Name:_________________________________

Math

Notebook

Teacher:______________________________

L.86 – L.120

Math Notebook Rules:

1. Keep this notebook in your binder when you are not using it. It has a lot of important information!

2. Use this Math Notebook to help you with your homework.

Today’s Topic is: L.86 Multiplying Round Numbers Mentally Today’s Date: _______________________

Important Words:

Steps:

1. Multiply the first digits of the factors.

2. Count and then attach the zeros.

Example:

(1) Multiply mentally: 60 x 80 = 4,800

6 x 8 = 48

There is one zero in 60 and one zero in 80, so we attach two zeros to 48. The product is 4,800.

(2) Multiply mentally: 30 x $7.00 = ______

(3) Multiply mentally: 400 x 700 = ______

Think

Today’s Topic is: L.87 Multiplying Two-Digit Numbers, Part 1 Today’s Date: _______________________

Important Words:

Steps:

1. Multiply the ___________ digit.

2. Multiply the ___________ digit.

3. ____________ the products.

Example:

(1)

3 4

x 1 2

(2)

3 1

x 2 3

Today’s Topic is: L.88 Remainders in Stories About Equal Groups Today’s Date: _______________________

Important Words:

Steps:

1. Divide. 2. Identify exactly what the

question is asking.

Example:

The packer needs to place 100 bottles into boxes that hold 6 bottles each.

(boxes)

R ___ 6 ) 1 0 0 (bottles left over)

(bottles)

a) How many boxes can be

filled? _______

b) How many bottles will be left over? _______

c) How many boxes are needed to hold all the bottles? _______

Today’s Topic is: L.89 Mixed Numbers and Improper Fractions Today’s Date: _______________________

Important Words:

___________________: Fractions that are greater than or equal to 1.

Steps:

1. Draw the __________.

2. __________ the shapes.

3. __________ to show the mixed number or improper fraction.

Example:

(1) Draw circles to show that 2 34

= 114

.

234 = + + =

114

234 =

114

(2) Draw circles to show that 1 34

= 74.

Today’s Topic is: L.90 Multiplying Two-Digit Numbers, Part 2 Today’s Date: _______________________

Important words:

Steps:

1. Multiply the ___________ digit.

2. Multiply the ___________ digit.

3. Carry over where needed.

4. ____________ to find the total.

Example:

(1) 4 6

x 2 7

(2) 4 6

x 7 2

Today’s Topic is: L.91 Decimal Place Value Today’s Date: _______________________

Important Words: Steps:

Compare: 23.25 23.250

1. Both numbers have the same digits in the same places.

2. The zero in the thousandths place of 23.250 adds no value.

Example:

Subtract: 4.37 – 1.146

Subtraction

(1) Line up the decimal points.

(2) Fill the empty place with a zero to subtract from.

Hun

dred

s

Tens

One

s

Tent

hs

Hun

dred

ths

Thou

sand

ths

3 1 4 . 3 7 0

(dim

es)

(pen

nies

)

Today’s Topic is: L.92 Classifying Quadrilaterals Today’s Date: _______________________

Important Words:

Quadrilateral: Any ________ sided polygon.

Steps:

1. Parallelogram: ___ pairs of parallel sides.

2. Trapezoid: ___ pair of parallel sides.

3. Rectangle: ___ right angles. 4. Rhombus: sides are ______ in

length. 5. Square: sides are _______ in

length and angels are all ______ angles.

Example:

Name the quadrilaterals.

__________

__________

__________

__________

Today’s Topic is: L.93 Estimating Multiplication and Division Answers Today’s Date: _______________________

Important words:

Product: Answer in a __________________ problem.

Quotient: Answer in a __________________ problem.

Steps:

Estimate the product of 38 and 53 by rounding the numbers.

Example:

Estimate the quotient when 1,845 is divided by 6 by choosing a number close to 1,845 that is easily divided by 6.

6 ) 1 , 8 4 5

→ ) .

Today’s Topic is: L.94 Two-Step Word Problems Today’s Date: _______________________

Important words:

Steps:

To help you solve two-step word problems:

1. Write down the given information.

2. Draw a picture.

Example:

(1) Jim is 5 years older than Ali. Ali is 2 years younger than Blanca. Blanca is 9 years old. How old is Jim?

Step 1 Step 2

Ali Blanca Jim 2 years younger

than Blanca

9 years old

5 years older than

Ali

= ___ yrs old

= ___ yrs old

(2) Carlos paid for 5 pounds of apples with a $10 bill. He got back $6. What was the cost of each pound of apples?

Step 1 ~Find out how much all 5 pounds of apples cost?

Step 2 ~ To find the cost of each pound of apples divide the cost for 5 pounds by 5.

$10.00

- $ 6.00 $ . .

$ . .

) $ . .

Today’s Topic is: L.95 Two-Step Problems about a Fraction of a Group Today’s Date: _______________________

Important Words:

Steps:

1. Divide to find the number in one part.

2. Multiply to find the number in more than one part.

Example:

There were 30 campers in the forest. Three fifths of them wore green jackets. How many campers wore green jackets?

35

𝑜𝑜𝑜𝑜 30 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = ___𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 Divide and multiply answer by the numerator.

(1) 0

5 ) 3 0

(2) __ x 3 = ___ campers

(3) 30 campers

35 wore green

jackets { (___) (___) (___)

25 did not wear

green jackets {

Today’s Topic is: L.96 Average Today’s Date: _______________________

Important words:

Average: also called the mean.

Steps:

(1) Add the numbers.

(2) Divide the sum by the number of items.

Example:

Jan scored 95, 85, 63, 52 and 100 on his last 5 math tests. What was the average of Jan’s tests?

(1) Add all the scores. (2) Divide the sum by the number of tests to get the average.

) .

Average = ______

Today’s Topic is: L.97 Mean • Median • Range • Mode Today’s Date: _______________________

Important Words:

____________: Average.

____________: Middle number.

____________: The difference between the smallest and biggest numbers.

____________: The number that appears most.

Important Words:

____________: a number that is distant from other numbers in a list.

Example:

Mean (average) 1. Add the numbers. 2. Divide by the number of items.

Example: Find the mean of the following scores – 70, 30 and 100.

70 30

+ 100 ___

) .

Median (middle number) 1. Arrange the numbers by size. 2. Identify the middle number.

2, 3, 6, 9, 11 3. If there are 2 middle numbers,

the median is their average. 2, 3, 6, 8, 9, 11

6 + 8 = ____ ÷ 2 = ___

Range (Difference between largest and smallest numbers)

1. Arrange the numbers by size. 2. Subtract the smallest number

from the largest number. 10, 80, 85, 85, 85, 90, 90

90 – 10 = ___

Mode (Number that occurs the most.)

80, 85, 85, 10, 90, 90, 85

___

Today’s Topic is: L.98 Geometric Solids Today’s Date: _______________________

Important Words:

Geometric Solids: Geometric shapes that take up __________. __________: A flat surface of a solid.

Important Words:

___________: Where two faces meet. ___________: Where three or more edges meet (corner). __________: More than one vertex (corners).

Example

Geometric Solids

Shape Name

Today’s Topic is: L.99 Decimal Numbers and Money Today’s Date: _______________________

Important Words:

Steps:

1. To write cents, we use a cent sign (₵) and do not use a decimal point.

2. To write dollars, we use a dollar sign ($) and a decimal point to show fractions of a dollar.

Example:

Something is wrong with this sign. Draw two different signs to show how to correct the error.

Kit Kats .50₵ each

Today’s Topic is: Investigation 10 Probability Today’s Date: _______________________

Important Words:

____________: result.

____________: the degree of likelihood of an outcome.

Steps:

The probability of an outcome can be expressed as a number ranging from ___ to ____.

The chance of an event is sometimes expressed as a percent from ___% to ____%.

Example:

Probability

0 – An outcome that ____________ happen.

1 – An outcome that is ____________ to happen.

An outcome that could happen, but is not certain to happen is expressed as a fraction between 0 and 1.

Example: What is the probability of rolling a 2 with one roll of a die?

___

Chance

0% chance means there is ____ chance of that event happening.

100% chance means the event is ____________ certain to happen.

Examples: (1) If the chance of rain is 20% is

it more likely to rain or not rain? ___________________

(2) There is 80% chance of snow.

What percent chance is there that it will not snow?

L.100 Follow the teacher’s directions to construct Geometric Models.

100% - 80%

%

Today’s Topic is: L.101 Tables • Schedules Today’s Date: _______________________

Important Words:

__________: another way of presenting number information.

__________: a list of events organized by the times at which they are planned to occur

Steps:

____________ when comparing numbers such as heights.

Example:

Heights of Major Mountains

Mountain Feet Meters Everest 29,035 8,850 McKinley 20,320 6,194 Kilimanjaro 19,340 5,895 Matterhorn 14,691 4,478 Pike’s Peak 14,110 4,301 Fuji 12,388 3,776

(1) How many meters taller is the Matterhorn than Pike’s Peak?

School-Day Schedule

6:30 a.m. Wake-up 7:30 a.m. Leave for school 8:00 a.m. School starts 12:00 p.m. Eat lunch/recess 2:45 p.m. School ends 9:00 p.m. Go to bed

(1) If lunch and recess together last 45 minutes, how many hours are spent in class?

Today’s Topic is: L.102 Decimal Number Line: Tenths and Hundredths Today’s Date: _______________________

Important Words:

Steps:

162 cm = ? meters

100 cm = 1 meter, so 162 cm is 1 meter plus 62 cm.

162 cm = . meters

Example:

↓

9 10

(1) What decimal number is the arrow pointing to?

__________

(2) Round 9.6 to the nearest whole number. (Halfway from 9 to 10 is 9.5. Think 9.6 is greater than 9.5).

__________

↓

7.5 7.6

(1) What decimal number is the arrow pointing to?

__________

(2) Round 7.52 to the nearest tenth. (Think - this is like rounding $7.52 to the nearest ten cents.)

__________

Today’s Topic is: L.103 Fractions Equal to 1 and ½ Today’s Date: _______________________

Fractions Equal to 1

22

33

44

55

A fraction equals 1 if its numerator and denominator are equal.

Write a fraction equal to 1 that has a denominator of 7. ___

Fractions Equal to ½

12

24

36

48

If the numerator of a fraction is half the denominator, then the fraction equals ½.

Example:

Compare:

38

12

�= 48�

The fraction 48 is equal to 1

2.

38 is less than 4

8, so 3

8 is ______

_____ 12.

Round:

6 710

to the nearest whole number.

Halfway between 6 and 7 is 6 12 or

6 510

.

6 710

is greater than 6 510

�6 12� so

6 710

is rounded to _____.

Today’s Topic is: L.104 Changing Improper Fractions to Whole or Mixed Numbers Today’s Date: _______________________

Important Words:

__________ __________: When the numerator is equal to or greater than the denominator.

Example: 124

Steps:

1. Divide

2. If there is no remainder, write the answer as a whole number.

3. If there is a remainder, the remainder becomes the numerator in a mixed number.

Example:

Write 135

as a mixed number. Draw a picture to show the improper fraction and the mixed number are equal.

02R3 5 ) 13

- 10 3

= 235

135 =

55 +

55 +

35 = 2

35

Today’s Topic is: L.105 Dividing by 10 Today’s Date: _______________________

Important Words: Steps:

1. Divide

2. Multiply

3. Subtract

4. Bring down.

(The remainder is the last digit of the dividend.) There is no remainder if the last digit of the dividend is 0.

Example:

R 10 ) 4 3 2

1. Put a placeholder above the “4”

2. Divide 43 by 10 and write “4” next to the placeholder.

3. Multiply 4 by 10 and write “40”.

4. Subtract 40 from 43 and write “3”.

5. Bring down the 2. 6. Divide 32 by 10 and

write “3”. 7. Multiply 3 by 10 and

write “30”. 8. Subtract 30 from 32

and write “2”. 9. There is no number to

bring down, write the “2” as a remainder.

Today’s Topic is: L.106 Evaluating Expressions

Today’s Date: _______________________

Important Words:

Evaluate: to find the value of an expression.

Expression: any combination of symbols, numerals or operators.

Steps:

1. Substitute the number in place of the letter.

2. Perform the calculation.

Example:

If R is 5, then what is the value of these expressions?

a) R + 3 b) R – 3 c) 3R

Today’s Topic is: L.107 Adding and Subtracting Fractions with Common Denominators Today’s Date: _______________________

Important Words:

23

Steps:

1. When adding/subtracting fractions, add or subtract the numerators only.

2. Keep the denominators the same.

Example:

(1) 35

+ 15

=5

(2) 35− 1

5=

1. When adding/subtracting mixed numbers, write the numbers above each other.

2. Add/subtract the fraction and then the whole number.

2 35

+ 3 15

=

235

+ 315

5

45

numerator

denominator

Today’s Topic is: L.108 Formulas • Distributive Property Today’s Date: _______________________

Important Words:

Formula: A rule, fact or relationship expressed by an equation.

Steps: Some Common Formulas

Area of a Rectangle 𝐴𝐴 = 𝐿𝐿𝐿𝐿

Area of a Triangle 𝐴𝐴 =𝑏𝑏ℎ2

Perimeter of a Rectangle

𝑃𝑃 = 2(𝐿𝐿 + 𝐿𝐿) 𝑃𝑃 = 2𝐿𝐿 + 2𝐿𝐿

Area of a Square 𝐴𝐴 = 𝑐𝑐2

Perimeter of a Square 𝑃𝑃 = 4𝑐𝑐

Example:

Distributive Property

𝑃𝑃 = 2(𝐿𝐿 + 𝐿𝐿)

8 cm 5 cm

𝑃𝑃 = 2 ( 8 𝑐𝑐𝑐𝑐 + 5 𝑐𝑐𝑐𝑐 )

16 𝑐𝑐𝑐𝑐 + 10 𝑐𝑐𝑐𝑐 = ___ 𝑐𝑐𝑐𝑐

(1)

(2)

Today’s Topic is: L.109 Equivalent Fractions Today’s Date: _______________________

Important Words:

Equivalent Fractions: Different fractions that name the same amount.

Steps:

1. Multiply a fraction by a fraction name for 1 to find an equivalent fraction.

Example:

Find four equivalent fractions to 12 by multiplying 1

2 by 2

2, 33, 44 and 5

5.

1. 12

× 22

= 24

=

2. 12

× 33

=

3. 1

2× 4

4=

4. 1

2× 5

5=

Today’s Topic is: L.110 Dividing by Multiples of 10 Today’s Date: _______________________

Important Words:

Multiples of 10: are the numbers we say when we count by 10 such as 10, 20, 30, 40, 50 etc.

Steps:

1. To help us divide by a two-digit number, we may think of dividing by the first digit only. (Ignore the last digit in each number when dividing.)

2. Multiply

3. Subtract

4. Bring down where needed

Example:

Do not write the 3 above the 7!

0 3R12 2 0 ) 7 2

- 6 0 1 2

0 0 4R7 3 0 ) 1 2 7

- 1 2 0 7

Think: 2 ) 7 Think: 3 ) 12

Today’s Topic is: Investigation 11 Volume Today’s Date: _______________________

Important Words:

Volume: the amount of __________ a shape occupies.

Cubic units: are used to measure volume. Examples – cubic feet, cubic inches, cubic cm and cubic meters.

Steps:

𝑉𝑉𝑜𝑜𝑉𝑉𝑉𝑉𝑐𝑐𝑐𝑐 = 𝐿𝐿 × 𝐿𝐿 × 𝐻𝐻

𝑉𝑉𝑜𝑜𝑉𝑉𝑉𝑉𝑐𝑐𝑐𝑐 = 𝑉𝑉𝑐𝑐𝑙𝑙𝑙𝑙𝑙𝑙ℎ × 𝑤𝑤𝑤𝑤𝑤𝑤𝑙𝑙ℎ

× ℎ𝑐𝑐𝑤𝑤𝑙𝑙ℎ𝑙𝑙 (𝑤𝑤𝑐𝑐𝑐𝑐𝑙𝑙ℎ)

Example:

2 cm (height)

2 cm (width)

3 cm (length)

𝑉𝑉𝑜𝑜𝑉𝑉𝑉𝑉𝑐𝑐𝑐𝑐 = ___ 𝑐𝑐𝑐𝑐 × ___ 𝑐𝑐𝑐𝑐 × ___ 𝑐𝑐𝑐𝑐 = ___ 𝑐𝑐𝑉𝑉𝑏𝑏𝑤𝑤𝑐𝑐 𝑐𝑐𝑐𝑐

Today’s Topic is: L.111 Estimating Area Today’s Date: _______________________

Important Words:

Steps:

1. Count all the entire squares. 2. Estimate the number of entire

squares that could be formed with the remaining partial squares or count all the squares that seem to have at least half their area.

Example:

Each small square represents one square inch.

Estimate the area of the bottle.

About ________ square inches.

Today’s Topic is: L.112 Reducing Fractions Today’s Date: _______________________

Important Words:

Reduce a Fraction means to find an equivalent fraction written with smaller numbers.

Steps:

• Only a fraction whose numerator and denominator can be divided by the same number can be reduced.

• To reduce a fraction, we will use a fraction equal to 1.

Example:

(1) 68

÷ 22

= (The numerator and denominator can both be divided by 2.)

(2) 36

÷ = (The numerator and denominator can both be divided by __.)

(3) 67

÷ 11

= * This fraction cannot be reduced. (The only number that divides both 6 and 7 is 1.)

Today’s Topic is: L.113 Multiplying a Three-Digit Number by a Two-Digit Number Today’s Date: _______________________

Important Words:

____________: the answer in a multiplication problem.

Steps:

1. Write the three-digit number above the two-digit number.

2. Line up the last digits in each number.

Example:

3 6 4 x 2 4

1. Multiply 364 by 4. 2. Put a ‘0’ placeholder and

multiply 364 by 2. 3. Add to find the product.

Today’s Topic is: L.114 Simplifying Fraction Answers Today’s Date: _______________________

Important Words:

Reduce: to rewrite a fraction in lowest terms.

Steps:

1. Write improper fractions as mixed numbers.

2. Reduce when possible.

Example:

Add: 23

+ 23

23

+ 23

= 43

= 43 is an improper fraction. Change

it to a mixed number.

Subtract: 34− 1

4

34− 1

4= 2

4=

Reduce: 24

÷ 22

=

1 R1 3 ) 4

- 3 1

113 Subtract: 6 5

8− 1 3

8

658− 1

38

= 528

5 28

=

Today’s Topic is: L.115 Renaming Fractions Today’s Date: _______________________

Important Words:

Steps:

1. When we multiply a fraction by a fraction name for 1, the result is an equivalent fraction.

2. Sometimes we must choose a particular multiplier that is equal to 1.

Example:

(1) Find the equivalent fraction for 14

whose denominator is 12.

To change 4 to 12, we must multiply by 3. So we multiply 1

4 by 3

3.

14 ×

33 =

The fraction 14 is equivalent to ______.

(2) Complete the equivalent fraction:

23 =

?15

23 × 5 = 15

The denominator is changed from 3 to 15. Since the denominator was multiplied by 5, the numerator must be multiplied by 5.

Today’s Topic is: L.116 Common Denominators Today’s Date: _______________________

Important Words:

Common Denominators: Two or more fractions that have equal denominators.

Example: 25

35

Steps:

To rename fractions so they have a common denominator, multiply each fraction by a fraction name for 1.

Example:

(1) Rename 23 and 3

4 so they have a common

denominator of 12.

23 × = 12

34 × = 12

(2) Rename 12 and 1

3 so they have a

common denominator.

This time we must find a common denominator by listing multiples of 2 and 3. Choose the least common denominator.

Multiples of:

2: 2, 4, 6, 8, 10, 12

3: 3, 6, 9, 12, 15

12 × = 6

13 × = 6

Today’s Topic is: L.117 Rounding Whole Numbers Through Hundred Millions Today’s Date: _______________________

Important Words: Steps:

Example:

(1) Round T TH38,274 to the nearest ten thousand.

38,274 is between the multiples 30,000 and 40,000.

Halfway between 30,000 and 40,000 is 35,000.

38,274 is greater than 35,000 so we round 38,274 to __________.

hund

red

mill

ions

ten

mill

ions

mill

ions

hund

red

thou

sand

s

ten

thou

sand

s

thou

sand

s

hund

reds

tens

ones

_ _ _, _ _ _, _ _ _

Today’s Topic is: L.118 Dividing by Two-Digit Numbers Today’s Date: _______________________

Important Words:

Steps:

1. Put placeholders in the answer.

2. Ignore the last digits.

3. Divide

4. Multiply (If bottom number is larger – Start over!)

5. Subtract

6. Bring down

Example:

(1) 0 0 6

4 3 ) 2 4 6 - 2 5 8

(2) Choose 1 digit less than 6

0 0 5 R31 4 3 ) 2 4 6

- 2 1 5 3 1

Start over! (258 is greater than 246)

Today’s Topic is: L.119 Adding and Subtracting Fractions with Different Denominators Today’s Date: _______________________

Important Words:

Steps:

1. Rename the fractions so they have common denominators.

~ Rename a fraction by multiplying it by a fraction name for 1.

Example:

Add: 14

+ 38

Rename

14 ×

22 =

28

+38 +

38

Today’s Topic is: L.120 Adding and Subtracting Mixed Numbers With Different Denominators Today’s Date: _______________________

Important Words:

Steps:

1. Rewrite the problem so that the fractions have common denominators

2. Add or Subtract. 3. Reduce the fraction part of

your answer when possible..

Example:

(1) Add 4 16

+ 2 12

Rename 12 so that it has a

denominator of 6 by multiplying 12

by 33.

(12

× 33

= 36)

416

+236

(2) Subtract 5 34− 3 5

8

Rename 34 so that it has a

denominator of 8 by multiplying 34

by 22.

(34

× 22

= 68)

568

−358