Fluency in Math: Examples & Non-Examples
▣ MA KE CONJECT URES FROM PATTERNS OR SETS OF EXAMP LES & NONEXAMPLES
▣ USE GEOMETRIC VOCABUL A RY TO DESCRIBE, COMPARE & CLASS IFY TWO –DIMENSIONAL FIGURES
Preparation
a worksheet for the given term for each student
Prerequisites
none
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 definitions.
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 finding their own connections. In fact, next time you are searching for fresh way to
teach a concept and are struggling to find 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 differences. Based on their observations students are then
given two or three new samples and are asked to decide if each of these fits in the category of “example” or “nonexample”. Students should then feel comfortable creating their own examples and non-examples, and ultimately
defining the concept in their own words. This definition 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 definition of _____ in your own words.
Encouraging Mathematical Reasoning: www.MathLessonBank.com
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Date:
Fluency in Math: Rectangles
Study the Venn diagram below showing examples and non-examples of rectangles.
Rectangles
1.
Based on the similarities and differences you see in the Venn diagram, is
a rectangle?
2.
Based on the similarities and differences you see in the Venn diagram, is
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 figures already given.
4.
What makes something a rectangle? List the characteristics.
5.
Do all of the rectangles in the Venn diagram fit your description in question #4?
a rectangle?
(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
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FLUENCY IN MA TH: R ECTAN LGES —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 differences you see in the Venn diagram, is
a parallelogram?
2.
Based on the similarities and differences you see in the Venn diagram, is
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 figures already given.
4.
What makes something a parallelogram? List the characteristics.
5.
Do all of the parallelograms in the Venn diagram fit your description in question #4?
a parallelogram?
(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
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FLUENCY IN MA TH: PA RALLELOG R AMS —WORKSHEET
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Date:
Fluency in Math: Quadrilateral
Study the Venn diagram below showing examples and non-examples of quadrilaterals.
Quadrilaterals
1.
Based on the similarities and differences you see in the Venn diagram, is
a quadrilateral?
2.
Based on the similarities and differences you see in the Venn diagram, is
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 figures already given.
4.
What makes something a quadrilateral? List the characteristics.
5.
Do all of the quadrilaterals in the Venn diagram fit your description in question #4?
a quadrilateral?
(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
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FLUENCY IN MA TH: Q UADR ILATER ALS —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 differences you see in the Venn diagram, is
a regular polygon?
2.
Based on the similarities and differences you see in the Venn diagram, is
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 figures already given.
4.
What makes something a regular polygon? List the characteristics.
5.
Do all of the regular polygons in the Venn diagram fit your description in question #4?
a regular polygon?
(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. 5 of 10
FLUENCY IN MA TH: R EGULAR POLYGONS —WORKSHEET
Name:
Name:
Date:
Study the Venn diagram below showing examples and non-examples of rhombi.
Rhombi
1.
Based on the similarities and differences you see in the Venn diagram, is
a rhombus?
2.
Based on the similarities and differences you see in the Venn diagram, is
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 figures already given.
4.
What makes something a rhombus? List the characteristics.
5.
Do all of the rhombi in the Venn diagram fit your description in question #4?
a rhombus?
(If the answer is “no”, you need to improve your response to question #4)
6.
Do all of the non-rhombi 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. 6 of 10
FLUENCY IN MA TH: RH OMBUS —WORKSHEET
Fluency in Math: Rhombus
Date:
Fluency in Math: Trapezoids
Study the Venn diagram below showing examples and non-examples of trapezoids.
Trapezoids
1.
Based on the similarities and differences you see in the Venn diagram, is
a trapezoid?
2.
Based on the similarities and differences you see in the Venn diagram, is
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 figures already given.
4.
What makes something a trapezoid? List the characteristics.
5.
Do all of the trapezoids in the Venn diagram fit your description in question #4?
a trapezoid?
(If the answer is “no”, you need to improve your response to question #4)
6.
Do all of the non-trapezoids 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. 7 of 10
FLUENCY IN MA TH: TRAPEZ OIDS —WORKSHEET
Name:
Date:
Fluency in Math: Convex Polygons
Study the Venn diagram below showing examples and non-examples of convex polygons.
Convex Polygons
1.
Based on the similarities and differences you see in the Venn diagram, is
a convex polygon?
2.
Based on the similarities and differences you see in the Venn diagram, is
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 figures already given.
4.
What makes something a convex polygon? List the characteristics.
5.
Do all of the convex polygons in the Venn diagram fit your description in question #4?
a convex polygon?
(If the answer is “no”, you need to improve your response to question #4)
6.
Do all of the non-convex 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. 8 of 10
FLUENCY IN MA TH: CONVEX POLYGONS —WORKSHEET
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Date:
Fluency in Math: Part-to-Part Ratios
These are examples of part-to-part ratios:
SSSSTTT
7 to 4
½
4/3
3/1
1 to 1
1:4
QQSSS
2:3
3/1
These are NOT examples of part-to-part ratios:
3 cats
2/3
4/8
Circle the ratios:
⌧⌧⌧
¼
6/2
£››
$$$
2/3
3
1/3
What is a part-to-part ratio? (Make sure the non-examples do NOT fit this description):
Create your own example of a ratio:
Encouraging Mathematical Reasoning
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1/2
2 to 1
FLUENCY IN MA TH: RA TIOS —WORKSHEET
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FLUENCY IN MA TH: P ROP OR TIONA L —WORKSHEET
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Fluency in Math: Proportional
These groups are proportional:
W
W
These groups are NOT proportional:
Circle the groups that are proportional:
⌧
›
›
⌧
$
What does proportional mean? (Make sure the non-examples do NOT fit this description):
Create your own group of proportional items:
Encouraging Mathematical Reasoning
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