Transcript 4-5 - PMS-Math

4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Warm Up
Simplify.
1. 52 25
2. 82
64
3. 122 144
5. 202. 400
4. 152
225
6. Evaluate (–3)4
81
7. Evaluate gh + 3k – gk for g = 2, h = 4, and k = 3.
8. Write the rule in words and as an equation.
7
X
5
10
15
20
Y
10
20
30
40
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
CMT Question of the day!
And Check Homework…
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
4-4 Lesson Quiz
Write each number in standard notation.
1. 1.72  104
17,200
2. 6.9  10–3
0.0069
Write each number in scientific notation.
3. 0.0053
5.3  10–3
4. 57,000,000
5.7  107
5. Write the rule in words and as an equation.
X
2
4
6
8
10
Y
1
2
3
4
5
Divide by 2, Y = x/2
T
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Learn to find square roots.
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Shade in graph paper to make each of the shapes below. Each shape is a
square.
Count and write the number of square tiles in each of the larger
squares below.
1.
2.
3.
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Count and write the number of square tiles in each of the larger
squares below.
1.
2.
3.
Continue to draw larger squares. Make one that is 7 tiles wide
and 7 tiles high; then make one that is 8 wide and 8 high. Count
the number of squares in each shape.
4. 7 by 7 = ___________
5. 8 by 8 = ______________
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Continue to draw larger squares. Make one that is 7 tiles wide and 7 tiles high;
then make one that is 8 wide and 8 high. Count the number of squares in each
shape.
4. 7 by 7 = ____
5. 8 by 8 = _______
Talk in your groups about the following questions. Be prepared
to discuss them if I call on you.
The numbers 1, 4, 9, 16, 25, etc. are known as perfect squares. Why
do you think they are called perfect squares?
How are the width and the height of the squares related? How are
they related to the total number of tiles?
How could you find the next numbers that are perfect squares without
tiles?
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Try This
Write down the first 10 perfect squares, starting with 0.
0, 1, 4, 9, ___, ___, ___, ___, ___, ___
Now subtract each number from the one after it.
1 , 3 , 5 , ___, ___, ___, ___, ___
What pattern do you see in the difference between two perfect
squares?
Use your answer from Exercise 3 above to find all perfect squares less
than 200.
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
-What’s the opposite operation to
addition?
-What’s the opposite operation to
multiplication?
-The opposite operation to squaring
a number is taking the square root.
62 = 36
36 = 6
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Find the two square roots of each number.
A. 49
–
49 = 7
49 = –7
B. 100
100 = 10
– 100 = –10
C. 225
–
7 is a square root, since 7 • 7 = 49.
–7 is also a square root, since
–7 • –7 = 49.
10 is a square root, since 10 • 10 = 100.
–10 is also a square root, since
–10 • –10 = 100.
225 = 15
15 is a square root, since 15 • 15 = 225.
225 = –15
–15 is also a square root,
since –15 • –15 = 225.
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Check It Out: Example 1
Find the two square roots of each number.
A. 25
–
25 = 5
25 = –5
B. 144
144 = 12
5 is a square root, since 5 • 5 = 25.
–5 is also a square root, since
–5 • –5 = 25.
12 is a square root, since 12 • 12 = 144.
– 144 = –12 –12 is also a square root, since
–12 • –12 = 144.
C. 289
289 = 17
–
17 is a square root, since 17 • 17 = 289.
289 = –17 –17 is also a square root, since
–17 • –17 = 289.
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Additional Example 2: Application
A square window has an area of 169 square
inches. How wide is the window?
Write and solve an equation to find the area of the
window.
132 = 169
So
169 = 13.
Use the positive square root; a negative length has
no meaning. The window is 13 inches wide.
Remember!
The area of a square is s2, where s is the
length of a side.
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Check It Out: Example 2
A square shaped kitchen table has an area of
16 square feet. Will it fit through a van door
that has a 5 foot wide opening?
Write and solve an equation to find the area of
the kitchen table
16 = 4
Use the positive square root; a negative length
has no meaning. So the table is 4 feet wide,
which is less than 5 feet, so it will fit through
the van door.
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Additional Example 3A: Evaluating Expressions
Involving Square Roots
Simplify the expression.
3 36 + 7
3 36 + 7 = 3(6) + 7
Evaluate the square root.
= 18 + 7
Multiply.
= 25
Add.
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Additional Example 3B: Evaluating Expressions
Involving Square Roots
Simplify the expression.
25 + 3
16
4
25 + 3 =
16
4
3
1.5625 +
4
25 = 1.5625.
16
= 1.25 + 3
4
Evaluate the
square roots.
=2
Add.
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Check It Out: Example 3A
Simplify the expression.
2
25 + 4
2 25 + 4 = 2(5) + 4
Evaluate the square root.
= 10 + 4
Multiply.
= 14
Add.
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Check It Out: Example 3B
Simplify the expression.
18 + 1
t2
4
18 + 1 = 9 + 1
t2
4
4
18 = 9.
t2
=3+ 1
4
Evaluate the square roots.
= 31
4
Add.
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Lesson Quiz
Find the two square roots of each number.
1. 81 9
2. 2500
50
Evaluate each expression.
3. 3 16 + 1
13
4. 7 9 – 2 49
7
5. Ms. Estefan wants to put a fence around 3 sides
of a square garden that has an area of 225 ft2.
How much fencing does she need?
45 ft
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Lesson Quiz for Student Response Systems
1. Find two square roots of each number.
64
A. 4
B. 8
C. 9
D. 16
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Lesson Quiz for Student Response Systems
2. Find two square roots of each number.
6400
A. 4
B. 8
C. 80
D. 800
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Lesson Quiz for Student Response Systems
3. Evaluate the expression.
A. 17
B. 17
C. 19
D. 72
4-5 Squares and Square Roots
Students will be able to find square roots.
Students will describe in writing what is meant by a perfect square.
Lesson Quiz for Student Response Systems
4. Evaluate the expression.
A. 4
B. 8
C. 16
D. 40