Fluency in Math: Examples & Non-Examples

Fluency in Math: Examples & Non-Examples

MAKE CONJECTURES FROM PATTERNS OR SETS OF EXAMPLES & NONEXAMPLES USE GEOMETRIC VOCABULARY TO DESCRIBE, COMPARE & CLASSIFY TWO?DIMENSIONAL FIGURES

Prerequisites none

Preparation a worksheet for the given term for each student

In a Nutshell In these activities students compare and contrast examples and non-examples to discover the meaning of key mathematic terms rather than memorizing and regurgitating textbook de nitions.

Math Content Traditional teaching methods such lecture, note taking, and drills are typically easier for teachers. Creating lessons in which students explore, predict, and discover generally require more thought and creativity ... except when it comes to "Examples and Non-Examples". They are as simple as any worksheet to write and best of all, they foster students making sense of information and nding their own connections. In fact, next time you are searching for fresh way to teach a concept and are struggling to nd an approach which is not leading, lecturing, and teacher-directed, consider applying the concept of "Examples and Non-Examples". Here's how it generally works: you introduce a new concept or term without any explanation as to its meaning. You then present examples and non-examples of this concept and ask students to look for similarities and di erences. Based on their observations students are then given two or three new samples and are asked to decide if each of these ts in the category of "example" or "nonexample". Students should then feel comfortable creating their own examples and non-examples, and ultimately de ning the concept in their own words. This de nition can then be checked against the examples and nonexamples for accuracy and completeness. When leading a class discussion around examples and non-example, I usually ask:

? What do you notice the examples have in common?

? What is wrong or missing from the non-examples?

? Here are two or three new situations to consider. Which category would each of these fall under, examples or non-examples?

? Create your own examples and non-examples.

? Write the de nition of _____ in your own words.

Encouraging Mathematical Reasoning: pg. P--21

FLUENCY IN MATH: RECTANLGES --WORKSHEET

Name:

Date:

Fluency in Math: Rectangles

Study the Venn diagram below showing examples and non-examples of rectangles. Rectangles

1. Based on the similarities and di erences you see in the Venn diagram, is

a rectangle?

2. Based on the similarities and di erences you see in the Venn diagram, is

a rectangle?

3. Add one of your own examples and non-examples to the Venn diagram. Make sure your drawings are not exactly the same as any of the gures already given.

4. What makes something a rectangle? List the characteristics.

5. Do all of the rectangles in the Venn diagram t your description in question #4? (If the answer is "no", you need to improve your response to question #4)

6. Do all of the non-rectangles in the Venn diagram fall short of your description in question #4? (If the answer is "no", you need to improve your response to question #4)

Encouraging Mathematical Reasoning: pg. G--22

FLUENCY IN MATH: PARALLELOGRAMS --WORKSHEET

Name:

Date:

Fluency in Math: Parallelograms

Study the Venn diagram below showing examples and non-examples of parallelograms. Parallelograms

1. Based on the similarities and di erences you see in the Venn diagram, is

a parallelogram?

2. Based on the similarities and di erences you see in the Venn diagram, is

a parallelogram?

3. Add one of your own examples and non-examples to the Venn diagram. Make sure your drawings are not exactly the same as any of the gures already given.

4. What makes something a parallelogram? List the characteristics.

5. Do all of the parallelograms in the Venn diagram t your description in question #4? (If the answer is "no", you need to improve your response to question #4)

6. Do all of the non-parallelograms in the Venn diagram fall short of your description in question #4? (If the answer is "no", you need to improve your response to question #4)

Encouraging Mathematical Reasoning: pg. G--22

FLUENCY IN MATH: QUADRILATERALS --WORKSHEET

Name:

Date:

Fluency in Math: Quadrilateral

Study the Venn diagram below showing examples and non-examples of quadrilaterals. Quadrilaterals

1. Based on the similarities and di erences you see in the Venn diagram, is

a quadrilateral?

2. Based on the similarities and di erences you see in the Venn diagram, is

a quadrilateral?

3. Add one of your own examples and non-examples to the Venn diagram. Make sure your drawings are not exactly the same as any of the gures already given.

4. What makes something a quadrilateral? List the characteristics.

5. Do all of the quadrilaterals in the Venn diagram t your description in question #4? (If the answer is "no", you need to improve your response to question #4)

6. Do all of the non-quadrilaterals in the Venn diagram fall short of your description in question #4? (If the answer is "no", you need to improve your response to question #4)

Encouraging Mathematical Reasoning: pg. G--22

FLUENCY IN MATH: REGULAR POLYGONS --WORKSHEET

Name:

Date:

Fluency in Math: Regular Polygons

Study the Venn diagram below showing examples and non-examples of regular polygons. Regular Polygons

1. Based on the similarities and di erences you see in the Venn diagram, is

a regular polygon?

2. Based on the similarities and di erences you see in the Venn diagram, is

a regular polygon?

3. Add one of your own examples and non-examples to the Venn diagram. Make sure your drawings are not exactly the same as any of the gures already given.

4. What makes something a regular polygon? List the characteristics.

5. Do all of the regular polygons in the Venn diagram t your description in question #4? (If the answer is "no", you need to improve your response to question #4)

6. Do all of the non-regular polygons in the Venn diagram fall short of your description in question #4? (If the answer is "no", you need to improve your response to question #4)

Encouraging Mathematical Reasoning: pg. G--22

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