2014 – 15 2nd Grade Math Concept Map – Unit 1
Big Idea – RT1: Number Systems
Students use multiple models (Rekenrek, number line, hundreds chart, base 10 blocks) to develop an understanding of the
base-ten numeration system and place-value concepts to 500. They compose and decompose numbers in multiple ways,
such as 340 = 340 ones, 3 hundreds and 40 ones, 34 tens, etc. Students understand that the base-ten system includes
ideas of counting in multiples of hundreds, tens and ones. They understand multi-digit numbers in terms of place value,
recognizing that place-value notation is shorthand for the sums of multiples of powers of 10.
Connections to the Big Idea
RT 2: Students continue to develop an understanding of numbers by representing, ordering, and comparing quantities to
500. They develop an understanding of the magnitude and position of numbers using various physical models and
representations (Rekenrek, hundreds chart, base 10 blocks). Through activities involving the number line, students gain an
understanding of number as a measure of distance (iteration). They represent whole numbers as lengths from 0 on a
number line with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and
differences within 100 on a number line.
RT3: Students solve contextual problems by applying their understanding of models, relationships and properties of number
(commutativity, associativity and identity), including odd and even. Students begin to develop efficient procedures for
adding and subtracting whole numbers, understand why the procedures work (on the basis of place value, properties of
operations, and/or the relationship between addition and subtraction), and use them to solve problems. Students work on
visualization and re-creation of images through activities such as using Rekenrek, ten-frames, number line and arrays to
develop a sense of quantity for addition and subtraction situations. Students use addition and subtraction within 500 to
solve word problems.
July 25, 2014
2014 – 15 2nd Grade Math Concept Map – Unit 1
RT1: Number Systems
PSa) Decompose numbers 10-500 using groups of hundreds, tens and ones (e.g., 853 as 8 hundreds, 5 tens and 3 ones)
2.NBT.1
PSb) Identify numerals 10-500 given a model that uses groups of hundreds, tens and ones (e.g., identify 2 hundreds, 4 tens and 8 ones as 248)
2.NBT.1
PSc) Rote count forward and backward between 0-1000 by ones, twos, fives, tens, and hundreds (e.g., count backward from 355-320 by fives)
2. NBT.2
PSd) Mentally add 10 or 100 to a given 3-digit number, and mentally subtract 10 or 100 from a given 3-digit number
2. NBT.8
RT3: Addition and Subtraction Computation
RT2: Number Relationships and Representations
PSa) Use numerals, pictures, objects, and words to represent quantity to 500
2.NBT.3
PSa) Use models to demonstrate an understanding of multi-digit addition and subtraction
within 500 (e.g., number line, 100 Rekenek, base ten blocks, 10 frames)
PSb) Compare and order numbers to 500 and use models (number line, base ten
blocks) to represent their relationship, including use of symbols <, >, =
2.OA.1, 2.NBT.7, 2.MD.6
2.NBT.4
PSb) Choose, combine and apply strategies for answering multi-digit addition and
subtraction problems, including contextual situations with unknowns in all positions
PSc) Identify, read, and write numerals and words 0-500
2.OA.1, 2.NBT.7
2.NBT.3
PSc) Add up to four two-digit numbers using strategies based on place value and
properties of operations
2.NBT.6, 2.NBT.7
July 25, 2014
2014 – 15 2nd Grade Math Concept Map – Unit 2
Big Ideas – RT1: Number Systems & RT3: Addition and Subtraction Computation
Students use multiple models (Rekenrek, number line, hundreds chart, base 10 blocks) to develop an understanding of the base-ten numeration system and placevalue concepts to 1000. They compose and decompose numbers in multiple ways, such as 850 = 850 ones, 8 hundreds and 50 ones, 85 tens, etc. Students
understand that the base-ten system includes ideas of counting in multiples of hundreds, tens and ones. They understand multi-digit numbers in terms of place
value, recognizing that place-value notation is shorthand for the sums of multiples of powers of 10.
Students develop quick recall of basic addition and related subtraction facts, and use efficient, accurate, and generalizable methods to add and subtract multi-digit
whole numbers. They solve contextual problems by applying their understanding of models, relationships and properties of number (commutativity, associativity and
identity), including odd and even. Students develop fluency** with efficient procedures for adding and subtracting whole numbers, understand why the procedures
work (on the basis of place value, properties of operations, and/or the relationship between addition and subtraction), and use them to solve problems. Students work
on visualization and re-creation of images through activities such as using Rekenrek, ten-frames, number line and arrays to develop a sense of quantity for addition
and subtraction situations. Students use addition and subtraction within 1000 to solve word problems, e.g., by using drawings and equations.
** Fluency is defined under the CCSS as “ the ability to use certain facts and procedures with enough facility that using them does not slow down or derail the problem solver as he or she works on more complex problems and being able to use
relevant ideas or procedures in a wide range of context.”
Connections to the Big Idea
RT 2: Students continue to develop an understanding of numbers by representing, ordering, and comparing quantities. They develop an understanding of the
magnitude and position of numbers using various physical models and representations (Rekenrek, hundreds chart, base 10 blocks). Through activities involving the
number line, students gain an understanding of number as a measure of distance (iteration). They represent whole numbers as lengths from 0 on a number line with
equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line.
RT 7: Students continue to develop an understanding of an unknown quantity represented as a symbol such as a box or picture, and solving for that unknown in
addition and subtraction situations. They continue to develop an understanding of equality around the equal sign (=) and generate equivalent equations in addition
and subtraction situations. Students continue to develop their understanding of patterns involving addition and subtraction. They make connections between their
work with patterns, and addition and subtraction situations, through activities such as skip counting forward and backward.
July 25, 2014
2014 – 15 2nd Grade Math Concept Map – Unit 2
RT3: Addition and Subtraction Computation
PSa) Use models to demonstrate an understanding of multi-digit addition and subtraction within 1000 (e.g., number line, 100 Rekenek, base ten blocks, 10 frames)
2.OA.1, 2.NBT.7, 2.MD.6
PSb) Choose, combine and apply strategies for answering multi-digit addition and subtraction problems, including contextual situations with unknowns in all positions.
2.OA.1, 2.NBT.7
PSd) Apply commutative and associative property of addition using whole numbers (e.g., 88+312=312+___)
2.NBT.7, 2.NBT.9
PSe) Demonstrate fluency* with basic addition and subtraction (mental math to 20, strategies to 100)
2.OA.2, 2.NBT.5, 2.NBT.8
PSf) Use addition to find the total number of objects arranged in arrays of up to 5 by 5 and write an equation matching the situation (3 by 3 array, 3+3+3=9)
2.OA.4
* Fluency is defined under the CCSS as “ the ability to use certain facts and procedures with enough facility that using them does not slow down or derail the problem solver as he or she works on more complex problems and being
able to use relevant ideas or procedures in a wide range of context.”
RT1: Number Systems
PSa) Decompose numbers 10-1000 using groups of hundreds, tens and ones (e.g., 853 as 8 hundreds, 5 tens and 3 ones)
2.NBT.1
PSb) Identify numerals 10-1000 given a model that uses groups of hundreds, tens and ones (e.g., identify 2 hundreds, 4 tens and 8 ones as 248)
2.NBT.1
RT7: Algebraic Thinking
PSa) Represent contextual problems that involve addition and subtraction of whole
numbers as a number equation using symbols and solve (e.g., box or picture to
represent the unknown)
RT2: Number Relationships and Representations
PSa) Use numerals, pictures, objects, and words to represent quantity to 1000
2.NBT.3
PSb) Generate equivalent equations (e.g., 24+26=100-50)
PSb) Compare and order numbers to 1000 and use models (number line, base ten
blocks) to represent their relationship, including use of symbols <, >, =
2.OA.1, 2.OA.4, 2.NBT.1, 2.NBT.4
2.NBT.4
PSc) Explain why addition and subtraction strategies work, using place value and the
properties of operations (models and drawings)
PSc) Identify, read, and write numerals and words 0-1000
2.OA.1
2.NBT.9
July 25, 2014
2.NBT.3
2014 – 15 2nd Grade Math Concept Map – Unit 3
Big Idea – RT5: Measurement Systems
Students develop their understanding of formal systems for measurement by investigating the units and tools used within
particular measurement systems. They develop an initial understanding by focusing heavily on the US and metric systems
for measuring length. Students continue work on iterating a unit (repeating a same sized unit), and develop an
understanding of partitioning (dividing a length into equal-sized units) and transitivity (if object A is longer than object B and
object B is longer than object C, then object A is longer than object C). Students understand the inverse relationship
between the size of a unit and the number of units used in a particular measurement (e.g., the smaller the unit the greater
the number of units for the same length). Once students have developed a foundation in formal measurements of length,
they extend their understanding to other measurement systems (units) and tools, including capacity, temperature, and
weight. The majority of the work on measurement systems can be embedded within Science RT 4.
Connections to the Big Idea
RT 8: Students extend their understanding of composing and decomposing two-dimensional shapes by partitioning shapes into their
fractional components. Students recognize that the fractional components compose the whole and that the same fractional component may
vary in size based on the size of the whole. As students combine figures, they recognize them from different perspectives and orientations,
describe geometric attributes and properties, and determine how the shapes are alike and/or different.
July 25, 2014
2014 – 15 2nd Grade Math Concept Map – Unit 3
RT5: Measurement Systems
PSa) Select and use appropriate units and tools to measure length, capacity, weight, and temperature using U.S. customary and metric units
2.MD.1, 2.MD.4
PSb) Use repetition of a single formal unit of length to measure something larger than the unit (iteration)
2.MD.4
PSc) Identify whether the number of units increases or decreases when the size of the unit changes (e.g., If a pencil is 4 inches long, when measured in centimeters will
the number be larger or smaller?)
2.MD.2
PSd) Estimate length using standard units (inches, feet, centimeters, meters)
2.MD.3
PSe) Recognize and represent time to five minute intervals using digital and analog clocks (including hour, half-hour, and quarter-hour)
2.MD.7
RT8: Geometric Figures
PSa) Recognize and draw 2D shapes given specific attributes (number of sides or angles)
2.G.1
PSb) Identify triangles, quadrilaterals, pentagons, hexagons and cubes
2.G.1
RT9: Data Collection / Representation
PSa) Generate measurement data by measuring lengths of several
objects to the nearest whole unit, or by making repeated measurements of
the same object. Show the measurements by making a line plot, where
the horizontal scale is marked off in whole-number units
PSc) Partition a rectangle into rows and columns of equal size and count to find the total number
2.MD.9
2.G.2
PSd) 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 equal shares of identical wholes need not have the same shape
PSb) Draw a picture graph and a bar graph (with single-unit scale) to
represent a data set with up to four categories. Solve simple put- together,
take-apart, and compare problems using information presented in a bar
graph.
2.G.3
2.MD.10
July 25, 2014