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Common Core Mathematics 4
Year at Glance
WHAT STUDENTS LEARN IN Mathematics 4
Mathematics Gr. 4 CA Framework
Overview
In grade four a critical area of instruction is developing understanding and fluency with multi-digit multiplication and
developing understanding of division to find quotients involving multi-digit dividends. In grade four students compare quantities
multiplicatively for the first time. Additionally, students solve multi-step word problems using the four operations, including
problems in which remainders must be interpreted. Students use estimation to solve problems. Students find all factor pairs for
whole numbers in the range 1–100. They extend the idea of decomposition to multiplication and learn to use the term multiple.
Understanding patterns is fundamental to algebraic thinking. In grade four students generate and analyze number and shape
patterns that follow a given rule. In grade four, students extend their work in the base-ten number system and generalize previous
place value understanding to multi-digit whole numbers (less than or equal to 1,000,000). At grade four, students become fluent
with addition and subtraction with multi-digit whole numbers to 1,000,000 using standard algorithms. In grade four students
extend multiplication and division to include whole numbers greater than 100. Students should use methods they understand and
can explain to multiply and divide. In grade four students also find whole number quotients with remainders. A critical area of
instruction in grade four is developing an understanding of fraction equivalence, addition and subtraction of fractions with like
denominators, and multiplication of fractions by whole numbers. In fourth grade students develop an understanding of decimal
notation for fractions and compare decimal fractions (fractions with denominator 10 or 100). This work lays the foundation for
performing operations with decimal numbers in grade five. Students learn to add decimal fractions by converting them to fractions
with the same denominator. Students compare two decimals to hundredths by reasoning about their size. They relate their
understanding of the place value system for whole numbers to fractional parts represented as decimals. Students compare
decimals using the meaning of a decimal as a fraction, making sure to compare fractions with the same denominator and that the
“wholes” are the same. Students in grade four begin using the four operations to solve word problems involving measurement
quantities such as liquid volume, mass, and time, including problems involving simple fractions or decimals. In grade four
students are expected to use formulas to calculate area and perimeter of rectangles; however, they still need to understand and
be able to communicate their understanding of why the formulas work. In grade four students make a line plot to display a data
set of measurements in fractions of a unit and they solve problems involving addition and subtraction of fractions by using
information presented in line plots. Students in grade four learn that angles are geometric shapes formed by two rays that share a
common endpoint. A critical area of instruction in grade four is for students to understand that geometric figures can be analyzed
and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and
symmetry.
IMP CC Mathematics Gr. 4 Course Outline 2014-­‐15 1 Mathematics 4
Year at Glance
Unit
Length
Unit Name & Sub-topics
Standards
Addressed
Prior Knowledge
Assessment
Guidelines
M = Major Cluster
A/S = Additional
or Supporting
Cluster
1 Week
Aug 11th15th
5 Weeks
Aug.18th to
Sept. 19th
0: Introductory Week
• Setting the tone
• Establishing Routines
1: Place Value & Fluency with
Addition/Subtraction
• Relationship of place value to
multiplication/division by 10 and the “role
Resources
of 0” in place value.
may be
• Read & write numbers to 1,000,000
found in:
• Expanded Notation- compose and
Synced Unit
decompose numbers
1, unit 2
• Comparing whole #’s using symbols
component • Rounding numbers and using that to
1, unit 3
estimate
component • Interpreting whole numbers in real world
1, & Unit 4
contexts
Component • “Play” with large numbers
1.
• Fluently add and subtract with an algorithm
(that students can explain)
• Calculate perimeter
• Extend number patterns involving addition
or subtraction.
5 Weeks
2: Multiplication Concepts
IMP CC Mathematics Gr. 4 Course Outline 2014-­‐15 NBT 1 (M), 2 (M),
3 (M), 4
OA 3 (M) ,
5(part)-A/S
MD 3 (part)- A/S
◊ Addition and
Subtraction of whole
numbers (an
algorithm)
◊ Basic Place Value
◊ Perimeter concept
◊ Basic Rounding
◊ Basic Patterns
OA 1 (M), 2 (M), 3
◊
Single-digit
◊ Unit One
Test
◊
Unit 4 Test
2 Sept. 22nd
to Oct. 24th
•
•
Resources
may be
•
found in:
Synced Unit •
3, 4, 5
•
Concept of multiplicative vs. additive
growth
Single-digit multiplication word problem
types and location of the unknown.
Using a variable to represent an unknown
in a word problem.
Bar models or tape diagrams for solving
multiplicative comparison problems
Use rounding and estimation with
multiplication word problems.
Factors and Multiples
Prime and composite numbers
Extend patterns involving multiplication or
multiplication and addition/subtraction.
4 Weeks
3: Multiplication of Whole Numbers and its
Oct. 27th to
applications
st
Nov. 21
• Area of rectangles and multiplication
• Multiply a single-digit by a 4-digit number
Resources
• Use place value to multiply with multiples
may be
of 10
found in:
• Use area model and generic rectangles to
Synced Unit
multiply
2
• Relative size of units: Liquid volume,
component
Mass, linear measurement
2,& Unit 6
• Convert units by using a table and
multiplication
• Solve word problems involving distance,
time or money
4 Weeks
4: Whole Number Division
Dec. 1st to
• Concept of a remainder
Jan. 9th
• Writing remainders as part of an equation
• Relationship between multiplication and
Resources
division
IMP CC Mathematics Gr. 4 Course Outline 2014-­‐15 (M), 4 (A/S), 5
(A/S)
multiplication
◊ Concept of
multiplication
◊ Basic multiplication
word problems
•
•
•
Unit 5 Test
NBT 5 (M)
MD 3 (part)- A/S
MD 1 (A/S), 2
(A/S)
◊ Concept of Area
◊ Liquid Volume and
units of mass
◊ Time
◊ Look in
Synced for
Performance
Tasks and/or
team may
create
assessments
in OARS to
monitor
progress
NBT 6 (M)
MD 2 (A/S)
OA 2 (M), 3 (M)
◊ Relationship
between multiplication
and division
◊ Look in
Synced for
Performance
Tasks and/or
team may
3 may be
found in:
Synced Unit
2
component
3, unit 6
component
2, unit 3
Jan 12-16th
create
assessments
in OARS to
monitor
progress
◊ Unit 2 Test
◊ Unit 3 Test
◊ Unit 6 Test
Properties of division
Use place value to divide by multiples of
10
• Divide up to a 4-digit whole number by a
single digit divisor.
• Illustrate and explain division using
equations connected to rectangular arrays
or an area model.
• Division as equal groups and as
measurement
• Finding the side length of a rectangle with
a given area and factor.
• Solve word problems involving distance,
time or money
Review, catch up, move forward
•
•
5 Weeks
Jan. 20th to
Feb. 27th
5: Fractions and Decimal Fractions
• Defining a fraction on the number line and
a
1
seeing as the sum of “a” ’s.
b
b
Resources
• Using a number line to define and write
may be
improper fractions as mixed numbers.
found in:
• Concept of equivalent fractions
€
Synced Unit • €Generate equivalent
fractions using an
7, 8, & 9
area model and number line
component • Understand, mathematically, why two
1&2
fractions are equivalent (without seeing it
as multiplication by 1).
• Compare two fractions using symbols and
justify with a visual representation.
• Use common denominators to compare
fractions.
• Use benchmark fractions to compare other
fractions.
IMP CC Mathematics Gr. 4 Course Outline 2014-­‐15 May use Unit 2
NF 1, 2, 3b, 4a, 5,
6, 7
All Major
◊ Concept of a unit
fractions and fractions
◊ Whole numbers as
fractions
◊ Basic equivalence
of fractions
◊ Basic comparisons
of fractions
◊ Fractions on a
number line.
◊ Measurement data
on a line plot
◊
Unit 7 Test
4 Concept of the WHOLE with fractions and
decimals.
• Decimal notation for fractions with
denominators of 10 and 100
• Placing fractions and decimals on the
number line
• Comparing decimal fractions using
symbols
• Naming a number with both its fraction and
decimal fraction name
• Adding tenths and hundredths on the
number line/meter stick (including
measurement amounts)
• Interpret line plots with fractional amounts
5 Weeks
6: Fraction Addition, Subtraction and
Mar. 2nd to
Multiplication
Apr. 10th
• Add and subtract fractions with like
denominators manipulatives or visuals
Resources
and connect this to the mathematics
may be
• Decompose a fraction into unit fractions or
found in:
combinations of smaller fractions.
Synced Unit • Using a number line to add fractions and
9 & 10
mixed numbers with like denominators.
• Using a number line to add decimal
fractions with denominators of 10 and 100
(review from prior unit)
• Understand mixed numbers as the sum of
a whole number and a fraction.
• Using a number line to multiply fractions
by whole numbers, being able to write the
whole number as in improper fraction.
• Area model to add and multiply fractions
with common denominators.
•
IMP CC Mathematics Gr. 4 Course Outline 2014-­‐15 Unit 8 Test
NF 3a, 3b, 3c, 3d,
4a, 4b, 4c (All
Major)
MD 4 (A/S)
◊
Prior unit
◊ Unit 9 Test
◊ After MD4,
give unit 10
Test
5 Word problems involving distance, time,
liquid volume, mass, and money with
simple fractions and decimals.
• Compare fractional amounts displayed in
line plots
Apr. 13 - 17 Review, catch up, move forward
4 Weeks
7: Angles and Polygons
Apr. 20th to
• Vocabulary- point, line, ray, angle, parallel
May 15
and perpendicular lines.
• Concept of an angle as formed by two
Resources
rays.
may be
• Benchmark angles
found in:
• Concept of angle measure as based on a
Synced Unit
circle of 360°.
11 & 12
• Measure angles with a protractor
• Sketch Angles
• Decompose angles and see measures as
additive
• Find measure of a missing angle, using a
variable to represent the unknown.
• Name angles as right, acute or obtuse.
• Classify polygons (triangles and
quadrilaterals) by angle measure and by
presence or absence of parallel or
perpendicular lines.
• Identify and draw lines of symmetry in
polygons.
th
May 18-28
Review & catch up
•
MD 5a, 5b, 6, 7
G 1, 2, 3
All A/S
◊ Shapes can belong
to more than 1
category (focus on
quadrilaterals)
◊ After MD
5a, 5b, 6, 7,
give Unit 11
◊ After G1,
G2, and G3,
give Unit 12
Test
v Indicates pre-­‐units to be taught to address standards that were taught in prior grades, but have moved grade levels and for which students need a first-­‐
teaching, or in which students need review. Pre-­‐units may be phased out over time. Notes: Major-­‐ Volume, PV, Mult., Dec and Fract. Units could be its own “unit” before Whole #’s or after it (but it was addressed some in grade 3). Fractions could all be in 1 unit with decimals after, but decimals need to be seen as the same concept. MD word problems throughout almost every unit! IMP CC Mathematics Gr. 4 Course Outline 2014-­‐15 6