon L. 6

Saxon L. 3








2.MD.8 (DOK 1)

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.



Identify and recognize the value of dollar bills, quarters, dimes, nickels, and pennies
Identify and $ and ¢ symbols
Think: Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies using $ and ¢ symbols appropriately

Saxon L. 109 (dollar); L. 9e(quarter); L. 28 (pennies and dimes); L. 46 (nickels)

Saxon L. 53 (¢)


Saxon L. 157







Represent and interpret data

2.MD.9 (DOK 1)

Generate measurement data by measuring lengths of objects to the nearest whole standard unit.

Show the measurements by making a line plot, using horizontal scale marked off in whole-number units.


Read tools of measurement to the nearest unit
Represent measurement data on a line plot

Measure length of several objects to the nearest whole unit

Measure length by making repeated measurements of the same object
Create a line plot with a horizontal scale marked in whole numbers using measurements


Saxon L. 99

Saxon L. 43 (extension)

Saxon L. 43

Saxon L. 43

Saxon L. 43 (extension)





Students may generate data by making repeated measurements of a growing or shrinking object over time or measuring several different objects.

2.MD.10 (DOK 1, 2)

Draw a picture graphs and bar graphs with single-unit scales to represent data sets with up to four categories.

Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.


Recognize and identify picture graphs and bar graphs
Identify and label the components of a picture graph and bar graph
Make comparisons between categories in the graph using more than, less than, etc.
Solve problems relating to data in graphs by using addition and subtraction

Draw a single-unit scale picture graph to represent a given set of data with up to four categories


Draw a single-unit scale bar graph to represent a given set of data with up to four categories

Saxon L. 17

Saxon L. 17

Saxon L. 39

Saxon L. 39

Saxon L. 82

Saxon L. 125-2









Geometry (G)

Reason with shapes and their attributes

2.G.1 (DOK 1)

Identify trapezoids, rhombuses, pentagons, hexagons, octagons, parallelograms, quadrilaterals, cubes, spheres, cylinders, cones, triangular prisms, and rectangular prisms.


Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.

Identify the attributes of triangles, quadrilaterals, pentagons, hexagons, and cubes (e.g., faces, angles, sides, vertices, etc.)
Identify triangles, quadrilaterals, pentagons, hexagons, and cubes based on the given attributes
Describe and analyze shapes by examining their sides and angles, not by measuring
Compare shapes by their attributes (e.g., faces, angles)
Draw shapes with specified attributes

Saxon L. 18; L. 101

Saxon L. 18; L. 101


Saxon L. 57


Saxon L. 18: L. 101

Saxon L. 57








2.G.2 (DOK 1)

Partition a rectangle into rows and columns of same-size squares and count to find the total number.



Define partition
Identify a row
Identify a column
Count to find the total number of same-size squares
Determine how to partition a rectangle into same-size squares

Augment
Saxon L. 129
Augment
Saxon L. 121

Saxon L. 129









2.G.3 (DOK 1)

Partition circles and rectangles into two, three, or four equal shares.


Describe the shares using the words halves, thirds, half of, a third, of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that identical can be equally divided in different ways.
Demonstrate understanding that partitioning shapes into more equal shares creates smaller shares.

Identify two, three, and four equal shares of a whole
Describe equal shares using vocabulary: halves, thirds, fourths, half of, third of, etc.
Describe the whole as two halves, three thirds, or four fourths
Justify why equal shares of identical wholes need not have the same shape

Saxon L. 19;

Saxon L. 34


Saxon L. 23



Saxon L. 24








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