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Standards-based assessment and Instruction

Math Pre K-K

Justin's Placemats

Task

Justin makes a placemat from a piece of paper just like the piece of paper you have. Justin draws a different pattern-block shape on each corner of the placemat. What could Justin's placemat look like? Show and tell how you know.

Alternative Versions

More Accessible Versions:

Justin makes a placemat from a piece of paper just like the piece of paper you have. Justin draws a pattern-block shape on each corner of the placement. What could Justin's placemat look like? Show and tell how you know.

More Challenging:

Justin makes two placemats from two pieces of paper just like the two pieces of paper you have. Justin draws a pattern-block shape on each corner of a placemat. Justin makes each placemat the same. What could Justin's two placemats look like? Show and tell how you know.

NCTM Content Standards and Evidence

Instructional programs from pre-kindergarten through grade 12 should enable all students to:

  • Recognize and name some variations of the circle, square, triangle and rectangle
  • Understand ideas such as over, under, corner and locate these positions
  • In this task, learners must be able to draw and name four different shapes, as well as identify the corners of the given rectangle.

Links

This task would link well to a celebration of Thanksgiving in which the children have worked to design placemats. Instruction in naming, describing and drawing shapes needs to have taken place.

Support

A child may need pattern blocks, pattern-block paper shapes, or stamps to represent/model the shapes to put on each corner of the placemat. The teacher can take a picture of the child's model. (Many children will select paper, pencil, crayon, etc. to show their solution.) A teacher, older student, paraprofessional, volunteer, etc. should scribe the child's solution so the teacher will have a complete record of the child's reasoning.

Task Specific Assessment Notes

General Notes: Many children will solve this task by placing pattern-block shapes on the corners of the paper provided and then trace the pattern-block shape. Other children may glue paper pattern-block shapes on the corners or use pattern-block stamps. Please note that all pattern blocks are not colored the same. Some companies will color the triangle green and others red. A child could decide to color the patternblock shapes on her/his paper, and the color choice does not matter.

Task Specific Rubric/Benchmark Descriptors
Click on a level for student example.
Novice The Novice will be unable to solve the task and could draw pattern-block shapes all over her/his paper or could draw shapes other than pattern-block shapes.
Apprentice The Apprentice will be able to partially solve the task. S/he will understand that the task involves pattern-block shapes but not understand the property of corner (vertex, angle). The Apprentice could demonstrate understanding of corner but not be able to place a different pattern-block shape in each corner. The Apprentice will attempt to communicate her/his reasoning by using a mathematical language term and/or number. The Apprentice will also attempt to make an appropriate representation. A connection may be attempted but it will not be mathematically relevant to the task.
Practitioner All the Practitioner criteria are evident and the Expert will be able to demonstrate a deeper understanding of the mathematical concept of geometric properties of pattern-block shapes. The Expert will also bring more mathematical language and/or numbers to the task than the Practitioner. Terms could include, but are not limited to - diagram, key, model, triangle, square, rhombus, trapezoid, hexagon, sides, angle, vertex, even, odd, more than, less than. The Expert will often use her/his representation to explore the underlying mathematical concepts in the problem. The Expert could, but is not limited to, conclude that the triangle has the least number of sides of all the pattern blocks and the hexagon has the most; that the hexagon is the "largest" shape to place on the placemat; that there are two remaining shapes (if you count the two rhombus shapes separately) for the next placemat and then you have to repeat shapes; and that each shape on the placemat will have four sides if you use the square, trapezoid, and two rhombi.
Expert The Practitioner will be able to correctly solve the task by demonstrating that a different pattern-block shape is on each corner of the paper. This would indicate a "correct answer." The Practitioner will use mathematical language and/or numbers. Terms could include but, are not limited to - diagram, square, triangle, rhombus, trapezoid, hexagon. The Practitioner will be able to construct an appropriate and accurate representation (many children will begin with a model and then represent the shapes with paper, tracing, stamps). The Practitioner will make a mathematically relevant observation (connection about her/his solution) such as there are four different shapes because there are four corners, the triangle only has three sides.

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Here's What People Are Saying

I am particularly charmed by the anchor papers. They provide an excellent indicator of what good work looks like so the teachers can immediately identify the levels of work that can be expected. In addition, the commentary on the anchor papers guide the teachers in using the rubrics so they may develop thoughtful and significant comments for the very important feedback they must give to their students.

E. Alquist

IB/PYP Consultant

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