Common Core Grade 3
Mathematics
Scope and Sequence
Overview and Guide
Overview1
In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of
multiplication and division and strategies for multiplication and division within 100; (2) developing
understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing
understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing
two-dimensional shapes
Four Critical Areas
Questions or Concerns?
1
From Common Core State Standards for Mathematics, PARCC Model Content Frameworks, FSiM, and assorted Progressions
Revised: 5/12
Page 2 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Overview and Guide
Please contact Stephanie Lyon (stephanielyon@achievementfirst.org.)
Revised: 5/12
Page 3 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Grade 3 Overview
Revised: 5/12
Page 4 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Grade 3 Standards
Revised: 5/12
Page 5 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Grade 3 Standards
Revised: 5/12
Page 6 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Grade 3 Standards
Revised: 5/12
Page 7 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Grade 3 Standards
Revised: 5/12
Page 8 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Grade 3 Standards
Revised: 5/12
Page 9 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Grade 3 Standards
Revised: 5/12
Page 10 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Grade 3 Standards
Revised: 5/12
Page 11 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Grade 3 Standards
Revised: 5/12
Page 12 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Glossary & Tables
Revised: 5/12
Page 13 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Glossary & Tables
Revised: 5/12
Page 14 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Glossary & Tables
Revised: 5/12
Page 15 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Glossary & Tables
Revised: 5/12
Page 16 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Interim Assessment One
Unit One: Multiplication, Division, & Area 1
Critical Area(s): (1) Developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) Developing
understanding of the structure of rectangular arrays and of area
Duration: 18 days
Strategies: Concrete – build arrays/groups; Pictorial – draw arrays/groups; Abstract – count on/skip-count, just know facts
*use tiled arrays consistently to link multiplication, division, and area
Major, Supporting, Additional
Common Core State Standard
Clusters
Major: Represent and solve
3.OA.1 Interpret 2products of whole numbers, e.g., interpret 5x7 as the total number of objects in 5 groups of 7 objects each.
problems involving
For example, describe a context in which a total number of objects can be expressed as 5x7.
multiplication and division
*FS: UO KU3
3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56÷8 as the number of objects in each share when
Major: Understand concepts of
56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8
area and relate area to
objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56÷8.
multiplication and addition
*FS: UO KU4
3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.
Major: Understand properties of
a) A square with side length 1 unit, called a “unit square,” is said to have “one square unit” of area, and can be used to
multiplication and the
measure area.
relationship between
b) A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
multiplication and division
*FS: UU KU3, UU KU4, DM KU3
3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
Major: Represent and solve
*FS: UU KU3, UU KU4, UU KU7
problems involving
3.MD.7 Relate 3area to the operations of multiplication and addition.
multiplication and division
a) Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be
found by multiplying the side lengths.
Additional: Use place value
*FS: IM KU1
understanding and properties of
3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For
operations to perform multiexample, determine the unknown number that makes the equation true in each of the equations 8 x ? =48, 5 = □ ÷ 3, 6 x 6 = ?.
digit arithmetic
*FS: UO KU3, UO KU4, UO KU5
3.OA.5 Apply properties of operations as strategies to multiply and divide. Examples: if 6x4=24 is known, then 4x6=24 is also
known. (Commutative property of multiplication.) 3x5x2 can be found by 3x5=15, then 15x2=30, or by 5x2=10, then 3x10=30.
(Associative property of multiplication.) Knowing that 8x5=40 and 8x2=16, one can find 8x7 as 8x(5+2)=(8x5)+(8x2)=40+16=56.
(Distributive property). (Don’t need to use the formal terms)
*FS: C KU1, C KU4, C KU5,
3.OA.6 Understand division as an unknown-factor problem. For example, find 32÷8 by finding the number that matches 32
when multiplied by 8.
*FS: UO KU5
3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9x80, 5x60) using strategies based on
place value and properties of operations.
*FS: C KU3
Review/Imbedded Standards
2.OA.4 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.
2.G.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
Focal Standards for
SMP1: Make sense of problems and persevere in solving them
Mathematical Practice
SMP4: Model with mathematics
SMP5: Use appropriate tools strategically
2
From Progression- OA: Students focus on understanding the meaning and properties of multiplication and division and on finding products of single-digit
multiplying and related quotients. These skills and understandings are crucial; students will rely on them for years to come as they learn to multiply and
divide with multi-digit whole numbers and to add, subtract, multiply, and divide with fractions and decimals. (multiplicative comparison first enters the
standards at Grade 4- 4.OA.1)
3
From Progression- OA: Area problems where regions are partitioned by unit squares are foundational for Grade 3 standards because area is used as a model
for single-digit multiplication and division strategies.
Revised: 5/12
Page 17 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Interim Assessment One
Unit Two: Graphing & Time
Critical Area(s):
Major, Supporting,
Additional Clusters
Major: Solve problems
involving measurement
and estimation of
intervals of time, liquid
volumes, and masses of
objects
Supporting: Represent
and interpret data
Review/Imbedded
Standards
Focal Standards for
Mathematical Practice
Duration: 10 days
Strategies: timeline – count up/back/on by hours and minutes
Common Core State Standard
3.MD.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word
problems involving addition and subtraction of time intervals in minutes, e.g., by representing the
problem on a number line diagram.
*FS: DM KU6
3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several
categories. 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 five pets.
2.MD.10 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.
3.OA.1 Interpret products of whole numbers, e.g., interpret 5x7 as the total number of objects in 5
groups of 7 objects each. For example, describe a context in which a total number of objects can be
expressed as 5x7.
3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56÷8 as the number of
objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares
when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context
in which a number of shares or a number of groups can be expressed as 56÷8.
SMP5: Use appropriate tools strategically
SMP6: Attend to precision
Revised: 5/12
Page 18 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Interim Assessment One
Fluency: Interim Assessment One
ST Math & Renaissance Learning – Math Facts in a Flash
Duration: IA cycle
Renaissance Learning – Math Facts in a Flash
ST Math
-
-
Students work for the first 5 minutes of Math
Fluency time daily
If using Math Facts in a Flash, begin the year with
the “Review: +, -“. (the baseline assessment may
start students on a different level – this is
acceptable)
If students using Math Facts in a Flash finish
“Review: +, -, x, ÷”, discontinue MFiaF and use the
full fluency time for ST Math
Multiplication Concepts: Build conceptual understanding of
multiplication using concrete representations and repeated
addition. Disambiguate multiplication and addition.
Division Concepts: Build conceptual understanding of division
using concrete representations. Students manipulate given
visuals to represent division problems and associate division with
dividing items into equal groups.
Multiplication: Multiply and Divide within 100.
Multiplication & Division Relationships: Explore the differences
between multiplication and division through the use of concrete
objects and the number line. Then, introduce the inverse
relationship between the two operations by viewing division as
an unknown-factor problem.
Scale & Measurement in Graphing: Read and graph quantities
when the axis is marked incrementally. Draw and read bar
graphs from scaled keys.
Time to the Minute: Identify parts of both analog and digital
clocks. Tell time to the minute using both analog and digital
clocks.
Intervals of Time: Determine time elapsed to 5 minute intervals
using analog clocks.
Revised: 5/12
Page 19 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Interim Assessment Two
Unit Three: Addition, Subtraction, & Perimeter
Critical Area(s):
Duration: 18 days
Strategies: Pictorial – number line (+/-);
Abstract – expanded notation (+/-), add by place (+), keep one number whole (+), compensate (+/-)
Major, Supporting,
Common Core State Standard
Additional Clusters
Additional: Recognize
3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100.
perimeter as an
*FS: UWDN KU6, C KU8
attribute of plane
3.NBT.2 Fluently4 add and subtract within 1000 using strategies and algorithms based on place value,
figures and distinguish
properties of operations, and/or the relationship between addition and subtraction.
between linear and
*FS: UWDN KU2, UWDN KU6, C KU2-KU6
area measures
3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding
the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the
Additional: Use place
same perimeter and different areas or with the same area and different perimeters.
value understanding
*FS: IM KU1, UU KU1
and properties of
operations to perform
multi-digit arithmetic
Review/Imbedded
Standards
Focal Standards for
Mathematical Practice
2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on
place value, properties of operations, and/or the relationship between addition and subtraction; relate
the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one
adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary
to compose or decompose tens or hundreds.
SMP1: Make sense of problems and persevere in solving them
SMP4: Model with mathematics
SMP5: Use appropriate tools strategically
SMP7: Look for and make use of structure
4
From Progression-NBT: They achieve fluency with strategies and algorithms that are based on place value, properties of operations, and/or the
relationship between addition and subtraction. Such fluency can serve as preparation for leraning standard algorithms in Grade 4, if the
computational methods used can be connected with those algorithms.
Revised: 5/12
Page 20 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Interim Assessment Two
Major, Supporting,
Additional Clusters
Major: Solve problems
involving measurement
and estimation of
intervals of time, liquid
volumes, and masses of
objects
Review/Imbedded
Standards
Focal Standards for
Mathematical Practice
Unit Four: Measurement
Critical Area(s):
Duration: 7 days
Common Core State Standard
3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g),
kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems
involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker
with a measurement scale) to represent the problem. (excludes multiplication comparisons- no “times
as much”; excludes cm3 and finding volume)
*FS: UU KU3, UU KU4, DM KU3, UU KU7
n/a
SMP1: Make sense of problems and persevere in solving them
SMP2: Reason abstractly and quantitatively
SMP3: Construct viable arguments and critique the reasoning of others
SMP4: Model with mathematics
SMP5: Use appropriate tools strategically
SMP6: Attend to precision
Revised: 5/12
Page 21 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Interim Assessment Two
Fluency: Interim Assessment Two
ST Math & Renaissance Learning – Math Facts in a Flash
Duration: IA cycle
Renaissance Learning – Math Facts in a Flash
ST Math
-
-
Students work for the first 5 minutes of Math
Fluency time daily
If using Math Facts in a Flash, begin the year with
the “Review: +, -“. (the baseline assessment may
start students on a different level – this is
acceptable)
If students using Math Facts in a Flash finish
“Review: +, -, x, ÷”, discontinue MFiaF and use the
full fluency time for ST Math
Place Value Concepts: Learn how to represent a quantity of
objects using groups of thousands, hundreds, tens and ones.
Students read and write four-digit numbers using the digits 0-9 by
writing the quantity of thousands, hundreds, tens and ones in the
correct order.
Rounding Three-Digit Numbers: Round two- and three-digit
numbers to the nearest ten or hundred. Students utilize the
number line and develop strategies based on palce value to
round whole numbers.
Place Value Bundles: Students build on place value knowledge
developed in earlier objectives to learn the relationship between
the ones and tens place and the tens and hundreds place.
Students develop and apply knowledge of a ten or hundred as a
bundle of 10 ones or tens. This objective prepares students to
learn addition and subtraction strategies based on place value by
developing the ability to compose and decompose tens and
hundreds.
Addition & Subtraction with Regrouping: Learn and apply
strategies for regrouping in addition and subtraction. Numbers
are restricted up through three digits.
Volume & Weight: Compare weight of up to four objects and
measure weight using scales. Using models, find the volume of a
solid object in cubic units.
Concepts of Area and Perimeter: Determine the area and
perimeter of rectangles. Generate different rectangles with given
areas and perimeters. Use models to solve problems involving
area.
Revised: 5/12
Page 22 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Interim Assessment Three
Unit Five: Fractions
Critical Area(s): Developing understanding of fractions, especially unit fractions (fractions with numerator 1)
*numerators 2, 3, 4, 6, 8
Major, Supporting,
Additional Clusters
Major: Develop
understanding of
fractions as numbers
Supporting: Reason
with shapes and their
attributes
Review/Imbedded
Standards
Focal Standards for
Mathematical Practice
Duration: 22 days
Common Core State Standard
3.NF.1 Understand5 a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b
equal parts; understand a/b as the quantity formed by a parts of size 1/b.
*FS: UFN KU2, UFN KU3
3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the
whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part
as ¼ of the area of the shape.
3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line
diagram.
a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole
and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of
the part based at 0 locates the number 1/b on the number line.
b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize
that the resulting interval has size a/b and that its endpoint locates the number a/b on the number
line.
*FS: UFN KU5
3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their
size.
a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a
number line.
b. Recognize and generate simple equivalent fractions, e.g., ½ = 2/4, 4/6 = 2/3. Explain why the
fractions are equivalent, e.g., by using a visual fraction model.
c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
Examples: express 3 in the form 3=3/1; recognize that 6/1=6; locate 4/4 and 1 at the same point of a
number line diagram.
d. Compare two fractions with the same numerator or the same denominator by reasoning about
their size. Recognize that comparisons are valid only when the two fractions refer to the same whole.
Record the results of comparisons with the symbols, >, =, or <, and justify conclusions, e.g., by using a
visual fraction model.
*FS: UFN KU4
2.G.3 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.
SMP4: Model with mathematics
SMP5: Use appropriate tools strategically
SMP8: Look for and express regularity in repeated reasoning
5
From Progression- NF: Grade 3 students should start with unit fractions, which are formed by partitioning a whole into equal parts and taking one
part, e.g., if a whole is partitioned into 4 equal parts then each part is ¼ of the whole and 4 copies of that part make the whole. Next, students build
fractions from unit fractions seeing the numerator 3 of ¾ as saying that ¾ is the quantity you get by putting 3 of the ¼’s together. They read any
fraction this way, and in particular there is no need to introduce “proper fractions” and “improper fractions” initially; 5/3 is the quantity you get by
combining 5 parts together when the whole is divided into 3 equal parts.
Revised: 5/12
Page 23 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
Interim Assessment Three
Unit Six: Measurement – Length
Critical Area(s): Developing understanding of multiplication and division and strategies for
multiplication and division within 100
Major, Supporting,
Additional Clusters
Supporting: Represent
and interpret data
Review/Imbedded
Standards
Focal Standards for
Mathematical Practice
Duration: 8 days
Common Core State Standard
3.MD.4 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.
*FS: DM KU4
2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers,
yardsticks, meter sticks, and measuring tapes.
2.MD.2 Measure the length of an object twice, using length units of different lengths for the two
measurements; describe how the two measurements relate to the size of the unit chosen.
2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters. (MMtg)
2.MD.4 Measure to determine how much longer one object is than another, expressing the length
difference in terms of a standard length unit.
2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced
points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences
within 100 on a number line diagram.
SMP3: Construct viable arguments and critique the reasoning of others
SMP5: Use appropriate tools strategically
SMP6: Attend to precision
Fluency: Interim Assessment Three
ST Math & Renaissance Learning – Math Facts in a Flash
Duration: IA cycle
Renaissance Learning – Math Facts in a Flash
ST Math
-
-
Students work for the first 5 minutes of Math
Fluency time daily
If using Math Facts in a Flash, begin the year with
the “Review: +, -“. (the baseline assessment may
start students on a different level – this is
acceptable)
If students using Math Facts in a Flash finish
“Review: +, -, x, ÷”, discontinue MFiaF and use the
full fluency time for ST Math
Fraction Concepts: Represent fractions using multiple visual
models as well as numerical notation. Represent a whole number
as a fraction.
Fractions on the Number Line: Represent fractions on the number
line. Represent a whole number on the number line.
Comparing Fractions: Compare fractions with either the same
numerator or same denominator using visual models as well as
the symbols <, >, and =.
Revised: 5/12
Page 24 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
End-of-Course
Unit Seven: Multiplication, Division, & Area 2
Critical Area(s): (1) Developing understanding of multiplication and division and strategies for multiplication and division within 100; (2)
Developing understanding of the structure of rectangular arrays and of area
Duration: 20 days
Strategies: draw arrays/groups, count on/skip-count, just know facts, distributive, associative
Major, Supporting,
Common Core State Standard
Additional Clusters
Major: Understand
3.MD.7 Relate 6area to the operations of multiplication and addition.
concepts of area and
a) Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as
relate to multiplication
would be found by multiplying the side lengths. (IA-1)
and addition
b) Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real
world and mathematical problems, and represent whole-number products as rectangular areas in mathematical
Major: Represent and
reasoning.
solve problems involving
c) Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c
multiplication and division
is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning.
d) Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlaping
Major: Multiply and divide
rectangles and adding the areas of non-overlapping parts, applying this technique to solve real world problems.
within 100
*FS: IM KU1
3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups,
arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number
to represent the problem.
*FS: UO KU3, UO KU4
3.OA.5 Apply properties of operations as strategies to multiply and divide. Examples: if 6x4=24 is known, then
4x6=24 is also known. (Commutative property of multiplication.) 3x5x2 can be found by 3x5=15, then 15x2=30, or by
5x2=10, then 3x10=30. (Associative property of multiplication.) Knowing that 8x5=40 and 8x2=16, one can find 8x7
as 8x(5+2)=(8x5)+(8x2)=40+16=56. (Distributive property). (Don’t need to use the formal terms)
*FS: C KU1, C KU4, C KU5,
3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and
division (e.g., knowing that 8x5=40, one knows 40÷5=8) or properties of operations. By the end of Grade 3, know
from memory all products of two one-digit numbers.
*FS: C KU3
3.OA.1 Interpret products of whole numbers, e.g., interpret 5x7 as the total number of objects in 5 groups of 7 objects each. For
Review/Imbedded
example, describe a context in which a total number of objects can be expressed as 5x7.
Standards
Focal Standards for
Mathematical Practice
3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56÷8 as the number of objects in each share when 56
objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8
objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56÷8.
3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.
a) A square with side length 1 unit, called a “unit square,” is said to have “one square unit” of area, and can be used to
measure area.
b) A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square
units.
3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For
example, determine the unknown number that makes the equation true in each of the equations 8 x ? =48, 5 = □ ÷ 3, 6 x 6 = ?.
3.OA.6 Understand division as an unknown-factor problem. For example, find 32÷8 by finding the number that matches 32 when
multiplied by 8.
3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9x80, 5x60) using strategies based on place
value and properties of operations.
SMP1: Make sense of problems and persevere in solving them
SMP3: Construct viable arguments and critique the reasoning of others
SMP4: Model with mathematics
SMP5: Use appropriate tools strategically
6
From Progression- OA: Area problems where regions are partitioned by unit squares are foundational for Grade 3 standards because area is used as a model
for single-digit multiplication and division strategies.
Revised: 5/12
Page 25 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
End-of-Course
Unit Eight: Geometry
Critical Area(s): Describing and analyzing two-dimensional shapes
Duration: 5 days
Major, Supporting,
Additional Clusters
Supporting: Reason
with shapes and their
attributes
Review/Imbedded
Standards
Focal Standards for
Mathematical Practice
Common Core State Standard
3.G.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may
share attributes (e.g., having four sides), and that the shared attributes can define a larger category
(e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and
draw examples of quadrilaterals that do not belong to any of these subcategories.
2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a
given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
SMP5: Use appropriate tools strategically
SMP7: Look for and make use of structure
Revised: 5/12
Page 26 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
End-of-Course
Unit Nine: Story Problems
Critical Area(s):
Duration: 15 days
Strategies: Operate – Visualize, Represent and Retell, Solve;
Represent – TD, BM, EQ
Calculate - expanded notation (+/-), add by place (+), compensate (+/-), count on/skip-count (m/d), just know facts (m/d),
distributive (m/d), associative (m/d)
Major, Supporting,
Common Core State Standard
Additional Clusters
Major: Solve problems
3.OA.8 solve two-step word problems using the four basic operations. Represent these problems using
involving the four
equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using
operations, and identify mental computation and estimation strategies including rounding. (addition and subtraction only)
and explain patterns in
*FS: C KU8, C KU10
arithmetic
3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and
eplain them using properties of operations. For example, observe that 4 times a number is always even,
and explain why 4 times a number can be decomposed into two equal addends. (addition and
subtraction only)
*FS: RANP KU3
Review/Imbedded
2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving
Standards
situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all
positions, e.g., by using drawings and equations with a symbol for the unknown number to represent
the problem.
2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are
given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol
for the unknown number to represent the problem.
3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal
groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for
the unknown number to represent the problem.
3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g),
kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems
involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker
with a measurement scale) to represent the problem. (excludes multiplication comparisons- no “times
as much”; excludes cm3 and finding volume)
*imbed further area, perimeter, graphing, and measurement work
Focal Standards for
SMP1: Make sense of problems and persevere in solving them
Mathematical Practice
SMP2: Reason abstractly and quantitatively
SMP3: Construct viable arguments and critique the reasoning of others
SMP4: Model with mathematics
SMP5: Use appropriate tools strategically
SMP6: Attend to precision
Revised: 5/12
Page 27 of 29
Common Core Grade 3
Mathematics
Scope and Sequence
End-of-Course
Fluency: Interim Assessment Four
ST Math & Renaissance Learning – Math Facts in a Flash
Duration: IA cycle
Renaissance Learning – Math Facts in a Flash
ST Math
-
-
Students work for the first 5 minutes of Math
Fluency time daily
If using Math Facts in a Flash, begin the year with
the “Review: +, -“. (the baseline assessment may
start students on a different level – this is
acceptable)
If students using Math Facts in a Flash finish
“Review: +, -, x, ÷”, discontinue MFiaF and use the
full fluency time for ST Math
Shapes: Identify 2D geometric shapes and their attributes,
including mame, type, number of edges, and number of vertices.
Shape Attributes: Identify 3D geometric shapes and their
attributes, including name, type, number of edges, number of
faces, and number of vertices.
Division: Practice interpreting division expressions and solving
division problems. Visual models strengthen the understanding
of division as dividing items into equal groups. Students also
discover that the quotient is the number of shares each group has
as a result of dividing equally.
Multiplication & Division Situations: Use multiplication and
division to solve problems in situations including equal groups.
Determine the unknown whole number in a multiplication or
division equation relating three whole numbers.
Unknowns in Two-Step Problems: Solve two-step word problems
using the four operations. Represent these problems using
equations.
Number Patterns: Show simple linear functions visually as
patterns. Connect linear equations to multiplication.
Patterns & Functions: Show simple linear functions as patterns,
both visually and as skip-counting. Connect linear equations to
multiplication, and introduce the table as an organizational tool
for functions.
Revised: 5/12
Page 28 of 29
Revised: 5/12
Page 29 of 29