Puzzling Relationships

• ## Puzzling Relationships

Periods: 2
Author: Carol Midgett

### Instructional Plan

Display the Tangram Puzzle Activity Sheet for the whole class to see and ensure that each student has access to the activity sheet and tangrams (cardstock is recommended).

Model how to fill the puzzles with the tangram pieces. For example, the Tangram School can be filled as shown below.

Discuss how it is necessary to turn over, rotate, or slide pieces to complete a puzzle by attending to precise vocabulary.

Have the students work in pairs to complete the tangram puzzles. Encourage them to discuss with each other what needs to be done to fit the pieces to match the outline of the puzzle. (This exercise focuses students' attention on the transformations required to make pieces fit. A turnover, rotation, or slide of pieces may be necessary to complete the puzzle.) This discourse facilitates students' problem solving and reasoning about the process. It connects actions with vocabulary and assists the students in relating what happens with concrete and virtual tools.

As a wrap up activity, pairs of students can share their work (what was most difficult, what feature they used the most, how long it took them, etc.).

### Assessments and Extensions

Assessment Options

1. By completing tangram puzzles, the students should demonstrate the ability to do the following:
• Interpret relative positions in space and apply ideas about relative position.
• Describe and interpret direction and distance in navigating space, and apply ideas about direction and distance.
2. Making notes about what the students do and do not understand is helpful when planning future instruction for individuals, groups of students, and the class as a whole. Collecting this data for future reference helps you understand the impact of your teaching strategies on students' learning. You may use the Class Notes recording sheet for this purpose.

Extensions

The students who find it easy to complete the puzzles could create new ones for the class to solve.

### Questions and Reflections

Questions for Students

1. What did you find when you tried to place the puzzle pieces in place?
2. What happens when you turn (or rotate) a puzzle piece?
3. What happens when you turn over a puzzle piece to fit it into place?
4. How many different ways did you find to fill the puzzle? What did you do to fill the puzzles in different ways? (This question focuses students' attention on different orientations of pieces and whether pieces must be turned over, rotated, or slid to fill the puzzle.)
5. What did you learn from other students as you watched them put their puzzle together?
6. If you were teaching this lesson, what would you tell your classmates about how to put the puzzle together?
7. Why is it necessary to turn over, rotate, or slide the tangram pieces to make them fit?
8. How did you decide which triangle would fit into the vacant space?
9. Which shape(s) caused you the most trouble? Why?

Teacher Reflection

• Which students demonstrate an understanding of how to solve puzzles by turning over, rotating, and sliding puzzle pieces? Which did not? What caused them difficulty?
• What other learning opportunities do these students need? What instructional strategies would provide these learning experiences?
• Were some students able to use more than one strategy to complete the puzzles?
• Which students were able to interpret and use relative position in space as a problem-solving strategy?
• Were all students able to describe how they solved puzzles? If not, what would help them do so?
• Which students demonstrate an understanding of the relative sizes among the tangram pieces by identifying the varying sizes of the triangles as small, medium, or large? For those who do not, what instructional experiences are needed?
• Which students do not realize that rotating or sliding changes the orientation of shapes? What experiences would help them learn this?
• Which students realize that turning over pieces can change the orientation of shapes? If not, what experiences would help them learn this?

### Objectives and Standards

Students will:

• Interpret relative positions in space and apply ideas about relative position.
• Describe and interpret direction and distance in navigating space and apply ideas about direction.
• Use tangram puzzles to experience turns, rotations, and slides.
Common Core State Standards – Mathematics

9th to 12th

• Stats & Probability
• CCSS.Math.Content.HSS-ID.A
Summarize, represent, and interpret data on a single count or measurement variable

Pre K to 2nd

• Kindergarten
• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP7
Look for and make use of structure.

Pre K to 2nd

• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP7
Look for and make use of structure.

Pre K to 2nd

• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP7
Look for and make use of structure.
Common Core State Standards – Practice
• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP7
Look for and make use of structure.