Mathematics Lesson Planning Guide IP4 Fourth Grade
Instructional Period 4
Content
Strand 1: Number and Operations
G.E.S.D. suggestion: distributed practice Concepts 1, 2 and 3
Strand 2: Data Analysis, Probability, and Discrete Math
G.E.S.D. suggestion: distributed practice Concepts 1, 2, 3 and 4
Strand 3: Patterns, Algebra, and Functions
G.E.S.D. suggestion: distributed practice Concepts 1, 3 and 4
Strand 4: Geometry and Measurement
Concept 1: Geometric Properties
PO1. Draw and describe the relationships between points, lines, line segments, rays, and angles
including parallelism and perpendicularity.
PO2. Justify which objects in a collection match a given geometric description.
PO3. Describe and classify triangles by angles and sides.
PO4. Recognize which attributes (such as shape or area) change and which do not change when
2-dimensional figures are cut up or rearranged.
PO5. Recognize and draw congruent figures, and match them in a given collection.
PO6. Draw right, acute, obtuse, and straight angles and identify these angles in other geometric
figures.
PO7. Recognize the relationship between a 3-dimensional figure and its corresponding net(s).
Concept 3: Coordinate Geometry
PO1. Name, locate, and graph points in the first quadrant of the coordinate plane using ordered
pairs.
PO2. Plot line segments in the first quadrant of the coordinate plane using a set of ordered pairs
in a table.
PO3. Construct geometric figures with vertices at points on the coordinate plane.
Concept 4: Measurement
PO4. Solve problems involving perimeter of 2-dimensional figures and area of rectangles.
PO5. Describe the change in perimeter or area when one attribute (length or width) of a rectangle
changes.
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Process
Strand 5: Structure and Logic
Concept 2: Logic, Reasoning, Problem Solving, and Proof
PO1. Analyze a problem situation to determine the question(s) to be answered.
PO2. Identify relevant, missing, and extraneous information related to the solution to a problem.
PO3. Select and use one or more strategies to efficiently solve the problem and justify the
selection.
PO5. Represent a problem situation using any combination of words, numbers, pictures, physical
objects, or symbols.
PO6. Summarize mathematical information, explain reasoning, and draw conclusions.
PO7. Analyze and evaluate whether a solution is reasonable, is mathematically correct, and
answers the question.
Mathematical Practices
MP1. Make sense of problems and persevere in solving them.
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP4. Model with mathematics.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
MP7. Look for and make use of structure.
MP8. Look for and express regularity in repeated reasoning.
Glendale Elementary School District| June 2011
Mathematics Lesson Planning Guide IP4 Fourth Grade
Instructional Period 4
Strand 4: Geometry and Measurement
Concept 1: Geometric Properties
Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.
In Grade 4, students deepen their understanding of 2-dimensional figures by classifying triangles and other two-dimensional polygons using properties and attributes. Students also recognize nets
for 3-dimensional figures.
Essential Questions: How does knowing the parts of a shape help to define it? What properties and attributes can be used to compare and classify shapes? How can a 3-dimensional figure be
represented 2-dimensionally (using nets)?
Big Ideas: 2- and 3-dimensional shapes/figures can be measured, described, compared, sorted, and classified.
Performance Objective
S4C1PO1. Draw and
describe the relationships
between points, lines, line
segments, rays, and angles
including parallelism and
perpendicularity.
Connections
Math: S4C1PO2, S4C1PO3,
S4C1PO6
Process Integration
Mathematical Processes
S5C2PO5. Represent a
problem situation using
any combination of words,
numbers, pictures,
physical objects, or
symbols.
A.V.
angle
intersect
line
line segment
parallel
perpendicular
ray
straight angle
Explanations and Examples
Examples of points, line segments, angles, parallelism, and perpendicularity can be
seen daily. Students do not easily identify lines and rays because they are more
abstract.
Students can arrange two pencils in as many different ways as possible to
determine that the 2 pencils might intersect in one point or may never intersect.
Further investigations could lead to pencils that are parallel, perpendicular or
intersecting in some other way. This can lead to a discussion on points, angles,
lines and rays.
Students should become familiar with parallelism and perpendicularity. Parallelism
is described as lines in the same plane that never intersect and are always
equidistant. Perpendicularity is described as two lines in the same plane that
intersect to form right (90º) angles.
Resources
Assessment
SFAW
SFAW ASB
8-3 Line, Line Segments, p. 97, #3
Rays, and Angles
p. 99, #19-20
p. 100, #3
ATM
p. 102, #19-20
More Explorations Using
the GeoBoard p. 125
TSCM2
Property Lists for
Quadrilaterals p. 226
Parallel and perpendicular
lines are shown below:
MP1. In fourth grade, students know that doing mathematics involves solving
problems and discussing how they solved them. Students explain to
themselves the meaning of a problem and look for ways to solve it. Fourth
graders may use concrete objects or pictures to help them conceptualize and
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Glendale Elementary School District| June 2011
Mathematics Lesson Planning Guide IP4 Fourth Grade
MP1. Make sense of
solve problems. They may check their thinking by asking themselves, “Does
problems and persevere this make sense?” They listen to the strategies of others and will try different
in solving them.
approaches. They often will use another method to check their answers.
MP4. Model with
mathematics.
MP4. Students experiment with representing problem situations in multiple
ways including numbers, words (mathematical language), drawing pictures,
using objects, making a chart, list, or graph, creating equations, etc.
Students need opportunities to connect the different representations and
explain the connections. They should be able to use all of these
representations as needed. Fourth graders should evaluate their results in
the context of the situation and reflect on whether the results make sense.
S4C1PO2. Justify which
S5C2PO6. Summarize Example:
objects in a collection match a mathematical information, • Identify which of these shapes have perpendicular or parallel sides and justify
given geometric description. explain reasoning, and
your selection.
draw conclusions.
Connections
Math: S4C1PO1, S4C1PO3, S5C2PO7. Analyze and
S4C1PO5, S4C1PO6,
evaluate whether a
S4C1PO7, S4C3PO3
solution is reasonable, is A possible justification that students might give is:
mathematically correct,
The square has perpendicular lines because the sides meet at a corner, forming
and answers the question. right angles.
SFAW
8-2 Polygons
8-9 Writing to Describe
TSCM2
Shapes & Properties
Activities p. 211-218
GESD Suggestions
Use example from
Examples and
Explanations column and
change details.
A.V.
geometric
MP1. Make sense of
problems and persevere MP1. In fourth grade, students know that doing mathematics involves solving
in solving them.
problems and discussing how they solved them. Students explain to
MP2. Reason abstractly themselves the meaning of a problem and look for ways to solve it. Fourth
graders may use concrete objects or pictures to help them conceptualize and
and quantitatively.
solve problems. They may check their thinking by asking themselves, “Does
MP3. Construct viable this make sense?” They listen to the strategies of others and will try different
arguments and critique approaches. They often will use another method to check their answers.
the reasoning of others
MP2. Fourth graders should recognize that a number represents a specific
MP5. Use appropriate
quantity. They connect the quantity to written symbols and create a logical
tools strategically.
representation of the problem at hand, considering both the appropriate
MP8. Look for and
units involved and the meaning of quantities. They extend this
express regularity in
understanding from whole numbers to their work with fractions and
repeated reasoning.
decimals. Students write simple expressions that record calculations with
numbers and represent or round numbers using place value concepts.
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Glendale Elementary School District| June 2011
Mathematics Lesson Planning Guide IP4 Fourth Grade
MP3. In fourth grade, students may construct arguments using concrete
referents, such as objects, pictures, and drawings. They explain their
thinking and make connections between models and equations. They refine
their mathematical communication skills as they participate in mathematical
discussions involving questions like “How did you get that?” and “Why is
that true?” They explain their thinking to others and respond to others’
thinking.
MP5. Fourth graders consider the available tools (including estimation) when
solving mathematical problem and decide when certain tools might be
helpful. For instance, they may use graph paper or a number line to
represent and compare decimals and protractors to measure angles. They
use other measurement tools to understand the relative size of units within a
system and express measurements given in larger units in terms of smaller
units.
MP6. As fourth graders develop their mathematical communication skills,
they try to use clear and precise language in their discussions with others
and in their own reasoning. They are careful about specifying units of
measure and state the meaning of the symbols they choose. For instance,
they use appropriate labels when crating a line plot.
MP7. In fourth grade, students look closely to discover a pattern or structure.
For instance, students use properties of operations to explain calculations
(partial products model). They relate representations of counting problems
such as tree diagrams and arrays to the multiplication principal of counting.
They generate number or shape patterns that follow a given rule.
MP8. Students in fourth grade should notice repetitive actions in
computation to make generalizations. Students use models to explain
calculations and understand how algorithms work. They also use models to
examine patterns and generate their own algorithms. For example, students
use visual fraction models to write equivalent fractions
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Glendale Elementary School District| June 2011
Mathematics Lesson Planning Guide IP4 Fourth Grade
S4C1PO3. Describe and
classify triangles by angles
and sides.
Connections
Math: S4C1PO1, S4C1PO2,
S4C1PO6
S5C2PO7. Analyze and
evaluate whether a
solution is reasonable, is
mathematically correct,
and answers the question.
A.V.
acute
equilateral
isosceles
obtuse
right
scalene
A triangle can be described in more than one way.
Examples:
 A right triangle can be both scalene and isosceles.
 A scalene triangle can be right, acute and obtuse.
Triangles can be classified by:
 Angles
o Right: The triangle has one angle that measures 90º.
o Acute: The triangle has exactly three angles that measure between 0º
and 90º.
o Obtuse: The triangle has exactly one angle that measures greater
than 90º and less than 180º.
 Sides
o Equilateral: All sides of the triangle are the same length.
o Isosceles: At least two sides of the triangle are the same length.
Scalene: No sides of the triangle are the same length.
SFAW
8-4 Triangles and
Quadrilaterals
TSCM2
Triangle Sort p. 225
http://www.geom.
uiuc.edu/~demo5
337/Group3/triang
le.html
GESD Suggestion
Internet search for triangle
classification quiz.
http://rpsec.usca.
edu/Classwork/70
3sp2004/RaceCa
r/triquiz.htm
MP1. Make sense of
MP1. In fourth grade, students know that doing mathematics involves solving
problems and persevere problems and discussing how they solved them. Students explain to themselves the
meaning of a problem and look for ways to solve it. Fourth graders may use concrete
in solving them.
objects or pictures to help them conceptualize and solve problems. They may check
MP2. Reason abstractly their thinking by asking themselves, “Does this make sense?” They listen to the
strategies of others and will try different approaches. They often will use another
and quantitatively.
method to check their answers.
MP3. Construct viable MP2. Fourth graders should recognize that a number represents a specific quantity.
arguments and critique They connect the quantity to written symbols and create a logical representation of
the reasoning of others the problem at hand, considering both the appropriate units involved and the
MP5. Use appropriate
tools strategically.
meaning of quantities. They extend this understanding from whole numbers to their
work with fractions and decimals. Students write simple expressions that record
calculations with numbers and represent or round numbers using place value
concepts.
MP3. In fourth grade, students may construct arguments using concrete referents,
such as objects, pictures, and drawings. They explain their thinking and make
connections between models and equations. They refine their mathematical
communication skills as they participate in mathematical discussions involving
questions like “How did you get that?” and “Why is that true?” They explain their
thinking to others and respond to others’ thinking.
MP5. Fourth graders consider the available tools (including estimation) when solving
mathematical problem and decide when certain tools might be helpful. For instance,
they may use graph paper or a number line to represent and compare decimals and
protractors to measure angles. They use other measurement tools to understand the
relative size of units within a system and express measurements given in larger units
in terms of smaller units.
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Glendale Elementary School District| June 2011
Mathematics Lesson Planning Guide IP4 Fourth Grade
S4C1PO4. Recognize which
attributes (such as shape or
area) change and which do
not change when 2dimensional figures are cut up
or rearranged.
S5C2PO5. Represent a Examples:
problem situation using
• Students should recognize that the area of the triangle and the area of the
any combination of words, rectangle are equal.
numbers, pictures,
physical objects, or
symbols.
ATM
GESD Suggestion
Pentominoes pp. 108-110 Exit ticket using
Pentominoes
MBL
The I Hate Mathematics! AIMS STTT
Book
#7
Connections
Math: S4C4PO4
S5C2PO7. Analyze and
evaluate whether a
solution is reasonable, is
mathematically correct,
and answers the question.
TSCM2
Pentominoes p. 243
• Students should recognize that when the shape is rearranged, the number of
MP1. Make sense of
sides and vertices change, but the area remains the same.
problems and persevere
in solving them.
MP5. Use appropriate
tools strategically.
MP8. Look for and
express regularity in
repeated reasoning.
MP1. In fourth grade, students know that doing mathematics involves solving
problems and discussing how they solved them. Students explain to
themselves the meaning of a problem and look for ways to solve it. Fourth
graders may use concrete objects or pictures to help them conceptualize and
solve problems. They may check their thinking by asking themselves, “Does
this make sense?” They listen to the strategies of others and will try different
approaches. They often will use another method to check their answers.
MP5. Fourth graders consider the available tools (including estimation) when
solving mathematical problem and decide when certain tools might be
helpful. For instance, they may use graph paper or a number line to
represent and compare decimals and protractors to measure angles. They
use other measurement tools to understand the relative size of units within a
system and express measurements given in larger units in terms of smaller
units.
6 of 17
Glendale Elementary School District| June 2011
Mathematics Lesson Planning Guide IP4 Fourth Grade
MP8. Students in fourth grade should notice repetitive actions in
computation to make generalizations. Students use models to explain
calculations and understand how algorithms work. They also use models to
examine patterns and generate their own algorithms. For example, students
use visual fraction models to write equivalent fractions.
S4C1PO5. Recognize and
draw congruent figures, and
match them in a given
collection.
Connections
Math: S4C1PO2, S4C1PO7
S5C2PO5. Represent a Figures are congruent if they have the same shape and are the same size.
problem situation using
any combination of words, Example:
numbers, pictures,
• Which of these figures are congruent?
physical objects, or
symbols.
MP1. Make sense of
problems and persevere
in solving them.
MP4. Model with
mathematics.
S4C1PO6. Draw right, acute,
obtuse, and straight angles
and identify these angles in
other geometric figures.
Connections
Math: S4C1PO1, S4C1PO2,
S4C1PO3
7 of 17
SFAW ASB
p. 97, #7
p. 100, #7
TSCM2
Congruent Parts p. 216
AIMS STTT
#28
MP1. In fourth grade, students know that doing mathematics involves solving
problems and discussing how they solved them. Students explain to
themselves the meaning of a problem and look for ways to solve it. Fourth
graders may use concrete objects or pictures to help them conceptualize and
solve problems. They may check their thinking by asking themselves, “Does
this make sense?” They listen to the strategies of others and will try different
approaches. They often will use another method to check their answers.
MP4. Students experiment with representing problem situations in multiple
ways including numbers, words (mathematical language), drawing pictures,
using objects, making a chart, list, or graph, creating equations, etc.
Students need opportunities to connect the different representations and
explain the connections. They should be able to use all of these
representations as needed. Fourth graders should evaluate their results in
the context of the situation and reflect on whether the results make sense.
Students use the benchmark angles of 90°, 180°, and 360° to approximate the
measurement of angles to draw or identify right, acute, obtuse, and straight angles.
S5C2PO5. Represent a
problem situation using
any combination of words,
numbers, pictures,
Example:
physical objects, or
symbols.
MP1. Make sense of
problems and persevere
in solving them.
SFAW
8-6 Congruent Figures
and Motion
http://www.woodl
andsjunior.kent.sch.u
k/maths/shapes/a
ngles.html#angle
s
http://www.legend
.yorks.com/~calve
rms/angl07pg.htm
Glendale Elementary School District| June 2011
Mathematics Lesson Planning Guide IP4 Fourth Grade
MP4. Model with
mathematics.
MP1. In fourth grade, students know that doing mathematics involves solving
problems and discussing how they solved them. Students explain to
themselves the meaning of a problem and look for ways to solve it. Fourth
graders may use concrete objects or pictures to help them conceptualize and
solve problems. They may check their thinking by asking themselves, “Does
this make sense?” They listen to the strategies of others and will try different
approaches. They often will use another method to check their answers.
MP4. Students experiment with representing problem situations in multiple
ways including numbers, words (mathematical language), drawing pictures,
using objects, making a chart, list, or graph, creating equations, etc.
Students need opportunities to connect the different representations and
explain the connections. They should be able to use all of these
representations as needed. Fourth graders should evaluate their results in
the context of the situation and reflect on whether the results make sense.
S4C1PO7. Recognize the
relationship between a 3dimensional figure and its
corresponding net(s).
Connections
Math: S4C1PO2, S4C1PO5
S5C2PO5. Represent a
problem situation using
any combination of words,
numbers, pictures,
physical objects, or
symbols.
Students will recognize the relationship between a figure and its net by:
• making a net(s) for a basic 3-dimensional figure,
• identifying the 3-dimensional figure that corresponds to a given net, and
• identifying the net that corresponds to a given 3-dimensional figure.
SFAW
8-1 Relating Solids and
Plane Figures
GESD Suggestion
Match 3 dimensional
figures to given nets.
TSCM2
Net Challenges p. 244
Notches and Holes p.244
S5C2PO6. Summarize
mathematical information,
explain reasoning, and
draw conclusions.
MP1. In fourth grade, students know that doing mathematics involves solving
problems and discussing how they solved them. Students explain to
MP1. Make sense of
themselves the meaning of a problem and look for ways to solve it. Fourth
problems and persevere graders may use concrete objects or pictures to help them conceptualize and
in solving them.
solve problems. They may check their thinking by asking themselves, “Does
this make sense?” They listen to the strategies of others and will try different
MP2. Reason abstractly approaches. They often will use another method to check their answers.
and quantitatively.
MP2. Fourth graders should recognize that a number represents a specific
MP3. Construct viable quantity. They connect the quantity to written symbols and create a logical
arguments and critique representation of the problem at hand, considering both the appropriate
the reasoning of others. units involved and the meaning of quantities. They extend this
understanding from whole numbers to their work with fractions and
MP6. Attend to
decimals. Students write simple expressions that record calculations with
precision.
numbers and represent or round numbers using place value concepts.
8 of 17
Glendale Elementary School District| June 2011
Mathematics Lesson Planning Guide IP4 Fourth Grade
MP7. Look for and make MP3. In fourth grade, students may construct arguments using concrete
use of structure.
referents, such as objects, pictures, and drawings. They explain their
thinking and make connections between models and equations. They refine
their mathematical communication skills as they participate in mathematical
discussions involving questions like “How did you get that?” and “Why is
that true?” They explain their thinking to others and respond to others’
thinking.
MP4. Students experiment with representing problem situations in multiple
ways including numbers, words (mathematical language), drawing pictures,
using objects, making a chart, list, or graph, creating equations, etc.
Students need opportunities to connect the different representations and
explain the connections. They should be able to use all of these
representations as needed. Fourth graders should evaluate their results in
the context of the situation and reflect on whether the results make sense.
MP6. As fourth graders develop their mathematical communication skills,
they try to use clear and precise language in their discussions with others
and in their own reasoning. They are careful about specifying units of
measure and state the meaning of the symbols they choose. For instance,
they use appropriate labels when crating a line plot.
MP7. In fourth grade, students look closely to discover a pattern or structure.
For instance, students use properties of operations to explain calculations
(partial products model). They relate representations of counting problems
such as tree diagrams and arrays to the multiplication principal of counting.
They generate number or shape patterns that follow a given rule.
9 of 17
Glendale Elementary School District| June 2011
Mathematics Lesson Planning Guide IP4 Fourth Grade
Strand 4: Geometry and Measurement
Concept 3: Coordinate Geometry
Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands.
In Grade 4, students use coordinates to describe positions in the first quadrant on a grid. They plot line segments and connect the segments to construct geometric figures.
Essential Questions: How do we use geometry to describe a location?
Big Ideas: Points can be described in terms of their location in a plane or space.
S4C3PO1. Name, locate, and
graph points in the first
quadrant of the coordinate
plane using ordered pairs.
Connections
Math: S4C3PO2, S4C3PO3
S5C2PO5. Represent a
problem situation using any
combination of words,
numbers, pictures, physical
objects, or symbols.
Example:
• Students can use a classroom size coordinate grid to physically locate the
coordinate point (5, 3) by starting at the origin point (0,0), walking 5 units along
the x axis to find the first number in the pair (5), and then walking up 3 units for
the second number in the pair (3). The ordered pair names a point on the grid.
A.V.
axis
ordered pair
plot
quadrant
SFAW
4-9 Graphing Ordered
Pairs
SFAW ASB
p. 71, #24-26
p. 74, #22-24
SSG
AIMS STTT
Coordinates and
#20
Distances on a grid p. 5-9
TSCM2
Location Activities p. 239
MBL
The Fly on the Ceiling
MP1. Make sense of
problems and persevere
in solving them.
MP4. Model with
mathematics.
10 of 17
MP1. In fourth grade, students know that doing mathematics involves
solving problems and discussing how they solved them. Students explain
to themselves the meaning of a problem and look for ways to solve it.
Fourth graders may use concrete objects or pictures to help them
conceptualize and solve problems. They may check their thinking by asking
themselves, “Does this make sense?” They listen to the strategies of others
and will try different approaches. They often will use another method to
check their answers.
Glendale Elementary School District| June 2011
Mathematics Lesson Planning Guide IP4 Fourth Grade
S4C3PO2. Plot line
segments in the first quadrant
of the coordinate plane using
a set of ordered pairs in a
table.
Connections
Math: S2C1PO1, S4C3PO1,
S4C3PO3
S5C2PO2. Identify
relevant, missing, and
extraneous information
related to the solution to a
problem.
As students plot line segments in the first quadrant of the coordinate plane, they
build on the skills learned in M04-S4C3-01.
MP1. In fourth grade, students know that doing mathematics involves
solving problems and discussing how they solved them. Students explain
to themselves the meaning of a problem and look for ways to solve it.
S5C2PO5. Represent a
Fourth graders may use concrete objects or pictures to help them
problem situation using any conceptualize and solve problems. They may check their thinking by asking
combination of words,
themselves, “Does this make sense?” They listen to the strategies of others
numbers, pictures, physical and will try different approaches. They often will use another method to
objects, or symbols.
check their answers.
SSG
GESD Suggestion
Coordinates and
Students create a table
Distances on a grid p. 5-9 with 4-8 ordered pairs to
form a polygon, challenge
another student to draw
the polygon based on the
ordered pairs.
AIMS STTT
#30
MP1. Make sense of
MP4. Students experiment with representing problem situations in multiple
problems and persevere ways including numbers, words (mathematical language), drawing pictures,
in solving them.
using objects, making a chart, list, or graph, creating equations, etc.
Students need opportunities to connect the different representations and
MP4. Model with
explain the connections. They should be able to use all of these
mathematics.
representations as needed. Fourth graders should evaluate their results in
the context of the situation and reflect on whether the results make sense.
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Glendale Elementary School District| June 2011
Mathematics Lesson Planning Guide IP4 Fourth Grade
S4C3PO3. Construct
geometric figures with vertices
at points on the coordinate
plane.
Connections
Math: S4C1PO2, S4C3PO1,
S4C3PO2
S5C2PO5. Represent a
problem situation using any
combination of words,
numbers, pictures, physical
objects, or symbols.
As students construct geometric figures on the coordinate plane, they practice the
skills used in previous performance objectives (M04-S4C3-01, M04-S4C3-02).
Students investigate the relationship of coordinates of squares, rectangles and
isosceles triangles to further enhance their understanding of coordinates and
properties of these shapes.
TSCM2
Coordinate Slides,
Reflections, & Dilations
pp. 240-241
MP1. Make sense of
MP1. In fourth grade, students know that doing mathematics involves
problems and persevere solving problems and discussing how they solved them. Students explain
in solving them.
to themselves the meaning of a problem and look for ways to solve it.
Fourth graders may use concrete objects or pictures to help them
MP4. Model with
conceptualize and solve problems. They may check their thinking by asking
mathematics.
themselves, “Does this make sense?” They listen to the strategies of others
and will try different approaches. They often will use another method to
check their answers.
GESD Suggestion
Students create a table
with 4-8 ordered pairs to
form a polygon, challenge
another student to draw
the polygon based on the
ordered pairs.
MP4. Students experiment with representing problem situations in multiple
ways including numbers, words (mathematical language), drawing pictures,
using objects, making a chart, list, or graph, creating equations, etc.
Students need opportunities to connect the different representations and
explain the connections. They should be able to use all of these
representations as needed. Fourth graders should evaluate their results in
the context of the situation and reflect on whether the results make sense.
Strand 4: Geometry and Measurement
Concept 4: Measurement
Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.
In Grade 4, students explore and develop an understanding of the relationship between area and perimeter of plane figures.
Essential Questions: How does measuring influence our understanding of geometry? How do we changes in the perimeter or area of a figure affect each other?
Big Ideas: The size and shape can be described using the distance around the shape or the amount of space it covers.
Performance Objective
12 of 17
Process Integration
Mathematical Practices
Explanations and Examples
Resources
Assessment
Glendale Elementary School District| June 2011
Mathematics Lesson Planning Guide IP4 Fourth Grade
S4C4PO4. Solve problems
involving perimeter of 2dimensional figures and area
of rectangles.
Connections
Math: S1C3PO2, S4C1PO4,
S4C4PO2, S4C4PO5
S5C2PO1. Analyze a
problem situation to
determine the question(s)
to be answered.
Students contrast the concepts and relationships of area and perimeter including SFAW
the units used to measure both. It is important for students to recognize that units 8-10 Perimeter
used to measure area are 2-dimensional and cover a space.
8-11 Area
8-12 Act It Out
In order to distinguish between perimeter and area students may need to
S5C2PO3. Select and use physically fill a rectangle with 1-inch color tiles or squares and use a string to
ATM
one or more strategies to measure around the rectangle to understand that area is a measure of the space Foot Area and Perimeter
efficiently solve the
within a specific region and perimeter is measuring the distance around a region. p. 78
problem and justify the
Squares can be cut from cardboard or construction paper. Square grid paper can Perimeter with Cuisenaire
selection.
also be used to measure area.
Rods p. 83
S5C2PO7. Analyze and
evaluate whether a solution
is reasonable, is
mathematically correct, and
answers the question.
A.V.
squared units
Students don’t usually connect to the formula l x w by filling a region with 1 unit
squares. That realization occurs when students make the connection between
multiplication and the rectangular array model.
Example:
• What is the area of the shape below?
2 in.
SFAW ASB
p. 98, #9-10, 16-17
p. 99, #21 & 23
p. 101, #9-10
p. 102, #16-17, 21, & 23
TSCM2
Area and Perimeter
p. 264-265
Expanded Lesson
p. 288-289
MBL
Spaghetti and Meatballs
for All!
5 in.
MP1. Make sense of
Using a grid will allow students to see the 5 square inches 2 times or the 2 square
problems and persevere inches 5 times.
in solving them.
MP1. In fourth grade, students know that doing mathematics involves
solving problems and discussing how they solved them. Students explain
MP4. Model with
to themselves the meaning of a problem and look for ways to solve it.
mathematics.
Fourth graders may use concrete objects or pictures to help them
conceptualize and solve problems. They may check their thinking by asking
MP5. Use appropriate
themselves, “Does this make sense?” They listen to the strategies of others
tools strategically.
and will try different approaches. They often will use another method to
check their answers.
MP4. Students experiment with representing problem situations in multiple
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Glendale Elementary School District| June 2011
Mathematics Lesson Planning Guide IP4 Fourth Grade
MP8. Look for and
express regularity in
repeated reasoning.
ways including numbers, words (mathematical language), drawing pictures,
using objects, making a chart, list, or graph, creating equations, etc.
Students need opportunities to connect the different representations and
explain the connections. They should be able to use all of these
representations as needed. Fourth graders should evaluate their results in
the context of the situation and reflect on whether the results make sense.
MP5. Fourth graders consider the available tools (including estimation)
when solving mathematical problem and decide when certain tools might be
helpful. For instance, they may use graph paper or a number line to
represent and compare decimals and protractors to measure angles. They
use other measurement tools to understand the relative size of units within
a system and express measurements given in larger units in terms of
smaller units.
MP8. Students in fourth grade should notice repetitive actions in
computation to make generalizations. Students use models to explain
calculations and understand how algorithms work. They also use models to
examine patterns and generate their own algorithms. For example, students
use visual fraction models to write equivalent fractions
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Glendale Elementary School District| June 2011
Mathematics Lesson Planning Guide IP4 Fourth Grade
S4C4PO5. Describe the
change in perimeter or area
when one attribute (length or
width) of a rectangle changes.
Connections
Math: S1C3PO2, S4C4PO4
S5C2PO3. Select and use
one or more strategies to
efficiently solve the
problem and justify the
selection.
As students explore problems (M04-S4C4-04), they begin to notice similarities
ATM
and differences in area and perimeter. They describe the relationship between the Squaring Up p. 79
two ideas.
The Perimeter Stays the
Same p. 80
Example:
Yarn Shapes p. 82
• Draw different rectangles, each with an area of 24 square units, and compare
The Area Stays the Same
S5C2PO6. Summarize
their perimeters. What patterns do you notice in the data? This data can be
p. 84
mathematical information, recorded in a table and graph.
Area and Perimeter p. 115
explain reasoning, and
Pick’s Theorem p. 129
draw conclusions.
MP1. In fourth grade, students know that doing mathematics involves
solving problems and discussing how they solved them. Students explain TSCM2
MP1. Make sense of
to themselves the meaning of a problem and look for ways to solve it.
Rectangle Comparisons –
problems and persevere Fourth graders may use concrete objects or pictures to help them
No Units p. 261
in solving them.
conceptualize and solve problems. They may check their thinking by asking Fill and Compare p. 263
themselves, “Does this make sense?” They listen to the strategies of others Rectangle Comparison –
MP2. Reason abstractly and will try different approaches. They often will use another method to
Square Units p. 264
and quantitatively.
check their answers.
Fixed Perimeters p.265
Fixed Areas p. 265
MP3. Construct viable
MP2. Fourth graders should recognize that a number represents a specific
arguments and critique quantity. They connect the quantity to written symbols and create a logical
the reasoning of others. representation of the problem at hand, considering both the appropriate
units involved and the meaning of quantities. They extend this
MP4. Model with
understanding from whole numbers to their work with fractions and
mathematics.
decimals. Students write simple expressions that record calculations with
numbers and represent or round numbers using place value concepts.
MP5. Use appropriate
MP3. In fourth grade, students may construct arguments using concrete
tools strategically.
referents, such as objects, pictures, and drawings. They explain their
GESD Suggestion
Journal idea: Which will
have a great area a long,
thin rectangle or a short,
fat rectangle with the
same perimeter?
http://www.primary
resources.co.uk/m
aths/mathsE4.htm
thinking and make connections between models and equations. They refine
MP6. Attend to precision. their mathematical communication skills as they participate in mathematical
discussions involving questions like “How did you get that?” and “Why is
MP7. Look for and make that true?” They explain their thinking to others and respond to others’
use of structure.
thinking.
15 of 17
Glendale Elementary School District| June 2011
Mathematics Lesson Planning Guide IP4 Fourth Grade
MP4. Students experiment with representing problem situations in multiple
ways including numbers, words (mathematical language), drawing pictures,
using objects, making a chart, list, or graph, creating equations, etc.
Students need opportunities to connect the different representations and
explain the connections. They should be able to use all of these
representations as needed. Fourth graders should evaluate their results in
the context of the situation and reflect on whether the results make sense.
MP5. Fourth graders consider the available tools (including estimation)
when solving mathematical problem and decide when certain tools might be
helpful. For instance, they may use graph paper or a number line to
represent and compare decimals and protractors to measure angles. They
use other measurement tools to understand the relative size of units within
a system and express measurements given in larger units in terms of
smaller units.
MP6. As fourth graders develop their mathematical communication skills,
they try to use clear and precise language in their discussions with others
and in their own reasoning. They are careful about specifying units of
measure and state the meaning of the symbols they choose. For instance,
they use appropriate labels when crating a line plot.
MP7. In fourth grade, students look closely to discover a pattern or
structure. For instance, students use properties of operations to explain
calculations (partial products model). They relate representations of
counting problems such as tree diagrams and arrays to the multiplication
principal of counting. They generate number or shape patterns that follow a
given rule.
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Glendale Elementary School District| June 2011
Mathematics Lesson Planning Guide IP4 Fourth Grade
Key for Resources
Adopted Text
Code
Resource Title
SFAW
SFAW TTP
SFAW 5th
DS
LTH
MT4
MML
PG
SD
SSS
SSG
TFS
Scott Foresman Addison Wesley Mathematics
Scott Foresman Addison Wesley Mathematics Test-Taking Practice
Scott Foresman Addison Wesley – 5th Grade
Investigations Different Shapes
Investigations Landmarks in the Thousandths
Investigations Mathematical Thinking at Grade 4
Investigations Money, Miles, and Large Numbers
Investigations Packages and Groups
Investigations Shape of the Data
Investigations Seeing, Solids, and Silhouettes
Investigations Sunken Ships and Grid Patterns
Investigations Three Out of Four Like Spaghetti
Code
Assessment Title
AIMS STTT
SFAW ASB
SFAW ASB 5th
INV ASB
AIMS Sample Test Think Throughs
Scott Foresman Addison Wesley Assessment Sourcebook
Scott Foresman Addison Wesley Assessment Sourcebook – 5th Grade
Investigations Assessment Sourcebook
Additional Resources (Ask Achievement Advisor)
Code
Assessment Title
ATM
BLM
CP:PS4
MBL4-6
PSSM
TSCM2
IC 3-5
IPS 3-5
IR 3-5
IRP 3-5
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About Teaching Mathematics
How the Brain Learns Mathematics
Creative Publications: Problem Solver
Marilyn Burns Classroom Math Library Grades 4-6
Principles and Standards for School Mathematics
Teaching Student-Centered Mathematics Volume 2: Grades 3-5
The Math Process Standards Series: Introduction to Connections Grades 3-5
The Math Process Standards Series: Introduction to Problem Solving Grades 3-5
The Math Process Standards Series: Introduction to Representation Grades 3-5
The Math Process Standards Series: Introduction to Reasoning & Proof Grades 3-5
**Used as a resource and/or assessment
**Used as a resource and/or assessment
**Used as a resource and/or assessment
**Used as a resource and/or assessment
Glendale Elementary School District| June 2011