Number, Operation, and Quantitative Reasoning Activity ...€¦ · mathematical language,...

Mathematics TEKS Refinement 2006 – 6-8 Tarleton State University

Number, Operation, and Quantitative Reasoning Grade 8 Fractions Within A Square

Number, Operation, and Quantitative Reasoning Activity: Fractions Within A Square TEKS: (8.1) Number, operation, and quantitative reasoning. The student

understands that different forms of numbers are appropriate for different situations.

The student is expected to: (A) compare and order rational numbers in various forms including

integers, percents, and positive and negative fractions and decimals;

(B) select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships;

(8.2) Number, operation, and quantitative reasoning. The student

selects and uses appropriate operations to solve problems and justify solutions.

The student is expected to: (A) select appropriate operations to solve problems involving

rational numbers and justify the selections; (B) use appropriate operations to solve problems involving rational

numbers in problem situations; (8.15) Underlying processes and mathematical tools. The student

communicates about Grade 8 mathematics through informal and mathematical language, representations, and models.

The student is expected to: (A) communicate mathematical ideas using language, efficient

tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models;

Overview: Students will develop an understanding of operations with fractions by

creating visual representations of fractional parts. Materials: 6 in. by 6 in. transparency and sheet marked at 1 in. intervals

Fractions Within a Square: Recording Sheet Fractions Within a Square: Answer Sheet Calculator to check work if needed Rulers in inches

Grouping: Individual, pairs, or groups of 3 Time: One to two 45 minute class periods



Lesson: Procedures Notes 1. Give each student a piece of paper with a

large 6x6 inch square and Fractions Within a Square: Recording Sheet and Answer Sheet.

2. Tell students that the area of this large square is 1 square unit with each side marked at 1 inch intervals.

3. Direct students to divide this square into polygons of various shapes and sizes by utilizing a straightedge and the small inch measurement marks indicated on each side of the square.

The area of these polygons must be determined by inspection. (No rulers will be needed to perform measurements, only a straightedge to check for point-to-point alignment.)

4. Inside each polygon the student must draw a picture or symbol that will represent the area inside that particular polygon.

Encourage students to use different pictures to represent different areas and the same picture to represent the same area. A possible extension would be for students to justify why different shaped polygons have the same area.

5. Students are then assigned to develop a minimum of twenty-five questions (complete with answer key) that will demonstrate their understanding of fractional values and competency in computation with fractions.

Questions should contain no words. Students will use the pictures or symbols for each polygon and the appropriate operation to write their questions. You can be more specific here. For example, 8 questions must be subtraction questions, etc.

6. Samples of student work are included. These samples could be made into transparencies to show students what the task is.

Students could also write comparative statements to show inequalities, along with decimal equivalents.

7. Have students write a paragraph about what



Procedures Notes they learned or discovered while doing this activity.

Homework: Have students develop another square concept activity to be given as

a class assignment. Assessment: This will be determined by the accuracy of their figures, areas and

computational exercises. Have students determine the value of each of the pieces of a tangram if the seven piece tangram is the whole.

Extensions: Students are to teach this concept and explain their activity sheet to

parents. Parents are to write back to the teacher their understanding of what their son/daughter has taught to them.

This activity has worked well because it allows for individual and creative student work while at the same time it graphically reinforces the concepts pertaining to fractions and gives a visual rationale to the computational process involved with fractions. In fact, many of the computational questions can be answered more readily from a visual mode than from an arithmetic mode. This assignment also allows for some nice student design and art work. Students tend to enjoy this activity and almost always try to develop incredibly difficult questions. Much revealing discussion arises in many critical concept areas of this assignment. Overall, this activity is one of the most enlightening lessons concerning fractions. Finding the area of various geometric shapes is also greatly enhanced by this activity. Evaluation of student work varies. Teams of students evaluate each piece of student work with their rationale. Their rationale helps to further clarify the expectations for the assignment.



Name: __________________________ Date: __________

Fractions Within A Square

The square below is one square unit. Using the small hash-marks placed at one inch intervals alone each side, divide the 6X6 inch square into at least 15 various shaped polygons. Create each polygon so that the area can be determined by inspection. Use your 15 polygons to create 10 computational questions (2 addition, 2 subtraction, 2 multiplication, 2 division, and 2 of your choosing) which demonstrate your understanding of operations with fractions.



Name: __________________________ Date: __________

Fractions Within A Square Recording Sheet

List your 10 computational questions. 1. _______________________ 2. _______________________ 3. _______________________ 4. _______________________ 5. _______________________ 6. _______________________ 7. _______________________ 8. _______________________ 9. _______________________ 10. _______________________



Name: __________________________ Date: __________

Fractions Within A Square Answer Sheet

Identify the value of at least 15 polygons. List your 10 computational questions

with answers 1. ___________________ 1. _______________________ 2. ___________________ 2. _______________________ 3. ___________________ 3. _______________________ 4. ___________________ 4. _______________________ 5. ___________________ 5. _______________________ 6. ___________________ 6. _______________________ 7. ___________________ 7. _______________________ 8. ___________________ 8. _______________________ 9. ___________________ 9. _______________________ 10. ___________________ 10. _______________________ 11. ___________________ 12. ___________________ 13. ___________________ 14. ___________________ 15. ___________________

Number, Operation, and Quantitative Reasoning Activity ...€¦ · mathematical language,...

Documents

Transcript of Number, Operation, and Quantitative Reasoning Activity ...€¦ · mathematical language,...