This book was created by 4th grade students in the Advanced Math Program at Latin American School in Monterrey, Mexico.
It contains Topics 8 to 15 of our curriculum.

This Is What We Have Learned 2

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BY:JOSE CARLOS, SANTIAGO ORTIZ, LEANDRO MAURICIO AND JIMENA ZAPATA.

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Common Factors and Greatest Common Factor

This is an example of how you can get the factors

The greatest common factor (GCF) of two numbers is the greatest number that is a factor of both.

This are the factors of 18 are 1,2,3,6,9,and 18

You put the to numbers that multiplied gives you the number on the top like 3x6=18 so in one side 3 and in the other side the 6

Their greatest common factor is 6 because 12 doesn’t have the factors 9 and 18 . And 18 don’t have the factor 12 so then the greatest factor that they have in common is 6

Blue geometrical pattern

We all know what are fractions but do you know how to multiply them?

For example to multiply 1/4 by 60 you convert the 60 into an improper fraction 60/1 and then you just do normal multiplication

Leaving James Harden GIF by Farmers Insurance ®

Remember that in some cases the fraction would contain factors so you would have to simplify your fraction and then continue multiplying.

Marble

To make an improper fraction to a mixed number you have to divide.

To make a mixed number to an improper fraction you have to multiply the whole number and the denominator and add the numerator, the answer is the numerator of the improper fraction and the denominator stays the same.

🍃 ᴇʟᴀᴘꜱᴇᴅ ᴛɪᴍᴇ 🍃

In elapsed time you can use a number line or  subtract whatever you choose

Martin is leaving at 2pm of his house,and he come at 5pm ¿How many hours it goes from his house?

Martin wasn’t in his house for 3h,then at 5pm he come to his house ¿At what hour Martin leave from his house?

5h 00min - 3h 00min ____________ 2h 00min

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Almost all solids have vertices, edges and faces. Vertex: a vertex is a point where two or more curves, lines, or edges meet. Edge: an edge is a particular type of line segment joining two vertices in a polygon. Face: a face is a flat surface that forms part of the boundary of a solid object.

There are 8 vertices, 12 edges, and 6 faces on this cube.

Name the edges, the vertices and the faces of the picture.

The vertices are the yellow circles, the edges are the lines of green, and the faces are the blue ones.

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Problem solving: use objects to solve a simpler problem 

Six people can be seated at the table . If tow tables are together , 10 people can be seated . How many tables are needed to make a long table that will be seat 22 people?

First we need to know that a parallelogram is a figure with all sides being parallel to each other; like in the example below.

The formula for getting the area of a parallelogram is multiplying base by height.

In this case the base is of 7.9 inches and the height is of 1.5 inches, so we need to multiply 7.9 in. by 1.5 in.

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𝙲𝚘𝚖𝚖𝚘𝚗 𝙼𝚞𝚕𝚝𝚒𝚙𝚕𝚎𝚜 𝚊𝚗𝚍 𝙻𝚎𝚊𝚜𝚝 𝙲𝚘𝚖𝚖𝚘𝚗 𝙼𝚞𝚕𝚝𝚒𝚙𝚕𝚎

Pablo wants to find the least common multiple of Step 1. Find the least common multiple of 8 and 3

Step 2. Make the least common multiple the least common denominator of both fractions.

Problem solving: draw an picture and write an equation 

In this topic you need to draw a picture in base of what it says in the problem 

In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or \pi /2 radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles.

An acute angle is an angle that is&nbsp;less than 90°, and these angles can be measured using a protractor.

In Mathematics, “an obtuse angle is&nbsp;an angle which is greater than 90° and less than 180°”. In other words, an obtuse angle is between a right angle and a straight angle.

🌲 ᴄᴏɴᴠᴇʀᴛɪɴɢ ᴄᴜꜱᴛᴏᴍᴀʀʏ ᴜɴɪᴛꜱ 🌲

Think: Quarts are larger than pints. If we convert pints to quarts, there will be a smaller number of quarts than there were pints. So we need to divide

Parallelogram: a quadrilateral with both pairs of opposite sides parallel and equal in length. Rectangle: a parallelogram with four right angles. Rhombus: a parallelogram with all sides the same length. square: a rectangle with all sides the same length. trapezoid: a quadrilateral with only one pair of parallel sides.

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The surface area is the sum of the areas of all the faces of a figure.

The formula to find the surface area of the rectangular prism below is:

surface area = 2(lxw) + 2(lxh) + 2(wxh) surface area = 2(15x5) + 2(15x8) + 2(5x8) surface area = 150 + 240 + 80 surface area = 470 in

Find the surface area of the figure below.

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Thanks Thank You Sticker by Have A Nice Day

🌿 ᴄᴏɴᴠᴇʀᴛɪɴɢ ᴍᴇᴛʀɪᴄ ᴜɴɪᴛꜱ🌿

1000 ml = 1L 5L = 5,000 ml 2000 m = 2 km 30 km = 30,000,000 mm 3kg = 3,000 g 10,000 mg = 10 g

THE VOLUME is the measure of the space inside the solid figure , it is measured in cubic units . A CUBIC UNIT is the volume of a cube which has edges that are 1 unit .

The formula of the volume is: V = l x w x h Example: V = l x w x h V = 3cm x 5cm x 8cm V = 120 cm

To find equivalent fractions, multiply or divide the numerator and denominator by the same number.

 When you have a table first you need to identify the operation like what you are doing or which is the correct pattern for example if you have a table that in letter x are the numbers 5 , 7 , 9 and in letter y you have the numbers 8, 10, 12 the pattern is add 3 so the equation will be Y = X + 3 

I hope you have learned a lot reading this book.

🍀 ᴘʀᴏʙʟᴇᴍ ꜱᴏʟᴠɪɴɢ: ᴛʀʏ, ᴄʜᴇᴄᴋ, ᴀɴᴅ ʀᴇᴠɪꜱᴇ 🍀

Then divide the floor into a whole number of rectangles that are 2 feet wide? or divide it into a whole number of rectangles that are 2 feet long?

If the answers are both yes, you can use the tiles to cover the floor without cutting them.

The first number of the division is the numerator and the second the denominator.

12 - 8 Problem Solving: Draw a Picture and Make an Organized List

For this you’ll need to learn that when there’s a word problem you can draw a picture of different ways of solving a problem, then create a list of your results like in the example below.

Maria wants to cover a 12 x 12 area of tiles and she doesn’t knows what type of tiles are better.

✩ Topic ✩ 🍀-𝟷𝟶 𝚊𝚗𝚍 𝟷𝟺-🍀

&nbsp;｡˚ᴛᴏᴘɪᴄ 10&nbsp;｡˚ -ᴀᴅᴅɪɴɢ ᴀɴᴅ ꜱᴜʙᴛʀᴀᴄᴛɪɴɢ ꜰʀᴀᴄᴛɪᴏɴꜱ ᴡɪᴛʜ ʟɪᴋᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀꜱ -ᴄᴏᴍᴍᴏɴ ᴍᴜʟᴛɪᴘʟᴇꜱ ᴀɴᴅ ʟᴇᴀꜱᴛ ᴄᴏᴍᴍᴏɴ ᴍᴜʟᴛɪᴘʟᴇ -ᴀᴅᴅɪɴɢ ꜰʀᴀᴄᴛɪᴏɴꜱ ᴡɪᴛʜ ᴜɴʟɪᴋᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀꜱ -ꜱᴜʙᴛʀᴀᴄᴛɪɴɢ ꜰʀᴀᴄᴛɪᴏɴꜱ ᴡɪᴛʜ ᴜɴʟɪᴋᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀꜱ -ᴀᴅᴅɪɴɢ ᴍɪxᴇᴅ ɴᴜᴍʙᴇʀꜱ -ꜱᴜʙᴛʀᴀᴄᴛɪɴɢ ᴍɪxᴇᴅ ɴᴜᴍʙᴇʀꜱ -ᴘʀᴏʙʟᴇᴍ ꜱᴏʟᴠɪɴɢ: ᴛʀʏ, ᴄʜᴇᴄᴋ, ᴀɴᴅ ʀᴇᴠɪꜱᴇ

&nbsp;｡˚ʟᴇꜱꜱᴏɴ 14 &nbsp;｡˚ -ᴄᴜꜱᴛᴏᴍᴀʀʏ ᴜɴɪᴛꜱ ᴏꜰ ᴄᴀᴘᴀᴄɪᴛʏ -ᴜɴɪᴛꜱ ᴏꜰ ᴡᴇɪɢʜᴛ ᴀɴᴅ ᴍᴀꜱꜱ -ᴄᴏɴᴠᴇʀᴛɪɴɢ ᴄᴜꜱᴛᴏᴍᴀʀʏ ᴜɴɪᴛꜱ -ᴄᴏɴᴠᴇʀᴛɪɴɢ ᴍᴇᴛʀɪᴄ ᴜɴɪᴛꜱ -ᴇʟᴀᴘꜱᴇᴅ ᴛɪᴍᴇ -ᴇʟᴀᴘꜱᴇᴅ ᴛɪᴍᴇ ɪɴ ᴏᴛʜᴇʀ ᴜɴɪᴛꜱ -ᴛᴇᴍᴘᴇʀᴀᴛᴜʀᴇ ᴄʜᴀɴɢᴇ -ᴘʀᴏʙʟᴇᴍ ꜱᴏʟᴠɪɴɢ: ᴍᴀᴋᴇ ᴀ ᴛᴀʙʟᴇ

For this lesson you just have to draw a picture and solve the problem using the information that you have 

If Duke has 1/1/2 of juice and wants 6 cups of juice how many 1/1/2 of juice he will need

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All solid shapes have a&nbsp;top view, a side view and a front view . Top View: The top view of a solid shape is the shape of an object when we see it from the top. Side View: The side view of a solid shape is the shape of an object when it is seen from one of its sides.

Example : what type of view you see in that examples ?

Comparing and ordering fractions and mixed numbers

We use&lt;,&gt; for a fraction greater than the other one, and we use = for the same fractions, you can multiply a fraction to get the fraction with or more less the denominator of the other fraction.

Hint: sometimes the fraction with the lowest denominator is the greatest fraction.

Points and lines are basic geometric ideas. Lines are sometimes described by relationships to other lines.

If you see a line crossing another line it means they intersect. In this example you can se line U intersects line P.

If you see this time a dot it means it is point (a letter or number). In this example point J.

Parallel lines can’t intersect because parallel means extending in the same direction, but without meeting.

12 - 1 Using Customary Units of Length 12 - 2 Using Metric Units of Length 12 - 3 Perimeter 12 - 4 Area of Squares and Triangles 12 - 5 Area of Parallelograms 12 - 6 Area of Triangles 12 - 7 Circles and Circumference 12 - 8 Problem Solving: Draw a Picture and Make an Organized List

🌴♡ꜱᴜʙᴛʀᴀᴄᴛɪɴɢ ꜰʀᴀᴄᴛɪᴏɴꜱ ᴡɪᴛʜ ᴜɴʟɪᴋᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀꜱ♡🌴

First we need to find the LCM (least common multiple) for example:

5 3 — - — 8 4

Because 16 is my LCM is also my LCD (least common denominator)

Now we write equivalent fractions with our LCD 10 12 — - — 16 16

Finally we just subtract the numerators because we already have the same denominator. But we can simplify if it’s possible 

2 1 — = — 16 8

Say that triangles u,a,c and d,b,k are congruent?

Both triangles are congruent because each is a half of a square and squares have 4 congruent sides and angles.

A polygon is a closed plane figure made up of line segments. Common polygons have names that tell the number of sides the polygon has.

You can make a 3D figure with a net, a net is a paper that if you fold it in a way you would make a 3D figure. Almost all figures have a net with sides a bottom and a top part.

This lesson is very easy. To multiply fractions you have to multiply the numerator times the numerator. (The same with the denominator)

🌴 ᴛᴇᴍᴘᴇʀᴀᴛᴜʀᴇ ᴄʜᴀɴɢᴇ 🌴

Tell if the difference is an increase and decrease.Scince the second temperature is less than the first temperature,there was a decrease

Remember that: Water freezes at 0 degrees Celsius, and boils at 100 degrees C, while in Fahrenheit, water freezes at 32 degrees F and boils at 212 degrees F. You see that Celsius has 100 degrees between the freezing and boiling point, whereas Fahrenheit has 180 degrees between these two points

All the points on a circle are the same distance from the center. The center of circle E is point E.

A radius goes from the center to any point on the circle. ___ QA is a radius of circle R.

A chord has both endpoints on a circle. ___ IA is a chord of circle W.

A diameter is a chord that passes through the center of a circle. ___ DT is a diameter of circle M.

A central angle is an angle whose vertex is the center. FWU is a central angle.

The circumference is the distance around a circle. The circumference equals the circle’s diameter multiplied by (3.1416). C D

Solving multiplication and division equations 

This topic is exactly the same like the 15-1 only that you multiply or divide here is the process

Remember that what you do in one side you need to do it in the other side

Relating division to multiplication of fractions 

This lesson is a little tricky ! You have to draw a picture based on the information that you have. For example if you have 3 divided by 1/2 you have to draw a picture of 3 rectangles and split those rectangles into two pieces 

Use this chart to estimate the circles infested with larva, using a benchmark fraction that is closer to the actual amount.

Normal circles circles infected with venom circles infested with pollution circles infested with larva

🍃 ᴀᴅᴅɪɴɢ ꜰʀᴀᴄᴛɪᴏɴꜱ ᴡɪᴛʜ ᴜɴʟɪᴋᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀꜱ 🍃

Step 1. Find the least common denominator of the two fractions 

Multiple of 5: 5 10 15 20 25 30 35 Multiple of 7: 7 14 21 28 35

Step 2. Now that you have equivalent fractions with the same denominator, add the numerators.

Step 3: Place the sum over the common denominator and simplify your fraction if possible.

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🌳 ᴘʀᴏʙʟᴇᴍ ꜱᴏʟᴠɪɴɢ: ᴍᴀᴋᴇ ᴀ ᴛᴀʙʟᴇ 🌳

A table can be used for a  schedule. For example in an airport there is a lot of schedules for people to know when their flight is leaving or information they need to know.

A bus station has 4 buses.Each bus leaves every 30min and they start leaving at 9:30a.m.The bus destination for all is from Monterrey to McAllen.It takes about 3 hours and a half to get from Monterrey to McAllen.At what time does the fourth bus get to McAllen?

The perimeter is the distance around the outside of a polygon .You can find the perimeter in two different ways.

There are two different ways to write a fraction in simplest form

Divide by the common factor until the only common factor is 1

If your fraction is only even numbers you can use the  number 2 to get it simply ,but if the two are even number you can’t use the 2

Imagine that I want to simplify 30 35 the factors of 30 are 1,2,3,5,6,10,15,30 and the factors of 35 are 1,5,7,35

Our greatest factor is 5 so divide by five the fractions

 But now you have 5 6 only one is even number and they don’t have any other number that they have in common  and if only the 1 is the common factor is it means that the fraction is simply 

🍃 ᴜɴɪᴛꜱ ᴏꜰ ᴡᴇɪɢʜᴛ ᴀɴᴅ ᴍᴀꜱꜱ 🍃

🌱 ꜱᴜʙᴛʀᴀᴄᴛɪɴɢ ᴍɪxᴇᴅ ɴᴜᴍʙᴇʀꜱ 🌱

First we need to write equivalent fractions with our LCM 4: 4, 8, 12, 16… 3: 3, 6, 12, 15…

Because we have the same denominator we subtract the whole ( 3 - 2 ) and then subtract 3/12 - 9/12

Solving addition and subtraction equations 

In this topic you need to find the value of a letter it seems difficult but is super easy,this is the process

Remember what you do in one side you need to do it in the other side

also there are subtractions where you need to find the value of a letter. Also when theres a negative number you need to convert all the process to an addition

To multiply a mixed number you have to convert the mixed number into an Improper fraction and then just do normal multiplication 

Fractions and Decimals on the Number Line

is showing the exact position in a number line like this

Is like if you want to know who got first to school Maria lives in 0.4 of the school. And Fernando is 0.8 of the school who gets first

When you are going to find the area of a triangle you need always to divide by two.

🍀ᴀᴅᴅɪɴɢ ᴍɪxᴇᴅ ɴᴜᴍʙᴇʀꜱ🍀

Step 1. Write equivalent fractions with the least common denominator.

Multiple of 7: 7 14 21 28 35 42 49 56 63 Multiple of 9: 9 18 27 36 45 54 63

Step 2: Add the fraction. Then add the whole numbers.

Step 3: If you see that the denominator is greater than the numerator you’ll need to simplify your mixed fraction 

🌿 ᴇʟᴀᴘꜱᴇᴅ ᴛɪᴍᴇ ɪɴ ᴏᴛʜᴇʀ ᴜɴɪᴛꜱ 🌿

Elapsed time is the amount of time that happens in a period.

If a party starts  at 4:00p.m an d ends a 7:30 p.m. What is the elapsed time of the party.

3h                                 30 min     

Other way you can do it is by converting the 4:00 into a 16:00 and add it with 7:30 (remember that all p.m. numbers can be converter) 1:00 = 13:00, 2:00 = 14:00, 3:00 = 15:00 , 4:00 = 16:00 , and so on

The Thousandths is another decimal place like the Tenths and Hundredths but the Thousandths are two spaces after the decimal place like this 0.003

This lesson is very simple you need to identify what represents the number line like this

Remember that when theres a close circle that means the the letter is greater than or equal to x number,also can mean that is less or equal to x number

Irregular shapes and solids

To find the AREA first separate the figure in two different rectangles and solve the area when you have both, add them up and it will be the area of the irregular shape 

A= l x w A= 8x4 =32 + A= 10x10 =100 A= 132m2

To find VOLUME of an irregular solid, first separate the Prisms and calculate the volume individually and add them up. 

V= l x w x h V= 12 x 6 x 7= 504 V= 8 x 5 x 7= 280 V= 784in3

Fractions can also be named using decimals

A decimal is a number that goes after the decimal point

There are tenths and hundredths the tenths are after the decimal point like this 0.2 like that but the hundred is one space after the decimal point like this 0.03 like that

1. Find the denominator(the total amount of circles).

2.find the numerator(the amount of shaded circles).

The answer is 2/4, and we can simplify it to 1/2.

8 - 1 Basic Geometric Ideas 8 - 2 Measuring and Classifying Angles 8 - 3 Polygons 8 - 4 Triangles 8 - 5 Quadrilaterals 8 - 6 Problem Solving: Make and Test Generalizations

ᴄᴜꜱᴛᴏᴍᴀʀʏ ᴜɴɪᴛꜱ ᴏꜰ ᴄᴀᴘᴀᴄɪᴛʏ

1 gallon = 4 quarts 1 qt = 2 pt 1 pt = 2 cp 2 g = 8 qt

ᴍᴇᴛʀɪᴄ ᴜɴɪᴛꜱ ᴏꜰ ᴄᴀᴘᴀᴄɪᴛʏ

2,400 ml = 2.4 L 10,000 ml = 10 L 2.3 L = 2,300 ml 0.9 L = 900 ml 8,548 ml = 8.548 L

🌿𝔸𝕕𝕕𝕚𝕟𝕘 𝕒𝕟𝕕 𝕊𝕦𝕓𝕥𝕣𝕒𝕔𝕥𝕚𝕟𝕘 𝔽𝕣𝕒𝕔𝕥𝕚𝕠𝕟𝕤 𝕨𝕚𝕥𝕙 𝕃𝕚𝕜𝕖 𝔻𝕖𝕟𝕠𝕞𝕚𝕟𝕒𝕥𝕠𝕣𝕤 🌿

Adding fractions with like denominators Step 1. Add the numerators. Step 2. Write the sum over the denominator. Step 3. Simplify the fraction if possible. Example:

4 4 8 2 4 2 — + — — ÷ — = — ÷ 2 = — 12 12 12 2 6 3 first add then if possible Simplest divide form

Subtract Fractions with like denominators Step 1. Subtract the numerators. Step 2. Place the difference over the denominator and simplify if possible. Example:

8 4 4 2 2 2 1 — - — — ÷ — = — ÷ — = — 12 12 12 2 6 2 3 First subtract Then divided simplest form