This Is What We Have Learned

Books created by Elementary students (2nd to 6th graders) in the Advanced Math Program at Latin American School in Monterrey, Mexico.

BOOKS BY AMP STUDENTS

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It is when you multiply the number by itself.

An irrational number is a real number that can’t be expressed as a ratio of integers.

When  you write irrational numbers as decimals they don’t terminate.

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Lesson 2: Units Rates and Proportional Reasoning

A unit rate is a rate for one of something. An example is: you run 250 miles in 5 hours. How many miles did you run in 1 hour, to find it you need to divide the denominator (that is 5) to the numerator (that is 250).

Note: Unit Rates can be used for any type of measure, like meters, miles, liters, etc.

Chapter 7: Geometry, Lines, Angles, Figures and Transformations

By: Andrea Arteaga, Mauricio Garza, Julio César González

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Percent of change is the percent that changes from a number to another number.

First, you subtract the whole, in this case 50 by 35 which gives 15. Now the 15=n so we can proceed with the proportion. P (percent) = 15 times 100 divided by 50. Which gives you 30. Now we have to find if it is decrease or increase in this case it is decrease because the $50 turns into $35.

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Chapter 5 Ratios, Rates, and proportions

By Eduardo Bernal, Gilberto Cavazos, and Rodrigo Garza

Here we have another two examples so we can solve in case that we don’t have the number or the whole or the number.

Chapter 6 lesson 5 Solving percent problems using proportions

First, this is the proportion you will be using to solve the problems.

For this example we need to solve what is the percent. In this, we could cross a zero for a zero and convert 90 to 9, and 100 to 10, then after you multiply 50 x 10, that is 500, you divide 500 divided by 9. The answer is 55.5%.

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A proportion is an equation in which two ratios are set equal to each other.

In the example above, both ratios are equal to each other, since when simplified, they both are equal to “1/2”.

This two sets of figures make a proportion.

The first one is 2/3 (2= number of stars | 3= number of shapes)

The second one is 4/6 ( 4= number of stars | 6= number of shapes)

When simplified, both proportions are to equal the same amount.

In the next lesson you will learn how to: Solve Proportions

These two triangles are have the same shape, but are different sizes. Both triangles have angles (A,B,C, and D,E,F), which are also equal to each other. (A = D)

Note: Shapes may rotate, but their angles will agree to each other even if they are at different places.

How to Find the value of a variable in similar shapes.

Step 1: Write the values of the shapes in two ratios.

Step 2: Write and solve an equation that looks like this. (The numbers that are multiplying are the numbers that are on the sides of the variable, and the denominator is the number in the opposite place of the variable)

You can simplify the numbers by a common number.

This works for any shape, you only need to write two ratios that are equal to both shapes, and you can solve the equation.

Chapter 6 Lesson 6 Solving percent using equations

The most fundamental part of solving percent problems using equations is to remember the image next to this (as mentioned in 6-5).

That is the key to solving the problems, since you just need to learn how to use them in their correct way.

Here is the way they are arranged in each problem:

A circle graph is a circle which has information inside of the circle of any topic using percentages. Circle graphs sometimes may or may not contain the percentage inside of them.

Constructions: to draw shapes, angles or lines precisely

To draw constructions you’ll have to use a compass, ruler, and pencil

(To make a circle graph you need the information, but how do you get it? You can go over your neighborhood, school, and other places and poll the people what you want your circle graph of. You can also just ask your friends and/or family.)

Lesson 7-4 Quadrilaterals and Other Polygons

Triangles can be classified by their angles and sides

Quadrilaterals can be classified by relationships of their sides and angles

Parallelogram: four-sided polygon with two pairs of parallel and equal sides

Rectangle: parallelogram with 4 right angles

Rhombus: a parallelogram with 4 equal sides

Trapezoid: a quadrilateral with only one pair of parallel sides 

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To solve a proportion you need to know how and this example will help you do that. example: the proportion is gonna be n/4 = 4/8, so here is how to solve them, you have to put the equation n= 4 x 4 divided by 8, so since not every proportion you solve is gonna be the same, a better way to say it would be n= denominator x numerator divided by other denominator (even if I say it this way a proportion is not a fraction)

The example’s answer is n=2 since 4x4 is 16 and 16 divided by 8 is 2

In the video shown here it shows how someone would do this process

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How do you get the volume of a rectangular prism?

This is the formula for a triangular prism:

The volume of this triangular prism is 42 cubic inches.

The formula for the volume of the cylinder is a little different, here it is:

You got it? The volume of this cylinder is 2035 cubic inches

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To find a percent of a number it is important that you do a ratio of the percent you want to find to the place value. After you do the ratio you can simplify or just multiply and then divide by the place value. Another way of finding the percent of a number is by just multiplying the decimal of a percent by the number you are finding the percent of.

Chapter 6 Lesson 4 Finding a percent of a number

The percent of a number shows part of a number.

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Line: a straight path of points that goes on forever in only one direction

Lesson 7-2 Identifying and Classifying Angles

Obtuse: between 91 degrees and 179 degrees

Parallel: in the same place but do not intersect

Vertical: a pair of angles formed by intersecting lines

Intersecting: pass through the same point

Complementary: two angles whose measures add up to 90 degrees

Supplementary: two angles whose measures add up to 180 degrees

Perpendicular: intersecting lines that form right angles

Adjacent: a pair of angles with a common vertex and a common side, but no common interior points

Thank you, we hope you understood this chapter, goodbye

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Let’s see a video of how we can find a the surface area!

Let’s try finding the surface area of a cylinder!

note: the surface area of a rectangular prism is different from the one of a cylinder

Let’s see a video explaining how to do it!

To find the tax you will need to find the percent of the number (as in 6-4). After you find the percent you will add it to the cost of the thing you bought. Example: You buy something for $20 and it has a 5% sales tax. 5% of $20 is $1 so add that $1 to $20 and your total cost is $21. For Commission and Tip you will only need to find the percent of a number. For example: You sell something for $2,500 and you have a commission of 7%, then you will have $175 in commission. Example for tax: You buy food for 15$ and you have to give a 15% tip to the waiter, 15% of $18= $2.70 so that is the tip.

Chapter 6 Lesson 7 Applications of Percent

Applications of percent can vary depending on the use of it. In this lesson we will only be using tax, commission, and tip. We will also be using the proportion used in lesson 6-5.

To convert a decimal to a percent you move the decimal point two times to the right, and to convert a percent to decimal you move the decimal point to the opposite side, so you move the decimal point two times to the left, and to change the decimal to a fraction you can put the decimal number on the numerator and to find the denominator you need to find the decimal’s place value.

Chapter 6 Lesson 3 Percents Greater than 100% or less than 1%

In this lesson, you will learn that you can have percents over than a 100% and less then 1%.

Here we have an example of two decimals converting into a percent. One is less than 1% and the other is greater than 100%.

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If you want to estimate the perimeter of this rectangle you got to know how many units the side of a square is. In this case the side of a square is 1 yd. For estimating the perimeter you need to count how many complete square sides are there. Then with the incomplete ones you can complete them with other incomplete ones.

For estimating the area of a figure you need to count the complete squares and the incomplete ones you complete them with other incomplete ones.

A pair of congruent figures are figures which have the same measurement, angles, and have the same dimensions. They have to agree in everything.

A circle is a closed round figure in which of all points the same distance away from the center, a circle has 360°. 

(Shapes can still be congruent even if the other shape is smaller, rotated, mirrored, etc. It just has to agree on what I said before already.)

A circle can have lots of parts in it! The parts being the diameter, radius, arc, sector, chord, center, circumference, segment, tangent and semicircle.

That is an example of a pair of congruent figures because both have the same shape, measurements, angles and basically everything.

But this ones are not congruent, even though the shapes and angles agree, the sizes do not, for it to be congruent it has to have everything the same.

We’ll use another formula for this one. The formula is b*h

How do we find the area and circumference of this circle?

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In the example below you can see that we use a proportion to find the length of the rectangle. In this other example we made a proportion that is x/8 = 63/9 to find the missing length.

To find the missing length of a figure you need to make a proportion. A proportion is an equation in which two ratios are set equal to each other. In this example I will how you the process to find the missing length of the rectangle.

Tip: You need to multiply the cross products and divide the one that is cross to X.

In this two other examples you will see that we make the proportion 15/30 = 5/x to get the square missing side. Also in the other square we make the proportion x/8 = 63/9 to find the rectangle missing length. In the first proportion we did 30 x 5/ 15 and that gave us 10. In the second proportion we did 63 x 8/ 9 and the answer was 56.

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A ratio is used to compare things like 2 apples to 3 bananas, but ratios can be written in other ways like 2:3 or 2/3 Tho even if a ratio can be written as a fraction,it is not a fraction

How to get equivalent ratios: this is a simple process, all you do is put the 2 ratios as if they were a fraction and then cross multiply them.

The video shows you how to do the process of this example

In the example showed above we know it’s equivalent because 6 x 3 is 18 and 2 x 9 is also 18

So since they are the same product the ratios are equivalent.

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Chapter 6 Lesson 1 Understanding Percents

A percent is a special kind of ratio in which the first term is compared to 100.

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The formula for the perimeter of a triangle is a+b+c. Try solving an example.

The formula for the area of a triangle is bh/2.

The faces are all the plain sides of the figure, the edges all the lines that form the figure, and the vertices are the corners of the figure.

How many faces, edges, and vertices does this figure have?

How to change from a percent to decimal and decimal to fraction

To change from a percent to a decimal you need to move the decimal point two times to the left. To change the decimal to a fraction you can put the decimal number on the numerator and to find the denominator you need to find the decimal’s place value.

Chapter 6 Lesson 2 Percents, Fractions, and Decimals

Percents, fractions, and decimals represent a part of a whole

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