March Math March Math AcademyAcademy

Dr. Rhonda BonnstetterDr. 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/mindre

ad/mindread.html• Gopher Math – • http://www.learnenglish.org.uk/

games/magic-gopher-central.swf

• Navigations book – pg. 59-62

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

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

Tiling Around the GardenCommit 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.

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

Garden 0 1 2 3 4 5 6 7 8 …

Tiles

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 membersCommit to an outcome: With your groupDecide 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.

y

Tiling Around the Garden (3)

y = 2x + 6y =2(47) + 6y = 94 + 8y = 100

y

Tiling Around the Garden (3)

y

Tiling Around the Garden (3)

• 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.

Perimeter and Area Activity

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?

• 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

Pattern Finding – Algeblocks Activity

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?

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!

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?

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

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

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

Pattern Finding – Algeblocks Activity

What expression does this represent?

3 = 3(x + 2)

= 3x + 6 x + 2Use the blocks to represent these expressions:• 4(x + 2)• -2x(3)• (2x)(x – 3)

Pattern Finding – Algeblocks Activity

NLVM website:http://nlvm.usu.edu/en/nav/category_g_3_t_2.html

Algeblocks Virtual Manipulatives

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!

MCA Test Prep

MDE website:http://www.education.state.mn.us/mde/index.html

Assessment & TestingMCA

see various categories

Texas Instruments Test Prep:http://education.ti.com Classroom activities State practice exams

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)

MCA Test Prep

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.

Closing