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UNIT 5 - 2-D GEOMETRY

DESIGNED TO GET YOUR STUDENTS ENGAGED FROM THE MINUTE THEY WALK INTO YOUR CLASS

Created by: THE HCPS MATHEMATICS CURRICULUM DEVELOPMENT TEAM

http://blogs.henrico.k12.va.us/math

NUMBER SENSE ROUTINES

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Hand Signals

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Number Talks - Number Strings

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Today’s Number

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Today’s Number

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Today’s Number

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Mystery Angle

My angle is acute

When you add me to another angle I create a right angle

7 is the square root of my complement

What’s my angle?

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Alike and Different

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Alike and Different

20⁰

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Math Yapper

DIRECTIONS:

Turn to someone beside you or behind you - have one person face the board and have the other person face the back wall.

Three words will appear on the board - the partner facing the board will try to describe the words WITHOUT using the word itself, so the partner can guess what the words are.

When your partner has guessed all three words, sit down silently!

Math Yapper - Partner A

REMEMBER - YOU CAN’T USE THESE WORDS!!

VERTEX

SUPPLEMENT

VERTICAL ANGLE

REMEMBER - YOU CAN’T USE THESE WORDS!!

COMPLEMENTARY ANGLES

CONGRUENT

ADJACENT

Math Yapper - Partner B

DIRECTIONS:

Now switch places with your partner.

Three NEW words will appear on the board - the partner facing the board will try to describe the words WITHOUT using the word itself, so the partner can guess what the words are.

When your partner has guessed all three words, sit down silently!

Teaching NOTE: PLAY this slide as you preview so that you can see how it will work! This content contained on this slide is the SAME as that on the next three slides!

Topic: Math Yapper/Angles

Routine: This number sense routine helps students consider key vocabulary in a unit. The teacher should ensure students are paired up and explain the rules, emphasizing that students can describe the words to their partners by using examples, vocabulary, etc. but cannot use the specific word shown. After both rounds, teacher should facilitate a student-led discussion to include observations, examples, etc.

Sample Responses/Teacher Talking Points:

What did you notice/wonder about this activity?
What did you use to describe your word? Does anyone have a different example?
What might have been difficult about this task?

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Math Yapper

DIRECTIONS:

Turn to someone beside you or behind you - have one person face the board and have the other person face the back wall.

Three words will appear on the board - the partner facing the board will try to describe the words WITHOUT using the word itself, so the partner can guess what the words are.

When your partner has guessed all three words, sit down silently!

Teaching NOTE: Use this slide in conjunction with the next two slides if you are “snipping” to include in a flipchart or other presentation. Use the version on the previous slide if you will conduct the Number Sense Routine through this presentation.

Topic: Math Yapper/Angles

Routine: This number sense routine helps students consider key vocabulary in a unit. The teacher should ensure students are paired up and explain the rules, emphasizing that students can describe the words to their partners by using examples, vocabulary, etc. but cannot use the specific word shown. After both rounds, teacher should facilitate a student-led discussion to include observations, examples, etc.

Sample Responses/Teacher Talking Points:

What did you notice/wonder about this activity?
What did you use to describe your word? Does anyone have a different example?
What might have been difficult about this task?

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Math Yapper - Partner A

REMEMBER - YOU CAN’T USE THESE WORDS!!

COMPLEMENTARY ANGLES

CONGRUENT

ADJACENT

Teaching NOTE: Use this slide in conjunction with the slides immediately before and after it, if you are “snipping” to include in a flipchart or other presentation. Use the other version (two slides previous) if you will conduct the Number Sense Routine through this presentation.

Topic: Math Yapper/Angles

Routine: This number sense routine helps students consider key vocabulary in a unit. The teacher should ensure students are paired up and explain the rules, emphasizing that students can describe the words to their partners by using examples, vocabulary, etc. but cannot use the specific word shown. After both rounds, teacher should facilitate a student-led discussion to include observations, examples, etc.

Sample Responses/Teacher Talking Points:

What did you notice/wonder about this activity?
What did you use to describe your word? Does anyone have a different example?
What might have been difficult about this task?

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Math Yapper - Partner B

REMEMBER - YOU CAN’T USE THESE WORDS!!

VERTEX

SUPPLEMENT

VERTICAL ANGLE

Teaching NOTE: Use this slide in conjunction with the two slides immediately before it, if you are “snipping” to include in a flipchart or other presentation. Use the other version (three slides previous) if you will conduct the Number Sense Routine through this presentation.

Topic: Math Yapper/Angles

Routine: This number sense routine helps students consider key vocabulary in a unit. The teacher should ensure students are paired up and explain the rules, emphasizing that students can describe the words to their partners by using examples, vocabulary, etc. but cannot use the specific word shown. After both rounds, teacher should facilitate a student-led discussion to include observations, examples, etc.

Sample Responses/Teacher Talking Points:

What did you notice/wonder about this activity?
What did you use to describe your word? Does anyone have a different example?
What might have been difficult about this task?

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Fill in the Blank

Directions: Using the digits 0 through 9 at most one time, fill in the boxes to make the statement true.

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Fill in the Blank

Directions: Using the digits 0 through 9 at most one time, fill in the boxes to make the sum of the interior angles of a triangle.

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Number Lines

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Number Lines

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How Do You Know?

How do you know these are vertical angles?

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Quick Images

Topic: SOL 8.5 - Angles

Routine: The teacher will click to display the image. The image will only be shown for 3 seconds. Once the image disappears, students are asked to tell the quantity or draw what they can remember seeing. When the teacher sees that most students have drawn all they can, he/she will click to display the image for three more seconds. Once the image disappears again students will continue drawing. At this time, students can compare drawings and either discuss in pairs or as a whole class how they developed their drawings. The Quick Images routine develops mental imagery, builds vocabulary, improves spatial memory, and teaches students to analyze mental images.

Guiding questions: “What did you see?” “How did you draw it?” “What are figures that you see?”

Sample Responses/Teacher Talking Points:

3 different colored angle images
Green image creates two angles that appear to be supplementary
Red angle is obtuse
Blue angle is acute
Red and blue angle look like they mirror the two angles in the green image
Red and blue angles could be supplementary
Blue angle is less than 90; red is more than 90

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Which One Doesn’t Belong?

Topic: SOL 8.5 - Angles

Routine (Which One Doesn’t Belong): Students will determine which figure(s)/statement(s) they think do not belong and provide a justification. There is no correct solution, but rather students should be encouraged to use their knowledge of symmetry to figure out a reason why each shape may not belong. This routine will strengthen students skills in comparative thinking, connecting and communicating mathematical ideas, and critical thinking.

Sample Responses/Teacher Talking Points:

Top Left: only one with pairs of vertical angles; only one with supplementary angles
Top Right: only one with a single angle shown (straight angle) instead of a pair; only one with 2 colors in the diagram
Bottom Left: only box with a border; only box with no color; the only complementary angles
Bottom Right: only rectangle that is not blue; only diagram with two separate angles; only pair of angles that are both congruent and supplementary

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Alike and Different

Topic: SOL 8.5 Angles

Routine (Alike and Different): Students are presented with two or more numbers, shapers, properties, etc. and are asked to think about and suggest the similarities and differences between the objects. The teacher can record the students ideas on the board in a T-chart. This routine will strengthen students skills in comparative thinking, connecting and communicating mathematical ideas, and critical thinking.

Sample Responses/Teacher Talking Points:

ALIKE: Same colors; both are traffic/street signs; both images in the signs create angles; both have a pair of supplementary angles; both images have adjacent angles; both appear to have right angles; neither have complementary angles
DIFFERENT: Signs are different shapes; one is for railroads, one is for roads; one has letters and the other does not have letters; the RR crossing sign has pairs of vertical angles, the other does not; the RR crossing sign has multiple pairs of supplementary angles, the other has only one pair; RR crossing sign has no straight angle.

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Today’s Numbers

5, 12, 13

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Fill in the Blank

Directions: What could the lengths of the legs be such that the lengths of the legs are integers and x is an irrational number between 5 and 7?

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Alike and Different

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Fill in the Blank

Use the numbers 1 thru 10 to fill in

the side lengths of the triangle so

that it creates a true right triangle.

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What Do You Know?

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Quick Images

Topic: Pythagorean Theorem

Image appears and disappears on mouse click.

Routine: The teacher will click to display the image. The image will only be shown for 3 seconds. Once the image disappears, students are asked to tell the quantity or draw what they can remember seeing. When the teacher sees that most students have drawn all they can, he/she will click to display the image for three more seconds. Once the image disappears again students will continue drawing. At this time, students can compare drawings and either discuss in pairs or as a whole class how they developed their drawings. The Quick Images routine develops mental imagery, builds vocabulary, improves spatial memory, and teaches students to analyze mental images.

Guiding questions: “What did you see?” “How did you draw it?” “What are figures that you see?”

Sample Responses/Teacher Talking Points:

A triangle with sides labeled a, b and c
Squares on each side on the triangle
A/B= legs
C= Hypotenuse

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Mystery Number

I am a side of a right triangle.

I am the longest side in the triangle.

One of my legs is the square root of 25.

My other leg is the square root of 144.

What is my length?

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Mystery Number

I am a 2 digit number.

I am the length of the hypotenuse in a right triangle.

The sum of my digits makes an odd number.

My first digit is even.

I am a perfect square number.

I am part of a Pythagorean Triple.

My longer leg measures 24 units.

My shorter leg measures 7 units.

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Alike and Different

Topic: Pythagorean Theorem

Routine (Which One Doesn’t Belong): Students will determine which figure(s)/statement(s) they think do not belong and provide a justification. There is no correct solution, but rather students should be encouraged to use their knowledge of symmetry to figure out a reason why each shape may not belong. This routine will strengthen students skills in comparative thinking, connecting and communicating mathematical ideas, and critical thinking.

Sample Responses/Teacher Talking Points:

Top left: Only one where the hypotenuse (which should be the longest side in a right triangle), is not; the 20 and 25 have been reversed

Top right: A true “pythagorean triple”

Bottom left: A pythagorean triple (3-4-5 times 10)

Bottom right: these could NOT be the sides of a right triangle

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Alike and Different

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Alike and Different

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Which One Doesn’t Belong

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Which One Doesn’t Belong?

okay

6, 8, 10	9, 12, 15
1, 4, 7	3, 4, 5

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Today’s Image

Topic: Pythagorean Theorem

Routine: Students are presented with an image that may or may not have an obvious answer. Students work individually, or in small groups, to think about the question, then discuss their explanations. This routine will strengthen students’ ability to defend their thinking with mathematical reasoning. This routine will place the emphasis on process and remind students that the thinking behind the answer is as important - or more so - than the answer itself.

Sample Responses/Teacher Talking Points:

The bunny sits 12 units/feet from the base of the tree.
The bunny sits 20 units/feet from the top of the tree.
There is a right triangle represented in the image.
The length of the hypotenuse is 20 units/feet.
One of the legs measures 12 units/feet.
The missing side can be found using the Pythagorean Theorem.
The tree is 16 units/feet tall.

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Prove Me Wrong

Antonio climbed a seven-foot ladder to the top of a slide. The slide is ten feet long. Approximately how far away is the bottom of the ladder from the end of the slide?

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How Do You Know?

This is a right triangle.

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Quick Images

Topic: Pythagorean Theorem

Image appears and disappears on mouse click.

Routine: The teacher will click to display the image. The image will only be shown for 3 seconds. Once the image disappears, students are asked to tell the quantity or draw what they can remember seeing. When the teacher sees that most students have drawn all they can, he/she will click to display the image for three more seconds. Once the image disappears again students will continue drawing. At this time, students can compare drawings and either discuss in pairs or as a whole class how they developed their drawings. The Quick Images routine develops mental imagery, builds vocabulary, improves spatial memory, and teaches students to analyze mental images.

Guiding questions: “What did you see?” “How did you draw it?” “What are figures that you see?”

Sample Responses/Teacher Talking Points:

There is a right triangle
The legs are 15 and 8
The hypotenuse is missing (x)
The value of x is 17

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How Do You Know?

You leave your house and travel 10 miles to the movie theater. After the movie you travel 6 miles to the bowling alley. At the end of the day you travel home. If your house, movie theater, and bowling alley create a right triangle, how do you know the missing length is less than 10 miles but more than 6 miles?

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Alike and Different

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Which One Doesn’t Belong?

Topic: Composite Figures

Routine (Which One Doesn’t Belong): Students will determine which figure(s)/statement(s) they think do not belong and provide a justification. There is no correct solution, but rather students should be encouraged to use their knowledge of symmetry to figure out a reason why each shape may not belong. This routine will strengthen students skills in comparative thinking, connecting and communicating mathematical ideas, and critical thinking.

Sample Responses/Teacher Talking Points:

Top left: Only one that is a rectangle, only one with 4 right angles, only one whose height is also the measure of a side

Top right: Only one that is a trapezoid, only one that has side (base) measures of 8 and 12.

Bottom left: Only one that is a triangle, and the only one whose area is not 40 square units

Bottom right: Only one that is a parallelogram that is not also a rectangle

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Which One Doesn’t Belong?

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Quick Images

Topic: Composite Figures

Image appears and disappears on mouse click.

Routine: The teacher will click to display the image. The image will only be shown for 3 seconds. Once the image disappears, students are asked to tell the quantity or draw what they can remember seeing. When the teacher sees that most students have drawn all they can, he/she will click to display the image for three more seconds. Once the image disappears again students will continue drawing. At this time, students can compare drawings and either discuss in pairs or as a whole class how they developed their drawings. The Quick Images routine develops mental imagery, builds vocabulary, improves spatial memory, and teaches students to analyze mental images.

Guiding questions: “What did you see?” “How did you draw it?” “What are figures that you see?”

Sample Responses/Teacher Talking Points:

There is a semi-circle and a rectangle
The radius of the circle is 5
Can find the area
It looks like a basketball free throw line or soccer field

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Quick Images

Topic: Composite Figure

Image appears and disappears on mouse click.

Routine: The teacher will click to display the image. The image will only be shown for 3 seconds. Once the image disappears, students are asked to tell the quantity or draw what they can remember seeing. When the teacher sees that most students have drawn all they can, he/she will click to display the image for three more seconds. Once the image disappears again students will continue drawing. At this time, students can compare drawings and either discuss in pairs or as a whole class how they developed their drawings. The Quick Images routine develops mental imagery, builds vocabulary, improves spatial memory, and teaches students to analyze mental images.

Guiding questions: “What did you see?” “How did you draw it?” “What are figures that you see?”

Sample Responses/Teacher Talking Points:

Broken into a rectangle and right triangle
Can find the area/perimeter

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Quick Images

Topic: SOL 8.10 - Composite Figures

Routine: The teacher will click to display the image. The image will only be shown for 3 seconds. Once the image disappears, students are asked to tell the quantity or draw what they can remember seeing. When the teacher sees that most students have drawn all they can, he/she will click to display the image for three more seconds. Once the image disappears again students will continue drawing. At this time, students can compare drawings and either discuss in pairs or as a whole class how they developed their drawings. The Quick Images routine develops mental imagery, builds vocabulary, improves spatial memory, and teaches students to analyze mental images.

Guiding questions: “What did you see?” “How did you draw it?” “What are figures that you see?”

Sample Responses/Teacher Talking Points:

What did you see: House, rectangle and triangle; graph; 2 x 4 rectangle; triangle is bigger than the rectangle; house

wiith a roof

Rectangle - area is 2 x 4 = 8 (l x w); Triangle - area is 0.5 x 6 x 3 = 9; total area: 8 + 9 = 17
Could split the triangle into two equal right triangles
Could find perimeter if you used Pythagorean Theorem on one small right triangle to find missing side and doubleed it
Perimeter - count the straight measures and add the perimeter of the triangle after P.T.

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Quick Images

Topic: Translations

Routine: The teacher will click to display the image. The image will only be shown for 3 seconds. Once the image disappears, students are asked to tell the quantity or draw what they can remember seeing. When the teacher sees that most students have drawn all they can, he/she will click to display the image for three more seconds. Once the image disappears again students will continue drawing. At this time, students can compare drawings and either discuss in pairs or as a whole class how they developed their drawings. The Quick Images routine develops mental imagery, builds vocabulary, improves spatial memory, and teaches students to analyze mental images.

Guiding questions: “What did you see?” “How did you draw it?” “What are figures that you see?”

Sample Responses/Teacher Talking Points:

Translation
Composite figure (inside 5 x 5 square)
17 dots (kids may say 18
Line of symmetry

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Math Yapper

DIRECTIONS:

Turn to someone beside you or behind you - have one person face the board and have the other person face the back wall.

Three words will appear on the board - the partner facing the board will try to describe the words WITHOUT using the word itself, so the partner can guess what the words are.

When your partner has guessed all three words, sit down silently!

Math Yapper - Partner A

REMEMBER - YOU CAN’T USE THESE WORDS!!

RADIUS

PERIMETER

CONGRUENT

REMEMBER - YOU CAN’T USE THESE WORDS!!

CIRCUMFERENCE

SUBDIVIDE

AREA

Math Yapper - Partner B

DIRECTIONS:

Now switch places with your partner.

Three NEW words will appear on the board - the partner facing the board will try to describe the words WITHOUT using the word itself, so the partner can guess what the words are.

When your partner has guessed all three words, sit down silently!

Teaching NOTE: PLAY this slide as you preview so that you can see how it will work! This content contained on this slide is the SAME as that on the next three slides!

Topic: Math Yapper/Composite Figures

Routine: This number sense routine helps students consider key vocabulary in a unit. The teacher should ensure students are paired up and explain the rules, emphasizing that students can describe the words to their partners by using examples, vocabulary, etc. but cannot use the specific word shown. After both rounds, teacher should facilitate a student-led discussion to include observations, examples, etc.

Sample Responses/Teacher Talking Points:

What did you notice/wonder about this activity?
What did you use to describe your word? Does anyone have a different example?
What might have been difficult about this task?

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Math Yapper

DIRECTIONS:

Turn to someone beside you or behind you - have one person face the board and have the other person face the back wall.

Three words will appear on the board - the partner facing the board will try to describe the words WITHOUT using the word itself, so the partner can guess what the words are.

When your partner has guessed all three words, sit down silently!

Teaching NOTE: Use this slide in conjunction with the next two slides if you are “snipping” to include in a flipchart or other presentation. Use the version on the previous slide if you will conduct the Number Sense Routine through this presentation.

Topic: Math Yapper/Composite Figures

Routine: This number sense routine helps students consider key vocabulary in a unit. The teacher should ensure students are paired up and explain the rules, emphasizing that students can describe the words to their partners by using examples, vocabulary, etc. but cannot use the specific word shown. After both rounds, teacher should facilitate a student-led discussion to include observations, examples, etc.

Sample Responses/Teacher Talking Points:

What did you notice/wonder about this activity?
What did you use to describe your word? Does anyone have a different example?
What might have been difficult about this task?

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Math Yapper - Partner A

REMEMBER - YOU CAN’T USE THESE WORDS!!

CIRCUMFERENCE

SUBDIVIDE

AREA

Teaching NOTE: Use this slide in conjunction with the slides immediately before and after it, if you are “snipping” to include in a flipchart or other presentation. Use the other version (two slides previous) if you will conduct the Number Sense Routine through this presentation.

Topic: Math Yapper/Composite Figures

Routine: This number sense routine helps students consider key vocabulary in a unit. The teacher should ensure students are paired up and explain the rules, emphasizing that students can describe the words to their partners by using examples, vocabulary, etc. but cannot use the specific word shown. After both rounds, teacher should facilitate a student-led discussion to include observations, examples, etc.

Sample Responses/Teacher Talking Points:

What did you notice/wonder about this activity?
What did you use to describe your word? Does anyone have a different example?
What might have been difficult about this task?

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Math Yapper - Partner B

REMEMBER - YOU CAN’T USE THESE WORDS!!

RADIUS

PERIMETER

CONGRUENT

Teaching NOTE: Use this slide in conjunction with the two slides immediately before it, if you are “snipping” to include in a flipchart or other presentation. Use the other version (three slides previous) if you will conduct the Number Sense Routine through this presentation.

Topic: Math Yapper/Composite Figures

Routine: This number sense routine helps students consider key vocabulary in a unit. The teacher should ensure students are paired up and explain the rules, emphasizing that students can describe the words to their partners by using examples, vocabulary, etc. but cannot use the specific word shown. After both rounds, teacher should facilitate a student-led discussion to include observations, examples, etc.

Sample Responses/Teacher Talking Points:

What did you notice/wonder about this activity?
What did you use to describe your word? Does anyone have a different example?
What might have been difficult about this task?

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Today’s Image

Topic: Pythagorean Theorem

Routine: Students are presented with an image that may or may not have an obvious answer. Students work individually, or in small groups, to think about the question, then discuss their explanations. This routine will strengthen students’ ability to defend their thinking with mathematical reasoning. This routine will place the emphasis on process and remind students that the thinking behind the answer is as important - or more so - than the answer itself.

Sample Responses/Teacher Talking Points:

The red, green, and red segments form a right triangle.
The length of the blue segment can be found by counting the horizontal distance between (-3, 2) and (4, 2).
The blue segment is 7 units long.
The length of the green segment can be found by counting the vertical distance between (-3, -1) and (-3, 2).
The green segment is 3 units long.
The length of the red segment cannot be found by counting on the coordinate plane.
The length of the red segment can be found using the Pythagorean Theorem.
The red segment is the square root of 58, or approximately 7.6 units long.

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How Do You Know?

The perimeter of the composite figure below is less than the perimeter of each figure separately.

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How Do You Know?

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Which One Doesn’t Belong?

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Quick Images - How Many Windows?

Topic: SOL 8.10 - Composite Figures

Routine: The teacher will click to display the image. The image will only be shown for 3 seconds. Once the image disappears, students are asked to tell the quantity or draw what they can remember seeing. When the teacher sees that most students have drawn all they can, he/she will click to display the image for three more seconds. Once the image disappears again students will continue drawing. At this time, students can compare drawings and either discuss in pairs or as a whole class how they developed their drawings. The Quick Images routine develops mental imagery, builds vocabulary, improves spatial memory, and teaches students to analyze mental images.

Guiding questions: “What did you see?” “How did you draw it?” “What are figures that you see?”

Sample Responses/Teacher Talking Points:

What shapes did you notice?
What strategies did you use to estimate the number of glass panes?
Bottom row - 3 sections each; in each section, two tall rectangles and 6 squares (total of 6 rectangles; 18 squares)
Middle row - 3 sections of 4 x 5 = 20 each; 60 total
Top - 2 rows of 5 (10) squares; semi-circle on top
How would we find the area of these windows? Perimeter?

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Prove Me Wrong

Topic: SOL 8.10 - Composite Figures

Routine: Students are presented with sample student work. They are asked to analyze the work to identify the error, explain the error, and fix the mistake. Students should be expected to explain their thinking and the sample student’s misconception(s).

Sample Responses/Teacher Talking Points:

What do you notice?
What information do you have with this image?
What information do you still need?
How do we find missing measures with a shape like this?

SOLUTION: (Starting with 2cm on the side and going clockwise): 2+4+1+2+4+2+1+4 = 20 cm

Students who incorrectly answered 12 - they just added the given sides

Students who incorrectly answered 18 - they did not count the two small 1 cm pieces

ALSO INCORRECT: Answer is given in inches, not cm as shown

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Would You Rather...

Your yard needs 1600 sq. feet of sod.

Would you rather use Sample A or Sample B?

Topic: 8.10 - Composite Figures

Routine: Would You Rather - students will explain their thought process on which option they would prefer and their reasoning behind this.

Guiding questions:

Have students explain what processes they used to break each part down in order to compare the two quantities
Which, if any, was more difficult to compute? Why?
What information would you want to consider when making this purchase?

Cost of each sample; if the size of the sample would require you to use more/less

Sample Responses/Teacher Talking Points:

SAMPLE A: Prefer the basic square shape; easy to calculate the area (l x w = 16) - would need 100 of them
SAMPLE B: Depending on the shape of the lawn, these might fit better?
NEITHER - the samples are the same area, although the shape is much different .

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Mystery Image

Topic: SOL 8.10 - Composite Figures

Routine: Students work individually, in pairs or in small groups to determine a mystery number when given a set of clues. Clues may be presented all together or given one at a time. The creation, sharing and use of clues provides a wealth of experiences with a variety of mathematical ideas. Some of the same ideas that are shared as part of “Today’s Number” may be presented in the clues for the mystery number, but these clues push for a higher level of reasoning.

Sample Responses/Teacher Talking Points:

What do you notice? What do you wonder?
The whole shape is: pink, looks like a duck, looks like a submarine
Could be broken down into several smaller shapes
Base can be broken into triangle, rectangle, trapezoid OR two trapezoids
“Flag” or “Head of the Duck” can be a trapezoid or a rectangle and triangle

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Mystery Image

Topic: SOL 8.10 - Composite Figures

Routine: Students work individually, in pairs or in small groups to determine a mystery number when given a set of clues. Clues may be presented all together or given one at a time. The creation, sharing and use of clues provides a wealth of experiences with a variety of mathematical ideas. Some of the same ideas that are shared as part of “Today’s Number” may be presented in the clues for the mystery number, but these clues push for a higher level of reasoning.

Sample Responses/Teacher Talking Points:

What do you notice? What do you wonder?
Does anyone see a different combination or image?
The whole shape is: blue/purple; shape looks like a boat?
Could be broken down into several smaller shapes
Base could be two triangles and a rectangle or one trapezoid
Top could be a paralellogram and triangle, or could be two triangles and a rectangle

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Number Task

You and a partner are tasked with laying the tile for this pool. What information will you need?

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Mystery Number

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Alike and Different

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Alike and Different

Topic: SOL 8.7 - Transformations

Routine (Alike and Different): Students are presented with two or more numbers, shapers, properties, etc. and are asked to think about and suggest the similarities and differences between the objects. The teacher can record the students ideas on the board in a T-chart. This routine will strengthen students skills in comparative thinking, connecting and communicating mathematical ideas, and critical thinking.

Sample Responses/Teacher Talking Points:

Alike:

Both are squares
Both squares are the same size
Both have point labeled A, B, C, D and A’, B’, C’, D’
Pre-image in both is in Quadrant II
Squares in example on the Left

Different

Image on the left shows a translation; image on the right shows a reflection
Images in both are in different quadrants
Color of both squares is different in image on the right, but the same in image on the left

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Alike and Different

Topic: SOL 8.7 - Transformations

Routine (Alike and Different): Students are presented with two or more numbers, shapers, properties, etc. and are asked to think about and suggest the similarities and differences between the objects. The teacher can record the students ideas on the board in a T-chart. This routine will strengthen students skills in comparative thinking, connecting and communicating mathematical ideas, and critical thinking.

Sample Responses/Teacher Talking Points:

Alike:

Both are triangles
Both show only Quadrant 1
Both show dilations

Different

Left image: graph counts by units of 1; right - units of 2
Left: Image gets smaller; right, image gets larger
Left: dilated by a scale factor that is a fraction; right is dilated by a scale factor that is a whole number
Left - triangles are solid colors; right - just outline

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Guess That Transformation

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Mystery Transformation

What transformation(s) could take place for Point C’ to be located in a different quadrant?

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Notice and Wonder

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Two Truths and a Lie

Which statement is NOT true about the image of Point A (-2, 4)?

1.) Point A’ will be in Quadrant I after a reflection across the

y-axis.

2.) Point A’ will be in Quadrant III after a translation of 5 units to the

right and 3 units down.

3.) Point A’ will be in Quadrant II after a dilation with a scale factor

of 2.

Topic: SOL 8.7 - Transformations

Routine: Two Truths and a Lie - students will read three statements/potential answers to a given question - two of the statements would be correct and one would be incorrect. Students can justify both how they know the one statement is a lie/incorrect as well as how they know the other two statements are truths/correct statements.

Sample Responses/Teacher Talking Points:

What do you wonder about this question?
What do you know about Point A? What do you need to know?

We know Point A is in Quadrant II originally (pre-image)
We know we start at the origin and go 2 left, 4 up to get to the pre-image of Point A
We need to know what quadrant it will be in after the transformation

Statement 1 - TRUE - if we reflect over the y-Axis, Point A’ will be at (2, 4), which is in the 1st quadrant
Statement 2 - FALSE/LIE - if you translate 5 right and 3 down, you will be in the 1st quadrant, not Quadrant III
Statement 3 - TRUE - if we reflect over the x-axis, Point A’ will be at (-2,-4)

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Transform This!

Describe how the image of this cup will look after a given transformation.

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Quick Images

Topic: Transformations

Image appears and disappears on mouse click.

Routine: The teacher will click to display the image. The image will only be shown for 3 seconds. Once the image disappears, students are asked to tell the quantity or draw what they can remember seeing. When the teacher sees that most students have drawn all they can, he/she will click to display the image for three more seconds. Once the image disappears again students will continue drawing. At this time, students can compare drawings and either discuss in pairs or as a whole class how they developed their drawings. The Quick Images routine develops mental imagery, builds vocabulary, improves spatial memory, and teaches students to analyze mental images.

Guiding questions: “What did you see?” “How did you draw it?” “What are figures that you see?”

Sample Responses/Teacher Talking Points:

Dilation- could be the smaller one multiplied by a whole number or the larger one multiplied by a fraction

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Quick Images

Topic: Transformations

Image appears and disappears on mouse click.

Routine: The teacher will click to display the image. The image will only be shown for 3 seconds. Once the image disappears, students are asked to tell the quantity or draw what they can remember seeing. When the teacher sees that most students have drawn all they can, he/she will click to display the image for three more seconds. Once the image disappears again students will continue drawing. At this time, students can compare drawings and either discuss in pairs or as a whole class how they developed their drawings. The Quick Images routine develops mental imagery, builds vocabulary, improves spatial memory, and teaches students to analyze mental images.

Guiding questions: “What did you see?” “How did you draw it?” “What are figures that you see?”

Sample Responses/Teacher Talking Points:

Reflection - the image has been reflected across the y-axis, then translated down 2 units and to the right one unit
Alternate interpretation - the image has been translated down 2 units and to the left 1 unit, THEN reflected across the y-axis

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Quick Images

Topic: SOL 8.7 - Transformations

Routine: The teacher will click to display the image. The image will only be shown for 3 seconds. Once the image disappears, students are asked to tell the quantity or draw what they can remember seeing. When the teacher sees that most students have drawn all they can, he/she will click to display the image for three more seconds. Once the image disappears again students will continue drawing. At this time, students can compare drawings and either discuss in pairs or as a whole class how they developed their drawings. The Quick Images routine develops mental imagery, builds vocabulary, improves spatial memory, and teaches students to analyze mental images.

Guiding questions: “What did you see?” “How did you draw it?” “What are figures that you see?”

Sample Responses/Teacher Talking Points:

Columns
Getting further away
Appear to be getting smaller from front to back or larger from back to front
Real world - they are probably the same size, so this is an example of a translation
Discussion about dilation - if we just used the image itself and took out the distance, it may appear as a dilation

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Prove Me Wrong

Point N’ will be in Quadrant 3 after a reflection about the x-axis and a translation of 5 down.