Download Math Grade 4 Sampler - Common Core Standards Plus

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Three Types of Lessons:
(Available in Print and Interactive Digital Format)
Daily Lessons and Weekly Assessments (Evaluations):
(15-20 minutes daily)
There are 34 weeks of daily lessons and assessments (evaluations) written directly to the standards.
A week of instruction is comprised of four lessons and a corresponding assessment. The daily
lessons are written to DOK Levels 1 and 2.
Daily Lessons &
Weekly Assessm
ents
Performance Lessons:
(3-5 days 30 minutes each day)
After one or more weeks of daily lessons written to a particular standard or topic, you will find
a Performance Lesson. Performance Lessons are written to DOK Level 3. These lessons require
that students apply what they have learned and use reasoning, planning, evidence, and a higher
level of thinking than the daily lessons. Many standards are assessed at this level of rigor on
state assessments.
Performance
Lessons
Integrated Projects:
(Multiple class sessions over several days or weeks)
Three Integrated Projects are located immediately after the supporting daily lessons, assessments,
and performance lessons. Integrated Projects require that students plan, synthesize information,
produce high-quality products, and present their findings. Integrated Projects are written to
DOK level 4.
2
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Integrated
Projects
Measuremen
Measurement and Data
and D4ata Sta
(Measurement (Measurement and Data Standards .MD.1 24 E6 22 25 23 26 24 27 E6 28 25 E7 26 P8 27 Using a Protractor to Sketch Angles specified measure. circle is called a “one-­‐degree angle,” and can be used to measure angles. b) An angle that turns through n one-­‐
degree angles is said to have an angle measure of n degrees. 4.MD.5, 4.MD.6 Evaluation – Measurement of Angles Using a Protractor to Measure Angles 4.MD.6: Measure angles in whole–number Composing and Decomposing Angles 4.MD.7: Recognize angle measure as additive. When degrees using a protractor. Sketch angles of Using a Protractor to Measure Angles an angle is decomposed into non-­‐overlapping parts, specified measure. Finding Unknown Angles the angle measure of the whole is the sum of the Using a Protractor to Sketch Angles angle measures of the parts. Solve addition and Finding Unknown Angles subtraction problems to find unknown angles on a 4.MD.5, 4.MD.6 Evaluation – Measurement of Angles diagram in real world and mathematical problems, Angles in Real World Problems e.g., by using an equation with a symbol for the Composing and Decomposing Angles 4.MD.7: Recognize angle measure as additive. When unknown angle measure. Evaluation – Angles an angle is decomposed into non-­‐overlapping parts, Finding Unknown Angles the angle measure of the whole is the sum of the Performance Lesson #8 – All About Angles (4.MD.5, 4.MD.6, 4.MD.7) angle measures of the parts. Solve addition and Finding Unknown Angles subtraction problems to find unknown angles on a 1 Points, Lines, and Line Segments diagram in real world and mathematical problems, 28 Angles in Real World Problems by using an equation with a symbol for the 2 Draw and Distinguish Between Rays and Angles e.g., unknown angle measure. – Grade 4 Common Core Standards Plus – M
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26 10 E2 27 11 28 P9 12 E7 of symmetry. 9 Line of Symmetry Evaluation – Lines of Symmetry 4.G.3: Recognize a line of symmetry for a two-­‐
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344 175 Line of Symmetry 350 Classify Special Triangles Classifying Quadrilaterals 4.G.2: Classify two-­‐dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Lessons at:
P9 Performance Lesson #9 – Lines, Angles, Figures (4.G.1, 4.G.2) http://standardsplus.org/about-our-digital-platform/
9 10 11 12 302 296 304 298 306 300 308 302 310 304 312 306 314 308 326 310 328 312 TE 330 314 169 Classify Two-­‐Dimensional Figures Based on Their Sides Classify Two-­‐Dimensional Figures Based on Angle Measurement 7 8 152 334 Evaluation – Identify Geometric Objects (Geometry Standards 4.G.1 – 4.G.3)
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Line of Symmetry matching parts. Identify line-­‐symmetric figures © 2016 Learning Plus Associates
and draw lines Line of Symmetry 346 177–179 3
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Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry
Focus: Points, Lines, and Line Segments
Lesson: #1
Standard: 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and
parallel lines. Identify these in two-dimensional figures.
Lesson Objective: Students will draw and distinguish between points, lines, and line
segments.
Introduction: “Today we are going to learn to draw points, lines, and line segments.”
Sample Daily Lesson- Teacher Lesson Plan
Instruction: “A point is a precise location or place, usually represented by a dot. Points are
given letter names. Point X is symbolized as a dot with the letter name. In geometry, a line
is defined as a straight line that goes on forever or infinitely. It is signified as a straight line
with arrows at both ends. Typically two points are labeled on the line, so we call the line by
those two points. Line AB is a line with arrows at each end, and two points labeled A and B.
Notice that there are two ways to write the name for a line. A line segment is a part of a line.
When a line segment is drawn, there are no arrows on the ends. It has a definite start and
finish point. Line segment CD is a straight line, with no arrows and two endpoints labeled
point C and point D. Notice the two ways to write the name.”
Guided Practice: “In the example we will complete the table by drawing the figures
indicated in each row. When we draw these geometric figures, it is important that we draw
and label them properly. For the first figure, we will draw Point T. When drawing a point,
simply draw a dot, and label it with a letter. Another way to indicate a point is to simply write
the letter. Notice the T in the last column. For the second figure, we will draw Line PQ.
When drawing a line, first draw a line, then add arrows to each end. Label two points on the
line with letters to name the line. Another way to indicate a line is to write the two letters and
draw a two-sided arrow above them. For the third figure, we will draw Line Segment XY.
When drawing a line segment, first draw the line, and then place endpoints on both ends.
This shows the line segment is finite, or having a definite beginning and end. Label the
endpoints of the segment with letters. Another way to write a line segment is to write the two
letters and draw a line with two endpoints above them.”
Independent Practice: “Complete problems 1-4 on your own. For problems 1-3, complete
the table by drawing each geometric figure stated in the left column and writing the object
name a second way. For problem 4, explain the differences between a line and a line
segment.”
Review: Discuss the answers to problems 1-4, taking the time to reinforce the difference
between a line and line segment.
Closure: “Today we reviewed how to draw and distinguish between points, lines, and line
segments. Turn to your partner and tell them how lines and line segments are related.”
Answers:
1.
2.
4
3. R
F, F
A
B
AB
S
RS
4. Answers may vary. Lines have arrows on
each end and are infinite. Line segments do
not have arrows and have a dot at the
beginning and end.
www.standardsplus.org - 1.877.505.9152
© 2016 Learning Plus Associates
Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry
Focus: Points, Lines, and Line Segments
Lesson: #1
Standard: 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and
parallel lines. Identify these in two-dimensional figures.
Point: a precise location or place, usually represented by a dot
Line: a straight line that goes on forever or infinitely
Line Segment: a part of a line
X
= Point X,
or X
A
B
= Line AB, or AB
C
D
= Line segment CD, or CD
Example: Draw and label the geometric objects in the table below. Write object names a
second way.
Draw the Object
Write Object Name
Another Way
Sample Daily Lesson - Student Response Page
Geometric Object Name
Point T
Line PQ
PQ
Line Segment XY
XY
Directions: Complete the Table.
Geometric Object Name
1.
Point F
2.
Line AB
3.
Line Segment RS
Draw the Object
Write Object Name Another
Way
4. Explain the difference between a line and a line segment.
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5
Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry
Focus: Draw and Distinguish Between Rays and Angles
Lesson: #2
Standard: 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular
and parallel lines. Identify these in two-dimensional figures.
Lesson Objective: Students will draw and distinguish between rays and angles.
Introduction: “Today we are going to learn to draw rays and angles. A ray is a portion of a
line that starts at a point and goes in a particular direction to infinity. An angle is a shape
formed by two rays that start from the same point. This point is called the vertex.”
Instruction: “To draw a ray, make a straight line with a point on one end and an arrow on
the other. Rays are given letter names so they can be recognized. Look at Example A. Ray
AB is symbolized as a point with the letter A next to it, and a letter B on the line toward the
arrow. When naming a ray, the letter at the endpoint always comes first, ray AB.
Sample Daily Lesson- Teacher Lesson Plan
Angles are named for the point on the two rays that meet at the vertex. For example, ray AB
and ray AC form angle BAC or angle CAB. The vertex of the angle is always the middle letter
in the angle name.”
Guided Practice: “Look at Example B. We will draw each figure described in the table.
First, we will draw Ray BC. When drawing a ray, draw a line with a point at one end and an
arrow on the other end extending out in one direction. (Model drawing the ray.) Label the
point B and label the arrow C. Next, we will draw Angle EFG. When drawing an angle, draw
two rays with a common vertex. (Model this.) Label the vertex F, and each of the rays E and
G.” Guide students through the rest of the objects in the table. Draw these objects on the
board for students to check their own work.
Independent Practice: “Complete problems 1–5 on your own. Complete the chart by
drawing the correct geometric figures and write your answer to question 5 on the lines
provided.”
Review: Discuss the answers to problems 1–5.
Closure: “Today we reviewed how to draw and discuss the attributes of rays and angles.”
Answers:
1. Angle ABC; ABC; students
draw and label an angle with a
vertex at B.
3. Angle PQR; PQR; students
draw and label angle PQR with the
vertex at Q.

2. Ray QR; QR ; students draw and
label ray QR with the endpoint at
Q.
4. Angle DEF; DEF; students draw
and label angle DEF with the vertex
at E.
5. Answers will vary. It is made with two rays that have the same endpoint,
called a vertex.
6
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Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry
Focus: Draw and Distinguish Between Rays and Angles
Lesson: #2
Standard: 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular
and parallel lines. Identify these in two-dimensional figures.
Example A:
Ray:
A
Angle:
B
= Ray AB, or AB.
B
A
= angle BAC, or  CAB.
Vertex
C
Example B: Draw the geometric objects in the table below.
Geometric
Object
Name
Draw the
Figure
Write Object
Name
Another Way
Geometric
Object
Name
Angle LMN
EFG
Angle EFG
Angle QRS
Directions: Complete the table.
Geometric
Object
Name
Draw
the
Figure
Write Object
Name
Another Way
Write Object
Name
Another Way
Sample Daily Lesson - Student Response Page
BC
Ray BC
Draw the
Figure
Geometric
Object Name
1. Angle ABC
3.
Angle PQR
2. Ray QR
4.
Angle DEF
Draw the
Figure
Write Object
Name
Another Way
5. Explain the attributes of an angle. Use the word vertex in your explanation.
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7
Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry Focus: Draw, Distinguish Between Parallel and Perpendicular Lines
Lesson: #3
Standard: 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and
parallel lines. Identify these in two-dimensional figures.
Lesson Objective: Students will draw and distinguish between parallel and
perpendicular lines.
Introduction: “Today we are going to learn about parallel and perpendicular lines.”
Instruction: “Look at the top of your page. Today we will be working with parallel
and perpendicular lines. Parallel lines are two lines that are the same distance apart
for their entire length. This means that parallel lines never cross or intersect.
Perpendicular lines are lines that cross or intersect at right angles (90o).”
Sample Daily Lesson- Teacher Lesson Plan
Guided Practice: “In Example A, look at the two lines. On the space below the lines
XY and CD, write if the two lines are parallel, perpendicular, or neither. These lines
are parallel because they are the same distance apart and they will never intersect.
Next, look at Example B. Read the statement and draw two lines that make this
statement true. Line QR is perpendicular to line ST because they intersect at right
angles. Make sure you draw two lines that intersect at 90o. Connect points S and T.
Then connect points Q and R.”
Independent Practice: “Complete problems 1-5 on your own. For problems 1-3
write if each pair of lines is parallel, perpendicular, or neither. Notice that the small
box in problem 1 indicates the angle is a 90o angle. In problems 4-5, draw pairs of
lines that will make the written statement true.”
Review: Review correct answers, emphasizing the justification for each pair of lines.
Closure: “Today we reviewed how to draw and distinguish between parallel and
perpendicular lines. Turn and tell your partner the most important thing to remember
about both parallel lines and perpendicular lines.”
Answers:
1.
2.
3.
4.
Perpendicular
Parallel
Neither
L
M
X
Y
F
5.
D
E
G
8
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© 2016 Learning Plus Associates
Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry Focus: Draw, Distinguish Between Parallel and Perpendicular Lines
Lesson: #3
Standard: 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and
parallel lines. Identify these in two-dimensional figures.
Parallel lines are two lines that never
cross because they are the same
distance apart for their entire length.
Perpendicular lines are lines that cross
or intersect at right angles (90°).
Examples:
A.
Y
B. Line QR is perpendicular to line ST.
C
D
S
Q
These lines are ___________________.
Sample Daily Lesson - Student Response Page
X
R
T
Directions: Write whether each pair of lines is parallel, perpendicular, or neither.
1.
2.
_______________
3.
_______________
_______________
Directions: Draw pairs of lines that make the statement true.
4. Draw line LM parallel to line XY.
5. Draw line DE perpendicular to line FG.
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9
Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry
Focus: Angles, Parallel and Perpendicular Lines in Figures
Lesson: #4
Standard: 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel
lines. Identify these in two-dimensional figures.
Lesson Objective: Students will identify angles, parallel lines, and perpendicular lines in
two-dimensional figures.
Introduction: “Today we are going to learn how to identify angles, parallel lines, and
perpendicular lines in two-dimensional figures. Two-dimensional shapes have only two
dimensions: width and height. They have no thickness.”
Sample Daily Lesson- Teacher Lesson Plan
Instruction: “Look at the top of your page. In Example A there are three types of angles.
An acute angle is any angle that is less than 90 degrees. An obtuse angle is any angle that
is greater than 90 degrees, and a right angle is one that is exactly 90 degrees and is formed
by two perpendicular lines. Perpendicular lines intersect or cross at a 90-degree angle.
Parallel lines are two lines that never cross because they are the same distance apart for
their entire length. We can find all types of angles around us, including those in twodimensional figures. A two-dimensional figure is a closed shape that is made up of a
combination of line segments and angles.”
Guided Practice: “In Example B, we see a quadrilateral, with four sides and four angles.
We can see that side AC and side CD are perpendicular because they form a right angle at
C. So, angle ACD is a right angle. Write the name of the right angle in the space provided.
Name the other right angle. Find the obtuse angle and write its name in the space provided
(ABD). Remember that an obtuse angle is greater than 90 degrees. (Guide students through
identifying and writing the acute angle.) Do you see a pair of parallel sides? (Students
should identify the top and bottom sides or line segments AB and CD.) Write in the space
provided: AB   CD. Do you see any perpendicular sides? (Students should identify line
segments AB and AC or AC and CD.) Write AB  AC and AC  CD.”
Independent Practice: “Complete problems 1-3 on your own. Identify all angles, parallel
sides, and perpendicular sides that you see in these figures. If the figure does not contain a
type of angle or set of lines, write the word none in the space provided.”
Review: Review correct answers.
Closure: “Today we reviewed how to identify angles, parallel lines, and perpendicular lines
in two-dimensional figures. Turn and tell your partner the most important types of angles and
lines they would find in a perfect square.”
Answers:
1. *Right angle:  MNP & NPO
*Obtuse angle: OMN
*Acute angle: MOP
*Parallel sides: MN   PO
*Perpendicular sides: NP  PO and
MN  NP
*Students may reverse the order of the
letters and still be correct.
2. *Right angles: none
*Obtuse angle: XWY & WXZ
*Acute angle: WYZ & XZY
*Parallel side: WX   YZ
*Perpendicular sides: none
*Students may reverse the order of
the letters and still be correct.
3. Answers may vary. Right angles are made from perpendicular sides.
If a shape has no perpendicular sides there cannot be a right angle.
10
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© 2016 Learning Plus Associates
Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry
Focus: Angles, Parallel and Perpendicular Lines in Figures
Lesson: #4
Standard: 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel
lines. Identify these in two-dimensional figures.
Parallel: two lines that never cross because they are the same distance for their entire
length
Perpendicular: lines that intersect or cross at a 90-degree angle
Example B:
Example A:
A
B
Q


R
S
Acute angle is less than 90°
C
D
X
Right angles (2)
Z
Obtuse angle is greater than 90°
Obtuse angle
Acute angle
M

Parallel sides
Perpendicular sides
O
N
Sample Daily Lesson - Student Response Page
Y
Right angle is exactly 90°
Notice the box in the corner. This
tells that it is a right angle.
1.
M
N
Right angles
Obtuse angle
Acute angle
O
2.
Parallel sides
P
W
Perpendicular sides
X
Right angle
Obtuse angles
Acute angles
Y
Z
Parallel sides
Perpendicular sides
3. Explain why a quadrilateral without perpendicular sides does not have any right angles.
_______________________________________________________________________
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11
Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry
Focus: Identify Geometric Objects
Evaluation: #1
The weekly evaluation may be used in the following ways:
 As a formative assessment of the students’ progress.
 As an additional opportunity to reinforce the vocabulary, concepts, and
knowledge presented during the week of instruction.
Standard: 4.G.1 Draw points, lines, line segments, rays, angles (right, acute,
obtuse), and perpendicular and parallel lines. Identify these in two-dimensional
figures.
Sample Assessment - Teacher Lesson Plan
Procedure: Read the directions aloud and ensure that students understand
how to respond to each item.
 If you are using the weekly evaluation as a formative assessment, have
the students complete the evaluation independently.
 If you are using it to reinforce the week’s instruction, determine the items
that will be completed as guided practice, and those that will be completed
as independent practice.
Review: Review the correct answers with students as soon as they are
finished.
Answers:
12
1. (4.G.1) Ray BA or BA
2. (4.G.1) MNO or OMN ( ONM, NMO)
3. (4.G.1)
A
C
or
B
C
B
A
4. (4.G.1) ST   VU and SV   TU
5. (4.G.1) Answers may vary. An obtuse angle is greater
than 90. A right angle is made from perpendicular
lines. The lines of an obtuse angle are not parallel
or perpendicular.
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Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry
Focus: Identify Geometric Objects
Evaluation: #1
Point
Line
Ray
Parallel Lines
Perpendicular Lines
Acute Angle
Obtuse Angle
Vertex
Right Angle
Directions: Write the correct answers on the line provided.
2. Name an acute angle in the
figure below.
Sample Assessment - Student Response Page
1. Write the correct name for this figure.
A
B
3. Draw angle
ABC. Make sure
you label the vertex correctly.
M
O
N
4. Name two sets of parallel sides in the figure below.
S
T
V
U
5. Explain the differences between a right angle and an obtuse angle.
______________________________________________________________
______________________________________________________________
______________________________________________________________
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13
Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry
Focus: Classify Two-dimensional Figures
Lesson: #5
Standard: 4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular
lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and
identify right triangles.
Lesson Objective: Students will classify two-dimensional figures based on the presence
or absence of parallel or perpendicular lines.
Introduction: “Today we are going to learn how to recognize parallel or perpendicular
lines in a two-dimensional figure and classify figures according to their sides. Lines can
be classified as parallel and perpendicular. Remember, two lines are parallel if they
never intersect or cross, and two lines are perpendicular if they intersect or cross at right
angles (90).”
Sample Daily Lesson- Teacher Lesson Plan
Instruction: “Many two-dimensional figures are made of line segments or sides. The
endpoints of the sides are called vertices. The plural of vertex is vertices. Look at the first
figure. This is a parallelogram. It has two sets of parallel sides. The next figure is called a
trapezoid and has only one pair of parallel sides. The last figure is a right triangle; it has one
pair of perpendicular sides.”
Guided Practice: “Look at the figures below the Venn Diagram. Let’s draw the figures in the
correct places on the Venn Diagram. A parallelogram has one set of parallel lines. We will
draw that on the left side of the diagram. Where would you draw the trapezoid? It has both
parallel sides and perpendicular sides so it goes in the oval in the middle of the diagram.
Now draw the right triangle and a rectangle in the Venn Diagram.” (The right triangle should
be on the right, and the rectangle should be in the center.)
Independent Practice: “You will now complete the Venn Diagram at the bottom of your
page on your own. Place the figures in the Venn Diagram by drawing them. Make sure you
can justify why you chose where to draw each of the figures.”
Review: Review how each figure should be classified. Draw the shapes on the projected
image. (Teacher draws or selects students to draw.)
Closure: “Today we reviewed how to classify two-dimensional figures based on their types
of sides. Turn and tell your partner the most important thing is why there is only one right
triangle on the perpendicular side of the Venn Diagram.”
Answers:
Parallel Sides
Perpendicular Sides
Both
14
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Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry
Focus: Classify Two-dimensional Figures
Lesson: #5
Standard: 4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular
lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and
identify right triangles.
Example:
Parallelogram
Trapezoid
Parallel Sides
Right Triangle
Perpendicular Sides
Both
Trapezoid
Right Triangle
Sample Daily Lesson - Student Response Page
Parallelogram
Rectangle
Directions: Draw the following figures on the Venn Diagram according to their sides.
Parallel Sides
Perpendicular Sides
Both
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15
Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry
Focus: Classify Two-dimensional Figures
Lesson: #6
Standard: 4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or
the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
Lesson Objective: Students will classify two-dimensional figures based on angle
measurement.
Introduction: “Today we will be using right, acute, and obtuse angles to classify figures. A
right angle measures 90 degrees, an acute angle measures less than 90 degrees, and an
obtuse angle measures greater than 90 degrees.”
Sample Daily Lesson- Teacher Lesson Plan
Instruction: “Today we will review how to recognize figures and classify them according to
their angles. Look at the figures at the top of the page. A right triangle always has a right
angle and two acute angles. A square has four right angles as shown. A parallelogram has
two acute angles and two obtuse angles. An equilateral triangle has three equal sides and
three equal acute angles.”
Guided Practice: “Look at the categories and notice how each is labeled. We are going to
sort the figures from the top of the page into categories according to their characteristics.
Let’s start with the right triangle. Why is it placed in the At Least One Right Angle category?
(Discuss.) You can see we have placed the right triangle in two categories. Why does it fit in
the second category? A right triangle has two acute angles. Could a right triangle fit in the
final category? No. A right triangle has one right angle and two acute angles, so it doesn’t fit
in the final category. Let’s sort the rest of the shapes together.” (last box)
Independent Practice: “You will now categorize the figures shown at the bottom of your
page on your own. Place the figures in the correct category. Make sure you can justify
where you placed each of the figures. Figures can be placed in more than one category.”
Review: Review what figures are in each category.
Closure: “Today we reviewed how to classify two-dimensional figures based on their angles.
Turn to your partner and try to think of a shape that you could place into the portion of the
diagram that has all three angles.”
Answers:
Students may use the figure letter or shape name
At Least One Right Angle
Rectangle
Right Triangle
Square
Pentagon
16
At Least One Acute Angle
Rhombus
Right Triangle
Equilateral Triangle
Parallelogram
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At Least One Obtuse Angle
Rhombus
Parallelogram
Pentagon
Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry
Focus: Classify Two-dimensional Figures
Lesson: #6
Standard: 4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or
the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
Right:
Acute:
Right Triangle
1 Right Angle
2 Acute Angles
Obtuse:
Square
4 Right Angles
4 Equal Sides
Parallelogram
Equilateral Triangle
2 Acute Angles
2 Obtuse Angles
3 Equal Sides
3 Equal Acute Angles
At Least One Right Angle
At Least One Acute Angle
Right Triangle
Right Triangle
Sample Daily Lesson - Student Response Page
Example: Classify each figure above (some figures fit into more than one category).
At Least One Obtuse Angle
Directions: Classify each figure below (some figures fit into more than one category).
At Least One Right Angle
Rhombus
Rectangle
At Least One Acute Angle
Right Triangle
Square
At Least One Obtuse Angle
Equilateral
Triangle
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Parallelogram
Pentagon
17
Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry
Focus: Classify triangles
Lesson: #7
Standard: 4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or
perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a
category, and identify right triangles.
Lesson Objective: Students will classify triangles, by angle and side.
Introduction: “Today we are going to review how to recognize and classify triangles.
Triangles are given names according to their angles as well as the length of their sides.”
Sample Daily Lesson- Teacher Lesson Plan
Instruction: “Look at the top of your page. The three names we give triangles according to
their angles are right, obtuse, and acute. A right triangle has one right angle, an obtuse
triangle has one obtuse angle, and an acute triangle has three acute angles. Additionally,
triangles are named for the length of their sides. The names triangles can be called based on
their sides are equilateral, isosceles, and scalene. An equilateral triangle has three sides that
are the same length, an isosceles triangle has two sides that are the same length, and a
scalene triangle has three sides that are all different lengths. Many times when we name
triangles, we just use one name. A triangle can be called by two names, by their angles or by
their side measures. For example, a right triangle that has two sides the same length is a
right, isosceles triangle. Usually, when a triangle is labeled with both names, the angle
classification is stated first.”
Guided Practice: “Look at the triangle in the example. First, we are going to classify
this triangle by its angles. This triangle has one angle that is obtuse; therefore it is an
obtuse triangle. Write obtuse in the first blank. Next, we will look at the length of its
sides. This triangle has three sides that are all different lengths, so it is a scalene triangle.
Write scalene in the second blank next to the triangle. We can call this triangle an obtuse,
scalene triangle.”
Independent Practice: “Complete problems 1-4 on your own. Write the name of the
triangle according to its angle in the first blank, and named by the sides in the second blank.”
Review: Review correct answers. Discuss any questions that come up.
Closure: “Today we reviewed how to classify triangles by their angles and lengths of their
sides. Turn and tell your partner the most important reason why an equilateral triangle could
also be considered an isosceles triangle.”
Answers:
18
1.
2.
3.
4.
acute, equilateral
obtuse, isosceles
right, scalene
acute, isosceles
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Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry
Focus: Classify triangles
Lesson: #7
Standard: 4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or
perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a
category, and identify right triangles.
Right
Triangle
Obtuse
Triangle
Classifying Special Triangles
Acute
Equilateral
Isosceles
Triangle
Triangle
Triangle
Example:
Scalene
Triangle
1'
Sample Daily Lesson - Student Response Page
2'
3'
________________
Angles
________________
Sides
Directions: Write the name of each triangle as it would be classified by both its angles
and sides.
1.
5"
Angles
5"
5"
2.
8"
________________
________________
________________
________________
8"
12"
3.
Sides
8"
4"
10"
________________
________________
4.
2"
2"
________________
________________
3"
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19
Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry
Focus: Classifying quadrilaterals
Lesson: #8
Standard: 4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or
the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
Lesson Objective: Students will classify and draw quadrilaterals according to specific
features.
Introduction: “Today we are going to review how to recognize and classify quadrilaterals.
Quadrilaterals are two-dimensional figures that have four sides and four angles. They are
classified according to their sides and angles.”
Sample Daily Lesson- Teacher Lesson Plan
Instruction: “Look at the top of your page. All four-sided objects are quadrilaterals.
Quadrilaterals are classified according to more than one feature. Like triangles, they are
classified by both their angles and side lengths. For example, a quadrilateral with two pairs
of parallel sides, four right angles, and opposite sides that are equal in length is classified as
a rectangle. A parallelogram is a figure that has two pairs of parallel sides and opposite sides
that are equal. A parallelogram is not a rectangle because it does not have right angles, but
a rectangle is a parallelogram since it has two pairs of parallel sides and opposite sides that
are equal. Additionally, a square is a rectangle and a parallelogram, but neither of them can
be a square, because a square also has all four sides of equal length.”
Guided Practice: “Look at the Venn Diagram. Take a moment to examine the quadrilaterals
in each section of the diagram, and how they are classified. What figure on the diagram is
incorrectly classified? Why?” Allow students time to discuss this with their partners before
calling on a student to answer. Discuss why the trapezoid in the upper left section should be
in the overlapping section with the parallel sides. Make sure students understand how to
read the Venn Diagram.
Independent Practice: “Complete problems 1-3 on your own. Use the diagram to help you
answer the questions.”
Review: Review and discuss correct answers to problems 1-3.
Closure: “Today we reviewed how to classify quadrilaterals according to their features.”
Answers:
1. The square fits in the center because it is a quadrilateral that has at
least one right angle, and at least one pair of parallel sides.
2. Circle the shape in the bottom left corner. It is a quadrilateral with
one right angle and no parallel sides.
3. Students should draw a rectangle or a trapezoid with a right angle in
the center.
20
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Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry
Focus: Classifying quadrilaterals
Lesson: #8
Standard: 4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or
the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
All four-sided, two- dimensional objects are quadrilaterals.
Rectangle:
Example:
Parallelogram:
Square:
Classifying Quadrilaterals
At least one
right angle
Both
At least one pair of
parallel sides
Sample Daily Lesson - Student Response Page
Directions: Using the diagram above, answer the questions below.
1. Why does the square fit into both sections of the diagram?
2. Circle the shape with exactly one right angle. Explain why it is in its appropriate
place on the diagram.
3. Draw a figure that is not a square but would still fit in the same Venn Diagram
section as the square.
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21
Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry
Focus: Classifying two-dimensional figures
Evaluation: #2
The weekly evaluation may be used in the following ways:
 As a formative assessment of the students’ progress.
 As an additional opportunity to reinforce the vocabulary, concepts,
and knowledge presented during the week of instruction.
Standard: 4.G.2 Classify two-dimensional figures based on the presence or
absence of parallel or perpendicular lines, or the presence or absence of angles
of a specified size. Recognize right triangles as a category, and identify right
triangles.
Sample Assessment - Teacher Lesson Plan
Procedure: Read the directions aloud and ensure that students understand
how to respond to each item.
 If you are using the weekly evaluation as a formative assessment, have
the students complete the evaluation independently.
 If you are using it to reinforce the week’s instruction, determine the items
that will be completed as guided practice, and those that will be completed
as independent practice.
Review: Review the correct answers with students as soon as they are
finished.
Answers: 1.
2.
3.
4.
5.
(4.G.2)
(4.G.2)
(4.G.2)
(4.G.2)
(4.G.2)
right, isosceles triangle
one
two
C
or equivalent
22
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Common Core Standards Plus® – Mathematics – Grade 4
Domain: Geometry
Focus: Classifying two-dimensional figures
Evaluation: #2
Equilateral
Isosceles
5'
6'
5'
Acute
5'
12'
Obtuse
6'
Parallel Lines
Scalene
15'
17'
Right
5'
Quadrilateral
Sample Assessment - Student Response Page
Directions: Answer problems 1-4.
In problem 5, draw the figure described.
1. What is the complete name of this figure? ________________________
2. How many pairs of parallel sides does this figure have? _____________
3. How many acute angles does this figure have? ____________________
4. Circle the letter next to the figure that has all of the features listed.
 Two pairs of parallel sides
A. square
B. rectangle
 Opposite sides that
C. parallelogram
are equal
D. trapezoid
 No right angles
5. Draw a quadrilateral that has two right angles, and one pair of
parallel sides.
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23
Teacher Lesson Plan
Common Core Standards Plus® – Mathematics – Grade 4
Performance Lesson #9 – Domain: Geometry
Standard Reference: 4.G.1: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular
and parallel lines. Identify these in two-dimensional figures.
4.G.2: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the
presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
Required Student Materials:
• Student Pages: St. Ed. Pgs. 177-179 (Student Worksheet)
• Protractor
Sample Performance Lesson - Teacher Lesson Plan
Lesson Objective: The students will classify two-dimensional figures by their lines or angles, recognize and
identify right triangles, and classify triangles by their measurement.
Overview: Students will review the content and academic vocabulary as addressed in Common Core Standards
Plus Geometry Lessons 1-8, E1-E2. The students will also review the content and academic vocabulary in the
Measurement and Data Standard 6.
Students will:
• Draw a two-dimensional figure that has parallel lines.
• Classify parallel and perpendicular lines in two-dimensional figures.
• Recognize and categorize right triangles.
• Classify triangles by measuring the interior angles of triangles.
• Explain their thinking when classifying figures.
Guided Practice: (Required Student Materials: St. Ed. Pg. 177)
• Review the vocabulary terms: parallel and perpendicular lines.
• Review the vocabulary terms: right angle, acute angle, obtuse angle, parallel lines, and
perpendicular lines.
• Review how to identify right triangles, acute triangles, and obtuse triangles.
• Review the symbol for a right angle and the symbols for other angles.
• Review how to use a protractor to measure an angle. (Angle measurement is covered in
Measurement and Data Standards 6 and 7.)
Independent Practice: (Required Student Materials: St. Ed. Pgs. 177-179)
• Students will work with a partner to complete the three problems.
• Remind students to check their work to be certain they complete all parts of each problem.
Review & Evaluation:
• Option 1: Students join another group and explain their work product to the new group. Students
collect any feedback prior to making revisions or additions to their papers.
• Option 2: Teacher selects students’ answers to display and discusses possible answers with the class.
• Option 3: Teacher collects students’ papers and evaluates them for students’ ability to demonstrate
conceptual understanding of the standard and ability to explain thinking.
24
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Student Page 1 of 3
Common Core Standards Plus® – Mathematics – Grade 4
Performance Lesson #9 – Domain: Geometry
Sample Performance Lesoon - Student Repsone Page
Vocabulary: Lines: • Parallel lines: Never intersect or meet and equal distance from one another. • Perpendicular lines: Intersect to form a right angle 90o. Angles: • Right angle: An angle of exactly 90o. @ • Acute angle: An angle of less than 90o . Y • Obtuse angle: Angle of more than 90o. K Triangles: Have three angles and three sides; the measurement of the 3 angles always total exactly 1800. • Right triangle: Includes a right angle 90o. • Acute triangle: All angles measure less than 90o. • Obtuse triangle: Has one angle with a measure greater than 90 o. Directions: Complete all parts of each problem. 1. a) Draw a two-­‐dimensional figure that has parallel lines. b) Label the parallel lines with the word parallel. c) Label the right angles in the figure with the right angle symbol  . d) Explain how you know the figure you drew has parallel lines. Explanation:___________________________________________________________
______________________________________________________________________
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Student Page 2 of 3
Common Core Standards Plus® – Mathematics – Grade 4
Performance Lesson #9 – Domain: Geometry
2. a)
b)
c)
d)
Look at the two-­‐dimensional figures below. Which of the figures has perpendicular lines? Label the figures that have perpendicular lines with the word perpendicular. Explain how you know the other figures do not have perpendicular lines. F
n
p
A
X
Sample Performance Lesson - Student Response Page
1: 2:
3:
4: 5:
Explanation:___________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________ 26
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Student Page 3 of 3
Common Core Standards Plus® – Mathematics – Grade 4
Performance Lesson #9 – Domain: Geometry
3. a)
b)
c)
d)
Look at the triangles below. Use a protractor to measure the interior angles of each triangle. Label each interior angle with its measurement. Classify each triangle (right, acute, obtuse) by the measure of its largest interior angle. e) Identify and label any right triangles. f) Explain how you know that a triangle is a right triangle. B C Sample Performance Lesoon - Student Repsone Page
A D Explanation:___________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
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Comm on Core Stand ards Plus - Math Grade 4 Lesso n Index
Common Core Standards Plus – Mathematics – Grade 4 Number and Operations in Base Ten (Number and Operations in Base Ten Standards 4.NBT.1 – 4.NBT.6) Domain Lesson 28
Focus Standard(s) 1 2 3 4 E1 5 6 7 8 E2 9 10 11 12 Identify Place Value E3 Evaluation – Comparing and Rounding Whole Numbers P1 13 14 15 16 Performance Lesson #1 – Understanding Numbers (4.NBT.1, 4.NBT.2, 4.NBT.3) E4 Evaluation – Add and Subtract Multi–digit Whole Numbers 17 18 19 20 E5 21 22 23 24 E6 25 26 27 28 E7 Multiplication of Whole Numbers P2 TE St. Ed. DOK Page Page Level 30 32 34 36 38 40 42 44 46 48 50 52 54 56 3 4 5 6 7 9 10 11 12 13 15 16 17 18 58 19 60 64 66 68 70 21–23 72 29 74 76 78 80 82 84 86 88 90 31 32 33 34 35 37 38 39 40 92 41 Evaluation – Dividing Whole Numbers 94 96 98 100 102 43 44 45 46 47 Performance Lesson #2 – Working with Operations (4.NBT.4, 4.NBT.5, 4.NBT.6) 104 49–52 3 Identify Place Value up to 1,000,000 Understand Place Value Patterns Understand Place Value Patterns 4.NBT.1: Recognize that in a multi-­‐digit whole number, a digit in one place represents ten times what it represents in the place to its right. Evaluation – Place Value Word Form of Numbers Expanded Form Standard Form Whole Number Forms Evaluation – Forms of Numbers Compare Numbers 4.NBT.2: Read and write multi-­‐digit whole numbers using base-­‐ten numerals, number names, and expanded form. Compare two multi-­‐
digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 4.NBT.2 Compare Numbers Rounding Numbers 4.NBT.3: Use place value understanding to round multi-­‐digit whole numbers to any place. Rounding Numbers 4.NBT.2, 4.NBT.3 Add Multi-­‐digit Whole Numbers Add Multi-­‐digit Whole Numbers Subtract Multi-­‐digit Whole Numbers Subtract Multi-­‐digit Whole Numbers 4.NBT.4: Fluently add and subtract multi-­‐digit whole numbers using the standard algorithm. 4.NBT.5: Multiply a whole number of up to four digits by a one-­‐digit whole number, and multiply Multiplication of Whole Numbers two two-­‐digit numbers, using strategies based on place value and the properties of operations. Multiplication of Whole Numbers Illustrate and explain the calculation by using Multiplication of Whole Numbers equations, rectangular arrays, and/or area Evaluation – Multiplication of Whole Numbers models. Dividing Whole Numbers Dividing Whole Numbers Dividing Whole Numbers Dividing Whole Numbers Evaluation – Dividing Whole Numbers 4.NBT.6: Find whole-­‐number quotients and remainders with up to four–digit dividends and one-­‐digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Dividing Whole Numbers Dividing Whole Numbers Dividing Whole Numbers 4.NBT.6 Dividing Whole Numbers www.standardsplus.org - 1.877.505.9152
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25 26 27 28 1-­‐2 1-­‐2 1-­‐2 3 1-­‐2 1-­‐2 1-­‐2 1-­‐2 Comm on Core Stand ards Plus - Math Grade 4 Lesso n Index
Common Core Standards Plus – Mathematics – Grade 4 Domain Lesson TE St. Ed. DOK Page Page Level Commutative Property of Multiplication 4.OA.2: See Week 2. 118 53 2 Represent Verbal Statements as Equations 120 54 3 Represent Verbal Statements as Equations 122 55 4 Represent Verbal Statements as Equations 4.OA.1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. 124 56 4.OA.1, 4.OA.2 126 57 128 59 130 60 132 61 134 62 136 63 138 65 140 66 142 67 144 68 5 Operations and Algebraic Thinking Standard(s) 1 E1 (Operations and Algebraic Thinking Standards 4.OA.1 – 4.OA.5)
Focus Evaluation – Multiplicative Comparison Multiplicative Comparison Problems 6 Multiplicative Comparison Problems 7 Multiplicative Comparison Problems 8 Distinguish Multiplicative & Additive Comparisons E2 4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Evaluation – Multiplicative Comparison 9 Multiplicative Comparison Problems 10 Multiplicative Comparison Problems 11 Multistep Word Problems 12 Multistep Word Problems E3 Evaluation –Word Problems 4.OA.2, 4.OA.3 146 69 13 Multistep Addition & Subtraction Word Problems 148 71 14 Multistep Multiplication Word Problems 150 72 15 Multistep Word Problems 152 73 16 Multistep Word Problems 154 74 E4 Evaluation – Multistep Word Problems 4.OA.3: Solve multistep word problems posed with whole numbers and having whole-­‐number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 156 75 17 Division Word Problems with Remainders 158 77 18 Division Word Problems with Remainders 160 78 19 Division Word Problems with Remainders 162 79 20 Division Word Problems with Remainders 164 80 E5 Evaluation – Solving Division Word Problems with Remainders 166 81 21 Multiples of Whole Numbers 168 83 22 Finding Factor Pairs for Whole Numbers 170 84 23 Finding Factor Pairs for Whole Numbers 172 85 24 Recognize Prime and Composite Numbers 174 86 E6 Evaluation – Multiples and Factors 176 87 P3 Performance Lesson #3 – Understanding Operations (4.OA.1, 4.OA.2, 4.OA.3, 4.OA.4) 178-­‐179 89–92 4.OA.2 4.OA.3 4.OA.3 4.OA.4: Find all factor pairs for a whole number in the range of 1-­‐100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-­‐100 is a multiple of a given one-­‐digit number. Determine whether a given whole number in the range 1-­‐100 is prime or composite. www.standardsplus.org - 1.877.505.9152
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1-­‐2 1-­‐2 1-­‐2 1-­‐2 1-­‐2 1-­‐2 3 29
Comm on Core Stand ards Plus - Math Grade 4 Lesso n Index
Common Core Standards Plus – Mathematics – Grade 4 (4.OA.1 – 4.OA.5) Operations and Algebraic Thinking Domain Lesson Focus 25 Generating Arithmetic Patterns 26 Identifying the Rule for Arithmetic Patterns 27 Generate Geometric Patterns 28 Identifying the Rule for Geometric Patterns E7 Evaluation – Pattern Rules 29 Identify and Explain Features of Arithmetic Patterns Identify and Explain Features of Geometric Patterns 30 31 32 E8 P4 Standard(s) 4.OA.5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. TE St. Ed. DOK Page Page Level 184 93 186 94 188 95 190 96 192 97 194 99 196 100 198 101 Evaluation – Feature of Patterns 200 202 102 103 Performance Lesson #4 – Generate and Analyze Patterns (4.OA.5) 204 105–106 3 209-­‐213 107–110 4 Generate Growing Shape Patterns 4.OA.5 Identify the Rule for Growing Shape Patterns Integrated Project 1: It’s a Number’s Game 1-­‐2 1-­‐2 (4.OA.1, 4.OA.2, 4.OA.3, 4.OA.4, 4.OA.5, 4.NBT.1, 4.NBT.2, 4.NBT.3, 4.NBT.4, 4.NBT.5, 4.NBT.6) Prerequisite Common Core Standards Plus Domains: Number and Operations in Base Ten and Operations and Algebraic Thinking Product: A board game that includes the game board, rules, and cards with at least 10 questions/problems (and their answers) related to each of nine categories. Overview: In this project the students will work in groups of 2–4 to create a board game that shows an understanding of all of the standards taught in the Number and Operations in Base Ten and Operations and Algebraic Thinking Domains. The students will write at least 90 (10 in each category) questions or problems with an answer key for each in the following categories: • Place Value of Whole Numbers • Representing, Comparing, and Rounding Numbers • Adding Multi–digit Numbers • Subtracting Multi–digit Numbers • Multiplying Multi–digit Numbers • Dividing Multi–digit Numbers • Writing Equations • Pattern Rules • Making a Model The students will write the rules of play, design the game board, and create the cards. They will include dice, a spinner, or any other item needed to play the game. They will present and explain their game to the class when the project is complete. 30
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Comm on Core Stand ards Plus - Math Grade 4 Lesso n Index
Common Core Standards Plus – Mathematics – Grade 4 Domain Lesson Relative Size of Measurement Units 2 Customary Measurement Equivalents 3 Comparing Customary Measurements 4 Relative Size of Measurement Units Evaluation – Customary Measurement Equivalents 4.MD.1: Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-­‐column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24),... TE Page St. Ed. DOK Page Level 230 111 232 112 234 113 1-­‐2 236 114 238 115 5 Measurement Conversion 240 117 6 Measurement Conversion 242 118 7 Metric Measurement Equivalents 244 119 1-­‐2 8 Comparing Metric Measurements 246 120 E2 Evaluation – Metric Measurement Equivalents 248 121 9 Word Problems Involving Measurement Units 250 123 10 Word Problems Involving Measurement Units 252 124 11 Word Problems Involving Measurement Units 254 125 1-­‐2 12 Word Problems Involving Measurement Units 256 126 E3 Evaluation – Word Problems with Measurement Units 258 127 P5 Performance Lesson #5 – Conversion Factor (4.MD.1, 4.MD.2) Common Core Standards Plus® – Language Arts – Grade 3 4.MD.1 4.MD.2: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. 13 14 15 16 E4 P6 Reading Literature 17 18 19 20 E5 P7 260 129–132 3 DOK Level
266 133 282 131 5 Parts of Stories Finding Area of a Rectangle RL.3.5: Refer to parts of stories, dramas, 284 132 6 Parts of Dramas 4.MD.3: Apply the area and perimeter formulas Perimeter/Area in Real World Problems and poems when writing or speaking for r
ectangles i
n r
eal w
orld a
nd m
athematical about a text, using terms such as chapter, Parts of a Poem 286 133 1‐2 7 268 134 270 135 1-­‐2 272 136 274 137 Perimeter of a Rectangle Standard(s) Strand Finding Lesson Focus (Reading Literature Standards: RL.3.1, RL.3.2, RL.3.3, RL.3.4, RL.3.5, RL.3.6, RL.3.7)
Measurement and Data Standard(s) 1 E1 (Measurement and Data Standards 4.MD.1 – 4.MD.7)
Focus problems. scene, and stanza; describe how each 8 Parts of a Poem Perimeter/Area in Real World Problems successive part builds on earlier sections. TE Page 288 St. Ed.
Page
134 290 135 E2 Evaluation – Stories, Poems, and Dramas Evaluation – Perimeter and Area of a Illustration and Mood 292 137 9 Rectangular Figure RL.3.7: Explain how specific aspects of a 294 138 10 Illustration and Setting Performance Lesson #6 – Area and Perimeter (4.MD.3) text’s illustration contribute to what is conveyed by the words in the story (e.g., 296 139 1‐2 11 Illustration and Character create mood, emphasize aspects of a Create a
L
ine P
lot Illustrations 298 140 12 character or setting.) 4.MD.4: M
ake a
l
ine p
lot t
o d
isplay set of 300 a data 141 E3 Evaluation – Illustrations Reading a Line Plot measurements in fractions of a unit (1/2, 1/4, 1/8). Performance – Reading Literature: Character Study and Comic Strip
(RL.3.1, RL.3.3, Solve problems involving addition and s143‐146
ubtraction 302‐303
3 of fractions by using information presented in line RL.3.2: Recount stories, including fables, lot find 147 and interpret plots. For example, from a line p308 folktales, and myths from diverse cultures: the difference in length between the longest and 310 148 determine the central message, lesson, or shortest specimens in an insect collection. moral, and explain how it is conveyed Fables, Folktales, and Myths 312 149 1‐2 through key details in the text. P5 Solve PRL.3.5, RL.3.7) roblems Using a Line Plot 13 Fables, Folktales, Myths, and Word Meanings
Solve roblems Using a Line Plot 14 PFables, Folktales, and Myths 15 Evaluation – Line Plots RL.3.4: Determine the meaning of words 16 Fables, Folktales, and Myths and phrases as they are used in a text, Performance Lesson #7 – Plotting Data (4.MD.4) distinguishing literal from nonliteral Evaluation – Fables, Folktales, Myths, and E4 Vocabulary language. 17 18 19 20 E5 314 150 316 151 Point of View 318 153 Point of View 320 154 322 155 324 156 326 157 Point of View Point of View RL.3.6: Distinguish their own point of view from that of the narrator or those of the www.standardsplus.org
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characters. Evaluation – Point of View © 2013 Learning Plus Associates
276 3 280 141 282 142 284 143 1-­‐2 286 144 288 145 290 1‐2 139–140 147–148 3 31
Comm on Core Stand ards Plus - Math Grade 4 Lesso n Index
Common Core Standards Plus – Mathematics – Grade 4 Domain Lesson Measurement and Data (Measurement and Data Standards 4.MD.1 – 4.MD.7)
21 (Geometry Standards 4.G.1 – 4.G.3)
Geometry TE Page St. Ed. DOK Page Level 4.MD.5: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a) an angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-­‐degree angle,” and can be used to measure angles. b) An angle that turns through n one-­‐
degree angles is said to have an angle measure of n degrees. Concepts of Angles 294 149 1-­‐2 22 Using a Protractor to Measure Angles 23 Using a Protractor to Measure Angles 24 Using a Protractor to Sketch Angles E6 Evaluation – Measurement of Angles 4.MD.5, 4.MD.6 25 Composing and Decomposing Angles 26 27 Finding Unknown Angles 28 E7 Angles in Real World Problems 4.MD.7: Recognize angle measure as additive. When an angle is decomposed into non-­‐overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. P8 Performance Lesson #8 – All About Angles (4.MD.5, 4.MD.6, 4.MD.7) 314 1 2 Points, Lines, and Line Segments 326 165 328 166 3 Draw and Distinguish Between Parallel and Perpendicular Lines Identify Angles, Parallel, and Perpendicular Lines in Two-­‐Dimensional Figures 330 167 1-­‐2 332 168 334 169 336 171 338 172 340 173 1-­‐2 342 174 344 175 4 32
Standard(s) Focus E1 5 6 7 8 E2 Finding Unknown Angles Evaluation – Angles Draw and Distinguish Between Rays and Angles 4.MD.6: Measure angles in whole–number degrees using a protractor. Sketch angles of specified measure. 4.G.1: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-­‐
dimensional figures. Evaluation – Identify Geometric Objects Classify Two-­‐Dimensional Figures Based on Their Sides Classify Two-­‐Dimensional Figures Based on Angle Measurement Classify Special Triangles Classifying Quadrilaterals 4.G.2: Classify two-­‐dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Evaluation – Classifying Two–Dimensional Figures P9 Performance Lesson #9 – Lines, Angles, Figures (4.G.1, 4.G.2) 9 Line of Symmetry 4.G.3: Recognize a line of symmetry for a two-­‐
10 Line of Symmetry dimensional figure as a line across the figure such that the figure can be folded along the line into 11 Line of Symmetry matching parts. Identify line-­‐symmetric figures and draw lines 12 Line of Symmetry of symmetry. Evaluation –
L
ines o
f S
ymmetry E3 P10 Performance Lesson #10 – Symmetry (4.G.3) www.standardsplus.org - 1.877.505.9152
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296 150 298 151 300 152 302 153 304 155 306 156 308 157 1-­‐2 310 158 312 159 346 161–163 177–179 3 3 350 181 352 182 354 183 1-­‐2 356 184 358 185 360 187–188 3 Comm on Core Stand ards Plus - Math Grade 4 Lesso n Index
Domain Lesson Common Core Standards Plus – Mathematics – Grade 4 Focus Standard(s) Integrated Project #2: A Place to Play (4.NBT.4, 4.NBT.5, 4.NBT.6, 4.MD.1, 4.MD.2, 4.MD.3, 4.MD.4, 4.MD.5, 4.MD.5a, 4.MD.5b, 4.MD.6, 4.MD.7, 4.G.1, 4.G.2, 4.G.3) TE Page St. Ed. DOK Page Level 365-­‐369 189–191 4 Prerequisite Common Core Standards Plus Domains: Measurement & Data and Geometry Product: A park design that includes specific features. Overview: In this project, the students will design a park that includes specified features. They will create a schematic for the park that shows every feature including: green spaces (grass, shrubs, trees), benches, walkways, playground equipment, ball fields, etc. They will use common tools to provide a precise visual of the park. Each student will present his/her park design orally. www.standardsplus.org - 1.877.505.9152
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Comm on Core Stand ards Plus - Math Grade 4 Lesso n Index
Common Core Standards Plus – Mathematics – Grade 4 Domain Lesson 1 Equivalent Fractions 2 Equivalent Fractions 3 Comparing Fractions 4 Comparing Fractions E1 Number and Operations – Fractions (Number and Operations – Fractions Standards 4.NF.1–4.NF.7)
5 4.NF.2 See Below 4.NF.1, 4.NF.2 Comparing Fractions Comparing Fractions 7 Equivalent Fractions 8 Equivalent Fractions E2 Standard(s) 4.NF.1: Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Evaluation – Equivalent Fractions and Comparing Fractions 6 Evaluation – Equivalent Fractions and Comparing Fractions 4.NF.2: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. TE Page St. Ed. DOK Page Level 382 193 384 194 386 195 1-­‐2 388 196 390 197 392 199 394 200 396 201 1-­‐2 398 202 400 203 Add and Subtract Like Fractions 4.NF.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. 402 205 10 Decomposing and Composing Fractions 404 206 11 Decomposing Fractions 406 207 1-­‐2 12 Decomposing Mixed Numbers 4.NF.3b: Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. 408 208 E3 Evaluation – Composing and Decomposing Fractions 4.NF.3a, 4.NF.3b 410 209 9 P11 Performance Lesson #11 – All About Fractions (4.NF.1, 4.NF.2, 4.NF.3, 4.NF.3a, 4.NF.3b) 13 Adding Mixed Numbers 14 Adding Mixed Numbers 15 Subtracting Mixed Numbers 16 Subtracting Mixed Numbers E4 412-­‐413 211–213 3 418 215 420 216 422 217 1-­‐2 424 218 Evaluation – Add and Subtract Mixed Numbers 426 219 17 Add Fractions to Solve Word Problems 428 221 18 Subtract Fractions to Solve Word Problems 430 222 432 223 1-­‐2 434 224 436 225 19 20 E5 P12 34
Focus Add/Subtract Fractions to Solve Word Problems Add/Subtract Fractions to Solve Word Problems Evaluation – Word Problems -­‐ Adding/ Subtracting Fractions 4.NF.3c: Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. 4.NF.3d: Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. Performance Lesson #12 – Adding and Subtracting Fractions (4.NF.3c, 4.NF.3d) www.standardsplus.org - 1.877.505.9152
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Common Core Standards Plus – Mathematics – Grade 4 Number and Operations – Fractions (Number and Operations – Fractions Standards 4.NF.1–4.NF.7) Domain Lesson TE Page St. Ed. DOK Page Level 4.NF.4a: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. For example use a visual fraction model to represent 5/4 as the product of 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). 4.NF.4b: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b.) 442 229 444 230 446 231 448 232 4.NF.4a, 4.NF.4b 450 233 4.NF.4c: Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. 452 454 456 458 235 236 237 1-­‐2 238 460 239 Focus 21 Multiply Fractions by Whole Numbers 22 Multiplying Fractions by Whole Numbers 23 Multiplying Fractions by Whole Numbers 24 Multiplying Fractions by Whole Numbers E6 Evaluation – Multiplying Fractions by Whole Numbers 25 Word Problems – Multiplying Fractions 26 27 28 Word Problems – Multiplying Fractions E7 Evaluation – Operations in Fraction Word Problems Operations in Fraction Word Problems Operations in Fraction Word Problems Standard(s) 4.NF.4c , 4.NF.3d: Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. 4.NF.3c, 4.NF.4d P13 Performance Lesson #13 – Multiplying Fractions 4.NF.5: Express a fraction with denominator 10 as an 29 Converting Fractions -­‐ 10ths to 100ths equivalent fraction with denominator 100, and use this technique to add two fractions with respective 30 Add Fractions denominators 10 and 100. 4.NF.6: Use decimal notation for fractions with 31 Convert Fractions to Decimals denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on 32 Decimals on a Number Line a number line diagram. 4.NF.5, 4.NF.6 E8 Evaluation – Converting Fractions 33 Compare Decimals 4.NF.7: Compare two decimals to hundredths by 34 Compare Decimals reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same 35 Compare Decimals whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by Compare D
ecimals 36 using a visual model. E9 Evaluation – Compare Decimals P14 Performance Lesson #14 – Fractions and Decimals (4.NF.5, 4.NF.6, 4.NF.7) Integrated Project #3: An Illustrated Guide to Equivalence (4.NF.1, 4.NF.2, 4.NF.3, 4.NF.3a, 4.NF.3b, 4.NF.3c, 4.NF.3d, 4.NF.4, 4.NF.4a, 4.NF.4b, 4.NF.4c, 4.NF.5, 4.NF.6, 4.NF.7) 462 1-­‐2 241–242 3 466 243 468 244 470 245 1-­‐2 472 246 474 247 476 478 480 482 484 249 250 251 1-­‐2 252 253 486-­‐487 255–257 3 493-­‐497 258–261 4 Prerequisite Common Core Standards Plus Domains: Number and Operations – Fractions Product: A booklet, pamphlet, or series of posters that explore and explain comparisons and equivalence between fractions, whole numbers, mixed numbers, and decimals. Overview: In this project, the students will each create an illustrated guide to equivalence that may be a booklet, a pamphlet, or a series of posters that use models and written explanations to teach the concepts of comparisons and equivalence between fractions, whole numbers, mixed numbers, and decimals. The students will write the text and draw models to explain all of the concepts. They will present their product to a group of peers and participate in a group discussion analyzing and commenting on each group member’s work. www.standardsplus.org - 1.877.505.9152
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