squaring off: connecting your knowledge

Unit 2: Looking for Pythagoras//Investigation 2//Connections

Name _______________________________________ Class ______________ Date ______________________________

Squaring Off: Connecting Your Knowledge

I can recognize and utilize the relationship between squares and square roots.

Math: ______ / 30 points

Reflection: _______ / 10 points

Total: ______ / 40 Points

For this packet, your goal is to earn 40 points. 30 points will be from the math problems. 10 points will be from the reflection section. Look at the point values of the following questions

and answer the questions that you feel most comfortable to answer.

1. Graph and label the following points:

A(2, 5) B(1, 1) C(4, 5) D(3, 2)

2. Graph and label the following points: J(-‐1, 4) K(-‐3, 3) L(-‐4, 5) M(-‐5, 2)

3. Graph and label the following points: P(4, -‐5) Q(0, -‐1) R(2, -‐3) S(1, -‐5)

4. Graph and label the following points: W(0, -‐2) X(-‐2, -‐1) Y(-‐5, -‐2) Z(-‐3, -‐5)

2 points

2 points

2 points

2 points

5. Find the positive and negative square roots of: 25



8. Solve for x:

9. Solve for x:

10. Solve for x:

11. Is the following statement TRUE or FALSE?

Explain or prove:

2 points

2 points

2 points

2 points

2 points

2 points

5 points

12. Is the following statement TRUE or FALSE?

Explain or prove:

13. Is the following statement TRUE or FALSE? 2 ⋅ 2 = 4

Explain or prove:

14. Find the area and side length of this square:

Area: Side Length:

5 points

5 points

5 points

15. In Problem 2.1, it was easier to find the “upright” squares. Two of these squares are represented on the coordinate grid below.

a. Are these squares similar? Explain.

b. How are the coordinates of the corresponding vertices related?

c. How are the areas of the squares related?

d. Add two more “upright” squares with a common vertex at (0, 0). How are the coordinates of the vertices of these new squares related to the 2 x 2 square?

e. How are their areas related?

10 points

16. Use the graph below to complete parts (a) – (c).

a. Add in points Q, R, and S so that you create a square (PQRS) with an area of 10 square units.

b. Name one vertex of your square that is 10 units from point P.

c. Give the coordinates of at least two other points (not on your square) that are also 10 units from point P.

17. The drawing below shows three right triangles with a common side.

a. Find the length of the common side.

10 points

10 points

b. Find the area of each of the three triangles:

c. Do the three triangles have the same area? Explain why or why not.

18. Find the areas of each of the triangles:

U: V: W: X: Y: Z:

10 points

Squaring Off: Reflection In this investigation you worked with square roots and explored squares and segments drawn on dot paper. You learned that the side length of a square is the positive square root of the square’s area. You also discovered that, in many cases, a square root is not a whole number. Answer the following questions in complete sentences. (This reflection is worth 10 of your total of 40 points.)

1. Describe how you would find the length of a line segment that connects two dots on dot paper. Explain

how you would find lengths of horizontal, vertical, and diagonal segments.

2. Explain what it means to find the square root of a number. (Think about what a square root is!)

3. Explain whether or not a number can have more than one square root. Include an example.

4. Why might it make more sense to keep a number written as a square root instead of simplifying to decimal form? For example, why might we want to write a number as 40 instead of simplifying it to 6.3?

5. How does the drawing of a square represent the relationship between a squared number and its square roots? (Think about parts of a square!)

squaring off: connecting your knowledge

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