What do you mean the math is

MORE RIGOROUS? What’s changed?

Judith T. Brendel

January 2011

Remember?“Just use the FORMULA!”

What is the average of these numbers? 80 85 90 85 70

Add them: 80 + 85 + 90 + 85 + 70 = 460Then divide: 460/5 = 92 is the average

What is the lowest grade Carl should get on his next project to keep the same average? His grades so far are 80 90 92 88 and 80

80+90+92+88+80 = 540 540 divided by 5 = 84 He needs to get at least an 84 on his next project.

Problem Solve not Memorize

What is the average of these four test scores? 80 85 90 85

Add them up and divide by 4. 340/4 = 85

The average of these four test scores is 85.

or just notice that you can borrow 5 from the 90, give it to the 80, and they’ll each be 85.

80 + 5 85 90 - 5 85

85 85 85 85

.

This was much fasterand

easier!

Why work in pairs?What should Alycia get on her next art

project to raise her average by one point? On her first 5 projects she averaged 85%.

Now: 85 x 5 = 425

Needs: 86 x 6 = 516

515 – 425 = 91

She needs to get at least 91%.

Now:

85 85 85 85 85

86 86 86 86 86 86

add 1 to each = + 6 more

85 + 6 = 91% on next project

I needed a

Numbers were easy;

I didn’t need a calculator.

Understand the Concept

The highest you can get on any test is 100%.

Is it still possible for Jim to get a 90% average if he has two more tests to take? His tests and project grades so far are:

88 84 93 and 80

+2 +6 (3) +10He needs = + 15

Yes, he needs 15 extra points. He could get

90 + 7 = 97 and 90 + 8 = 98

Yes, he needs 15 extra points. He could get

90 + 7 = 97 and 90 + 8 = 98

What is the lowest he can get on one of the tests and still have a 90% average? Explain!He can get a 95% on one and 100% on the other.

Why memorize facts?

1) X2 + 13x + 36 = 0 (x ) (x ) = 0 x + 4 = 0 x + 9 = 0 x = - 4 x = -9

Check: x2 + 13x + 36 = 0 (-4)2 + 13(-4) + 36 ? 0 16 – 52 + 36 = 0

-36 + 36 = 0

(-9)2 + 13(-9) + 36 ? 0 81 - 117 + 36 = 0

-36 + 36 = 0

2) X2 - 16x - 36 = 0 (x ) (x ) = 0

3) X2 + 9x - 36 = 0 (x ) (x ) = 0

+ 4 + 9 -18+ 2

+12- 3

4) X2 -37x + 36 = 0 (x ) (x ) = 0- 1 - 36

Why is it so important to be neat and organized?

48/4 = 12

12 x 12 = 144

6 x 3 = 18

(8x3)/2=12

Total = 30 sq.

SEE the CHANGES?

1) Area of rectangle? 2) Area irregular shape

3) Perimeter is 48; what is area of square?

4) Area shaded region?

area sq.=144

6

3 3

6

14

12

12

Shaded area =- s

Area of the square = 144 sq.units

3

Today’s math is MORE RIGOROUS

for ALL students