Grade 3 Geometry and Perimeter Sdadfa;Sdklfjas;Unit Overview

Grade 3 Geometry and Perimeter SDadfa;sdklfjas;Unit Overview

Reason with shapes and their attributes.

1. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

8. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Day 1: Investigations Unit 4
Session 3.1 Building Triangles / Day 2: Investigations Unit 4
Session 3.3 Squares, Rectangles, and Other Quadrilaterals
Although it is not required for students to name acute, obtuse, and right angles, this lesson will help students use appropriate language as they categorize quadrilaterals by attributes.
*Keep one or two examples of a triangle with a right angle to use Day 2. / During the introduction, hold up the triangles from yesterday with the right angle. Ask students what they notice about the angle in the triangle and the angles in the rectangle and square.
Skip 2B – LogoPaths Activity: Feed the Turtle as this is 4th grade angle work.
The discussion “Squares and Rectangles” is vital to this session. When discussing the shapes of the corners, use “right or square” angle as a reference.
Day 3: Investigations Unit 4
Session 3.4 Right Angles and Not-Right Angles / Day 4 / Day 5
This lesson will help students begin to see different categories of quadrilaterals.
Instead of Activity 2: Finding Angles –Tell students today they will be creating quadrilaterals that are not rectangles or squares.
As students work, look for some examples of a rhombus (you will want to use these during the discussion).
Discussion: Hold up the examples of rhombuses. Ask, What is the same about these quadrilaterals? What is different?
Next, put up an example of a rectangle and a rhombus, ask students to think, pair, share about how these quadrilaterals are the same and how they are different. Create an anchor chart as students share to compare rectangles and rhombus (how they are the same, how are they different – see example on Investigations page 122). Create a second chart in the same manner comparing squares and rhombuses.
See exit ticket (attached) / More Quadrilateral work
Intro trapezoid. Then have students sort quadrilaterals / Not quadrilaterals
Day 6 / Day 7 / Day 8 / Day 9 / Day 10
Shapes culmination
The Greedy Triangle / Measuring Around shapes with square tiles and centimeter cubes / Ordering shapes by perimeter and intro Missing Measuring LogoPaths / Mystery Perimeters
-logopaths / Perimeters of building shapes sab p.17

Day 3 Exit Ticket Name: ______

Like Me, Like Me Not

Both of these shapes have 4 sides and 4 corners.

1. What is another attribute that they have in common?

2. Describe an attribute that is different between the two shapes above.

Day 3 Exit Ticket Name: ______

Like Me, Like Me Not

Both of these shapes have 4 sides and 4 corners.

1. What is another attribute that they have in common?

2. Describe an attribute that is different between the two shapes above.

Day 4: Sorting Quadrilaterals

Reason with shapes and their attributes.

3.G.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. / Emphasized Standards for Mathematical Practice:
3. Construct viable arguments and critique the reasoning of others
5. Use appropriate tools strategically.
6. Attend to precision.
Materials:
-Defining Quadrilaterals – overhead or record on poster
-Venn Diagram (sorting circles) for each pair of students- make out of large construction paper or string
-quadrilateral set (attached)
-What’s the Rule? Exit ticket / Words that you should hear students using in mathematical conversations:
corner (angle) quadrilateral
opposite sides equal (congruent)
opposite sides won’t meet (parallel)
Ten Minute Math:
Practicing Place Value: Write 538 on the board and have students practice saying it to a partner. Make sure all students can read, write, and say this number correctly. Ask students to find and sketch 5-6 different ways to make 538 using only strips of 10 and single stickers.
Collect a few examples and ask students how they found their answers. Ask all students, “Did anyone notice a pattern?”
Before:
Defining Quadrilaterals. Have students look closely at the rhombuses and copy them in their math notebook. Then have students record observations about rhombuses. Repeat with squares. Next, ask students “what would need to be done to this rhombus to make it a square?” Why is there a square in the group of rhombuses?” After students have had some time to think and write independently, have them get into groups of 4 and create a statement: For a rhombus to become a square…
During:
Yesterday, we spent some time sorting quadrilaterals using different attributes (re-visit anchor chart). Today, we are going to use Venn Diagrams to sort quadrilaterals. In a Venn Diagram all of the shapes in a circle follow the same rule. Shapes in the part that overlap follow the rules in both circles. Today you are going to continue sorting quadrilaterals using more than one attribute. You will choose two attributes from our anchor chart. Place shapes in the circle that matches the attributes you selected. Remember to place shapes that have both attributes in the part of the circle that overlap so that it is in both circles. If you have time, try to repeat with two new attributes.
Partner groups sort quadrilaterals using Venn Diagrams and attributes identified yesterday.
After:
One group had the attributes “all opposite sides will not meet” and “at least 1 square corner” Ask students, where should they put the parallelogram (k), the right trapezoid (m), and the square (a)? Ask students to explain how they decided to put it where they did in the Venn Diagram.
Evaluation:
What’s the Rule

Day 4: Before

Defining Quadrilaterals

Directions:

Look closely at the shapes in each group. What do all of the shapes in the group have in common? What do you notice about the length of the sides? What do you notice about the corners? Will the opposite sides ever meet each other?

These are all rhombuses.

Observations about rhombuses

These are all squares.

Observations about squares.

When does a rhombus become a square?

MATHEMATICS • GRADE 3• UNIT 5: Geometry Georgia Department of Education
Dr. John D. Barge, State School Superintendent May 2012 • All Rights Reserved

Day 4: Exit Ticket – What’s the Rule?

Name:______

Draw each shape where it belongs in the Venn Diagram.

All Opposite Sides Equal No Square Corners All opposite sides equal in length No square angles (corners)

Day 5: Properties of Quadrilaterals

Reason with shapes and their attributes.

3.G.A.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. / Emphasized Standards for Mathematical Practice:
3. Construct viable arguments and critique the reasoning of others
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
Materials:
-Defining Quadrilaterals poster or overhead
-Triangle, dot or graph paper (students should choose which to use) to create polygons
-Quadrilateral Riddles
-Square Disguise Exit Ticket / Words that you should hear students using in mathematical conversations:
corner (angle) quadrilateral
sides opposite sides
equal (congruent) opposite sides won’t meet (parallel)
Ten Minute Math:
Practicing Place Value: Say “one hundred twenty-three” and ask students to write the number. Make sure all students can read, write, and say this number correctly. Ask students to solve these problems mentally
-what is 123+20? 123+40? 123+60? 123+200? 123+400? 123+600?
-Write each answer on the board. Ask students to compare each sum or difference with 637
-Which places have the same digits? Which do not? Why?
If time remains, pose additional similar problems using 261 and 198.
Before:
Defining Quadrilaterals. Have students look closely at the rectangles and copy them in their math notebook. Then have students record observations about rectangles. Repeat with trapezoids. Next, ask students “what would need to be done to a trapezoid to make it a rectangle?” After students have had some time to think and write independently, have them get into groups of 4 and create a statement: For a trapezoid to become a rectangle…
During:
Read the book the Greedy Triangle to introduce students to shapes that aren’t quadrilaterals or rectangles. Ask students, “What shapes did the triangle want to turn into? What did the triangle have to do to become a square” A hexagon?” (Students have had experiences with many of these shapes in 1st and 2nd grade so this lesson is just a review). The work in this lesson is designed to help students not only remember these shapes, but to also see different representations of each of these shapes.
List all of the shapes in the Greedy triangle on a chart/poster and ask students what’s different about each shape.
Tell students that today they will be creating shapes using triangle, dot or graph paper.
After:
Have students bring their drawings to the discussion area. Ask students to quickly hold up their work and point to a pentagon. Ask, “How do you know all of these shapes are pentagons?” Draw a regular pentagon (all sides the same length and all angles equal) and a square on the board. Ask students, “What attribute does the pentagon share with the square?” Students may say, all straight lines, closed figure. Tell students to look closely at the length of the sides of the pentagon. Students should notice that all the sides are the same length. Say, “find shapes on your paper that would match the attribute ‘all sides the same length’.
Evaluation: Square Disguise Exit Ticket

Day 5: Before - Defining Quadrilaterals

These are all rectangles.

Observations about rectangles.

These are all trapezoids.

Observations about trapezoids.

“What would need to be done to a trapezoid to make it a rectangle?”

MATHEMATICS • GRADE 3• UNIT 5: Geometry Georgia Department of Education
Dr. John D. Barge, State School Superintendent May 2012 • All Rights Reserved

Day 5: Shapes that aren’t Triangles or quadrilaterals

Name:______

Creating Polygons

Directions: Use the triangle paper below to create 2-3 different examples of each of the following: triangles, quadrilaterals, pentagons, hexagons, octagons, decagons. Label each shape.

Name:______

Creating Polygons

Directions: Use the dot paper below to create 2-3 different examples of each of the following: triangles, quadrilaterals, pentagons, hexagons, octagons, decagons. Label each shape.

Day 5 Exit Ticket

Day 6: Shapes Culminating Activity

Reason with shapes and their attributes.

3.G.A.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. / Emphasized Standards for Mathematical Practice:
3. Construct viable arguments and critique the reasoning of others
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.
Materials:
Quadrilateral Riddles
The book, The Greedy Triangle
Materials for students to make Shape --shifter books / Words that you should hear students using in mathematical conversations:
corner (angle) sides
opposite sides equal (congruent)
opposite sides won’t meet (parallel)
quadrilateral, parallelogram, trapezoid, rhombus, rectangle, square
Ten Minute Math:
Quick Images: 2D Show images 2 and 3 (one at a time from Quick Images T52 and follow the procedure for the basic routine. For each image, students discuss how they drew their figures, including any revisions they made after each viewing. Ask students
-How did you remember the parts of the image?
-For shape 2, is this shape made up entirely of rectangles? How do you know?
-For both shapes, make sure students are using precise language (smaller than square corners, opposite sides equal, etc).
Before:
Introduce Quadrilateral Riddles. Show the first part of the riddle: If I were a rhombus I would have 4 equal sides and 4 angles (corners). But I would not have 4 square corners, because that would be a ______and have students turn and talk with a partner to determine the missing shape.
Re-read The Greedy Triangle. Explain to students that they will be creating their own Shape-Shifter book..
Provide the following list of shapes they must use in their book:
Square, Pentagon, Rhombus, Octagon, Trapezoid, Rectangle
Explain to students that they need to use all of the shapes above, but can use them in any order. They may also add more shapes if they choose.
During:
As students work, notice the explanations they use to change their shapes from one to another. Prompt students to use precise language. Students should mention the lengths of sides, size of angles and number of sides as they move from shape to shape.
Students create their book with a partner or independently. If time permits, have some students create Quadrilateral riddles to use throughout the year.
After:
Choose a discussion topic based on the needs of your class.
Evaluation: students complete 1 quadrilateral riddle.

Name ______Date ______

Quadrilateral Riddle

Choose two quadrilaterals that are similar but have at least one difference. The first three lines of the riddle refer to one quadrilateral and its attributes. The last two lines of the riddle refer to the second quadrilateral and its attribute(s) that make it different from the first quadrilateral. Use specific math vocabulary to describe the attributes.

If I were a______

I would have ______and

I would have______.

But I would not have______

because that would be a ______!

Optional: try another riddle using two new quadrilaterals.

If I were a______

I would have ______and

I would have______.

But I would not have______

because that would be a ______!

Day 7: Measuring quadrilaterals

Cluster:

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. / Emphasized Standards for Mathematical Practice:
4. Model with mathematics
5. Use appropriate tools strategically.
6. Attend to precision.
Materials:
-centimeter cubes and square tiles
-electrical or painters tape (Create 8 shapes on the floor that have sides that are whole number amounts 4 to be measured with square tiles and 4 to be measured with centimeter cubes).
-What’s the Perimeter? Recording sheet
-What’s the Perimeter? Exit ticket / Words that you should hear students using in mathematical conversations:
sides
triangle, quadrilateral, pentagon, hexagon, octagon,
sum
perimeter
length
centimeter, inches, feet
Ten Minute Math:
Quick Images: 2D Show images 11 and 15 (one at a time from Quick Images T53-T54 and follow the procedure for the basic routine. For each image, students discuss how they drew their figures, including any revisions they made after each viewing. Ask students
-How did you remember the parts of the image?
-What did you notice about the relationship of the parts of the image?
-What helped you remember the whole image, so you could draw your design?
For both shapes, make sure students are using precise language (smaller than square corners, opposite sides equal, etc).
Before:
What are some of the attributes that we have been using to put polygons into groups? (equal sides, square corners, opposite sides never meet)
Today, we are going to talk about another attribute of polygons. Sometimes mathematicians want to know how far it is…the length….around the outside of a polygon. When mathematicians find the length around the outside of a polygon, they say they are finding the perimeter. Today, we are going to find the perimeter around a variety of shapes. How do you think a mathematician might find the length around the outside of a shape? Today, we are going to use centimeter cubes, inch square tiles, and 1-foot rulers to measure the perimeter of shapes. Let’s practice measuring the perimeter of a polygon using square tiles. (Model measuring and recording the perimeter of a polygon emphasizing finding the length of each side, no gaps or overlaps, and then finding the sum of the sides). Give directions for how students will visit each center (centimeters, inches, feet)
During:
Students measure and record the perimeter of polygons using centimeter cubes and inch tiles. (As students work, listen for strategies that students use. Some students might notice that they don’t need to measure both of the opposite sides of a rectangle because they are congruent. Other students may notice that for a triangle it is the sum of 3 sides, a quadrilateral 4 sides, etc. If students are noticing those strategies, have them share those strategies with class as part of the discussion).
After:
How is measuring perimeter like and different from measuring a line? (Also have students share interesting strategies that may emerge as they work-see During).
Evaluation: What’s the Perimeter? Exit Ticket

What’s the Perimeter? Recording Sheet