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  • GENERAL INFORMATION AND SUMMARY
    • Title: Pattern Block Puzzles
      Resource ID: 12937
      Description:
      The students use pattern blocks to complete puzzles with outlined shapes, partially outlined shapes, and open patterns in order to determine the exact number of pattern blocks, the greatest number of pattern blocks, and the least number of pattern blocks needed to complete the puzzle.
      Subject(s):
      NGSSS: Mathematics
      Grade Level(s):
      1
      Intended Audience:
      Special Materials Needed:
      • Pattern Blocks (if pattern blocks are not available, use Resource available in Word, see Attachments section)
      • Pattern Block Activity Cards (available in Word, see Attachments section)
      Freely Available: Yes
      Instructional Component Type(s):
      Formative Assessment (Primary Type)
      Attachments: MFAS_PatternBlocks_Resource.doc , MFAS_PatternBlockActivityCards_Worksheet.doc
      Resource Collection: MFAS

  • RELATED STANDARDS (1)

  • FORMATIVE ASSESSMENT TASK
    • Instructions for Implementing the Task
      1. Prior to presenting the task to the student, the teacher should print the worksheets (see Attachments section) and complete the task to ensure the printer or computer did not distort or re-scale the figure.
      2. The teacher provides the student with ample pattern blocks to complete the puzzle block activity cards in multiple ways. 
      3. The teacher asks the students to explore different ways to fill in the same design using the pattern blocks and the procedure below: 
      • For puzzles #1-6:
      • "Fill in the pattern block puzzle using the pattern blocks outlined.  When you are finished, record how many blocks you used."  The teacher allows the student ample time to complete the puzzle using the outlined pieces and to record the number of pattern blocks used.  "How many pattern blocks did you use?"  When the student has finished explaining, the teacher asks the student to clear his or her pattern block puzzle.
      • "Now, fill in the pattern block puzzle using the greatest number of pattern blocks possible.  It is okay to use shapes that cross the interior lines, but stay within the border of the outlined shape.  Record how many pattern blocks you use this time."  The teacher allows the student ample time to complete the puzzle using the greatest number of blocks possible.  When the student finishes, the teacher asks, "Tell me how you determined that you would have the greatest number of pattern blocks by selecting these pieces."   When the student completes his or her explanation, the teacher asks the student to clear his or her puzzle for the next step.
      • "Finally, fill in the pattern block puzzle using the least number of pattern blocks possible.  Again, it is okay to cross the interior lines, but stay within the border of the outlined shape.  Record how many blocks you used."  The teacher allows the student sufficient time to complete the puzzle using the least number of pattern blocks possible.  When the student finishes, the teacher asks, "Tell me how you determined you would have the least number of pieces by selecting these pattern blocks." When the student completes his or her explanation, the teacher asks the student to clear his or her puzzle for the next activity card.
      • For puzzles #7-8
      • "Fill in the pattern block puzzle using the pattern blocks outlined in one of the halves of the puzzle."  The teacher shows the student the area to be filled, if the student does not understand the concept of one-half.  Make the same pattern in the other half.  When you are finished, record how many pattern blocks you used." The teacher allows the student ample time to complete the puzzle using the outlined pieces, repeat the pattern in the unmarked half of the puzzle, and record the number of pieces used to complete the puzzle.  The teacher asks, "How many pattern blocks did you use?" When the student completes his or her explanation, the teacher asks him or her to clear the puzzle for the next step. 
      • "Now, fill in the pattern block puzzle using the greatest number of pattern blocks possible.  It is okay to use shapes that cross the interior lines, but stay within the border of the outlined shape.  Record how many pattern blocks you use this time."  The teacher allows the student ample time to complete the puzzle using the greatest number of blocks possible.  When the student finishes, the teacher asks, "Tell me how you determined that you would have the greatest number of pattern blocks by selecting these pieces." The teacher asks the student to clear his or her puzzle for the next step.
      • "Finally, fill in the pattern block puzzle using the least number of pattern blocks possible.  Again, it is okay to cross the interior lines, but stay within the border of the outlined shape.  Record how many blocks you used."  The teacher allows the student sufficient time to complete the puzzle using the least number of pattern blocks possible.  When the student finishes, the teacher asks, "Tell me how you determined you would have the least number of pieces by selecting these blocks." When the student completes his or her explanation, the teacher asks the student to clear his or her puzzle for the activity card.
      • For puzzles #9-10
      • "Fill in the pattern block puzzle using as many different types (colors, shapes) of the pattern blocks as you can.  When you are finished, record how many pattern blocks you used."   The teacher allows the student ample time to complete the puzzle using as many possible colors/shapes as possible.  The teacher asks the student, "How many different shapes/colors did you use to complete the puzzle?  How many total blocks did you use?"  When the student completes his or her explanation, the teacher asks him or her to clear the puzzle for the next step.
      • "Now, fill in the pattern block puzzle using the greatest number of pattern blocks possible.  It is okay to use shapes that cross the interior lines, but stay within the border of the outlined shape.  Record how many pattern blocks you use this time."  The teacher allows the student ample time to complete the puzzle using the greatest number of blocks possible.  When the student finishes, the teacher asks, "Tell me how you determined that you would have the greatest number of pattern blocks by selecting these pieces." When the student is finished with her or her explanation, the teacher asks the student to clear his or her puzzle for the next step.
      • "Finally, fill in the pattern block puzzle using the least number of pattern blocks possible.  Again, it is okay to cross the interior lines, but stay within the border of the outlined shape.  Record how many blocks you used."  The teacher allows the student sufficient time to complete the puzzle using the least number of pattern blocks possible.  When the student finishes, the teacher asks, "Tell me how you determined that you have the least number of pieces by selecting these blocks."

      Notes to the teacher:
      This task requires a large number of pattern blocks per student, so the teacher may wish to administer this task to individuals or small groups of students.
      The teacher may wish to laminate the activity cards for repeated use.
      If administering task to a small group, the teacher may wish to give students different activity cards.
      Vocabulary Associated with the Assessment compose, decompose, pattern block puzzle, more, less, triangle, square, rhombus, hexagon

  • Task Rubric
    • Level I
      The student does not begin the task or identify a strategy to begin solving the problem. The student may guess an answer or copy what another student is doing without demonstrating understanding. The student appears not to understand the problem the task is asking him or her to solve.
      Misconception / Error

      The student does not understand the vocabulary least and most.

      The student lacks the visual/spatial sense to complete the task.
      Examples of Student Work at this Level
      The student is unable to accurately fill in the puzzle using the pattern blocks.
      Questions Eliciting Thinking
      What shape do you think you can start with?

      Where on the puzzle do you think you should place the first shape?
      Instructional Implications
      Have the student start off with easy pattern block puzzles consisting of only a couple of different shapes and pieces. (Puzzles #1, 2, 3 require one shape; puzzle #5 requires three shapes to complete.)

      Level II
      The student demonstrates errors in reasoning or fundamental misconceptions related to the learning goal. The student may not understand key mathematical terms in the problem and/or may be unable to describe or justify the strategy he or she uses.
      Misconception / Error
      The student may not complete the puzzle but has attempted to use a variety of blocks.
      Examples of Student Work at this Level
      The student is able to fill in the entire pattern block puzzle. An attempt is made to use more or less blocks, but the student is not making the connection between part-whole relationships and the composition and decomposition of shapes.
      Questions Eliciting Thinking
      How can you change some shapes in the puzzle in order to place a larger/smaller shape here?

      What happens to the number of shapes when you use larger pattern blocks?
      Instructional Implications
      Provide the student with opportunities to practice with a variety of pattern block puzzles. 
      Provide the student time to create shapes on his or her own using a variety of pattern blocks.

      Level III
      The student selects an appropriate strategy for solving the problem but may make an error(s) in computation. The student is unable to clearly articulate his or her thinking and/or to justify the strategy used to solve the problem.
      Misconception / Error
      The student is able to complete the pattern block puzzle but cannot explain the part-whole relationship.
      Examples of Student Work at this Level
      The student is able to complete the pattern block puzzle. The student is able to use more or less pattern blocks, but the student is unable to articulate the connection between part-whole relationships and the composition and decomposition of shapes.
      Questions Eliciting Thinking
      What happens to the number of shapes, when you use bigger pattern blocks?
      Instructional Implications
      Have the student create a hexagon using as many different pattern block shapes as possible. Discuss what happens to the number of pieces as the pieces get larger.

      Level IV
      The student solves the problem, uses formal mathematical terms correctly to explain how he or she arrived at the solution, and justifies why the solution is correct.
      Misconception / Error

      The pattern block puzzle may have some holes.
      There are no misconceptions or errors.

      Examples of Student Work at this Level
      The student completes the pattern block puzzle (may have some holes) with at least two different pattern blocks and explains what happens to the number of shapes as you change the size of the shape used.
      Questions Eliciting Thinking
      Is there a relationship between the size of the shape and the number of pattern blocks used?

      How can you apply what you just discovered for a different pattern block puzzle?
      Instructional Implications
      Provide the student time to experiment with more difficult pattern block puzzles.
      Encourage the student to create pattern block puzzles for his or her classmates.






  • SOURCE & ACCESS INFORMATION
    • Name of Author/Source: MFAS FSU
      E-Mail of Author/Source: mfas@lsi.fsu.edu
      Is this Resource freely Available? Yes
      Access Privileges: Public
      License:
      CC Attribution Non-Commercial Share Alike

* Please note that examples of resources are not intended as complete curriculum.

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