Math Pre K-K
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.
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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.
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.
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.
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.
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.|
The child's placemat showing a hexagon pattern-block shape near a corner ("This is the sun."), flowers and rain would not work to solve this problem and demonstrates incorrect reasoning.
The child uses no mathematical language or numbers.
The child's drawing cannot be considered a representation because the diagram does not support any mathematical reasoning. The one pattern block (hexagon) is not considered for a corner but to show the "sun."
The child is unable to make a mathematically relevant observation because s/he demonstrates no understanding of the underlying mathematical concept of "corner" or different pattern-block shapes for each corner.
The child's strategy of diagramming pattern-block shapes on each corner indicates correct reasoning for "corner." The child does not place a different patternblock shape in each corner even when the task was reread using a new term for "different." The child is not able to arrive at a complete correct answer.
The child correctly uses the mathematical terms - square, triangle, rectangle and orally counts the shapes from one to four correctly.
The child diagrams a pattern-block shape in each corner of her/his paper. This representation is appropriate but not accurate. The child does not indicate a different pattern-block shape in each corner. Two corners have a square pattern block.
The child solved the problem and made a mathematically relevant observation about her/his solution. The child states, "Justin's paper is a rectangle. That is not a patternblock shape."
The child's strategy of diagramming a square, trapezoid, triangle and rhombus on the placemat would work to solve this problem. The child's answer is correct because s/he used four different pattern-block shapes.
The child correctly uses the mathematical terms - rectangle, square, shapes, triangle and sides. The child's placement of four different pattern-block shapes on the placemat and tracing them to complete the diagram is appropriate and accurate to the task.
The child makes mathematically relevant observations about the properties of the patternblock shapes. "They are all different but three shapes got four sides. The triangle only has three sides," and, "This one (the hexagon) has six sides."
The child's strategy of putting pattern-block shapes in each corner of the paper placemat to finish the diagram would work to solve the problem and the answer is correct. The child uses four different shapes. The child then uses the geometric properties of the shapes to refl ect how the placemat could look as well as determining the surface area of each pattern-block shape.
The child correctly uses the mathematical terms - right, square, left, rhombus, triangle, corner, shapes, sides, rectangle, circle and row. The child correctly notates each shape from one to four. The child's ability to use so many correct geometric terms earns an Expert Level. The child completes the diagram by correctly placing four different pattern-block shapes in each corner. The child then makes a diagram to show which shapes have more than four sides and which shapes have four sides. The child makes another diagram to show the order of some pattern-block shapes from "smallest" to "biggest."
The child demonstrates a strong understanding of the geometric properties of pattern-block shapes as well as correctly naming the square, rhombus, triangle, as well as rectangle and circle. The child explores the geometric property of side and arranges the pattern blocks correctly in her/his diagram. Using this information the child states, "Justin can't just use four sides because the placemat has four corners. He needs four of them. Justin can do 1-3 side (one, three-sided) 1-6 side (one, six-sided) and 2-4 sides (two, four-sided) if he wants."
The child comments that there are no rectangle and circle pattern blocks and decides that there are more missing pattern-block shapes. The child then determines and places the pattern-block shapes in order according to the surface area of each. "Now I put them in a row from smallest to biggest." The child shares her/his thinking. "Put the triangle on the square. You still see orange. I can put three triangles on the red one and lots on the yellow."
(The rhombus does have more surface area than the square. Older children would find the area of a triangle and double the area to determine the area of the rhombus. Children would find the area of the square and compare the two shapes.) Visually comparing the area of a rhombus and square pattern block is difficult, but this young mathematician is beginning her/his geometric journey.