2014 – 15 3rd Grade Math Concept Map – Unit 1
Big Idea – RT4: Multiplication and Division Computation
Students understand the meanings of multiplication and division of whole numbers through the use of representations, such as equal-sized
groups, arrays, area models and number lines for multiplication, and repeated subtraction, partitioning and sharing for division. They use
properties of addition and multiplication (identity, zero, commutative, associative & distributive) to multiply whole numbers and apply
increasingly sophisticated strategies to solve contextual problems. Through their work with multiple strategies, students relate multiplication
and division as inverse operations. By the end of the unit the students should fluently multiply and divide within 100.*
Connections to the Big Idea
RT 1&2: Students extend their understanding of place value to multi-digit numbers in various situations, including understanding how place value relates to addition,
subtraction, multiplication, and division. They compose and decompose numbers in multiple ways, such as 3420 = 3420 ones, 3 thousands + 4 hundreds + 2 tens,
342 tens, etc.
RT 3: Students continue to develop their understanding of addition and subtraction of multi-digit whole numbers including building their facility with mental arithmetic
(e.g., 250 + 600 or 203-199) and by using computational estimation to judge the reasonableness of results. They select and apply appropriate methods to estimate
sums and differences or calculate them mentally depending on the context and numbers involved. They apply their understanding of repeated addition and/or
subtraction to multiplication and division.
RT6: Students understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular
arrays of squares, students connect area to multiplication and justify using multiplication to determine the area of a rectangle.
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
computation situations including multiplication and division. They continue to develop an understanding of equality around the equal sign (=) and generate equivalent
equations in computation situations including multiplication and division. Students continue to develop their understanding of patterns by describing and extending
them. Their work with multiplication and division strategies should involve analysis of the patterns that exist within these operations. Students work with various
models such as number lines, ratio tables and arrays, and should embed the analysis of the patterns that exist.
* 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.”
July 25, 2014
2014 – 15 3rd Grade Math Concept Map – Unit 1
RT4: Multiplication and Division Computation
PSa) Use models (number line, arrays, ratio table) to demonstrate an understanding of multiplication of whole numbers up to 10 x 10, and a whole number by multiples of 10
including contextual situations
3.OA.1, 3.OA.3, 3.OA.8, 3.NBT.3
PSb) Use models to demonstrate an understanding of division of numbers related to the 10 x 10 multiplication facts
3.OA.2, 3.OA.3, 3.OA.6
PSc) Fluently* multiply and divide within 100 (1 digit facts from memory by the end of 3rd grade)
3.OA.7, 3.NBT.3
PSd) Apply properties of operations as strategies to multiply and divide (students need not use formal terms for these properties)
3.OA.5, 3.OA.7, 3.OA.9, 3.NBT.3
* 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 relavant ideas or procedures in a wide range of context.”
RT6: Dimensional Measurement Relationships
RT1&2: Number Systems, Relationships and Representations
PSa) Compose and decompose multi-digit numbers (using groups
of thousands, hundreds, tens and ones) to support operations
PSa) Measure area by counting the unit squares and relate area to the operations of multiplication and
division (arrays and area models)
3.MD.6, 3.MD.7
3.NBT.2
RT7: Algebraic Thinking
RT3: Addition and Subtraction Computation
PSa) Demonstrate fluency* with addition and subtraction within 1000 using models, strategies and algorithms including
contextual situations
3.OA.8, 3.NBT.2
PSb) Assess the reasonableness of answers using mental computation and estimation strategies including rounding
3.OA.8, 3.NBT.1
PSa) Recognize, describe, and extend patterns, including patterns within the
multiplication chart (e.g., observe that 4 times a number is always even and explain
why 4 times a number can be decomposed into two equal addends)
3.OA.9
PSb) Represent contextual problems (one and two step) that involve computation of
whole numbers as an equation using symbols (box or picture to represent the
unknown)
3.OA.3, 3.OA.6, 3.OA.8
* 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 relavant ideas or procedures in a wide range
of context.”
PSc) Solve missing number equations
3.OA.4
PSd) Generate equivalent equations (e.g., 3x5=3+3+3+3+3 or 4x3=6x2)
3.OA.1, 3.OA.2, 3.OA.6
July 25, 2014
2014 – 15 3rd Grade Math Concept Map – Unit 2
Big Idea – RT 1&2: Number Systems, Relationships and Representations
Students develop an understanding of fractions to represent part(s) of a whole, part(s) of a set, or distance(s) on a number
line. They understand that the size of a fractional part is relative to the size of the whole (unitizing), and they use fractions to
represent numbers that are equal to, less than or greater than one. They use models, such as benchmark fractions (halves,
thirds, fourths, sixths and eighths) common numerators or denominators, and measurement tools (ruler) to solve problems
that involve comparing, ordering and identifying equivalent fractions.
Connections to the Big Idea
RT 5: Students continue to develop their understanding that measurement systems utilize standardized tools and units to measure attributes
of length. Students use rulers, yardsticks and meter sticks as distance models (number lines) in order to solidify their understanding of
fractional parts.
RT 7: Students continue to develop an understanding of equality around the equal sign (=) and generate equivalent fractions. Students
continue to develop their understanding of patterns by describing and extending patterns.
RT 8: Students partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole. For example,
partition a shape into four parts with equal area, and describe the area of each part as ¼ of the area of the shape.
RT9: Students continue to develop understanding of data representation and analysis by creating and using picture and bar graphs. They
use measurement data to draw a scaled picture graph and a scaled bar graph that represent a data set with several categories. Students
solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example,
draw a bar graph in which each square in the bar graph might represent 5 animals in an ecosystem.
July 25, 2014
2014 – 15 3rd Grade Math Concept Map – Unit 2
RT1&2: Number Systems, Relationships, and Representations
PSb) Use numerals, words and models (number line, arrays, Cuisenaire rods, pattern blocks, fraction bars) to represent whole numbers and fractions
3.NF.1, 3.NF.2
PSc) Compose and decompose fractions (e.g., 3/4 = 1/4 + 1/4 + 1/4, 5/2 = 1/2 + 1/2 + 1/2 + 1/2 + 1/2)
3.NF.1, 3.NF.2, 3.NF.3
PSd) Use visual fraction models and number lines, symbols (<, >, =), and words to compare and order whole numbers and fractions by reasoning about their size
3.NF.2
PSe) Identify equivalent fractions using a model
3.NF.3
PSf) Identify a fraction as less than, equal to, or greater than 1 (e.g., 1/2 is less than 1, 3/3 is equal to 1, 4/3 is greater than 1)
3.NF.3
Grade 3 expectations limited to denominators 2, 3, 4, 6, and 8
RT5: Measurement Systems
RT7: Algebraic Thinking
PSa) Recognize, describe and extend patterns involving fractions
3.NF.1, 3.NF.2
PSe) Represent equivalent fractions in an equation (e.g., 4/8 = 2/4
= 1/2)
RT8: Geometric Figures
PSb) Partition shapes into parts with equal areas and
express the area of each part as a unit fraction of the
whole
3.G.2
PSa) Generate measurement data by measuring lengths
using rulers marked with halves and fourths of an inch.
Show the data by making a line plot, where the horizontal
scale is marked off in appropriate units— whole numbers,
halves, or quarters.
3.MD.4
3.NF.3
RT9: Data Collection, Representation and Analysis
PSa) Draw a scaled picture graph and a scaled bar graph to represent a data set with several
categories
3.MD.3
PSb) Solve one- and two-step “how many more” and “how many less” problems using
information presented in scaled bar graphs
July 25, 2014
3.MD.3
2014 – 15 3rd Grade Math Concept Map – Unit 3
Big Idea – RT6: Dimensional Measurement Relationships
Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape by finding the total number of samesize units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for
measuring area. Students understand that rectangular arrays can be decomposed into identical rows or into identical columns. By
decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using multiplication to
determine the area of a rectangle. Students develop an understanding of perimeter and area as an extension of measuring length and can
select appropriate units, strategies and tools to solve problems related to perimeter and area.
Connections to the Big Idea
RT 3: Students use their understanding of addition and subtraction of whole numbers in order to solve problems involving perimeter of twodimensional figures and use computational estimation to judge the reasonableness of results. They select and apply appropriate methods to
estimate sums and differences or calculate them mentally depending on the context and numbers involved.
RT4: Students relate area and array models to demonstrate an understanding of multiplication of whole numbers up to 10 x 10, including
contextual situations.
RT 5: Students continue to develop their understanding that measurement systems utilize standardized tools and metric units to measure
attributes of objects. They utilize formal units and tools to measure attributes of liquid volume, weight, and time. In addition, students work on
estimating the number of units needed for a particular measurement. The majority of the work on measurement systems can be embedded
within Science RT4 which focuses on changes and measures of matter.
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 situations involving perimeter and area of two dimensional figures. They continue to develop an understanding of equality
around the equal sign (=) and generate equivalent equations in situations involving perimeter and area.
RT 8: Students describe, analyze, compare and classify two dimensional shapes by their attributes to create definitions of shapes. They
recognize area as an attribute of two-dimensional regions.
July 25, 2014
2014 – 15 3rd Grade Math Concept Map – Unit 3
RT6: Dimensional Measurement Relationships
PSa) Measure area by counting the unit squares and relate area to the operations of multiplication and division
3.MD.6, 3.MD.7
PSb) Multiply side lengths (whole number) to find the area of rectangles
3.MD.7
PSc) Solve real world and mathematical problems involving the perimeter of polygons
3.MD.8
RT4: Multiplication and Division Computation
RT3: Addition and Subtraction
Computation
PSc) Choose, combine and apply strategies for
answering multi-digit addition and subtraction
problems, including contextual situations (e.g., find
the perimeter)
PSa) Use models (arrays, area models) to demonstrate an understanding of multiplication of
whole numbers up to 10 x 10, including contextual situations
3.MD.7
3.MD.7, 3.MD.8
RT5: Measurement Systems
PSb) Tell and write time to the nearest minute and measure time intervals in
minutes
RT7: Algebraic Thinking
PSb) Represent contextual problems that involve perimeter and or area as a number equation
using symbols (e.g., box or picture to represent the unknown side length of geometric figure)
3.MD.1
PSc) Measure and estimate liquid volumes and masses of objects using standard units of
grams (g), kilograms (kg), and liters (l).
3.MD.2
3.OA.8
PSc) Solve missing number equations (e.g., perimeter and area problems)
3.MD.8
PSd) Generate equivalent equations (e.g., if two different rectangles have the same perimeter of
36, what could their side lengths be? 9+9+6+6 = 30 =10+10+5+5)
3.MD.8
RT8: Geometric Figures
PSa) Recognize area as an attribute of a plane figure, understand the concept of area measure and explain why area
is measured in square units
3.MD.5
PSc) Classify 2D shapes according to their properties and develop definitions for classes of shapes (e.g.,
quadrilaterals, polygons, rhombuses)
3.G.1
July 25, 2014