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POD 12/10

POD 12/10. 1. Find the volume of the following figure. 10 cm. 3 cm. 12 cm. Jumping to Conclusions. Two frogs, Alice and Fred, are near a path in the forest. Suddenly they hear footsteps on the path. To avoid possible danger, they jump away from the path.

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POD 12/10

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  1. POD 12/10 1. Find the volume of the following figure 10 cm 3 cm 12 cm

  2. Jumping to Conclusions • Two frogs, Alice and Fred, are near a path in the forest. Suddenly they hear footsteps on the path. To avoid possible danger, they jump away from the path. • Alice begins 8 decimeters from the path and Fred begins 18dm from the path. Each takes several jumps, then stops. What information would you need to find their new distances from the path? What information would you need to find their new distances from the path?

  3. What information would you need to find their new distances from the path?

  4. Suppose that Alice and Fred travel the same distance with each jump, but Alice takes 5 jumps and Fred takes 3 jumps. The diagram below illustrates their new positions. Alice 8 Fred 18 1a. Suppose that Alice and Fred travel 4 dm with each jump. Find the distance from the path to each frog's new position. Draw a diagram of this situation.

  5. 3. Suppose the frogs finish their jumps at exactly the same distance from the path, and you want to know the distance of each jump and each frog's final distance from the path. • Come up with a method in your group.

  6. Box A 8 x x x x x 8x + 5 = 18 + 3x x 18 x x • Explain how the equation • 8x + 5 = 18 + 3x describes the diagram in Box A.

  7. Explain the equation in Box B and describe how the diagram was changed from Box A to B. Box A 8 x x x x x 8x + 5 = 18 + 3x x 18 x x Box B x x 8 8 + 2x = 18 18

  8. Explain the equation in Box C and describe how the diagram was changed from Box B to C. Box B x x 8 8 + 2x = 18 18 Box C x x 2x = 10 10

  9. Explain the equation in Box D and describe how the diagram was changed from Box C to D. Box C x x 2x = 10 10 Box D x x = 5 5

  10. 10a. Write a 'frog problem' and an equation to represent the diagram below. x 14 6 x x x x x

  11. b. Draw the diagram for the next step in finding the value of x and write the equation for your diagram. • c. Complete the sequence of diagrams and equations.

  12. 11. Here is an equation: 12 + 2x = 6 + 4x. • Use a sequence of boxes to solve the equation. Start by drawing a diagram to represent each side of the equation. 12. a) Describe the equation 11 + 9x = 26 + 4x as a 'frog problem' b) Find the value of x in the equation and explain the steps of your solution.

  13. 13. Solve each equation for its unknown value and explain your method. How can you be sure if your answers are correct? a) 100 + w + w = 75 + w + w + w + w b) y + 42 + y = 12 + 3y + 2y c) 144 + z = 120 + 9z

  14. Exit Ticket!

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