Commutative Property: Associative Property

Section 5.1 Mental Computations

Multiplication:

Commutative Property: Associative Property:

3(5)(5)(2) 3(5)(5)(2)

Distributive Property: Order of operations:

52+3 52+3

720+30 720+30

13∙18-13∙15 17∙5+17∙15

51(30) 101(47)

49(30) 98(25)

725+27 7198

Commutative and associative with factors:

24(5) Hint: 2∙12∙5 44(75) Hint: 4∙11∙25∙3

35(12) 25(18)

Powers of 10

12100 13(200)

Additive Identity and Multiplicative Identity:

3 + = 3 3 ( ) = 3

List the fact families for these:

1) 1)

2) 2)

Also: -3+3=0 3)

Special factors: 5X2=10 50X2=100 25X4=100 0.3X10 =3 0.06X100 = 6

Multiply by a number and then divide later. 3÷3=1 and 1∙a=a

130(5) Hint: 135(10) 44(25) Hint: 11(100)

35(0.2) 25(0.03)

13(15) Hint: 13(10+5) 16(15) Hint: 16(10+5)

16(35) Hint: 16(10+10+10+5) or 16(10+10+10+10-5)

Addition:

Arrays for addition

289+597 725+568

Add using place values. 289+597

Commutative Property: Associative Property:

3+5+5+2+3 2+5+5+2+3

Try: 13+2+5+7+15+21

Adding up and subtracting down: Taking from one add end and giving to the other:

3 - 3 = 0 and 0+a=a

3 + 2

199+17 236+198

283+105 106+259

Subtraction:

Adding up:

3-(3)=0

276-158 185-97 255-168

Subtracting down:

-3-(-3)=0

276-158 185-97 255-168

Division:

8÷2=4 , why?

Find 38÷3 without our standard algorithm.

Hint: 3X10=

3X2=

Find 210÷4 without our standard algorithm.

Using factors

Find 126÷18 without our standard algorithm.

Hint: 18=2∙9

126÷2= ÷2=

2∙632∙9=

Find 80÷5 without our standard algorithm.

Find 4500÷250 without our standard algorithm.

Using 3÷3=1: Multiplying and multiplying or/and dividing and dividing

Find 80÷5 without our standard algorithm.

Find 4500÷250 without our standard algorithm.

Find 220÷4 without our standard algorithm.

Please put away your calculators. Do the following problems mentally. There is only one rule: you cannot use the standard paper and pencil algorithms for the four operations, even if you are doing them without pencil and paper. Write out the mental steps you took to calculate the answer. And, yes, it takes longer to write out the steps than to do the calculation in your head! Try as many different strategies as you can think of.

a) b)

c) d)

e) f)

g) h)

i) j)

k) m)

n) o)

Mental Calculations for percents:

Answer the following mentally (no calculator):

1Find 10% of the following

a) $35 b) $40 c) 70 people d) 50 cents

2) Find the given percentage of 50: a) 10% b) 20% c) 60% d) 5% e)1%

3) Find the given percentage of 40: a) 10% b) 20% c) 60% d) 5% e)1%

4) Find the given percentage of 25: a) 10% b) 20% c) 60% d) 5% e)1%

(No calculator)

i)You are looking at shirt that costs $40 and you have a 20% off coupon. How much will you pay before tax?

ii) What if you find a 25% of coupon. How much will you pay before tax? (hint:25% = 20%+5%)

iii) You find a Vase that is originally priced $60 and is clearance 50%. How much will you pay before tax if you use your 25% off coupon?

iiii) If your bill comes out to $44.05 including tax. Approximately what tip should you leave if the customary tip is 15%?

On the back of this paper, complete the following review questions:

1) Determine the following mentally, writing enough to make your mental work clear.

A) 40% of 80 B) 15% of 300 C) 20% of 14 D) 100% of 71

E) 5% of 60 F) 120% of 20 G) 15 is 25% of ? H) 14 is 50% of ?

2) For each, describe two different strategies for performing the following computation mentally.

A) 29 + 58 / B) 74 – 24 / C) 8 15

Section 5.2 Estimation

Discuss in Groups:

Try the following and ask yourself, "is your estimate quick and accurate?"

We want estimates to be accurate and relatively quick. Good number sense helps with this.

Estimate the following:

Try the following alone and then discuss your answers in a group.

A) 391 × 612

B) 0.74 × 798

C) Is 40 ¸ 1.99 less than, equal to, or greater than 20? Explain, showing your understanding of a meaning of division.

D) 75.48% ´ 883.375 ´ is about ______.

Is your estimate (less than, equal to, greater than) the exact answer? (Don't figure the exact answer out!) ______because______

Estimate the indicated quantity and tell how you did it.

A) 15% of $51.07

B) 25% of 1998

C) 196% of 47

D) 48% of 212

E) A $215.87 bike is offered at 25% off. About how much is the discount? The sale price?

Section 5.3 Estimating Values of Quantities using Benchmarks

Benchmarks are personally meaningful and recognizable amounts that can be used to make size estimates. Benchmarks give us a reference point to compare to other amounts or values.

Part I

Part II

Part III

1. / Approximately how long is this line segment, in inches or in centimeters? Be sure to name the measuring unit you use.
______
What benchmark did you use?
2. / Name an item that costs approximately $500,000.
A) / A family car
B) / A jet plane
C) / A nice home
D) / A stereo
3. / If a paperclip is about 1 gram. What does a "kilo" in all of those drug movies represent.
4. / You pick up a 30 pound child. You are going to pick up your 150 lb friend. Can you imagine the amount of force you will need? What is your benchmark?
5. / You push your 150 lb. friend. You are going to push your 30 lb. brother. Can you imagine the amount of force you will need? What is your benchmark?
6. / i) Name two types of estimates you use in daily life.
ii) Name the benchmarks.
iii) Use the benchmark to estimate something.

5.4 SCIENTIFIC NOTATION

3,654,000,000,000,000,000 0.000000000123

1) 32300000000

2) 2588800000000000

3) 56575

4) 0.000000000562

5) 0.789

6) 0.000000589

7) 56.8

8) 99999

9) 123.55

10) 0.0000000005065

Scientific Notation to Decimal form

Estimate in standard notation:______

Answer in standard notation:______

Estimate in standard notation:______

Answer in standard notation:______

Estimate in standard notation:______

Answer in standard notation:______

Estimate in standard notation:______

Answer in standard notation:______

Extra: The earth is 150,000,000,000 meters from the sun, and the speed of light is 300,000,000 meters per second. How many seconds does it take light to reach the earth from the sun? Express your answer in scientific notation.

Extra: A tube of steel is 50 meters long. A washer, 0.0004 meters thick, can be cut from the tube. Each cut removes 0.0001 meters of material. About how many washers can be made from the 500 meter tube?