Overview
Using pattern blocks, square tiles, snap cubes and the "Shapes" computer software, students learn to recognize, name and classify 2- and 3-dimensional shapes. They also examine ways that shapes can be decomposed or put together into other shapes. They investigate the structure of rectangular arrays and find halves of rectangles and other shapes. They explore symmetry by making symmetrical designs and pictures.
Materials
Materials used in this sequence include Geoblocks, Color tiles, Snap cubes, Mirrors, Pattern blocks, Chart paper, construction paper and indexcards.
Daily Routines
Suggestion: Have your students make math folders to collect daily work. You might want folders to include a log of daily work. Make a log sheet each week that includes a box for each math class. At the end of each class, give the students a few minutes to make a short entry in their log that describes what they did that day.
Suggestion: Create some variety by setting aside a brief period for a math game. This could be used as an opportunity to refresh material from other lessons.
Lesson 1. Shapes Around Us
Time required: 1 class period
Skills taught
Procedure
Read and discuss "Shapes, Shapes, Shapes." Have the students look around the classroom to find various shapes. Suggest that they try to find shapes within other shapes.
Play the "Sorting Shapes" game. Students form groups at tables. Each student chooses a shape card. A volunteer places his/her card in the center of a table and tells one thing about the shape. Students with shapes that match the description, place their shapes in the center. Repeat until all shape cards are sorted. (See attached shape card copies.) Discuss with students. When class agrees that the shapes are sorted correctly, students retrieve their cards and the game is repeated. The students must say something different about their shape each time. Distribute a set of shape cards to each group of 2 or three students. Explain that students are to sort their cards in at least two different ways. They sort them into two, three or four groups so that every card has a place.
Assessment
Walk around and observe students ask questions such as: Which shapes seem to go together? What do you call these shapes? Why did you place this shape in this group instead of that one?
Make shape posters. Each group makes a poster by choosing one way that they sorted their shapes and gluing on their shape cards to illustrate. Each group labels their poster. (ex: long and pointy)
Homework: Students look at home and bring back 5 examples of different shapes. They write about or draw pictures of what they see.
Lessons 2 and 3. Seeing Shapes Within Shapes
Time required: 2 class periods.
Skills taught
Procedure
Covering Pattern Blocks. After students have had a chance to freely explore their pattern blocks, instruct them to make some of the pattern block shapes by putting other blocks together (ex: 3 green triangles make a red trapezoid) Students work to find and display all the different ways they can make each shape.
Assessment
Walk around room as students work. Make notes on student understanding. *Does student try several ways to cover a pattern block or do they try covering another block after finding just one way? *Does the student share and compare his/her way with others in the group?
Make a class chart
After discussing the activity, Students share their results and record on a chart that shows all six pattern blocks.(ex. yellow hexagon= 6 green triangles or 2 red trapezoids etc.)
Predict and cover. Students predict how many blocks it takes to cover shapes
(see attached shape work mats) Model activity using transparency of work mat A. Ask "How many blue rhombuses do you think it will take to cover it?" "Make a prediction." Share predictions and have students check by placing blocks on shape to cover it. Students continue activity on their own by first recording predictions and then testing them.
Homework
Students write about and make drawings of at least three shapes within shapes they see at home (ex: a rectangular window that has 4 rectangular panes)
Choice Time
As students learn the activities in this unit , they are placed in centers to be done independently. Predict and cover is the first activity that works well as a choice during "Choice Time"
Lessons 4 and 5. Building Buildings
Time required: two ar three class periods.
Skills taught
Procedure
Activity one: Choose two students to play "The Last Block Game" on the overhead using transparent pattern blocks and a transparency of student sheet chosen from sheets 3-6 (see attached copy). The students take turns placing a pattern block in a shape. The players try to be the last player to place a block on the shape. The shape must be covered completely with no gaps.
Activity two: "Cube Building." Students use snap cubes to build buildings. Each cube is a room. Floors are constructed out of a chosen number of rooms. Floors are added. Each floor must have the same number of rooms and the same shape as the first floor. The teacher directs students to build a building that has one story and 3 rooms. Have students add floor #2,3,4.... and record the number of rooms after 2 floors, 3 floors, 4 floors. Ask students to predict the number of rooms their building would have if it were ten stories high. Students work independently to build five more buildings shown on student sheet 12. (attached). The students record the number of rooms in their building as it grows up to ten stories high. Model how to record data using transparency of sheet 12.
Activity three: Class discussion-Ask students to build a building 5 stories high with 5 rooms in each story. Ask: How many rooms are in your building? How did you figure this out? As students list results, record on class chart. Ask If you look at these numbers what do you notice? Continue discussion of other buildings made.
Extension
Students build building of choice
Choice Time
The "Last Block Game" and "Build a Building" are added to choice time activities.
Assessment
(The Last Block Game) Circulate to observe students making notes to reflect: Do students start planning a move several moves before last block is placed? Do students consider what could happen if they place a particular block in a particular place at a particular time?
Homework
Students cut squares into two triangles(see attached copy) They use the resulting triangle to make new shapes. Students make at least 4 new shapes and trace to record(see attached record sheet)
Lesson 7. Investigating Quadrilaterals
Skills taught
Sorting and identifying quadrilaterals in different ways
Procedure
"Guess My Shape Game"
Provide Groups with sets of attribute blocks or shape cards. Start the game by deciding on a rule such as: "My shape has 4 corners." Students choose one of their shapes to ask "Does it fit your rule?" Make 2 groups of shapes, those that fit and those that don't fit. After a few students have been directed as to which group their shape belongs, have students choose into which group their remaining shapes should be placed.
Homework
At home, students collect examples of rectangles and quadrilaterals. They bring items to share with class (Envelopes, stamps, pictures or drawings of requested shapes)
Lesson 8. Which Rectangle is Biggest?
Skills taught
Procedure
Provide each student with several rectangles to cut out (see attached rectangle black lines) Ask questions such as : Which rectangle do you think is the biggest? The smallest? Students work with partners to order rectangles largest to smallest. Pairs record order they used. Seat students in a circle on the floor. Ask one pair to share how the ordered their rectangles by arranging in center of circle . Ask for pairs to share that have a different order. Each pair explains why the ordered the rectangles as they did. Rotate the selected biggest rectangle from long side vertical to long side horizontal and ask "Do you still think this rectangle is the biggest? Ask " what if I rotated all the rectangles, would the order change? Why? Why not? Students check their order by covering each rectangle with color tiles. They record the number of tiles needed to cover each rectangle.
Lesson 9. Building Rectangles.
Skills taught
Procedure
Instruct students to build a rectangle using 6 color tiles. Next, students record their rectangle on grid paper. Volunteers describe their rectangle and build on the overhead. Discuss generated figure. Is it a rectangle? Can anyone describe the rectangle in a different way? Invite volunteers to show different rectangles and repeat discussion. (Vocabulary: Congruent Rectangles)
Activity
"How many rectangles"
Procedure
Have students make as may different rectangles as they can out of 12 color tiles. After class has had ample time to work, construct a chart that records all the different rectangles the students describe. Encourage students to find all possible rectangles.
Choice time
For new choice time activity, Students constuct a rectangle from a selected number of tiles. They record rectangle on inch graph paper. Next students work with apartner to construct all possible rectangles using one or two of the numbers, 16, 18, 24, 36. Studnent trace all possible rectangles on to graph paper, cut out and glue on construction paper.
Evaluation
Circulate and make notes : What stategies do students use to build rectangles?
Can they accurately record rectangles on graph paper? How do they describe their rectangles in writing? Do satudents have a strategy for finding different rectangles for a givien number? Do students realize the relationship between 5- by- 3 and 3- by-5?
Homework
Provide students with 12, 1"inch squares. Instruct them to find all the numbers between 1 and 12 that only make one rectangle. They record numbers and write about what they noticed.
Lesson 10. Describing Rectangles
Skills taught
Visualizing and reproducing rectangles
Procedure
Provide students with color tiles. Flash a teacher constructed array on the overhead for 3 seconds. Instruct students to build the rectangle they saw. Flash the rectangle again for 3 seconds.Students check their work and make changes if they choose to. Finally turn on overhead so that everyone can check their work. Ask students to describe what they saw. Repeat for several more rectangles
Homework
Provide inch graph paper. Assign students a number. Students must dreaw all possible rectangles for assigned number.
Lesson 11. Picturing Rectangles
Skills taught
Procedure
Provide each group with color tiles and a written description of a rectangle. Students use description to build rectangle described. Group members decide on a rectangle that reflects their description and draw it.A group member reads their description and the rest of the class tries to build it. Students show various rectangles drawn and class discusses results. Discuss what helps to make a description clear?
Assessment
On the overhead slowly construcxt a rectangular array. Allow students to look at it for 3 seconds and then turn off overhead. Students are instructed to: Draw the rectangle and give a written description explaining to someone else how to build it.
Lesson 12. Fractions of Geometric Shapes
Skills taught
Lesson 13. Halves of Rectangles and solids
Materials
color tiles, inch graph paper, crayons
Procedure
Teacher models making a rectangle using 6 tiles. One-half of the rectangle is red one- half is green. Have students work independently to construct a similar rectangle using 8 tiles. They record and color their rectangles on inch graph paper. During class discussion, ask volunteers to show their drawings. Ask class to decide if rectangles are one-half red and one-half green. Find rectangles that are different. Model a rectangle that has two colors but the colors represent "unequal parts." Ask students to make a rectangle one- half red and one-half green using 7 tiles. After a few minutes ask students what they discovered.
Choice Time
During choice time, pairs of students try to find which numbers will create half and half rectangles. Students color rectangles they find on graph paper.
Assessment
Students fill in blanks for rectangles made with red and green. " I used ____ tiles. Each half has ____ tiles.
Provide students with worksheet(see attached) Students use 2 colors to color a pair of rectangles and decide which rectangle shows halves and which do not. Do students understand that halves are always two parts and that the two parts are always equal?
Homework
Provide inch graph paper. Assign numbers for students to investigate. Can they be divided into 2 colors equally ?
Lesson 14. Cutting congruent halves
Skills taught
Procedure
Provide students with paper rectangles. Instruct students to fold it in half. Students cut halves and share results with class. Discuss results. Provide outlines of several different shapes. Students work to find ways to divide them in half and then glue on construction paper. Make a class chart. List numbers that make halves and those that don't.
Choice Time
Provide students with copy of shapes (see attached) . They discover shapes that can be cut in half and paste on paper to record results.
Assessment
Do students easily cut shapes into halves? Do they look for other ways to cut the shape in half? What kind of shapes do they draw? Ask" How do you know the shape is divided into halves? What stategies do they use to find conguent halves?
Lessons 15 and 16 : Fold and cut a figure to show symmetry
Skills taught
Procedure
Model folding a rectangle, drawing one-half of the figure on the fold and cutting the figure.
Display shape and discuss mirror symmetry. Provide small rectangles . Instruct students to make a figure that has mirror symmetry. Provide mirrors for students to test for symmetry. Students share their figures explaining how they made it and showing the line of symmetry. Have students explore mirror symmetry using mirrors and "Line-Symmetry" work sheet (see attached).They draw the line where they need to put the mirror to create line of symmetry. Next, students find symmetrical patterns by sliding a mirror across the page of "Kaleidoscope".(see attached).
Procedure
Students place one pattern block in corner of hinged mirror. They look in the mirror and build what they see. Students record shapes they have built by tracing pattern blocks on paper and coloring. They draw a line to show where their mirror was placed. Ask them if this line also shows a line of symmetry. Have students share results and explain how they used their mirrors to draw their shapes and find lines of symmetry.
Choice Time
"Fold and Cut." Provide paper, glue, scissors and shape word cards (heart, diamond, triangle,sun...) Students draw a card, fold paper in half , draw and cut out their shape.
Class discussion: How do you prove that a shape has a line of symmetry?
Assessment
Students choose one symmetry picture or cut-out that they have made and write sentences explaining how their shapes or pictures are symmetrical and what it means for a shape to have line otr mirror symmetry.
Literature Connections
Hoban, Tana. Shapes, Shapes, Shapes
Fraction Action
Burns, Marilyn. The Greedy Triangle
Hutchins, Pat. The Doorbell Rang
Birmingham, Duncan. Look Twice
Software
Macintosh "Shapes"