My Math Journal Grade 6

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René Descartes

René Descartes was a French
mathematician and philosopher during
the 17th century. René Descartes is most
commonly known for his philosophical

statement, “I think, therefore I am”
(originally in French, but best known by its

Latin translation: "Cogito, ergo sum”). In
the mathematics sphere, his primary

contribution came from bridging the gap
between algebra and geometry, which
resulted in the Cartesian coordinate
system still widely used today.

Algebra

In A.D. 820, Al-Khwārizmī, a faculty member of the
House of Wisdom of Baghdad, published "Al-jabr wa'l
muqabalah," or "The Compendious Book on Calculation
by Completion and Balancing." It is from "al-jabr" that
we derive our word "algebra." Arabic word Al-jabr
means the "reunion of broken parts"

Algebra is a branch of mathematics
dealing with symbols and the rules for
manipulating those symbols. In
elementary algebra, those symbols (today
written as Latin and Greek letters)
represent quantities without fixed values

Mathematicans who study algebra are known as "Algebraists"

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FUN TIME

1.Think of a number. Add 3.
2. Double the result. Subtract 4.
3.Divide the result by 2.
4. Subtract your original number.
5.Compare your results with your friends.

YOUR TURN

As far as you understand the strategy of "think of a number"
problems, write your own "think of a number" problem.

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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?

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If you want to visualize this unit what would it be like?
You may design a cover page for your Booklet #4

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VOCABULARY

SELF ASSESSMENT

I can use ratio to compare quantities and show
ratio in different ways.
In cases where a whole is divided into two
parts, I can determine the ratio of the two parts
to each other or each part to the whole; I can
find the ratio when the other is given.
I can determine the rate or ratio of two
quantities.
I can write an algebraic expression suitable for
a verbally given situation and a verbal situation
suitable for a given algebraic expression.
I can calculate the values of the algebraic
expression for different number values that the
variable will take.
I can explain the meaning of simple algebraic
expressions.
I can use terminology about ratio and algebraic
expressions.

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STATISTICS

Collection of data
Display of data - Double bar graphs
Analysis of data - Mean and range

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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?

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If you want to visualize this unit what would it be like?
You may design a cover page for your Booklet #5

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VOCABULARY

SELF ASSESSMENT

I can write research questions that require
comparing two sets of data.
I can show the data of two groups with
frequency table or double graph.
I can calculate and interpret the range of a
dataset.
I can calculate and interpret the arithmetic
mean of a data set.
I can use arithmetic mean and range to
compare and interpret data from two groups.
I can use terminology about data analysis.

TEACHER NOTES

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GEOMETRY

Angles
Units of area
Measuring land
Height of a parallelogram
Area of parallelogram
Height of a triangle
Area of triangle
Area of composite shapes
Circle - basic elements
Circumference of a circle

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Angles-Types of angles

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Angles-Types of angles

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Measuring area - Measuring land

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Height - Area of parallelogram - Area of triangle

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Area of composite shapes

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Directions:You will be creating a clinometer ?
to help you indirectly measuring
height of really tall objects !

STEP 1: Create your

Materials needed

protractor
scissors
plastic drinking straw
tape
string or thread
a small weight (a binder clip, an eraser, a coin, a piece of stick tag, etc.)

STEP 2: Making your CLINOMETER

Tape a straight, plastic drinking straw on or near
the straight edge of the protractor. Make sure
the straw passes through the two 0º or zero
marks on opposite ends of the straight edge.

Tie a string through the small hole on the
straight edge.

Attach a small weight to the dangling end of
the string. Tie a paper clip, coin, or other small
weight to the end of the string. When you hold
the clinometer so the string falls past the
circular rim of the protractor, the weight will
pull the string straight down past an angle mark
on the protractor.

STEP 3: Measuring height with a clinometer

A clinometer that was invented in 1889 by William B. Melick, is
still used today to measure the heights of objects that are
difficult or cannot be directly measured, like tall things that you
can't possibly reach to the top of, flag poles, buildings, trees.

You will need two people:
one to look through the
straw and site the top of an
object and one to read the
degrees that the string
makes with the protractor.

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Find a tall tree (or building, flag pole etc.) in a place where there is plenty of
space to move away from the object that you are measuring.
Look through the straw and find the top of the tree.
Ask your friend to read the angle being recorded on the clinometer. This is read
where the string or cotton is touching the protractor.
Keep moving back (or forward if you've gone too far) until you have the
clinometer angle measuring 45 degrees. With a 45 degree angle your job will be
much easier as the distance from you to the tree will be equal to the distance
from the ground to the top of the tree.
Measure the distance between where you are standing and the base of the tree.
Measure the distance from your eyes to the ground (this is where your partner is
indispensible!)
Add these two distances together - because to be most accurate the triangle
has to finish at your feet not your eyes.
You now have a very close approximation of the height of the tree, building or
other tall structure.

height of the tree : h

h = h1+ h2

h h1

450 h2

h1

You, the base of the tree and the top of the tree, form an isosceles triangle
meaning the distance from you to the base of the tree is equal to the height of
the tree (from the viewer's eyes to the top).

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WEEKS Weekly Plan / Main Topics

Week 30
April 24-28

Week 31
May 1-5

Week 32
May 8-12

Week 33
May 15-19

Week 34
May 22-26

Week 35
May 29-June 2

Week 36
June 5-9

Week 37
June 12-16

June 19
September 4

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Basic elements of circle

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Circumference

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Circumference

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All about PI

Interesting Facts

ADD UP THE FIRST 144 DIGITS OF PI AND THE ANSWER IS 666,
SAME WITH 144 = (6+6) X (6+6). SCHOLARS CALL 666 THE
“THE MARK OF THE BEAST.
ALFRED HITCHCOCK’S FILM TORN CURTAIN AND IN THE NET
WHICH STARS SANDRA BULLOCK UTILISED THE PI AS THE
SECRET CODE.
CALCULATING THE VALUE OF PI SERVES AS A DIGITAL
CARDIOGRAM OR STRESS TEST TO INDICATE A COMPUTER
PROCESSOR’S ACTIVITY LEVEL.

HTTPS://HOMEMADEHEATHER.COM/FREE-PI-DAY-ACTIVITY-PRINTABLES/

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CHALLENGE TIME

Bicycles from the 1800s look very different
from the bikes we see today.
In the given image, the bicycle’s back wheel
has a radius of 20 cm, and the front wheel
has a diameter of 100 cm.
If the back wheel makes 10 turns,
how many turns does the front wheel make?
(Take = 3.)

Is it possible to say that there is a relationship between the number
of turns and the radius of the circles? If yes what kind of?

-123-

Constructing The “Seed of Life” pattern- a classic geometric construction
With only a compass, one may contstruct this primal form. Starting
with a circle, center the next one on the edge and then use each new
intersection as the next center.

To construct the Seed of Life pattern:
1) Fix your compass to the size desired for the center circle and make a
circle.

2) Move the pivot point of the compass to the edge of the center circle
and make another circle. (This creates the familiar “eye” archetype of
the vesica piscis shape which sybolizes communion, relationship and
much more.)

3) Move the pivot point of the compass to the edge of the center circle
where the first two circles intersect and make the next circle.

4) Move the pivot point of the compass to the edge of the center circle
where the center and third circles intersect and make the next circle.

5) Move the pivot point of the compass to the edge of the center circle
where the center and fourth circles intersect and make the next circle.

6) Move the pivot point of the compass to the edge of the center circle
where the center and fifth circles intersect and make the next circle.

7) Move the pivot point of the compass to the edge of the center circle
where the center and sixth circles intersect and make the next circle.

That does it! You’ve just constructed the classic “Seed of Life” pattern.

***https://www.geometrycode.com/free/seed-of-life-pattern-construction-using-

compass/

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Your turn

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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?

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If you want to visualize this unit what would it be like?
You may design a cover page for your Booklet #6

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VOCABULARY

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SELF ASSESSMENT

I can identify the angle which is formed by
two rays with the same starting point and
represent it with a symbol.

I can draw an angle congruent to an angle.

I can discover properties of adjacent,
supplementary, complementary and vertical
angles and solve related problems.

I can calculate the area of the triangle and
solve related problems.

I can calculate the area of the parallelogram
and solve related problems.

I can identify the units of area measurement
and convert m2-km2, m2-cm2-mm2 units to
each other.
I can identify land measurement units and
associate them with the standard area
measurement units.

I can solve area problems.

By drawing a circle, I can identify its center,
radius, and diameter.

I can determine by measuring that the ratio
of a circle's length to its diameter is a
constant value.

I can calculate the circumference of a circle
when the diameter or radius is given.

I can use terminology about angles, area and
circle unit.

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GEOMETRIC CROSSWORD

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resting F
p 10: Inte acts abo
Pi is an infinitely long, ut To The symbol for pi is the
irrational number and lowercase Greek letter π,
its exact value cannot and is taken from the Greek
word perimetros, which
be known. Since Pi's means circumference.
exact value cannot be
known, we can never
find the exact area or

circumference of a
circle.

The first 100 digits of pi are 3.1415926535 8979323846
2643383279 5028841971 6939937510 5820974944
5923078164 0628620899 8628034825 3421170679

Pi day is Pi is a part of Egyptian Some people are known
celebrated mythology. It is being to practice piphilology,
annually every said that the Pyramids or the practice of
March 14 and of Giza are built with memorizing large
legendary the principles of Pi. numbers of digits of π
mathematician through the use of
Albert Einstein's mneumonic techniques.
birth
anniversary falls The record for The value of the Pi was first
on Pi day. reciting the most calculated by Archimedes.
number of decimal
In 2016, a Swiss scientist, Peter places of Pi was The protagonist of Carl Sagan’s
Trueb, used a computer with 24 achieved by Rajveer 1985 novel "Contact," astronomer
hard drives and a program called Meena. He was able Ellie Arroway, seeks evidence of
y-cruncher to calculate pi to more to recite 70,000 extraterrestrial civilizations by
than 22 trillion digits — the current decimal places. listening for signals from space —
world record for the enumeration and later looks for hidden patterns
of pi. If you read one digit every -131- in the digits of pi.
second, it would take you just
under 700,000 years to recite all
those digits.

SOLIDS_VOLUME AND CAPACITY

Solids
Units cube
Finding volume
Units of volume
Capacity

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Solids- Volume

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Units of Volume _Capacity

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Fill up the 5L container. Dump all water you can into 3L container.HOW TO GET 4 LITER FROM
Empty 3L container. Dump 2L remaining from 5L to 3L once again.TWO CONTAINERS OF SIZE
3 LITER AND 5 LITER ?
Once again fill up the 5L container and dump 1L into 3L.
Bingo!-136-

Rubik's Cube Facts

Professor Ernő Rubik invented in
1974, it took the inventor over a

month to solve it.

The Rubik’s Cube is the bestselling
toy of all time. Over 350 million
sold since 1980

It has been calculated that there are Add a little bit of body textIf you manage to
43,252,003,274,489,856,000 possible turn the Rubik's Cube once every second, it
permutations* of the Rubik's Cube. will take you 1.4 trillion years to go through all
That is 43 quintillion, 43 followed by 18 zeros! If
you had 43 quintillion dollars, you can spend a the permutations.
trillion dollars a day for the next 118 thousand

years.

The world record for solving the A robot made of Legos solved the
Rubik's Cube is 3.47 seconds by Rubik's Cube in 3.253 seconds

Yusheng Du

Guinness World
Records;

The largest
order Rubiks /
magic cube is

33x33x33

Permutation is ,basicly, number of possible arrangements
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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 #7

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VOCABULARY

SELF ASSESSMENT

I can understand that the number of cubes
placed inside the rectangular prism in such a
way that there is no space is the volume of
that object and I can calculate the volume of
the given object by counting the unit cubes.
I can construct different rectangular prisms of
a given volume with unit cubes and explain
that volume is the product of the area of the
base and the height.

I can identify standard volume measurement
units and convert mm3, cm3, dm3 and m3
units to each other.
I can calculate the volume of the rectangular
prism and solve related problems.

I can estimate the volume of the rectangular
prism.

I can identify liquid measurement units and
convert them to each other.

I can associate volume measurement units
with liquid measurement units.

I can solve problems with liquid measurement
units.
I can use terminology about volume and
capacity unit.

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MY MATH DICTIONARY







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