Download 5th Grade - Northeastdifferentiation

4th
4th Grade
Nine Weeks Math
Domain:
Geometry
Cluster:
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
Common Core Standards:
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.
4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be
folded along the line into matching parts. Identify the line-symmetric figures and draw lines of symmetry.
Key Vocabulary
Line Symmetry
Plane
Congruent
Congruence
Similar
Line of Symmetry
Reflection
Line of Reflection
Line
Horizontal
Line Segment
Ray
Angle
Vertex
Oblique
Perpendicular
Right Angle
Parallel
Quadrilateral
Vertical
Trapezoid
Isosceles Trapezoid
Parallelogram
Rhombus
Rectangle
Square
Acute
Angle
Edge
Diagonal
Equivalent
Intersecting lines
Obtuse angle
Parallel lines
Perpendicular Lines
Plane
Point
Straight Angle
Symmetric
Two-Dimensional
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Habits of Mind
 Persistence
 Striving for Accuracy
 Remaining Open to Continuous Learning
 Thinking/Communication with Clarity &
Precision
2
Domain: Geometry
Cluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
Common Core 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.
What does this mean? This standard asks students to draw two-dimensional geometric objects and to also identify them in
two-dimensional figures. This is the first time that students are exposed to rays, angles, and perpendicular and parallel lines.
Math Practices:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Essential Question:





How does geometry better describe objects?
How do geometric shapes help with problem solving?
How are angles categorized?
How are shapes categorized by their angles?
Learning Targets (KUD)
K: vocabulary associated with lines and angles;
U: criteria for categorizing lines and angles
D: use measurements to categorize lines and angles, draw
Criteria for Success for Mastery
Students should be able to:

Identify (by name) points, lines, line segments, rays, angles
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examples of a point, line, line segment, ray, right angle, acute
angle, obtuse angle, perpendicular lines, and parallel lines; use
pictures to explain lines and angles

I can:
 draw an example of a point, line, line segment, ray, right
angle, acute angle, obtuse angle, perpendicular lines, and
parallel lines.
 look for and identify the following in a given twodimensional figure: point, line, line segment, ray, right
angle, acute angle, obtuse angle, perpendicular lines, and
parallel lines.
 use pictorial representations to explain lines and angles.
(acute, right, and obtuse), parallel lines, and perpendicular
lines within diagrams and two-dimensional figures.
Draw points, lines, line segments, rays, angles, and
perpendicular and parallel lines in two-dimensional figures.
Examples
Right angle
Segment
Acute angle
Line
Obtuse angle
Ray
Straight angle
Parallel Lines
Perpendicular Lines
4
Textbook Resources
Houghton Mifflin Harcourt Unit 6 Chapter 12: Motion Geometry 378A-378B. 378-381
Math Expression: 215J, 220-224, 226-238, 437J, 438-446, 456-457, 461-463, 774
Houghton Mifflin (Turtle) Chapter 16, Lesson 1, 2, 4, 5-404-409, 412-417,; Chapter 17, Lesson 4-440-443
Supplemental Resources
STAMS
Math Madness
Buckle Down
Houghton Mifflin Math Chapter Challenges
North Carolina Mathematics Coach
Math Intensive Intervention (Houghton Mifflin)
Houghton Mifflin Harcourt Strategic Intervention
Houghton Mifflin Harcourt Assessment Guide
Houghton Mifflin Harcourt Problem Solving Practice Book
Houghton Mifflin Harcourt Resource Book
Media Resources
Geometry by John Burstein
Sir Cumference and the Great Knight of Angleland : A Math Adventure by Cindy Neuschwander
What's your angle, Pythagoras? : A Math Adventure by Julie Ellis
Web Resources
http://www.math-drills.com
http://www.brainpop.com/
5
Domain: Geometry
Cluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
Common Core 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.
What does this mean? Two-dimensional figures may be classified using different characteristics such as, parallel or
perpendicular lines or by angle measurement.
Math Practices:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Essential Question:



How does geometry better describe objects?
What characteristics can be used to categorize two-dimensional shapes?
What primary characteristic identifies a right triangle?
Learning Targets (KUD)
K: vocabulary associated with lines and angles
U: criteria for categorizing lines, angles, right triangles, and
Criteria for Success for Mastery
Students should be able to:
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two-dimensional shapes; the use of a protractor when
classifying shapes by their attributes
D: use 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; identify right
triangles
I can:
 classify two-dimensional shapes into the following
categories: those with parallel lines, those with
perpendicular lines, those with both parallel and
perpendicular lines, those with no parallel or
perpendicular lines.
 classify two-dimensional shapes into categories based on
the presence or absence of acute, obtuse, or right angles.
 identify a right triangle.
 recognize right triangles.
 determine attributes of specific shapes using a
protractor.




Classify shapes by attributes such as presence of right
angles, parallel and perpendicular line segments, number of
sides, and congruency.
Identify and classify triangles based on properties such as
angles and side lengths.
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.
Examples
Which figure in the Venn diagram below is in the wrong place? Explain how you know.
at least one set of
parallel sides
A
at least one
right angle
B
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Do you agree with the label on each of the circles in the Venn diagram above? Describe why some shapes fall in the overlapping
sections of the circles.
Textbook Resources
Houghton Mifflin Harcourt Unit 6 Chapter 12: Motion Geometry 378A-378B. 378-381
Math Expression: 215J, 220-224, 226-238, 437J, 438-446, 456-457, 461-463, 774
Houghton Mifflin (Turtle) Chapter 16, Lesson 1, 2, 4, 5-404-409, 412-417,; Chapter 17, Lesson 4-440-443
Supplemental Resources
STAMS
Math Madness
Buckle Down
Houghton Mifflin Math Chapter Challenges
North Carolina Mathematics Coach
Math Intensive Intervention (Houghton Mifflin)
Houghton Mifflin Harcourt Strategic Intervention
Houghton Mifflin Harcourt Assessment Guide
Houghton Mifflin Harcourt Problem Solving Practice Book
Houghton Mifflin Harcourt Resource Book
Media Resources
Geometry by John Burstein
Sir Cumference and the Great Knight of Angleland : A Math Adventure by Cindy Neuschwander
What's your angle, Pythagoras? : A Math Adventure by Julie Ellis
Web Resources
http://www.math-drills.com
8
http://www.brainpop.com/
TEACHER NOTE: In the U.S., the term “trapezoid” may have two different meanings. Research identifies these as inclusive and exclusive
definitions. The inclusive definition states: A trapezoid is a quadrilateral with at least one pair of parallel sides. The exclusive definition
states: A trapezoid is a quadrilateral with exactly one pair of parallel sides. With this definition, a parallelogram is not a trapezoid.
North Carolina has adopted the exclusive definition. (Progressions for the CCSSM: Geometry, The Common Core Standards Writing Team,
June 2012.)
Domain: Geometry
Cluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
Common Core Standard:
4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded
along the line into matching parts. Identify the line-symmetric figures and draw lines of symmetry.
What does this mean? Students need experiences with figures which are symmetrical and non-symmetrical. Figures include
both regular and non-regular polygons. Folding cut-out figures will help students determine whether a figure has one or more
lines of symmetry.
**This standard only includes line symmetry not rotational symmetry.
Math Practices:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Essential Question:

How does geometry better describe objects?
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

How can lines of symmetry be drawn for two-dimensional figures?
How can you identify examples and non-examples of lines of symmetry in two-dimensional figures?
Learning Targets (KUD)
K: vocabulary associated with lines and angles
U: criteria for categorizing lines, angles, right triangles, and
two-dimensional shapes
D: find lines of symmetry using symmetrical and nonsymmetrical figures; determine whether a figure has one or
more lines of symmetry; explore lines of symmetry using cutout figures
I can:
 find lines of symmetry using cut-out figures.
 define line symmetry.
 draw lines of symmetry in two-dimensional figures.
 identify examples and non-examples of line symmetry in
two-dimensional figures.
Criteria for Success for Mastery
Students should be able to:
 Define line symmetry.
 Identify examples and non-examples of line symmetry in twodimensional figures.
 Draw lines of symmetry in two-dimensional figures.
Examples
For each figure, draw all of the lines of symmetry. What pattern do you notice? How many lines of symmetry do you think there
would be for regular polygons with 9 and 11 sides. Sketch each figure and check your predictions. Polygons with an odd number
of sides have lines of symmetry that go from a midpoint of a side through a vertex.
Textbook Resources
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Houghton Mifflin Harcourt Unit 6 Chapter 12: Motion Geometry 378A-378B. 378-381
Math Expression: 215J, 220-224, 226-238, 437J, 438-446, 456-457, 461-463, 774
Houghton Mifflin (Turtle) Chapter 16, Lesson 1, 2, 4, 5-404-409, 412-417,; Chapter 17, Lesson 4-440-443
Supplemental Resources
STAMS
Math Madness
Buckle Down
Houghton Mifflin Math Chapter Challenges
North Carolina Mathematics Coach
Math Intensive Intervention (Houghton Mifflin)
Houghton Mifflin Harcourt Strategic Intervention
Houghton Mifflin Harcourt Assessment Guide
Houghton Mifflin Harcourt Problem Solving Practice Book
Houghton Mifflin Harcourt Resource Book
Media Resources
Geometry by John Burstein
Sir Cumference and the Great Knight of Angleland : A Math Adventure by Cindy Neuschwander
What's your angle, Pythagoras? : A Math Adventure by Julie Ellis
Web Resources
http://www.math-drills.com
http://www.brainpop.com/
11
Domain:
Measurement and Data
Cluster:
Geometric measurement: Understand concepts of angle and measure angles
Common Core Standards:
4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand
concepts of angle measurement.
4.MD.5a 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.
4.MD.5b An angle that turns through n one degree angles is said to have an angle measure of n degrees.
4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
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.
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Key Vocabulary
Degrees
Protractor
Acute angle
Obtuse angle
Right angle
Straight angle
Center
Radius
Diameter
Chord
Ray
End point
Intersect
One degree angle
Vertex
Angle
Parallel lines
Intersecting lines
Perpendicular lines
Measure
Point
Decompose
Circle
Habits of Mind
 Persistence
 Striving for Accuracy
 Thinking Flexibly
 Remaining Open to Continuous Learning
 Thinking/Communication with Clarity &
Precision
 Questioning and Posing Problems
13
Domain: Measurement and Data
Cluster: Geometric measurement: Understand concepts of angle and measure angles
Common Core Standard:
4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand
concepts of angle measurement.
4.MD.5a 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.
4.MD.5b An angle that turns through n one degree angles is said to have an angle measure of n degrees.
What does this mean?
5a Use a circle to measure angles and determine that an angle measurement is not related to an area. An angle is the union of
two rays, a and b, with the same initial point P.
5b Determine that the number of times you turn one degree is the measure of the angle. This standard calls for students to
explore an angle as a series of “one-degree turns.”
Math Practices:
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1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Essential Question:





How do you determine an angle measurement in reference to a circle?
How is the measurement of an angle related to the area of a circle?
How are one-degree angles used to measure the total angle measurement?
Why does “what” we measure influence “how” we measure?
Why display data in different ways?
Learning Targets (KUD)
K: vocabulary associated with geometric measurement and
data
U: how to use appropriate tools for measurement
D: use a circle to measure angles and determine that the
angle measurement is not related to an area
I can:
 identify the parts of an angle.
 explain that an angle is measured in degrees related to
the 360 degrees in a circle.
 demonstrate how to measure angles using a circle.
 demonstrate that a 1/360 is a one degree angle.
 determine angle measurements in reference to a circle by
using given angle measurements.
 determine that three 30-degree angles make a 90-degree
Criteria for Success for Mastery
Students should be able to:



Demonstrate how to measure angles using a circle (right,
acute, and obtuse).
Demonstrate that a 1/360 is a one degree angle. (A 30
degree angle is 30/360 degree angle which simplified is 1/12
of the circle.
o Example: Create small groups of students and give each
group a 30, 45, and 90 degree angle. Give students a
variety of sizes of circles. Have students place one
angle over two different sizes of circles and discuss if
the angle measurement changed or not. Have students
practice this over and over again to determine that the
angle measurement does not change no matter the size
of the circle it is placed over.
Demonstrate an understanding that 25 one degree angles
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

angle AND two 45-degree angles make a 90-degree angle
AND two 90-degree angles make 180 degrees which is a
straight angle.
determine that a circle has 360 degrees.
demonstrate an understanding that 25 one-degree angles
measures the same as a 25-degree angle.
measures the same as a 25 degree angle.
Examples
a. The diagram below will help students understand that an angle measurement is not related to an area since the area between
the 2 rays is different for both circles yet the angle measure is the same.
b. A water sprinkler rotates one-degree at each interval. If the sprinkler rotates a total of 100º, how many one-degree
turns has the sprinkler made?
Textbook Resources
Math Expression: 226, 229,438-446, 437K
Houghton Mifflin (Turtle) Chapter 16, Lesson 16.3 and Lesson 16.7—410-411, 422-425
Supplemental Resources
STAMS
Math Madness
Buckle Down
Houghton Mifflin Math Chapter Challenges
North Carolina Mathematics Coach
Math Intensive Intervention (Houghton Mifflin)
Houghton Mifflin Harcourt Strategic Intervention
Houghton Mifflin Harcourt Assessment Guide
16
Houghton Mifflin Harcourt Problem Solving Practice Book
Houghton Mifflin Harcourt Resource Book
Media Resources
Geometry by John Burstein
Sir Cumference and the Great Knight of Angleland : A Math Adventure by Cindy Neuschwander
What's Your Angle, Pythagoras? : A Math Adventure by Julie Ellis
Web Resources
http://www.math-drills.com
http://www.brainpop.com/
Domain: Measurement and Data
Cluster: Geometric measurement: Understand concepts of angle and measure angles
Common Core Standard:
4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
What does this mean?
Use a protractor to measure and create angles.
Math Practices:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
17
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Essential Question:


Why does “what” we measure influence “how” we measure?
Why display data in different ways?

How do you use a protractor to measure and create angles?
Learning Targets (KUD)
K: vocabulary associated with geometric measurement and
data; measure of benchmark angles (45º, 90º, 180º)
U: how to use appropriate tools for measurement
D: use a protractor to measure angles; create pictorial
representations of benchmark angles
Criteria for Success for Mastery
Students should be able to:




I can:

understand how to use a protractor and measure a given
angle in whole-number degrees.

determine that obtuse angles are greater than 90 degrees.

determine that acute angles are less than 90 degrees.

determine that right angles are 90 degrees.

determine that a straight angle is 180 degrees.

create pictorial representations of angles.

sketch angles with a given measurement.

Measure given angles using a protractor.
Create obtuse angles and give the angle measurement using a
protractor.
Create acute angles and give the angle measurement using a
protractor.
Create right angles and give the angle measurement using a
protractor.
Create straight angles and give the angle measurement using
a protractor.
Examples
Students should measure angles and sketch angles
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120 degrees
135 degrees
As with all measurable attributes, students must first recognize the attribute of angle measure, and distinguish it from other
attributes. As with other concepts students need varied examples and explicit discussions to avoid learning limited ideas about
measuring angles (e.g., misconceptions that a right angle is an angle that points to the right, or two right angles represented
with different orientations are not equal in measure). If examples and tasks are not varied, students can develop incomplete and
inaccurate notions. For example, some come to associate all slanted lines with 45º measures and horizontal and vertical lines
with measures of 90º.
Textbook Resources
Math Expression: 226, 229,438-446, 437K
Houghton Mifflin (Turtle) Chapter 16, Lesson 16.3 and Lesson 16.7—410-411, 422-425
Supplemental Resources
STAMS
Math Madness
Buckle Down
Houghton Mifflin Math Chapter Challenges
North Carolina Mathematics Coach
Math Intensive Intervention (Houghton Mifflin)
19
Houghton Mifflin Harcourt Strategic Intervention
Houghton Mifflin Harcourt Assessment Guide
Houghton Mifflin Harcourt Problem Solving Practice Book
Houghton Mifflin Harcourt Resource Book
Media Resources
Geometry by John Burstein
Sir Cumference and the Great Knight of Angleland : A Math Adventure by Cindy Neuschwander
What's Your Angle, Pythagoras? : A Math Adventure by Julie Ellis
Web Resources
http://www.math-drills.com
http://www.brainpop.com/
Domain: Measurement and Data
Cluster: Geometric measurement: Understand concepts of angle and measure angles
Common Core Standard:
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.
What does this mean?
This standard addresses the idea of decomposing (breaking apart) an angle into smaller parts. Use angle measurements to solve
word problems.
20
Math Practices:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Essential Question:




Why does “what” we measure influence “how” we measure?
Why display data in different ways?
How do you solve multi-step word problems using measurement?
How do you decompose a specific benchmark angle?
Learning Targets (KUD)
K: vocabulary associated with geometric measurement and
data; measure of benchmark angles (45º, 90º, 180º)
U: how to use appropriate tools for measurement
D: solve word problems involving unknown angles; use
addition and subtraction to solve for missing angle
measurements
I can:

determine how to break apart or decompose an angle.

explain that the angle measurement of a larger angle is the
sum of the angle measures of its decomposed parts.

write an equation with an unknown angle measurement.

use addition and subtraction to solve for the missing angle
Criteria for Success for Mastery
Students should be able to:

Demonstrate how to solve addition and subtraction problems
using angles and decompose those angles.

Demonstrate how to solve addition and subtraction problems
using angles, a variable, and an equation and decompose those
angles.
o Example: A 10 degree angle is made up of 10 one degree
angles.
o Example: You have a pie that half of the pie has been
eaten. You have three pieces of the pie left. One piece of
the pie shows a 30 degree angle. How many one degree
angles make up that 30 degree angle? You have another
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
measurements.
piece that shows a 90 degree angle. How many one
solve word problems involving unknown angles.
degree angles make up that 90 degree angle? Use the
measurements of the given pieces of pie to determine the
other piece of pie. (30+90=120, THEN 180-120=60)
Examples
A lawn water sprinkler rotates 65 degrees and then pauses. It then rotates an additional 25 degrees. What is the total degree of the water sprinkler
rotation? To cover a full 360 degrees how many times will the water sprinkler need to be moved?
If the water sprinkler rotates a total of 25 degrees then pauses. How many 25 degree cycles will it go through for the rotation to reach at least 90
degrees?
Textbook Resources
Math Expression: 226, 229,438-446, 437K
Houghton Mifflin (Turtle) Chapter 16, Lesson 16.3 and Lesson 16.7—410-411, 422-425
Supplemental Resources
STAMS
Math Madness
Buckle Down
Houghton Mifflin Math Chapter Challenges
North Carolina Mathematics Coach
Math Intensive Intervention (Houghton Mifflin)
22
Houghton Mifflin Harcourt Strategic Intervention
Houghton Mifflin Harcourt Assessment Guide
Houghton Mifflin Harcourt Problem Solving Practice Book
Houghton Mifflin Harcourt Resource Book
Media Resources
Geometry by John Burstein
Sir Cumference and the Great Knight of Angleland : A Math Adventure by Cindy Neuschwander
What's Your Angle, Pythagoras? : A Math Adventure by Julie Ellis
Web Resources
http://www.math-drills.com
http://www.brainpop.com/
23