February 23, Chapter 1. and Surface Area

Transcription

1 Chapter 1 and Surface Area

2 1. By tracing lines on the 1 cm graph paper provided, create three different sized squares. 2. Label the area of each square 3. Label the side length of each square How many different ways can you write the side length?

3 1. Draw three different squares at different angles but so that the points still match up with points on the graph paper (example below) 2. Label the area and side length of each - be ready to discuss how you obtained your answers What are some of the differences between the first set of squares you drew, and the second set?

4 Perfect Squares vs. Non Perfect Squares February 23, 2012

5 1. On your page, draw a square within a square (this will be easier if you simply trace the lines) 2. Can you express the small (inner) square's side length and area as a fraction? February 23, 2012

6 1. Sketch a Cube (anywhere on your page) 2. If you find this easy, try sketching a two cubes together, or a pyramid of cubes... February 23, 2012

7 1. Using a piece of 1 cm cardstock graph paper, create a net for a cube. 2. Cut our your net and build your cube. 3. Determine the total surface area of your cube (and be able to explain how you did so) February 23, 2012

8 1. Find a partner and compare your two cubes. Do they have the same surface area? Do they have the same volume? What is the combined surface area of your two cubes? 2a) Easy: Make a new object (tower) by stacking your two cubes). What is the new surface area? 2b) Harder: Create a "barbell" by inserting a pen or pencil into one side of each of your cubes. What is the surface area of your object?

9 1.1 Square Roots of Perfect Squares This playground has an area of 400 m 2. What length of fence is required to surround the playground?

10 1.1 Square Roots of Perfect Squares A square root is a number which when multiplied by itself, results in another number (called a square) Ex. 5 x 5 = = 5 Without using your calculator, make a list in your notebook of the squares of all whole numbers between 1 and 20: Square Root Square

11 The square of the side length of a square give us the area: A = bh or A = s 2 What is the area of a square with a side length of 11 cm? What is the side length of a square with an area of 11 cm 2 A = 81 m 2 Calculator Check! Know how to use square root and square buttons! What about with a fraction?

12 A square can be either perfect or non-perfect. A square is perfect if it's square root is a rational number.* *Rational numbers include integers, fractions, and all decimal numbers that either "end" or have repeating sequences Square: 4 cm 2 5 cm 2 25 cm cm cm cm 2 Side Length/ Square Root: Perfect (Y/N):

13 Also, a fraction in simplest form is a PERFECT SQUARE if it can be written as a product of 2 equal fractions. 7 9 x 7 9 = is therefore a perfect square Also, if the numerator is a perfect square AND the denominator is a perfect square, then the entire fraction is a perfect square! (Also called rational numbers) Which of the following are perfect squares?

14 Is it possible for a square to be smaller than it's square root? Working with decimals: - When you square a decimal, the product is smaller: 0.5 x 0.5 = x 0.8 = Decimal numbers follow the same patterns as non-decimals: 3 x 3 = x 0.3 = x 0.03 x x 300 = = = = = 300

15 Arrange the square roots on the number line without using your calculator:

16 Practice P Numbers: 3abc, 5abefg, 7bcefgh, 8a-f, 9bdfh, 10d, 12b Numbers: 13 Numbers: 14, 18, 19

17 1.2 Square Roots of Non-Perfect Squares 5 m A 5 m ladder is placed against a wall. The base of the ladder is 1.5 m from the wall. How far up the wall does the ladder reach? 1.5 m

18 What happens when you try to find the square root if 5.5 on your calculator? 5.5 =? To find the square root of a non-perfect square, we can benchmark, estimate, or use a calculator! Benchmarking Estimating Calculator 27 =? =? 0.38 =?

19 What happens when you try to find the square root of 5.5 on your calculator? 5.5 =? To find the square root of a non-perfect square, we can benchmarks & estimates, or use a calculator! Benchmarking & Estimating Calculator 27 =? =? 31 8 =? 0.38 =?

20 The Pythagorean Theorem often involves non-perfect squares: a 2 + b 2 = c 2 c b a h 14 cm 18 cm Steps: 1. Identify the hypotenuse (c 2 ) 2. Replace known variables 3. Solve for the unknown using your mad square root skills!

21 Find the value of the unknown side x 4 mm 2.7 mm 2 m h 14 cm x

22 Practice P Numbers: 4ab, 5abc, 6ab,7ac, 9ac, 10abd, 13, 17 Number: 14 Numbers: 16b, 19ab, 20b, Numbers: 22, 24

23 Section 1.1 and 1.2 Quiz February 23, 2012

24 Each of you have been given a different model made from blocks. Using a piece of graph paper, make a 2D drawing of the front, back, top, bottom, left side, and right side of your model. Tips to make it easier: - Make you drawing so that one square on the graph paper equals one block - You may write "front", "back" etc on your model as long as you erase it after When finished, assume one face of each cube has an area of 1 unit 2 and calculate the surface area of the model you were given.

25 1.3 Surface Area of Objects Made from Right Rectangular Prisms There are several different strategies to determine the surface area of composite objects made from rectangular prisms. 1. Count the number of exposed faces from a model or; 2. Create a top, bottom, front, back and side views and determine the area of each then add together or; 3. Determine the total surface area of each block and subtract the overlapping areas.

26 Method 1: Method 2: Method 3:

27 Sometimes you have to combine different stragtegies: 50 m 50 m 114 m 50 m 50 m 50 m 50 m

28 How would it change if this part was added? 50 m 50 m 114 m 50 m 50 m 50 m 30 m 50 m 30 m 30 m Would sketching side top, bottom, front, back, and side views work to calculate surface area for this object?

29 What if it was a building and had 4 m by 15 m door... and only the outside walls needed to be painted? 50 m 50 m 114 m 50 m 50 m 50 m 30 m 50 m 30 m 30 m

30 Practice P Numbers: 4cdef, 5, 6, 7, 8a,b Numbers: 10 Numbers: 11 Numbers: 12 And 17 for fun!!!!

31 1.4 Surface Areas of Other Composite Objects Review of Area formulas: Area of a Rectangle: A = bh (or if it's a square!) Area of a Triangle: Area of a Circle: A = bh 2 A = πr 2 Also, circumference will be important: c = πd

32 Calculate the total surface area of this cabin. 3.5 m 8 m 5 m

33 Calculate the total surface area of this cylinder: 18 cm 80 cm

34 One last one... and it's a tough one! Excluding the bow how many cm 2 of icing is required for this cake? (There is icing on the top of each layer, but not the bottom) 20 cm 16 cm 16 cm 40 cm 40 cm 14 cm 50 cm 14 cm

35 Practice P Numbers: 3de, 4b, 5 Numbers: 7 Numbers: 8, 11, 12, 14

36 Section 1.3 and 1.4 Quiz February 23, 2012

37 Unit Problem Complete the Project on Page 49. Your Project will be marked using the rubric provided. Have fun!