MIDDLE SCHOOL CONTENT ACADEMY

GeometrySOL 6.11, 6.12, 6.13, 7.7, 7.8, 8.8, 8.9, 8.10, 8.11 February 12, 2015

CURRICULUM FRAMEWORK Geometry strand information!

REPORTING CATEGORY: MEASUREMENT AND

GEOMETRY Let’s examine the SOL in this reporting category strand.

Which are in the Geometry reporting category?

CURRICULUM FRAMEWORK – UNPACK THE STANDARD

What are th

e

verbs?

HENRICO CURRICULUM GUIDE http://blogs.henrico.k12.va.us/math/courses/

PACING

SOL 6.11, 6.12, 6.13

SOL 7.7, 7.8

SOL 8.8, 8.9, 8.10, 8.11

REPORTING CATEGORY: MEASUREMENT AND GEOMETRY

Grade 62011-122012-132013-14

Grade 72011-122012-132013-14

Grade 82011-122012-132013-14

Look for trends!

FORMULAS

What formulas do students need to know related to the Geometry strand?

What formulas are provided on the formula sheet related to the Geometry strand?

Focus: Properties and RelationshipsFocus: Relationships between FiguresFocus: Problem Solving with 2- and 3-Dimensional Figures

VERTICAL ARTICULATION OF CONTENT

2014 SPBQ DATA – 6.11, 7.8, 8.8Grade Description of Question % Correct in

Division

6 Assign points to the correct quadrants or axes without graphing.

59

6 Use coordinates to graph points on the coordinate plane.

76

6 Assign points to the correct quadrants or axes. 88

7 Apply a transformation to the graph or coordinates of a figure and determine the graph or coordinates for the image.

50

7 Identify and recognize congruent images resulting from transformations.

63

7 Identify the resulting image of a transformation. 64

8 Apply transformations to plane figures and identify applications of transformations.

77

8 Identify the resulting image of a transformation 62

8 Apply transformations to plane figures. 67

PERFORMANCE ANALYSIS COMPARISONSOL 6.11, 7.8, 8.82012SOL 6.11

a) identify the coordinates of a point in a coordinate plane; andb) graph ordered pairs in a coordinate plane.

SOL 7.8 - The student, given a polygon in the coordinate plane, will represent transformations (reflections, dilations, rotations, and translations) by graphing in the coordinate plane.

SOL 8.8 - None

2013SOL 6.11 – None

SOL 7.8 - The student, given a polygon in the coordinate plane, will represent transformations (reflections, dilations, rotations, and translations) by graphing in the coordinate plane.

SOL 8.8c) apply transformations to plane figures; andd) identify applications of transformations.

2012 - SUGGESTED PRACTICE FOR SOL 6.11Students need additional practice recognizing the location of points that lie on the x- or y-axis.

1. Identify the location of the point (10,0).a) In Quadrant Ib) In Quadrant IIIc) On the x-axisd) On the y-axis

2. Select the two points that are located on the y-axis.

(0,0) (0,1) (1,1) (-1,-1) (1,0)

Common Errors? Misconceptions?

2012 - SUGGESTED PRACTICE FOR SOL 7.8Students need additional practice applying transformations to a given figure on a coordinate plane.a) Identify the coordinates of the image of triangle

ABC after a dilation about the origin by a factor of 2.

b) Identify the coordinates of the image of triangle ABC after a rotation of 180 degrees counterclockwise about the origin.

c) Identify the coordinates of the image of triangle ABC after a reflection over the y-axis.

d) Identify the coordinates of the image of triangle ABC after a translation 5 units to the right.

A (-7,3) B (-7,-2) C (-1,-2)

A

CB

Common Errors? Misconceptions?

2013 - SUGGESTED PRACTICE FOR SOL 7.8

1. Identify the coordinates of the image of triangle ABC after a dilation about the origin by a factor of 2.

2. Identify the coordinates of the image of triangle ABC after a rotation of 180 degrees clockwise about the origin.

3. Identify the coordinates of the image of triangle ABC after a reflection over the y-axis.

A (-2,4) B (-2,-3) C (-4,-3)

y

x

A

BC

Students need additional practice applying transformations to a given figure on a coordinate plane.

Common Errors? Misconceptions?

2013 - SUGGESTED PRACTICE FOR SOL 8.8AStudents need additional practice determining the coordinates of a figure after it is rotated about the origin in the counterclockwise direction.

This polygon is rotated 270° counterclockwise about the origin. Plot the image of point D (-4, 5) and name the coordinates.

D

(5, 4)

D ’

Common Errors? Misconceptions?

Focus: Properties and RelationshipsFocus: Relationships between FiguresFocus: Problem Solving with 2- and 3-Dimensional Figures

VERTICAL ARTICULATION OF CONTENT

2014 SPBQ DATA – 6.13, 7.7

Grade Description of Question % Correct in Division

6 Use attributes of quadrilaterals to solve problems. 74

7 Classify quadrilaterals based on properties. 82

7 Use properties to compare and contrast quadrilaterals. 46

7 Classify quadrilaterals based on properties. 72

PERFORMANCE ANALYSIS COMPARISONSOL 6.13, 7.72012SOL 6.13 – The student will describe and identify properties of quadrilaterals.SOL 7.7 – The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid.

2013SOL 6.13 – NoneSOL 7.7 – The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid.

2012 - SUGGESTED PRACTICE FOR SOL 6.13Students need additional practice describing and identifying properties of quadrilaterals.

a) Name each figure using the given attributes with its most precise name.

b) What term most accurately classifies all of these figures?c) What term most accurately classifies figures 1, 3, 4, and 6?d) What term most accurately classifies figures 1 and 3?

1 2

3 4 5 6

Each angle is 90°

Each angle is 90°

square trapezoid rhombus rectangle kite parallelogram

quadrilateralparallelogram

rhombus

Common Errors? Misconceptions?

2012 - SUGGESTED PRACTICE FOR SOL 7.7The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid.a) Identify the classifications to which this figure belongs.

Parallelogram Trapezoid Quadrilateral Rhombus Rectangle

b) Select each figure that appears to be a rectangle.

All angles in this figureare 90 degrees.

All angles in this figureare 90 degrees. Common Errors?

Misconceptions?

2013 - SUGGESTED PRACTICE FOR SOL 7.7Students need additional practice classifying an image of a rhombus.

Which classifications describe this figure?

Parallelogram Trapezoid Quadrilateral Square Rhombus Rectangle

Common Errors? Misconceptions?

2013 - SUGGESTED PRACTICE FOR SOL 7.7Students need additional practice differentiating between an image of a rhombus and a parallelogram.

Which classifications appear to describe both of these figures?

Parallelogram Trapezoid Quadrilateral Square Rhombus Rectangle

Common Errors? Misconceptions?

2013 - SUGGESTED PRACTICE FOR SOL 7.7Students need additional practice identifying the properties of a rhombus.

Select each property that is true for any rhombus.

There is exactly one pair of parallel sides.

There are exactly two pairs of parallel sides.

There are exactly four congruent sides.

There are exactly four right angles.

There are exactly two pairs of congruent opposite angles.

There are exactly four congruent angles.Common Errors? Misconceptions?

Focus: Properties and RelationshipsFocus: Relationships between FiguresFocus: Problem Solving with 2- and 3-Dimensional Figures

VERTICAL ARTICULATION OF CONTENT

2014 SPBQ DATA – 6.12, 8.10Grade Description of Question % Correct in

Division

6 Use attributes to identify congruent polygons. 67

8 Verify and apply the Pythagorean Theorem to find any missing side of a right triangle.

46

8 Verify and apply the Pythagorean Theorem to find any missing side of a right triangle.

36

8 Verify and apply the Pythagorean Theorem to find any missing side of a right triangle.

59

PERFORMANCE ANALYSIS COMPARISONSOL 6.12, 8.102012SOL 6.12 – NoneSOL 8.10 – None

2013SOL 6.12 – NoneSOL 8.10 – None – Really???

Focus: Properties and RelationshipsFocus: Relationships between FiguresFocus: Problem Solving with 2- and 3-Dimensional Figures

VERTICAL ARTICULATION OF CONTENT

2014 SPBQ DATA – 8.11

Grade Description of Question % Correct in Division

8 Solve practical area and perimeter problems involving composite plane figures.

44

8 Solve practical area and perimeter problems involving composite plane figures.

23

PERFORMANCE ANALYSIS COMPARISONSOL 8.112012SOL 8.11 – The student will solve practical area and perimeter problems involving composite plane figures.

2013SOL 8.11 – The student will solve practical area and perimeter problems involving composite plane figures.

2012 - SUGGESTED PRACTICE FOR SOL 8.11Students need additional practice using addition and subtraction to calculate area and perimeter in problems involving composite plane figures.

a) Find the area and perimeter of this composite figure.

b) A semicircle with a diameter of 2 centimeters is added to the side of the figure labeled 2 cm. Find the approximate area and perimeter of the new figure after this addition.

4 cm

6 cm

10 cm

9 cm

2 cm

Common Errors? Misconceptions?

2012 - SUGGESTED PRACTICE FOR SOL 8.11Students need additional practice solving practical area problems involving composite plane figures.

An artist created a geometric design on a wall. She began by painting a blue circle and then painting a yellow isosceles right triangle on top of the blue circle. This figure shows the artist’s beginning steps.

Point A is the center of the circle. Points B and C lie on the circle. The diameter of the circle is 12 feet.

What is the area of the interior of the circle not covered by triangle ABC, rounded to the nearest whole number?

Common Errors? Misconceptions?

2012 - SUGGESTED PRACTICE FOR SOL 8.11Students need additional practice finding the area and perimeter of composite figures.

Bobby is painting a figure on a banner for a homecoming parade. The figure he is painting consists of an isosceles triangle, a rectangle, and a semicircle, as shown.

a) What is the total area of the figure, rounded to the nearest tenth?

b) What is the total perimeter of the figure, rounded to the nearest tenth?

3ft

10 ft

8 ft5ft

117.1 sq ft

42.6 ft Common Errors? Misconceptions?

RESOURCES

1. ExamView Banks

2. NextLesson.org

3. HCPS Math Website - http://teachers.henrico.k12.va.us/math/courses/

VDOE Enhanced Scope and Sequence Skills - JMU Pivotal Items

4. ExploreLearning

Teaching Strategies

Student Engagement

Activities