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 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. pg. P 21
Fluency in Math: Rectangles Study the Venn diagram below showing examples and non-examples of rectangles. Rectangles FLUENCY IN MATH: RECTANLGES WORKSHEET 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 a rectangle? 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? 6. Do all of the non-rectangles in the Venn diagram fall short of your description in question #4?
Fluency in Math: Parallelograms Study the Venn diagram below showing examples and non-examples of parallelograms. Parallelograms FLUENCY IN MATH: PARALLELOGRAMS WORKSHEET 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 a parallelogram? 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? 6. Do all of the non-parallelograms in the Venn diagram fall short of your description in question #4?
Fluency in Math: Quadrilateral Study the Venn diagram below showing examples and non-examples of quadrilaterals. Quadrilaterals FLUENCY IN MATH: QUADRILATERALS WORKSHEET 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 a quadrilateral? 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? 6. Do all of the non-quadrilaterals in the Venn diagram fall short of your description in question #4?
Fluency in Math: Regular Polygons Study the Venn diagram below showing examples and non-examples of regular polygons. Regular Polygons FLUENCY IN MATH: REGULAR POLYGONS WORKSHEET 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 a regular polygon? 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? 6. Do all of the non-regular polygons in the Venn diagram fall short of your description in question #4?
Fluency in Math: Rhombus Study the Venn diagram below showing examples and non-examples of rhombi. Rhombi FLUENCY IN MATH: RHOMBUS WORKSHEET 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 a rhombus? 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? 6. Do all of the non-rhombi in the Venn diagram fall short of your description in question #4?
Fluency in Math: Trapezoids Study the Venn diagram below showing examples and non-examples of trapezoids. Trapezoids FLUENCY IN MATH: TRAPEZOIDS WORKSHEET 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 a trapezoid? 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? 6. Do all of the non-trapezoids in the Venn diagram fall short of your description in question #4?
Fluency in Math: Convex Polygons Study the Venn diagram below showing examples and non-examples of convex polygons. Convex Polygons FLUENCY IN MATH: CONVEX POLYGONS WORKSHEET 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 a convex polygon? 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? 6. Do all of the non-convex polygons in the Venn diagram fall short of your description in question #4?
These are examples of part-to-part ratios: Q Q S S S 2 : 3 Fluency in Math: Part-to-Part Ratios 7 to 4 ½ S S S S T T T 4/3 FLUENCY IN MATH: RATIOS WORKSHEET 3/1 1 to 1 1 : 4 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 1/2 2 to 1 What is a part-to-part ratio? (Make sure the non-examples do NOT fit this description): Create your own example of a ratio: pg. P 22
These groups are proportional: Fluency in Math: Proportional W W FLUENCY IN MATH: PROPORTIONAL WORKSHEET 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: pg. P 22