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General Rubric for Determining Achievement Levels in Problem-Solving |
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Thread |
Level 1 |
Level 2 |
Level 3 |
Level 4 |
Level 5 |
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Persistence |
You need help, even for very simple tasks.
You give up quickly, often just wanting someone to give you the answer. |
You can do simple parts of the problem with little help.
You start working on the harder parts but unless you have much help, you give up. |
You work by yourself to complete simple parts of the problem.
For hard problems, you proceed by yourself after you get help, but may return for help often. |
You try very hard on your own and only get help once you have tried many strategies and thought hard. |
You like working hard on challenging questions and don’t need much help.
You may extend your thinking beyond the problem and make new ones.
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Strategies used |
It is hard to identify any strategy used.
You may only re-copy the given data and shown no understanding. |
There is some evidence of a strategy although its use is unclear or flawed.
You may have tried one approach that did not work and then gave up. |
The strategy used is clear and appropriate but it was not carried out far enough to reach a solution or was incorrectly used. |
An appropriate strategy was successfully carried out for a relatively complex task.
There is no evidence that you tried to think about a possible better strategy. |
You use a variety of strategies and often select ones which are most appropriate to the complex tasks.
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Conceptual understanding |
You show very little understanding, even for simpler tasks.
You may only re-copy the given data and shown no understanding. |
You understand and apply basic concepts in isolation for simple problems. |
You understand and can apply combinations of a couple of basic concepts as problems get a little more complex. |
You understand and apply complex concepts and/or combinations of several concepts when working with difficult problems. |
Your work on the problems may allow you to develop an understanding of related concepts that you have not yet studied.
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Accuracy of Work |
You make a lot of calculation and copying mistakes. |
You only make occasional mistakes with basic number concepts, but make several mistakes with more advanced number concepts. |
You make a few calculation and copying mistakes. You usually need someone to point them out to you before you correct them. |
You make occasional calculation and copying mistakes. Once you know the answer is wrong, you tend to find and correct most of these mistakes yourself. |
You make few careless errors, thoroughly checking your work and correcting your own mistakes before handing in your work.
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Communication |
You do not give explanations or show your work. |
Your explanations are not complete and they are very hard for the reader to follow.
You do not accurately use math terminology. |
Your explanations are not precise, but the reader has a general idea of what you mean.
You use some basic math terminology, where appropriate. |
Your work is organized is a clear, systematic way and your explanations are clear and complete.
You use math terminology effectively to add to your precision. |
Your work and explanations are clear, concise and complete.
You use a variety of ways to communicate your answer (words, terminology, pictures, graphs, symbols, etc.)
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Which achievement level fits best? Dimes and Quarters |
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Level 1 |
Level 2 |
Level 3 |
Level 4 |
Level 5 |
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You were able to answer question 1 (simple multiplication and addition operations)
You have made lots of calculation mistakes.
You get confused when there are a lot of details in the question.
You might have included nickels or other coins in the problem.
You needed help for almost every part of the problem.
You did not give explanations or nobody could understand what you were explaining or showing.
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You were able to answer question 2.
You might have made some calculation mistakes.
You understand some conditions and details for the harder questions, but not all of them.
Your explanations are not complete or they are hard to understand.
You need some help, but can do some parts on your own, once you have the idea.
You did not try very hard on the extra questions. You gave up quickly when the questions got hard. |
You explain that all the coins cannot be just quarters or just dimes so others can understand.
You almost always do the calculations correctly. Any little mistake you make is from not being careful.
You get most of your answers using trial and error. Your work is not systematic and isn’t very organized.
You may have created a new question very similar to the Dimes and Quarters problem (Extra Questions).
You can work by yourself for the easier questions.
You give up quite quickly when the questions are hard and want ongoing help with the harder questions. |
With little help, you can answer questions 1-4.
If you are told you are not correct, you review your work, find and correct your mistakes.
You work with all the details and conditions of the questions. You might have only found one possible answer for question 5.
You get your answers by using a systematic and organized method involving different strategies.
The extra questions you create are quite different than the Dimes and Quarters problem.
You try very hard on your own and only get help once you have tried many strategies and thought hard. |
You need little help and answer most questions correctly. You find and correct your mistakes.
You give clear and complete explanations for the questions. You can explain well both by writing or by telling others.
You can find and explain the pattern in the Extra Questions.
You create interesting extra questions.
You like working hard on challenging questions.
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Which achievement level fits best? Making Change |
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Level 1 |
Level 2 |
Level 3 |
Level 4 |
Level 5 |
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You were able to answer question 1.
You could only list a few ways to return change of 27 cents.
Your work is scattered and hard to follow.
If you don’t understand the question, you quickly give up.
You needed help for most parts of the problem.
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You give a reasonable solution to question 2.
You list several ways to return change of 27 cents. Your work is not well-organized and you might repeat some of these ways.
You might have made some calculation mistakes.
You need some help, but can do some parts on your own, once you have the idea.
You might have started some of the work for the extra questions but stopped when it became a lot of work. |
You did very well finding the ways you can return change of 27 cents. You might have missed a couple.
Your work in finding these ways is quite organized.
You can find at least a couple of ways of returning $1.00 of change using at least two coins of each type.
You give up on the last extra question because of its many possibilities.
You mostly work without needing a lot of extra help. |
You can find all the ways of returning change of 27 cents.
This work is well-organized and systematically presented.
You can find a set of coins to satisfy question 4 (but you might have some extra coins).
You list a number of ways to return $1.00 of change as required in the extra questions.
You try very hard on your own and only get help once you have tried many strategies and thought hard. |
You need little help and answer most questions correctly. You find and correct your mistakes.
You can correctly answer question 4.
You persist and find almost all the ways to return $1.00 of change as required in the extra questions.
You create and solve other interesting questions.
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Which achievement level fits best? Talking About Shapes |
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Level 1 |
Level 2 |
Level 3 |
Level 4 |
Level 5 |
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You could make few observations without getting a lot of help.
You incorrectly named and described many features of the shapes.
Your descriptions and work was confusing and hard to follow.
You could probably name the shapes as a square and a triangle.
You might have stated the number of sides for each shape.
You don’t talk of any past experience or uses of these shapes.
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You make observations about the number of sides, number of angles, names of the figures.
If you are given a hint about what else you can find out, you can carry on with the idea but you have trouble coming up with any more ideas.
You might introduce other terminology (words) such as quadrilateral, equilateral triangle, 2-dimensional, plane.
You might have measured the lengths of the sides of the shapes.
Your descriptions are not always complete and you don’t use all the math terminology but the reader understands what you are describing. |
You mention or describe about half of the following:
- Vertices (corners)
- Parallel lines
- Perpendicular lines
- Quadrilateral
- Equilateral triangle
- Rectangle
- Right angles
You measured and compared the lengths of the sides.
You may have talked about (or calculated) the perimeter of the shapes.
You may have compared the size of the angles – observed equal angles within each shape – square has the larger angles.
You show good use of basic math terminology in your descriptions.
You might talk of some of the uses or your experiences with these shapes. |
You describe most of these features.
You calculated and compared the perimeters of the shapes.
You may identify or describe a few of the following:
- Acute and right angles
- Rhombus
- Parallelogram
- Symmetry
- Rotation
- Tessellating shapes
- Diagonals and their lengths
You might calculate the area of the square.
You might discuss sectioning the square into triangles.
You include details and math terminology in your descriptions. |
You describe many of these features.
You compare the areas of the figures, describing the square as having greater area than the triangle.
You might calculate or approximate the area of the triangle.
You might discuss and measure the height of the triangle.
You might discuss, compare, or determine the sum of the angles for each of the shapes.
You might discuss, compare, or identify the lines of symmetry for each shape.
Your descriptions are detailed and insightful.
You show a broad understanding of the uses and importance of these shapes in the world.
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