engaging students with manipulatives and interactive ... materials/2017... · 17.04.2012  ·...

Engaging Students with

Manipulativesand

Interactive TechnologyGrades 5-8, 9-12

Maria Diamantis Heather Sauer

Southern Connecticut State University Branford High School

diamantism1@southernct.edu hsauer@branfordschools.org

Warm up exercise

How many triangles and trapezoids will be needed for the 34th design?

a)How many parallelograms will be needed for the 100th design?

b)Can a design be created using exactly 2209 parallelograms?

Warm up exercise

Agenda

1.Canoe problem and Tower of Hanoi

Manipulatives

Interactive Technology

2.Angle Sum Theorem

Pattern Blocks

Geogebra software

CCSSM for Mathematical Practice

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.3. Construct viable arguments 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 regularity in

repeated reasoning.

Canoe problemTen people are fishing from a canoe. The seats in the canoe are just wide enough for one person to sit on and the center seat is empty. The 5 people in the front of the canoe want to change seats, and so do the 5 people who sit in the back. A person changing seats may move to the next empty seat or step over one other person to reach an empty seat. What is the minimum number of moves needed to exchange 5 people in the front with the 5 in the back?

• CCS of Mathematical Practice : 1, 2, 3, 4, 6, 7

Let’s try a simpler case!

As you make the moves, record them as S for Slide and J for Jump.

Let’s Make a Table

Number of People

Number of Pairs

Number of Minimum Moves

Sequence of Moves

(Slide, Jump)

2 1 3 SJS

4 2 8

6 3 15

8 4

10

N

Tower of Hanoi

Let’s experience with two discs….

Discover the pattern as you generate a table (# of discs and least number of moves)

Number of discs Number of Minimum

Moves

Sequence of Moves(Slide, Jump)

2 3S J S

3 7 J SS J SS J4 15

5

n

Tower of Hanoi

Tower of Hanoi:Interactive Technology• Tower of Hanoi – Interactive website

•History of the Tower of Hanoi – Some background information

•NCTM Illuminations Activity – Lessons & activities

•Model with a function – discuss what patterns you observe.

Sum of the Interior Angles of a Polygon

Sum of the Interior Angles of a Polygon

• Pattern Blocks [square, triangle, hexagon, trapezoid and parallelograms (two)]

Determine the measure of each interior angle of each pattern block. You may use ONLY the fact that the square has four right angles. HINT: you may place combinations of blocks on top of a block to assist in determining the measures of the angles.

• CCS of Mathematical Practice : 2, 4, 5, 6, 7, 8

Use the pattern blocks to construct convex polygons…

a) Construct a pentagon and find the Sum of the Measures of the Interior Angles:

b) Heptagon

Make a table and find patterns…

Number of Sides Sum of the Measures of Interior Angles

3

4

5

6

7

8

9

n9

Angle Sum Theorem:

• Using Angle Measures to Find Polygon Angle Sums

• Using Diagonals to Find Polygon Angle Sums

• Discovering the Sum of Exterior Angles of a Polygon

• GeogebraTube!

Bibliography

1. Building Algebraic Thinking with Progressive Patterns – Pattern Blocks. Bob Willcutt, Critical Thinking Press

2. Mathematics Activities. Dan Dolan, Mari Muri, Jim Williamson, 12th ed., Pearson

3. Algebra in a Technological World. NCTM Addenda Series grades 9-12.

4. Principles to Actions, Ensuring Mathematical Success for All. NCTM.

Websites

1. http://www.coolmath-games.com/0-tower-of-hanoi

2. https://en.wikipedia.org/wiki/Tower_of_Hanoi3. http://illuminations.nctm.org/Activity.aspx?id=4

1954. http://tube.geogebra.org/material/simple/id/19

583255. http://tube.geogebra.org/m/19583316. http://tube.geogebra.org/m/5148977. http://tube.geogebra.org/

Thank you!!!

Hope you enjoyed our session and keep on teaching fun

mathematics!!!