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March Math Academy

March Math Academy. Dr. Rhonda Bonnstetter Dr. Debbie VanOverbeke. Please sit with your school group. Opening Activity. Check out these websites for fun ‘Mathemagic’ activities! Crystal Ball Math- http://kids.niehs.nih.gov/mindread/mindread.html Gopher Math –

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March Math Academy

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  1. March Math Academy Dr. Rhonda Bonnstetter Dr. Debbie VanOverbeke Please sit with your school group.

  2. Opening Activity • Check out these websites for fun ‘Mathemagic’ activities! • Crystal Ball Math- • http://kids.niehs.nih.gov/mindread/mindread.html • Gopher Math – • http://www.learnenglish.org.uk/games/magic-gopher-central.swf • Navigations book – pg. 59-62

  3. Review of February topics: • Role of Properties in Algebra • Importance of Order of Operations in solving algebraic equations • Mathemagic – writing algebraic expressions • Closed, Open-Middled, and Open-Ended questions, and how to write them

  4. Today’s Agenda • Pattern finding – Tiling activity • Working with Perimeter and Area • Using Algeblocks in the Algebra classroom, grades 5-8 • Websites for ‘virtual’ Algeblocks! • MCA test prep – sharing and ideas

  5. Tiling Around the Garden • Commit to an Outcome: By self • How many tiles must be added to form the 6th garden? • Each successive garden? (Recursive rule- each term of a recursive expression as determined by application of a rule or formula to its preceding terms) • Expose beliefs: Share your answer with your group members. • Confront beliefs: Decide on a recursive rule to share with the class.

  6. Tiling Around the Garden (2) A table can help communicate the number of tiles that must be added form each successive garden.

  7. Tiling Around the Garden (3) • Commit to an Outcome: By self • Physical objects can help find the explicit rule to determine the number of tiles around a garden of size n. • What patterns do you see when using the tiles? • What explicit rule (functional relationship - rule that determines the number of elements in a step from the step number) • Expose beliefs: Share your answer with your group members • Commit to an outcome: With your group • Decide on an explicit rule and write your rule and a rational with a diagram of tiles to share with the class. • Create a coordinate grid graph to display the data.

  8. y Tiling Around the Garden (3) y = 2x + 6 y =2(47) + 6 y = 94 + 8 y = 100

  9. y Tiling Around the Garden (3)

  10. y Tiling Around the Garden (3)

  11. Perimeter and Area Activity • Review perimeter and area of rectangles • The Puppy Pen Activity • Please work on this activity at your table; be prepared to share your results with the group. • When finished, discuss how You could use this with your students.

  12. Using the Basic Mat • Compare the yellow rod(x) to the green unit block. • How can you describe the dimensions of the yellow rod in terms of the green rod? • What is the perimeter of this piece? • What is the area of the yellow rod? • Build rectangles with areas of 16 units, 18 units, 7 units. • Which numbers can build squares? • What numbers have only one rectangular shape possible? • Why do some numbers have more than one rectangular shape?

  13. Pattern Finding – Algeblocks Activity • Used to help students make the connection between concrete and abstract manipulations • Helps develop comprehension of key concepts • Blocks represent constants (1) and variables: x, x2, x3, y, y2, y3, xy, x2y, and xy2 • Three mats: Basic Mat, Quadrant Mat, Sentences Mat • Factor Track allows students to use +/- factors & polynomial models in all four quadrants

  14. Using the Basic Mat • Define the green block as a unit representing 1 • Use green blocks to build the number 7 • Use the green blocks to build the number -3 • Put one block on each side of the mat; what numbers are represented? What happens when you combine the numbers?

  15. Using the Basic Mat • Use the green blocks to show the equation 5 + 3 = _____ • Use the blocks to show the equation 9 + (-7) = _____ • Now build three ways to show the number 4 • Try using more than two numbers • Try using both positive and negative numbers!

  16. Using the Basic Mat • Use 12 units to build as many rectangles as possible with different dimensions • Why are there so many ways? What are the different ways? • Build rectangles with areas of 16 units, 18 units, 7 units. • Which numbers can build squares? • What numbers have only one rectangular shape possible? • Why do some numbers have more than one rectangular shape?

  17. Using the Basic Mat • Use the yellow rod(x) to represent the following situations: • Robert has five times as many baseball cards as Kirsten does • Model x and -2x on your mat • In one month, Dion ate six times as much fish as he did ham. • In your group, design and describe your own situation • Share with the large group

  18. Pattern Finding – Algeblocks Activity • What equation does this model represent? • 2x + 3 • What do the yellow blocks represent? • What do the green blocks represent? How would you represent –(2x + 3)?

  19. Pattern Finding – Algeblocks Activity Does this model represent 2x or x + 2? x + 2 Use the blocks to represent these expressions: • 3x + 1 • x – 6 • 2x – x + 4 - 2

  20. Pattern Finding – Algeblocks Activity What is the relationship between these two blocks? x x2 Use the blocks to represent these expressions: • x2 + x • 4x2 -7 • 3x2

  21. Pattern Finding – Algeblocks Activity What expression does this represent? 3 = 3(x + 2) = 3x + 6 x + 2 Use the blocks to represent these expressions: • 4(x + 2) • -2x(3) • (2x)(x – 3)

  22. Algeblocks Virtual Manipulatives NLVM website: http://nlvm.usu.edu/en/nav/category_g_3_t_2.html

  23. MCA Test Prep What are you doing in your district to help to prepare students for MCA testing? • test question prep? • Textbooks/supplementary materials used? • Websites you would recommend? SHARE with the whole group!

  24. MCA Test Prep MDE website: http://www.education.state.mn.us/mde/index.html Assessment & Testing MCA see various categories Texas Instruments Test Prep: http://education.ti.com Classroom activities State practice exams

  25. MCA Test Prep Minnesota Perspective (Pearson and State of MN): http://perspective.pearsonaccess.com/perspective/appmanager/mn/educator/ • Learning Locator # from MCA test Study Island: http://www.studyisland.com/demoAsk.cfm?myState=MN • Cost involved (Purchase per class or per person) Practice Planet: http://www.practiceplanet.com/pricing.php • Cost involved (Purchase per school, class or per person)

  26. Closing Thanks for coming today! Please fill out the evaluation forms and leave them on your tables. A copy of the Puppy Pen worksheet and the MCA Test Prep ideas will be posted on the Moodle site.

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