This is What We Have Learned 2

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

A proportion is an equation with a ratio on each side. It is a statement that two ratios are equal.&nbsp; 3/4&nbsp;=&nbsp;6/8 is an example of a proportion. When one of the four numbers in a proportion is unknown, cross products may be used to find the unknown number. This is called solving the proportion.

Marble

To learn about percents, decimals, and fractions. You need to know how to change your percent to fraction, to write a decimal as a percent, and to write a percent as a decimal. Here I show you how to do it.

After you learned all of this, here we will show you some examples.

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A&nbsp;cross product&nbsp;is the result of multiplying the numerator of one&nbsp;ratio with the denominator of another. If the&nbsp;cross products&nbsp;are equal, then the&nbsp;ratios&nbsp;are proportional.

Lesson 4 Area of other figures

To find the area of the trapezoid the first thing you need to do is to put the formula. Next you add the base 1 plus the base 2 and if you can simplify, you need to simplify the height to make it more easily. Then you multiply the height and the answer of the base 1+base 2 and then you will have your answer but if you can’t simplify you divide the answer of height+(base1+base2) by 2.

A percent is a special kind of ratio in which the first term is compared to 100. The percent is the number of hundredths that represents the part of the whole. A percent represents a part of a whole, just like a fraction and a decimal. Here are some examples.

Lesson 9 Surface Area of prisms and cylinders.

To find the surface area of a prism you need to find the top, bottom, front, back, and sides to multiply them and add them.

But not with a triangular prism, it depends of the type of triangle (equilateral, isosceles, scalene) to find the surface area.

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A&nbsp;unit rate&nbsp;is a&nbsp;rate&nbsp;with 1 in the denominator. If you have a&nbsp;rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate&nbsp;unit rate&nbsp;or price per&nbsp;unit&nbsp;by completing the division operation: numerator divided by denominator.

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Similar figures

To find the surface area of a cylinder you need to multiply 2x 3.14 x radius to the second power, then add that with height x 3.14 x diameter of a cylinder.

A&nbsp;proportion&nbsp;is a name we give to a statement that two ratios are equal. It can be written in two ways: two equal fractions, or, using a colon, a:b = c:d.

To find a central angle in a circle graph, you have to do proportions. First all your data you add it up. Then you do a proportion where the hole will be equal to 360° and a part will be equal to x. Then you do cross products, x times 360 divided by T (total). And then you will find the central angle that belong to the part.

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

Rhombus: parallelogram with four equal sides

Rectangle: a rectangle is a parallelogram with 4 right angles

Trapezoid: quadrilateral with only one pair of parallel sides

Similar figures are two&nbsp;figures&nbsp;are&nbsp;similar&nbsp;if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal.&nbsp;

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<a href="bookcreator://page/2ns5c28qR36o3TR3zZrbqQ">1</a>. Understanding Percents <a href="bookcreator://page/-PnNnx1hTU-WpocjyNdqhA">2</a>. Percents, Fractions, and Decimals <a href="bookcreator://page/nRqhve8EQTytXS_lY3XIPg">3</a>. Percents Greater Than 100% and Less Than 1% <a href="bookcreator://page/vqu4IhqlRkKcZLBzDup4rQ">4</a>. Finding a Percent of a Number <a href="bookcreator://page/cfUzYe7VQPuD9mzGVqr5aw">5</a>. Solving Percents Problems Using Proportions and Equations <a href="bookcreator://page/so_FF9snS8yvY0JkVsniOg">6</a>. Applications of Percent <a href="bookcreator://page/pQrWepzQRRKCBJXCR9XDyA">7</a>. Finding Percent of Change

Triangles can be classified by various properties relating to their angles and sides.

Right triangle: one angle exactly 90 degrees 

Acute triangle: all 3 angles less than 90 degrees

Obtuse triangle: one angle more than 90 degrees

The numbers or measurements being compared in a ratio are called the terms of the ratio. A&nbsp;rate&nbsp;is a special ratio in which the two terms are in different&nbsp;units. When&nbsp;rates&nbsp;are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called&nbsp;unit rates.

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A number that cannot be expressed as a ratio of integers is an irrational number. When they are written as decimals, they neither terminate, nor repeat.

27.5 isn’t an irrational number. The square root of 2 is an irrational number. 0.3434343434343434... isn’t an irrational number. The square root of 37 is an irrational number.

A scale drawing is an enlarged or reduced drawing of an object.

Lesson 5 Circumference and area of a circle

To get the area, the first thing you need to do is to make the formula. Then because the radius is squared you need to multiply the radius by itself. Next you multiply 3.14 by the radius that is now a diameter. Finally you will have the answer.

The first thing you need to do is to put the formula like in all equations. Next you need to multiply 3.14 by the diameter. Finally you will have your circumference.

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When we express ratios in words, we use the word "to" -- we say "the ratio of something to something else" -- for example, the ratio of circles to triangles in the illustration above.

<a href="bookcreator://page/rTj1hu27SVuA_joJohWTfw">Lesson 1</a> <a href="bookcreator://page/ek89CVEgS7a7JnLQXT0c4Q">Lesson 2</a> <a href="bookcreator://page/pAF2y9ypQOy9J96HIwsyCA">Lesson 3</a> <a href="bookcreator://page/0LfXmw1QT7eEg-OMZkw8bw">Lesson 4</a> <a href="bookcreator://page/O9o3_7mzQJaVApPBHl06Gg">Lesson 5</a> <a href="bookcreator://page/qFKCPq6lRnqTxL6kY20LdQ">Lesson 6</a> <a href="bookcreator://page/z4nHPEaHROi65e3KSHL3wg">Lesson 7</a> <a href="bookcreator://page/zc0ZUZ4oQiypk_By-73iVQ">Lesson 8</a> <a href="bookcreator://page/3tVq5koLTICdk5SF-6hZYA">Lesson 9</a> <a href="bookcreator://page/qNPq2u0FThmDrrZCP7qMLQ">Lesson 10</a>

A ratio is a comparison of two quantities. The quantities in the ratio are called terms. The first term is a, and the second term is b (b ≠ 0). A ratio can compare a part to a whole, a part to another part of the whole, or the whole to a part.

Intersecting lines: pass through the same point

Line: a straight path with two points that goes on forever.

Parallel Lines: two lines that don’t and will never touch

Line segment: part of a line with two endpoints 

Perpendicular lines: are intersecting lines that form right angles (square corners)

Ray: part of a line, with one endpoint, extending forever in only one direction

Skew lines: lie in different planes. They do not intersect and are not parallel 

Midpoint: the point halfway between the endpoints of a line segment 

Congruent Line Segments: two line segments with the same length

Plane: a flat surface that extends forever in all directions 

By: Fernanda Perez, Luis Fernando Ortiz, Galia Roffe, and Paula Treviño

Solving Proportions

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A chord is any line segment that connects two points in the circle 

A diameter is any line segment through the center that connects two points in a circle

A radius is any line segment that connects the center to a point on the circle

A circle is a closed plane figure made up of all points the same distance from a point called the center

An arc is part of a circle connecting two points of the circle. An arc that connects the endpoints of a diameter is a semicircle 

<a href="bookcreator://page/ZbR66LPJS0WQCSfWeGT9yA">Lines and planes</a> <a href="bookcreator://page/kjFeMVhjQGuzejffOuJCwA">identifying and classifying angles</a> <a href="bookcreator://page/I5MD9dkkSKOOI8V_fpSmYQ">Triangles</a> <a href="bookcreator://page/nVucBn59R2GG6HGH-tMnew">Congruent Figures</a> <a href="bookcreator://page/G3kmxO3BQKyFwOdj22bmEg">Types of Quadrilaterals</a> <a href="bookcreator://page/cTbdfPJ2R5mA98fjQn6TzA">Circles</a> <a href="bookcreator://page/DczTvxJZRsuIATkBtGEVfg">Circle Graphs</a> <a href="bookcreator://page/lL_rkWYcTTuDkyiT_YRDIw">Line Segment Construction</a>

Solving Percent Problems Using Proportions and Equations

You can use the proportion p/100 = n/w, where p stands for percent, n for number, and w for the whole. For example, in the question, 48 is 60% of what number? n=48, p=60, so 60/100=48/w, so we need to find w. The equation to find w will be: w=n*100/p. So in this case will be w=48*100/60. So the value fit w is 80. But what about if we are missing n? It’s the same first formula to find the proportion. For example, in the question, what is 50% of 42.88, p=50 and w=42.88. To find n, you just need to multiply p(w), so n=21.44. But maybe you’re still wondering, what about if p is the one missing? You will use the same first proportion. For example, if I tell you, what percent of 90 is 50? w=90 and n=50. The equation to find p is p=n*100/w, in this case p=50*100/90. So n=55.5

Clouds pattern

By: Joaquín Ramírez, Paulina Herrera, and Cecilia Montenegro

For the area of a parallelogram we multiply the base times the height.

In this example we need to use A=bh. If we substitute we get A=52ft*67ft so A=3,484 ft^2

A=bh then we substitute, we get A=12*5=60 units^2

<a href="bookcreator://page/_n9dMyHMQ0mS0S1_5DMCTg">Chapter 5</a>

<a href="bookcreator://page/dRbYV7h1QmG2g33AK4Q3SQ">Chapter 6</a>

<a href="bookcreator://page/pj7IzOKJQ5GffcaTt82lZg">Chapter 7</a>

<a href="bookcreator://page/hiv-_mq4TBmsW8FQd7EiRw">Chapter 8</a>

Acute: angle that measures between 0° and 90°

Complementary: two or more adjacent angles that together form 90°

Obtuse: angles that measures between 90° and 180°

Supplementary: two or more angles that together form a 180° angle

Straight: angle that measures exactly 180°

Congruent: two or more angles have the same measures

Vertical angles: a pair of angles formed by intersecting lines, they have no side in common, and are congruent.

Adjacent: two angles that share a common vertex and side, and are next to each other.

To construct a segment that is congruent to AB:

Open the compass to the length AB. Draw a ray with endpoint C that is at least as long as AB

Place the end of the compass on C and draw an arc that intersects the ray. Label the point of intersection as endpoint D. CD is congruent to AB

Without changing the opening, move the compass tip to B. Draw another arc.

Open the compass more than half the length of AB. With the compass tip on A, draw an arc.

Draw CD through the intersections of the arcs. CD is the bisector of AB. Point M is the midpoint of AB.

Percent greater than 100% or less than 1%

You can express a percent that is less than 1% or greater than 100% as a decimal and as a fraction. A percent that is less than 1% is a quantity 1 that is less than 100. A percent that is greater than 100% is a quantity that is greater than 1.

When two or more figures are the same size, (all its sides have the same measurements) they are called congruent figures.

If two figures seem alike, but don’t have the same shape, and have the same proportional size (ten sides are identified similar or not by proportion, multiplying, or dividing) they are similar figures.

Lesson 3 Area and Perimeter of a triangle

In the examples on the top the areas would be: 1) A=bh/2,A=

For the perimeter of a triangle we will find the sum of the sides.

Here the perimeter would be 12 in.Perimeter is always expressed in units.

🔴Remember the units🔴

If we have our triangle and paste a congruent triangle on the side we get a parallelogram (see <a href="https://app.bookcreator.com/4">Lesson 2</a> for understanding ) so the area should be A=bh/2

The percent of change is the percent something increases or decreases from its original amount. To find the percent of change you need to subtract. For example, if the original price was 12 and then, it increased to 18, you need to subtract 18 minus 12, which is 6. Now, the proportion to solve the percent of change is: change/original = percent/100. In this case it’ll be 6/12 = p/100. Then you just divide 6/12 (which is 0.5) so the percent of change is 50%.

Warp red

The square root of a number is the number that multiplied by itself gives you that number, for example the square root of 16 is 4, since 4 times 4 is 16. The square root of 4 is 2, since 2 times 2 is 4. The symbol of square root is √.

If you want to estimate the square root of a number that doesn’t has any exact square root, then find the square root of the two numbers that are between that number, the numbers need to have an exact square root. After that find what number is closer to the one that doesn’t has an exact number. There is your answer.

Lesson 10 Volume of Prisms and Cylinders

The volume of a 3D figure is the number of cubic units needed to fill the space inside the figure. 

REMEMBER TO LABEL YOUR ANSWER AND ADD THE CUBIC UNIT!

Perimeter:  the distance around a polygon.

We can use percents on mostly anything that involve a fraction of decimal, but most people use to find taxes and commissions.

sales tax = percent of tax * purchase price Find the amount of sales tax on a television that costs $350 with an 8% sales tax. sales tax = 8% ? $350 sales tax = 0.08 ? 350 sales tax = 28 The sales tax is $28. How much does the television cost with sales tax?

commission = commission rate * sales Find the commission earned with a 3% commission rate on $3,000 in sales. commission = 3% ? $3,000 commission = 0.03 ? 3,000 commission = 90 The commission earned is $90. How much do you earn if you have a base salary of $500 plus 3% commission on sales of $3,000?

To find the percent of a number you need to multiply the number and the percent, but the number that will be the percent needs to be move to places to left. Here are some examples.

The Pythagorean Theorem declares that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the legs (a and b) in any right triangle.

To get the hypotenuse of a right triangle you need to sum the squares of the legs which would be the square of the hypotenuse, then find the square root of that number.

To get a leg you need to subtract the squares of the hypotenuse and of the other leg, then you need to find the square root of that number.

- A polyhedron is a three dimensional figure made of flat shaped- polygon figure which are called faces.

-The point where several edges meet is called a vertex.

-The line segment where two segments intersect its called edges.

A net is a plane figure pattern that makes a three dimensional figure.

Name

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