50 Ideas in 60 MinutesAdd Differentiation toYOUR Math Classrom

Suzanne CulbrethSpain Park High School

sculbreth@hoover.k12.al.us

WHY???Differentiated Instruction: “a teacher’s response to learner’s needs”

“using various instructional methods to meet the needs of all students in the classroom”

Ways to differentiate:• Content• Process• Product• Learning Environment

Models &

Manipulatives

Technology

Cooperative

Activities

Models & Manipulatives1. Pythagorean Theorem Proof2. Tri-Square Rugs3. Homemade Trig Table4. Lily / Lulu / Lola5. Statue of Liberty’s Nose6. Pt/Lines/Planes Models7. Pt/Lines/Planes w/ Index Cards8. Patty Paper Parallel Lines9. Patty Paper Pts of Concurrency10. Patty Paper Parabola11. Shape Sorting12. Congruent Triangle Theorems13. Area Circle / Regular Polygon14. Types of Quadrilaterals15. Paper Plate Unit Circle16. Roller Coaster Slopes17. Volume of Sphere18. Surface Area of Sphere19. Foldables20. Graphic Organizers / Charts21. Puzzles for Reinforcement / Review22. Puzzles for Multistep Problems

Technology

Cooperative Activities

1. Lion / Tiger2. Mix & Match3. Mix Pair4. Round Table5. Pass Around Proofs6. Divide & Conquer 7. Inside / Outside Circle8. Fan-N-Pick9. Examples vs. Non-Examples10. Sequencing11. Pair / Share 12. Draw What I Say or Say What I Draw13. I have….Who has?14. LineUps

50 Ideas in 60 MinutesAdd Differentiation toYOUR Math Classrom

Suzanne CulbrethSpain Park High School

sculbreth@hoover.k12.al.us

Tri-Square Rug Game A rug designer decided to make a rug consisting of three separate square pieces sewn together at their corners, with an empty triangular space between them. The rug was an immediate hit, the designer decided to make more of them. She called these creations “tri-square rugs.” A sample rug is shown here.

Al and Betty thought these tri-square rugs could be used to make a great game. They made up these rules:

Let a dart fall randomly on the tri-square rug. If it hits the largest of the three

squares Al wins. If it hits either of the other two

squares Betty wins. If the dart misses the rug simply let

another dart fall.

Your challenge is to design 4 rugs - one each for Al wins, Betty wins, and Fair Game plus one of any type. Glue your rugs to unlined paper. Label who wins and total area on each square. On Al’s winning rugs, color the triangle red. On Betty’s winning rugs, color the triangle blue. On the Fair Game rugs, color the triangle green.

Analyze each triangle and see if you can determine a pattern as to who the winner will be.

Homemade Trig Table

The trigonometric functions are defined as ratios of the lengths of the sides of certain right triangles. One way to understand how these functions work is to draw the triangles and measure the sides to find the ratios.

Begin w/ a line 8 cm, 10 cm or 12 cm (one per each group member) and construct your smallest angle from one endpoint and 90° angle from other endpoint. Extend lines if necessary to form a right triangle. Measure sides to the nearest tenth of a centimeter. Label both angles and sides with their measurements.

Calculate sine, cosine and tangent of each acute angle rounding the ratio to the nearest thousandths. Record your calculations showing the ratio and the result of your division. Copy the tally chart from the back of this sheet and combine your ratios. (If one value is substantial different from the others, check the construction, the measurements and the calculations). Record your findings on the class chart.

Analyze the class results:

What happens to the sine ratio as the angle increases? What happens to the cosine ratio as the angle increases? What happens to the tangent ratio are the angle increases? WHY?? What is the range of the sine of an angle? What is the range of the cosine of an angle? What is the range of the tangent of an angle?

Activity 2: How to Shrink It? Lola, Lily and Lulu love Renata’s house, but find it a little too large. In other words, they want to shrink the house down to a smaller size while keeping exactly the same shape. After a long discussion, each came up with a different strategy. Lola’s Way: Keep all the angles as they are and subtract 5 cm from each side Lily’s Way: Keep all the lengths as they are and divide all the angles by two. Lulu’s Way: Keep all the angles as they are and divide the lengths of all the sides

by two. Try to shrink the house by using each of the methods above. Show what results each method produces (It is NOT necessary to redraw the original house, just the new one based on each different strategy) Explain why the method does or does not work. Each method should be on a separate sheet.

Points Lines and Planes

Given: lines l and m Plane A with points Y and Z Plane B with points W and X. Plane C

Model these relationships using the manipulatives. “Odd” partners demonstrates odd questions as “even” partner reads / “Even” partner demonstrates even questions as “odd” partner reads. Complete #16 & #17 in today’s notes using complete sentences. 1. Line l and m intersect at a point. 2. Line m intersect plane A at point Y. 3. Line l intersects plane B at W. 4. Planes A and B intersect in a line. 5. Panes A and B are parallel planes. 6. Line m intersects plane C at point V. 7. Line m is parallel to plane B 8. Planes A and B are parallel; and line m intersects plane A and B at points Y and X respectively.

Square

Pentagon

Hexagon

Octagon

LION• Listener• Recorder• Checker

Tiger• Talker• Give instruction

“Use Pythagorean Theorem to…..”

Write the formula for your shape with “B” replaced with the formula for area of the base. Analyze your shape and plug in the given values. Calculate perimeter if possible. (Do NOT calculate anything else.) Circle your answer, initial your work. Pass it in the clockwise direction when instructed.

On the new paper, check the previous work and coach if necessary. Place a checkmark by the circled work with your initials. Draw and label the auxiliary triangle. Compute the needed missing side (or altitude) of the triangle. Circle your answer, initial your work. Pass it in the clockwise direction when instructed.

Volume & Surface Area of Pyramids

A. Surface area = ? B. Volume = ? C. Surface area = ? D. Volume = ?

10 m

12 m

On the new paper, check the previous work and coach if necessary. Place a checkmark by the circled work with your initials. Draw and label the base. Compute the area of the base. Circle your answer, initial your work.

Pass it in the clockwise direction when instructed

≅ ∆ Proof Practice Pass Around Proofs: In your group, one person will write #1 while the rest of the group gives input.

Pass the paper to the next person to write #2. Continue until all proofs are complete. YES, you must include ALL five parts of the proof – given, prove, drawing, statement, reason.

1. Given: RS ≅ TS V is midpoint of RT Prove: △RSV ≅ △TSV 3. Given: ∠D ≅ ∠F GE bisects ∠DEF Prove: DG ≅ FG 5. Given: EG ≅ IA ∠EGA ≅ ∠IAG Prove: ∠GEN ≅ ∠AIN

2. Given: S is midpt of QT QR ∥ TU Prove: △QSR ≅ △TSU 4. Given: DA ∥ YN DA ≅ YN Prove: ∠NDY ≅ ∠DNA 6. Given: GH ∥ KJ GK ∥ HJ Prove: ∠K ≅ ∠H

Person A: __________________________ Person X: _________________________

Person A: Find the slope of each side of the quadrilateral

Person X check & initial _____

Person X: Name the sides which are legs and sides which are bases.

Person A check & initial _____

Person A: Find the length of the legs.

Person X check & initial _____

Person X: Name the type of quadrilateral.

Person A check & initial _____

Determine the type of quadrilateral: A (-5, -3) B(1, -2) C(6, 3) D(5, 7) #1

Person A: ___________________ _______ Person X: _______________________ __

Person X: Find the slope of each side of the quadrilateral

Person A check & initial _____

Person A: Name the sides which are legs and sides which are bases.

Person X check & initial _____

Person X: Find the length of the legs.

Person A check & initial _____

Person A: Name the type of quadrilateral.

Person X check & initial _____

Determine the type of quadrilateral: W(1, 4) X(4, 3) Y(-1, -2) Z(-2, 1) #1