# 4 Piece Jigsaw Puzzle Template

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```					                         Fourth Grade – 3rd 9 Weeks
Unit 2: Probability, Measurement, and Geometry

Focus of Unit: The study of translations, rotations, and reflections.

Investigation 1: Geometry

Part 1: Introduction to Translations, Rotations, and Reflections

Part 2: Reflection and Symmetry                          Note: Use SBISD
lessons as good first
Part 3: Translations – A Tessellation lesson             instruction and
textbook lessons as
Part 4: Rotation – A Tessellation lesson                 supplemental
resources.
Part 5: How to use translations, rotations, and reflections as a tool

Workstations

HSP Math Lesson Correlation
Unit 4 Geometry
Chapter 11 Transformations, Symmetry, & Congruence
 11.1 Congruent Figures                                    Note: 11.7
 11.2 Translations                                         Tessellations
 11.3 Rotations                                            may be used as
 11.4 Reflections                                          enrichment
 11.5 Symmetry
 11.6 Problem Solving Strategy: Act it Out

Hands-On Standards – Book 3-4
Geometry
 Lesson 8 Congruent & Similar Figures
 Lesson 9 Symmetrical Figures
 Lesson 10 Tangram Puzzles
 Lesson 11 Tiling Patterns
 Lesson 12 Tessellations
 Lesson 14 Flips(Reflections)
 Lesson 15 Rotational Symmetry
 Lesson 16 Vertical & Horizontal Line Symmetry

Grade 4 – 3rd 9 Weeks                   1
SBISD 2006-2007
Unit 2: Probability, Measurement, and Geometry

Notes
Problem Solving Investigation 1: Geometry
“In a differentiated
Part 1: Introduction of Translation, Rotation, and Reflection                     classroom, the teacher
(Physical Lesson)                                                                 proactively plans and
carries out varied
TEKS:                                                                             approaches to content,
4.9A Demonstrate translations, reflections, and rotations using concrete          process, and product
models (TAKS 3)                                                             in anticipation of and
4.9B Use translations, reflections, and rotations to verify that two shapes       response to student
are congruent (TAKS 3)                                                      differences in
4.9C Use reflections to verify that a shape has symmetry (TAKS 3)                 readiness, interest,
and learning needs.”
4.14A Identify the mathematics in everyday situations (TAKS 6)
Carol Ann Tomlinson,
4.14B Use problem solving model (TAKS 6)                                          How to Differentiate
4.14C Independently use the problem solving model and apply strategies            Instruction in Mixed
(TAKS 6)                                                                    Ability Classrooms
4.14D Use tools to solve problems (TAKS 6)
4.15A Explain/ record observations (TAKS 6)                                       Review your
4.15B Relate informal language to math language and symbols (TAKS 6)              Mathematics
4.16A Make generalizations (TAKS 6)                                               Standards to
4.16B Justify why an answer is reasonable and explain the solution process        understand how this
(TAKS 6)                                                                    concept is assessed
on TAKS and to guide
you in your evaluation
Vocabulary:                                                                       of students’ progress.
Translation            Traslación
Rotation               Rotación                                                   Display Vocabulary
Reflection             Reflexión                                                  on a Math Work Wall
Horizontal             Horizontal                                                 for future reference
Vertical               Vertical                                                   and activities
Parallel               Paralelo
Perpendicular          Perpendicular
Attribute              Atributo

Materials:
Pentominoes                                                                       Using the SBISD Fact
Strategy Packet
Literature:                                                                       strengthens and
The Greedy Triangle by Marilyn Burns                                              reinforces facts at
The Amazing Book of Shapes by Lydia Sharman (includes projects)                   individual student’s
Reflections by Ann Jonas                                                          level of ability. TEKS
4.4C, 4.6A
Student Handouts:                                                                 & subtraction to 18;
Paper letters (ex. Die Cut letters) – 1st initial letter of each student’s name   multiplication and
related division fact
Procedures:                                                                       families: x1, doubles
Practice Facts Daily                                                              (x2), doubles and
double again (x4), x5,
x10, x11, squares,
double & one more set
(x3), x9, x12, half then
double (x6, x8), x7
Grade 4 – 3rd 9 Weeks                          2
SBISD 2006-2007
Opening Activity: Parallel and perpendicular lines review:
Have students find 3 examples of parallel lines and three examples of                Notes
perpendicular lines in the classroom. Give them a 2 minute time limit
and then share findings.

Mini Lesson:
1. Remind students that shapes have attributes. Ask for examples of
attributes such as angles and sides.
2. Ask students “Will the attributes of a shape change if we changed the
position of the shape?” (No)
3. Tell students that there are three ways that a shape can move and
that they’re going to use some body movements to help them
remember.
4. The first is translation, which is a sliding action. Link “SL” in
translation to a slide. Have students move their hands or their body to
demonstrate a slide.
5. The second is rotation, which is turning in a clockwise or counter
clockwise direction. Link “T” in rotation to turning. Have students
again demonstrate the turning motion with their hands or their bodies.
6. The third motion is reflection, which is a flipping action (like a mirror
image). Link the “FL” in reflection to flipping. Have student
demonstrate with their hand or their bodies the flipping action.
7. Say, “Knowing these movements can tell us whether a shape has
changed or not.”
8. Provide students with examples. Display a pentominoe on the
overhead. Trace it on a transparency. Draw a vertical line next to the       *Any object can be
pentominoe vertically. Flip the pentominoe and trace it again. Ask           used if pentominoes
students how the pentominoe moved. How do the two tracings look in           are not available.
relation to each other? Remind students that this is an example of a
reflection.
9. Repeat the process of flipping shapes over a line in various directions.
Before flipping have students predict what the shape will look like
after it is flipped. They can describe it verbally or illustrate it.
10. Provide students with a die-cut of the first initial of their name.
11. Tell students to place the letter on paper and trace it. Then flip the
letter over a vertical line and trace it again. You should continue this
process in order to make a pattern.
12. Discuss the patterns:
- How many times did you flip your initial before it looked as it
did originally?
- How would the pattern change if you flipped it over a
horizontal line?
- What do you think the pattern will look if you flipped your initial
horizontally then vertically?
13. Use their initial to show a translation and a rotation. Record by
tracing and labeling.

Reflection:
What body parts may be considered as reflected images of each
other?

Grade 4 – 3rd 9 Weeks                         3
SBISD 2006-2007
Part 2: Reflection and Symmetry                                                  Notes

TEKS:
4.9A    Demonstrate translations, reflections, and rotations using concrete
models (TAKS 3)
4.9B    Use translations, reflections, and rotations to verify that two shapes
are congruent (TAKS 3)
4.9C    Use reflections to verify that a shape has symmetry (TAKS 3)
4.14A   Identify the mathematics in everyday situations (TAKS 6)
4.14B   Use problem solving model (TAKS 6)
4.14C   Independently use the problem solving model and apply strategies
(TAKS 6)
4.14D   Use tools to solve problems (TAKS 6)
4.15A   Explain/ record observations (TAKS 6)
4.15B   Relate informal language to math language and symbols (TAKS 6)
4.16A   Make generalizations (TAKS 6)
4.16B   Justify why an answer is reasonable and explain the solution
process (TAKS 6)

Vocabulary:
Congruent              Congruente
Symmetry               Simetría
Line of symmetry       Línea de simetría
Horizontal             Horizontal
Vertical               Vertical

Materials:
Geoboards
Rubber bands
Dot Paper Transparency

Student Handouts:
Dot Paper

Procedures:
Practice Facts Daily

Opening Activity:
Write several words on a transparency (without students seeing). Flip
the transparency over and display the words. Students will try to figure
out what the words are. Ask students what this activity was a model of
(reflection).

Mini Lesson:
1. Draw a rectangle on the dot paper transparency. Give students a
geoboard and one rubber band. Tell students to make a square that is
congruent to your square. Students hold their board to their chest until
you ask them all to reveal their square.

2. Ask a volunteer to verify that his or her square is congruent. “What
Grade 4 – 3rd 9 Weeks                        4
SBISD 2006-2007
Notes

does congruent mean?” (The figure has the same size and shape.)
3. Draw your triangle on dot paper transparency. Ask students to make a
triangle that is congruent to yours. Again ask students to cover their
sample until everyone is done. When all students are done, have all
students reveal their model. Ask a volunteer to verify and explain how
s/he knows that his or her creation is correct.
4. Use the rubber band to make the letter “O” on your dot paper
transparency. Ask students if they could draw a line through the letter
“O” where one side would be the mirror image or reflection of the other
half. Let a volunteer go to the overhead and draw a line between the two
parts. Confirm with the class that the volunteer completed the task
correctly.
5. Say, “Does anyone know what this line is called?” (Line of symmetry)
Define for students that an object with one line of symmetry can be cut in
half and each half would be the mirror image of the other; one half would
be symmetrical to the other half.
6. To demonstrate symmetry further, show students a piece of rectangular
8 x 11 paper. Fold the paper along the vertical midline and ask whether
or not both sides are symmetrical. Next, fold the paper along the
horizontal midline and ask whether or not both sides are symmetrical.
Does the rectangle have a diagonal line of symmetry? Ask students to
estimate. Then fold the paper along the diagonal to show that one side
would not disappear behind the other, therefore, the rectangle only has
two lines of symmetry, a horizontal and vertical.
7. For an independent activity, ask students to create each letter of their
first name on the geoboard. Record the letters and identify the lines of
symmetry of each letter on dot paper. Find the total number of lines of
symmetry that are in their name.

Reflection:
Find a word whose letters have at least 6 lines of symmetry. Explain
how you found the word.

Grade 4 – 3rd 9 Weeks                      5
SBISD 2006-2007
Part 3: Translation* - A Tessellation Lesson

TEKS:
Notes
4.9A   Demonstrate translation, reflections, and rotations using concrete
models (TAKS 3)
A tessellation is a
4.9B   Use translations, reflections, and rotations to verify that two shapes      repeated pattern of
are congruent (TAKS 3)                                                      polygons covering an
entire area. Ceiling
Vocabulary:                                                                        tiles, floor tiles, a
Tessellation                                                                       honeycomb are all
Translation            Traslación                                                  examples of
Reflection             Reflexión                                                   tessellations. The
Rotation               Rotación                                                    artist Escher used
tessellations to create
elaborate art from a
Materials:                                                                         single shape. Search
Pattern blocks                                                                     for Escher prints on
3 x3 squares (cut index cards or manila folders)                                   the internet to show
White construction paper                                                           students examples of
Scissors                                                                           his work.
Crayons or map pencil
Tape
Teaching Tessellation
Procedures:                                                                        Art
By Jill Britton and
Practice Facts Daily                                                               Walter Britton.
Opening Activity:                                                                  Seymour Publications
Give students 2 pattern blocks to create a design. The students are to          is a good resource if
use their design to show a translation, rotation and reflection, tracing it     you’re interested in
all three ways. Check with a partner.                                           delving further.

Mini Lesson:
1. Define what a tessellation is to students and give an example of
Escher’s art, which used tessellations to create dramatic designs.
2. Give students each a 3 x 3 card stock (index card) square.
Demonstrate to students on transparency before students begin.
Students will cut a small design off the right hand edge of the square.
Slide and tape it to the left hand edge of the square. (Step 1 & 2 – see
below)
3. Apply the same procedure to the bottom edge. Cut, slide, and tape it to
the top edge of the square. This is the students’ template for their
translation. (Step 3 & 4)
4. Have students rotate their shape to see if they can visualize a design.
Students have to give meaning to their shape. For example, when a
person looks at a cloud formation, s/he may see an ice cream cone
where someone else sees a clown. Ask students what their shape
suggests.
5. Afterwards, have students trace their template on paper, translate it so
there is not a gap and continue translating until s/he runs out of room.
Begin a second and third row translating the template.
Once the tracing is done, have students draw in the details and color
their tessellation. Students will then give their artwork a title and write a
brief (3 to 4 sentences) description of how it was created. Be certain
Grade 4 – 3rd 9 Weeks                         6
SBISD 2006-2007
that students include that they used translation to create the effect.           Notes
(Step 5)

Step 1                                 Step 2                         The shaded portion is
the portion that has
been cut out,
translated and taped.

*Assessment – You
may evaluate the
students description of
his/her artwork as one
form of evaluation.
You may also use
Step 3                                      Step 4
worksheet No. 1 on pp
106-107 (English) and
pp 108- 109 (Spanish)
to evaluate students’
understanding of
symmetry.

*After students create
Step 5                                                                tessellation art, they
can try their hand at
Tessellmania, a
software program.
(Check with your
technology SIS to see
if your school has the
software.)

http://www.coolmath.c
om/tesspag1.htm also
provides some
information on
tessellations and its
use with regular
Reflection:                                                                 polygons.
Describe what a tessellation is and give examples of tessellation
designs in real life.

Grade 4 – 3rd 9 Weeks                        7
SBISD 2006-2007
Part 4: Rotation - A Tessellation Lesson                                                 Notes
TEKS:
4.9A    Demonstrate translations, reflections, and rotations using concrete      Be sure to study the
models (TAKS 3)                                                          model and practice
4.9B    Use translations, reflections, and rotations to verify that two shapes   creating designs
are congruent (TAKS 3)                                                   yourself until you feel
4.9C    Use reflections to verify that a shape has symmetry (TAKS 3)             comfortable.
4.14A   Identify the mathematics in everyday situations (TAKS 6)                 Experiment with the
4.14B   Use problem solving model (TAKS 6)                                       shape. It will take
4.14C   Independently use the problem solving model and apply strategies         more than one try
(TAKS 6)                                                                 before you feel at ease
with manipulating the
4.14D   Use tools to solve problems (TAKS 6)                                     shape.
4.15A   Explain/ record observations (TAKS 6)
4.15B   Relate informal language to math language and symbols (TAKS 6)
4.16A   Make generalizations (TAKS 6)                                            Suggestion: Begin
4.16B   Justify why an answer is reasonable and explain the solution process     cutting the design from
(TAKS 6)                                                                 the corner of the
shape and paste the
Vocabulary:                                                                      cut-out on the other
Rotation               Rotación                                                  corner.
Reflection             Reflexión
Translation            Traslación
Vertical               Vertical
Horizontal             Horizontal
Congruent              Congruente
Tessellation

Materials:
3 x 3 square (made from index card or manila folder)
White construction paper
Student Geoboards
Shapes

Procedures:
Practice Facts Daily

Opening Activity:
Use an overhead geoboard to create a shape. Ask students to create a
shape that is congruent to yours. Once students have created the
shape, have the students make a reflection of your shape, and then
rotate it clockwise. Ask students to show their designs by holding it up
when teacher says, “go.”

Grade 4 – 3rd 9 Weeks                       8
SBISD 2006-2007
Notes
Mini Lesson:
1. Show students basic shapes such as

2. Using these shapes, if students rotate the shape at one vertex, how
many turns would the shape take to arrive back at its original shape?
(4, 6, and 4)
3. Tell students that in today’s activity, they are going to using translations,
reflections, and rotations to create their tessellations. Share with
students that they will be experimenting with squares again. Give
students each a 3 x 3 card stock (index card) square. Demonstrate to
students on transparency before they begin. Students will cut a small
design off half of the top left hand edge of the square and reflect twice.
The first reflection is a reflection horizontally. The second reflection is
vertical. Slide and tape it to the other half of the same edge. (Step 1)
4. Apply the same procedure to the right edge. Cut, reflect horizontally
and vertically, slide, and tape it to the other half of the same edge.
(Step 2)
5. Repeat again to the bottom and left edge of square. This is the
students’ template. (Step 3 and 4)
6. Have students rotate their shape to see if they can visualize a design as
they did in Part 3. Ask students what their shape suggests.
7. Afterwards, have students trace their template on paper, rotate it so
there is not a gap and continue rotating until s/he runs out of room.
Students will have to try different rotation configurations until they find
edges that fit like a jigsaw puzzle. (Step 5 and Step 6)
8. Once the tracing is done, have students draw in the details and color
their tessellation. Students will then give their artwork a title and write a
brief (3 to 4 sentence) description of how it was created. Be certain that
students include that they used translation to create the effect.

Step 1                             Step 2

The shaded portion is
the cut-out that is
reflected twice,
translated and taped.

Grade 4 – 3rd 9 Weeks                         9
SBISD 2006-2007
Notes

Step 3               Step 4

Step 5

Rotate until an
edge fits
another edge
like a jigsaw
puzzle.

Grade 4 – 3rd 9 Weeks        10
SBISD 2006-2007
Notes
Step 6

Reflections: What kind of everyday objects rotate? What objects
translate?

Grade 4 – 3rd 9 Weeks                   11
SBISD 2006-2007
Part 5: Using Translation, Reflection and Rotation as a Tool
How Many Different Rectangles Can You Find?                                      Notes

TEKS:
4.8C Use essential attributes to define two-and three-dimensional
geometric figures (TAKS 3)
4.9B Use translations, reflections, and rotations to verify that two
shapes are congruent (TAKS 3)
4.9C Use reflections to verify that a shape has symmetry (TAKS 3)
4.14A Identify the mathematics in everyday situations (TAKS 6)
4.14B Use problem solving model (TAKS 6)
4.14C Independently use the problem solving model and apply strategies
(TAKS 6)                                                            Objective 6 –
4.14D Use tools to solve problems (TAKS 6)                                Mathematical
4.15A Explain/ record observations (TAKS 6)                               Reasoning also
4.15B Relate informal language to math language and symbols (TAKS         includes problems in
6)                                                                  which students have to
4.16A Make generalizations (TAKS 6)                                       distinguish between
4.16B Justify why an answer is reasonable and explain the solution        examples and non-
examples. See your
process (TAKS 6)
Mathematics
Standards Document
Vocabulary:                                                               for clarification.
Example                Ejemplo
Nonexample             No ejemplo
Rectangle              Rectángulo
Rhombus                Rombo
Trapezoid              Trapezoide, trapecio

Materials:
Geoboards
Geoboard transparency
Rubber bands

Student Handouts:
Dot Paper

Procedures:
Practice Facts Daily

Opening Activity:
Review division with this word problem:
Maria has 76 geometric designs she wants to display on 3 poster
boards. How many designs will she put on each poster, if she puts an
equal amount on each?

Mini Lesson:
Grade 4 – 3rd 9 Weeks                         12
SBISD 2006-2007
1. Display a rectangle and a square and tell students that these are
examples of a rectangle. Have students record on paper that the                         Notes
rectangle and square are rectangles. Ask students to define what are
the attributes of a rectangle.                                                  *Creative Publications
2. Be sure students understand that a rectangle is any quadrilateral with          - Geoboards
four right angles.
3. Next, hold up a trapezoid or a rhombus and ask with a show of thumbs
whether these are examples or non-examples of a rectangle. Ask
students to explain why.
4. After introducing the idea of examples and non-examples, explain to
students that their task today is to fine as many different examples of         *If students are given
rectangles as they can make on a geoboard. *                                    one rubber band , they
5. Show students on dot paper transparency an example of a square.                 will be able to focus on
Then show the same square, only rotate it this time and ask students            one shape at a time,
whether or not you can count it as a second rectangle. Ask, “How can            recording it before
reflection, translation, or rotation help us to decide whether or not the       they construct the next
shape that you create is a repeat example of a shape that has already           shape.
been counted?”
6. Let students work in pairs. Some students may find all 16 rectangles
and some may not. The important focus is for students to practicing
using rotation, translation, or reflection as a tool to help them decide
whether or not they’ve created a new rectangle.
7. When all groups are finished, have students post their findings. Ask
students to reflect on their strategies for finding the different rectangles.

Reflection:
How would you describe a rectangle and a square to someone who
doesn’t know what they are?

Grade 4 – 3rd 9 Weeks                         13
SBISD 2006-2007
Workstations:
1. Multiplication Transformation - A Problem Solving Station                   Notes
Students solve a multiplication word problem and create a division
problem using the same numbers, including the product, and subject
matter.

2. Wrangler
Materials: 0-5 cube, paper, pencil, plastic animals (optional)
Players: 2-4

The object of this game is to capture as many remainders/ horses (any
animal) as possible. The person with the highest total of remainders
at the end of a 15 minute round is the winner. Students must use the
long division algorithm in this game.

To play, the students have a herd of 50 horses. The players want to
capture as many remainders/horses as possible. The first player rolls
a low die and divides the 50 horses by the number rolled. For
instance, if the player rolls a 2, then 50 divided by 2 is 25. The horses
split off into two groups with 25 in each group. There are no leftovers.
Player does not score.

The next player rolls a 3. The herd is divided into 3 groups and flees.
50 divided by 3 is 16 with 2 left over. So 2 horses are captured
reducing the herd to 48. Player one now plays with 48 horses and
rolls his die. This time he rolls a 5 and divides 48 by 5. The horses
split off into 5 groups with 9 in each group. There are 3 horses left out
of the group and the first player scores 3. At this point, player one has
a score of 3 and player 2 has a score of 2. Play continues until 15
minutes are over or all the animals have been captured.

3. Triangle Area Search
Materials: Geoboards, geoboard dot paper (end of investigation)
Have students find triangles on their geoboard that have an area of 5
and 8 square units Record findings on geoboard dot paper. Students
will display their finding on butcher paper for the class to see.

4. Partner Design Construction:
Materials: Geoboards, geoboard dot paper (end of investigation)
Students will work in pairs. One student will make a design on his/her
geoboard. The partner will then make a congruent design on his/her
geoboard. Together they will find the area of the design and its lines of
symmetry. Record design and lines of symmetry on geoboard dot
paper. Label what the area of the design is on the paper.

Grade 4 – 3rd 9 Weeks                       14
SBISD 2006-2007
Worksheet 1

1. What is true about a figure if it has one line of symmetry?

2-5 Draw the lines of symmetry found in each of the pictures below. Be sure to draw more
than one line if a figure has more than one line of symmetry.

Look at the figures below. Circle the congruent shapes.

6.

7.

Write whether each pair of figures shows a translation, rotation, or reflection.

8.                                         9.                                 10.

Grade 4 – 3rd 9 Weeks                      15
SBISD 2006-2007
Worksheet 2 Examples and Non-Examples

1. These are swigwams.

Which of these is a swigwam?

2. These are rectangles.

Which of these is a rectangle?

3. These are Reflectors.

Which of these is NOT a Reflector?

Grade 4 – 3rd 9 Weeks                 16
SBISD 2006-2007
Hoja 1

1. ¿Qué es verdadero sobre una figura que tiene solo una línea de simetría?

2-6 Dibuja las líneas de simetría en cada uno de los siguientes dibujos. Asegúrate de
dibujar más de una línea si la figura tiene más de una línea de simetría.

Mira las figuras de abajo. Circula las figuras congruentes.

6.

7.

Escribe si cada par de figuras es una traslación, rotación, o reflexión.

8.                                         9.                              10.

Grade 4 – 3rd 9 Weeks                      17
SBISD 2006-2007
Hoja 2 Ejemplos y no ejemplos

1. Estas son swigwames.

¿Cuál de estas figuras es una swigwam?

3. Estas figuras son rectángulos.

¿Cuál de estas figuras es un rectángulo?

3. Estas figuras son reflectores.

¿Cuál de estas figuras NO es un reflector?

Grade 4 – 3rd 9 Weeks                      18
SBISD 2006-2007
Answer Key Worksheet 1

1. What is true about a figure if it has one line of symmetry?

A figure that has one line of symmetry has two sides that are mirror images of one

another. If you fold one side behind the other one part will disappear behind the other.

Each side is in exact agreement with the other in size and shape.

2-5 Draw the lines of symmetry found in each of the pictures below. Be sure to draw more
than one line if a figure has more than one line of symmetry.

Look at the figures below. Circle the congruent shapes.

6.

X

7.

X

Write whether the examples below are examples of translation, rotation, or reflection.

8.                                           9.                                 10.

translation                            rotation                          reflection

Grade 4 – 3rd 9 Weeks                        19
SBISD 2006-2007
Worksheet 2 Examples and Non-Examples

1. These are swigwams.

Which of these is a swigwam?

X

4. These are rectangles.

Which of these is a rectangle?

X

3. These are Reflectors.

Which of these is NOT a Reflector?

X

Grade 4 – 3rd 9 Weeks                 20
SBISD 2006-2007
Grade 4 – 3rd 9 Weeks   21
SBISD 2006-2007

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