1 / 14

Choosing Tasks that Encourage Students to Use Mathematical Practices

Choosing Tasks that Encourage Students to Use Mathematical Practices. When you were working did you…. make sense of a problem and persevere in solving? reason abstractly and quantitatively? construct a viable argument and critique the reasoning of others?. 4. model with mathematics?

mahina
Télécharger la présentation

Choosing Tasks that Encourage Students to Use Mathematical Practices

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Choosing Tasks that Encourage Students to Use Mathematical Practices

  2. When you were working did you… • make sense of a problem and persevere in solving? • reason abstractly and quantitatively? • construct a viable argument and critique the reasoning of others? 4. model with mathematics? 5. use appropriate tools strategically? 6. attend to precision? 7. look for and make use of structure? 8. look for and express repeated reasoning?

  3. Stein, Smith, Henningsen, & Silver (2009). Implementing standards-based mathematics instruction. A casebook for professional development. New York: Teachers College Press

  4. http://classroom.westsidehsfaculty.org/webs/jschroe1/upload/worksheet_12.5_volume_of_pyramids_new.pdfhttp://classroom.westsidehsfaculty.org/webs/jschroe1/upload/worksheet_12.5_volume_of_pyramids_new.pdf

  5. Blocks measure 1 1/2 inches on each edge. A cube one foot high, one foot wide, and one foot deep is made with these cubes. How many little blocks are in the large cube of blocks?The area of the floor of a rectangular room is 315 sq. ft. The area of one wall is 120 sq. ft. and the area of another is 168 sq. ft. The floor and ceiling are parallel. What is the volume of the room? Source: Wheatley, G. & Abshire, A.  (2007). Developing mathematical fluency: Activities for grades 5-8. Tallahassee, FL: Mathematics Learning.

  6. To create a cone,Cut out the circle below.Cut through to the center on the radius line.You will slide the radius line to different points on the circle to create cones. Try the different cones. Predict the cone you believe will have the greatest volume. http://middlemathccss.wordpress.com/8th-grade-math/8th-d4-geometry/volume-of-cylinders-cones-spheres/

  7. Complete the table and then plot your Radius and Volume on the graph below. Label your points with the appropriate letter. Which point has the maximum volume? _______ How does the data below help you better estimate the position for the maximum volume? Make a second prediction for maximum volume. Use your prior knowledge to solve for the height using the length (l) and the radius (r). Show all work. h = ___________________________ Using the formula for volume of a cone, find your maximum cone volume in cubic centimeters. Show all work. V = ______________________

  8. What happens to the volume of a rectangular prism if one, two, or all dimensions are doubled? (begin with a 2 x 3 x 1)Source:Chapin, S. H. & Johnson, A. (2006) Math Matters: Understanding the math you teach, Grades K-8 (Second Edition). Sausalito, CA: Math Solutions.

  9. Use a centimeter ruler to measure the l, w, and h of a block. Build larger and larger cubes using blocks. Record the number of blocks on any edge and the volume for each of these larger cubes. What patterns do you observe? Generalize to a formula for volume of a cube. Source:Hatfield, Edwards, Bitter, & Morrow (2008). Mathematics Methods for Elementary & Middle School Teachers

  10. A swimming pool is 8 m long, 6 m wide and 1.5 m deep. The water resistant paint needed for the pool costs $6 per square meter. How much will it cost to paint the interior surfaces of the pool? http://www.vitutor.com/geometry/solid/volume_problems.html

  11. Making tasks more challenging… • Open Tasks – framed in such a way that a variety of strategies or solutions are possible • Parallel Tasks – sets of related tasks at different levels that are close enough in context that they can be discussed simultaneously Small, M. (2009). Good questions: Great ways to differentiate mathematics instruction. New York: Teachers College Press

  12. Open Tasks A shape has a triangle for a cross-section. What could the shape be? One vertex of a triangle is at the point (1,2). After a reflection, one vertex is at the point (5,8). Name all three vertices of the original and final triangles. • Small, M. (2009). Good questions: Great ways to differentiate mathematics instruction. New York: Teachers College Press

  13. Parallel Tasks Option 1: A and B are the location of Arjun’s and Bob’s homes. They want to meet equally far from both homes. Where could they meet? Option 2: Carol is joining Arjun and Bob. Locate a meeting place equally far from all three homes. A B C • Small, M. (2009). Good questions: Great ways to differentiate mathematics instruction. New York: Teachers College Press

  14. Changing Textbook Tasks http://classroom.westsidehsfaculty.org/webs/jschroe1/upload/worksheet_12.5_volume_of_pyramids_new.pdf

More Related