My Math Journal Grade 6

CHALLENGE YOURSELF!

In a survey of university students,
64 had taken mathematics course, 94 had taken chemistry
course, 58 had taken physics course, 28 had taken mathematics
and physics, 26 had taken mathematics and chemistry, 22 had
taken chemistry and physics course, and 14 had taken all the
three courses. Find how many had taken one course only.

-47-

Integers

-48-

Integers

-49-

What did you learn in this unit? Have you ever thought
Can you briefly summarize? "WHY" while working ?
Where can you use these
subjects in your daily life?

If you want to visualize this unit what would it be like?
You may design a cover page for your Booklet #2

-50-

VOCABULARY

SELF ASSESSMENT

I can understand the basic concepts of sets.
I can identify integers and plot them on the
number line.
I can compare and order the integers.
I can identify the absolute value of an
integer.
I can use terminology about sets and
integers.

-51-

GUESS THE GUINNESS
WORLD RECORDS

81 +162 -89 834 100 -2 217 2910

........... laptops toppled
like dominoes

to break world record

World's largest ...........°C degrees is the
vegan burger smashes lowest temperature
recorded on Earth.
record at whopping
........... kg

Lewis Pugh swam 18
minutes 50 seconds in
the Arctic Ocean and the
water temperature was
approximately...........°C

Most football touches Ashrita Furman
in one minute balanced ......... glasses

whilst wearing 5 kg on his chin for 12.10
ankle seconds.

weights is ........... A new record for the most
varieties of cheese on a
Ashrita Furman
crammed .......... pizza has been set by three
chefs in Lyon, France. The
scoops of
chocolate ice pizza was topped with
cream onto a ........... different varieties of
single cone.
cheese.

A)+162 B)2910 C)-89 D)217 E)-2 F)81 G)100 H)834

ARRANGING
INTEGERS

Positive and Negative Integers

Learning goal: To practice arranging positive and negative integers
in ascending and descending order.

Arrange the following sets of numbers in ascending order:
3, -2, 13, -10, 2, -3, 4 , |-12|, -1

-101, 111, -51, |15|, -151, 5, |-15|, -15

-205, -25, 20, 5, -2, 102, -105, 152

Arrange the following sets of numbers in descending
order:
13, 11, -13, -4, 8, -6, 3, |-3|, -3, -16

-1, -15, 13, 12, -8, -16, 7, 2, 0
202, -10, -11, -21, 102, -2, 120, |-203|, 22

-53-

KEN KEN PUZZLE

YOUR GOAL IS TO FILL IN THE WHOLE GRID WITH NUMBERS, MAKING SURE
NO NUMBERS IS REPEATED IN ANY ROW OR COLUMN.
IN A 3X3 PUZZLE, USE THE NUMBERS 1–3. IN A 4X4 PUZZLE, USE THE
NUMBERS 1–4, AND SO ON.
THE MATH OPERATION TO USE CAN BE ADDITION, SUBTRACTION,
MULTIPLICATION AND DIVISION. THE OPERATION TO BE USED IS
INDICATED AT THE CORNER OF THE RELATED AREA.

-54-

KAKURO

EACH PUZZLE CONSISTS OF A BLANK GRID WITH SUM-CLUES IN VARIOUS PLACES.
THE OBJECT IS TO FILL ALL EMPTY SQUARES USING NUMBERS 1 TO 9 SO THE SUM OF
EACH HORIZONTAL BLOCK EQUALS THE CLUE ON ITS LEFT, AND THE SUM OF EACH
VERTICAL BLOCK EQUALS THE CLUE ON ITS TOP.
NO NUMBER MAY BE USED IN THE SAME BLOCK MORE THAN ONCE.

-55-

FRACTIONS & DECIMALS

Let's remember fractions
Comparing fractions
Addition and subtraction of fractions
Multiplication and division of fractions
Estimation and problems with fractions
Conversion and expanded form of decimals
Rounding decimals
Multiplying decimals
Division with decimals
Problems with decimals

-56-

Fractions - Review

Efqruacivtaiolennst Find the missing parts.

-57-

Fractions - Review

-58-

Comparing fractions

Cformacptiaorninsg Use <, = , > symbols to show which fraction is greater.

-59-

Additions and Subtraction of fractions

SSTSTETEEPPPTTHOWRNOEEE:: AG: SDEITDMAPOLRCIOFSYMUTBMHTOERNARDCETESNUTHOLTEMINIFNUNAMETEEODRRAE. DTO. RS.
-60-

Additions and Subtraction of fractions

-61-

Solve every questions carefully. Simplify your results. Find your
answer and shade related box as shown on model.

-62-

-63-

Multiplications of fractions

-64-

Division of fractions

-65-

Problems with fractions

Let's remember fractions
Comparing fractions
Addition and subtraction of fractions
Multiplication and division of fractions
Estimation and problems with fractions
Conversion and expanded form of decimals
Rounding decimals
Multiplying decimals
Division with decimals
Problems with decimals

-66-

SELF ASSESSMENT

I can compare and order fractions and plot
them on the number line.
I can add and subtract fractions.
I can multiply a natural number by a fraction
and identify it.
I can solve problems about four operations.
I can multiply two fractions and identify it.
I can divide a natural number into a fraction
and a fraction into a natural number and I
can identify this operation.
I can divide two fractions and identify this
operation.
I can estimate the result of operations with
fractions.
I can solve problems that require operations
with fractions.
I can associate the notion of fraction with
division.

-67-

MUSIC and FRACTIONS

"Math is everywhere" you may
have told that several times by

your teachers.
Let's watch the video to see how

the math and music is linked.
Reflect on the video. How the math is used in music?

.........................................................................................
.........................................................................................
.........................................................................................
.........................................................................................
.........................................................................................

Now, search and take note of which fraction represents which notes.

-68-

MUSIC and FRACTIONS

Let's see another video and then sing together.

till 8.45

Create Your Song

Use fraction pies and notes together with Aztec Drum Syllables

Write the related notes on the staff.

-69-

Decimals

-70-

Rounding decimals

-71-

Operations on decimals

-72-

Operations on decimals

-73-

-74-

What did you learn in this unit? Can you briefly summarize?

Have you ever thought "WHY" while working ?
Where can you use these subjects in your daily life?

-75-

If you want to visualize this unit what would it be like?
You may design a cover page for your Booklet #3

-76-

VOCABULARY

-77-

SELF ASSESSMENT

I can write the expanded form of decimals.
I can round decimals to a certain digit.
I can do multiplication with decimals.
I can do division with decimals.
I can multiply and divide decimals by
powers of 10.
I can estimate the result of operations with
decimals.
I can solve problems that require operations
with decimals.
I can use terminology about fractions and
decimals.

TEACHER NOTES

-78-

My Plan

Write three words in each category.

Three people you will spend time with
Three places you will visit
Three activities you will do
Three things you will buy
Three songs you will listen
Three movies you will watch
Three desserts you will eat

Three colors you connect with your holiday

Three games you will play
Three lessons you will study

-79-

RMidatdhles

-80-

KAPREKAR'S CONSTANT
6174

What is 6174?

6174 is known as Kaprekar's constant as it
was invented by Indian mathematician DR
Kaprekar in 1949.

What is special about it?

Kaprekar constant, or 6174, is a

constant that arises when we take a
4-digit integer, form the largest and

smallest numbers from its digits, and
then subtract these two numbers.

Continuing with this process of

forming and subtracting, we will
always arrive at the number 6174.

Let's Watch Let's try :)

3872

-81-

We are introduced to a “pyramid” of numbers
of sorts in chapter 7.
What is the name of this famous triangle?
Fill all the boxes below and color.

-82-

Describe what the
Number Devil means
by this – using your
own words , the
information and
pictures on chapter 7.
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________

-83-

Scientists and engineers across the world are currently 1)................................
trying to develop better ways to generate the electricity 2)................................
needed to power the world. One way that is already in use 3)................................
is solar panels.
List at least three places different from the pictures
above where you see these panels are being used.

There are many different ways of generating
electricity such as using renewables such as wind,
wave and hydroelectric power, using nuclear
power or burning fossil fuels such as coal and gas.
What are the advantages and disadvantages of
solar panels over other ways of generating
electricity?

...............................................................

...............................................................

...............................................................

-84-

Our School has planted about 3596 solar panels
(area of one panel is approximately 5 meter
square) on rectangular region. Each solar panel
produces 270 Watt of energy.
MAKE A FIELD TRIP TO OUR SCHOOLS SOLAR
PANELS FIELD. THEN ANSWER THE QUESTIONS
BELOW:
A) WHAT IS THE TOTAL AREA OF THE SOLAR
PANELS?

B) IF ONE PANEL IS 350 US DOLLARS THEN WHAT IS
THE TOTAL PRICE OF THE SOLAR PANELS?

C) WHAT IS THE TOTAL ENERGY OF THE SOLAR
PANELS (IN WATTS)?

D) IF THE AVERAGE ANNUAL ENERGY CONSUMPTION
OF OUR SCHOOL IS 3.9 MEGAWATT, CALCULATE
THE PERCENT OF ENERGY THAT WILL BE PROVIDED
BY THE SOLAR PANELS.
(1 MEGAWATT IS 1 000 000 WATTS)

-85-

WEEKS Weekly Plan / Main Topics

Week 20 SPRING BREAK
February 6-10
-86-
Week 21
February 13-17

Week 22
February 20-24

Week 23
Feb 27-March 3

Week 24
March 6-10

Week 25
March 13-17

Week 26
March 20-24

Week 27
March 27-31

Week 28
April 3-7

Week 29
April 10-14

April 17-21

PRE-ALGEBRA

ALGEBRA

GEOMETRY

STATISTICS

NUMBERS

Equivalent ratios
Rate vs unit rate
km/h to m/s
Algebraic expression
Substitution
Simplifying algebraic expression

-87-

Equivalent ratios

-88-

Rate vs unit rate
km/h to m/s

-89-

-90-

-91-

Nature, The Golden Ratio
and Fibonacci

Plants can grow new cells in spirals, such as

the pattern of seeds in this beautiful

sunflower. The spiral happens naturally

because each new cell is formed after a His real name was Leonardo Pisano Bogollo, and he
lived between 1170 and 1250 in Italy.
turn. "New cell, then turn,
"Fibonacci" was his nickname, which roughly means
then another cell, then turn, ..." "Son of Bonacci".

So, if you were a plant, how much of a turn would you have
in between new cells?
If you don't turn at all, you get a straight line.But that is a
very poor design ... you want something round that will
hold together with no gaps.
Any number that is a simple fraction (example: 0,75 is 3/4,
and 0,95 is 19/20, etc) will, after a while, make a pattern of
lines stacking up, which makes gaps.

But the Golden Ratio (its symbol is the Greek letter Phi, shown at left) is an expert at
not being any fraction. It is an Irrational Number (meaning we cannot write it as a
simple fraction), but more than that ... it is as far as we can get from being near any
fraction.

There is a special relationship between the Golden Ratio
and Fibonacci Numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, ... etc,
each number is the sum of the two numbers before it).
When we take any two successive (one after the other)
Fibonacci Numbers, their ratio is very close to the Golden
Ratio

***https://www.mathsisfun.com/numbers/nature-golden-ratio-fibonacci.html

-92-

Are you a person?

-93-

-94-

-95-

Algebraic expressions
Key words

-96-