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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Subtracting integers is the same as adding two positive numbers, you only need to add a negative sign before the number.

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

Rectangle: A rectangle is a parallelogram with 4 right angles.

Trapezoid: A trapezoid is a quadrilateral with only one pair of parallel sides.

Square: A square is a rectangle with 4 equal sides.

Rhombus: A rhombus is a parallelogram with 4 equal sides

An equation with more than one operation is like a normal equation but with more steps

In this equation there are 2 equations: (12) and +24. The first thing to do is to find the operation that is farthest to the variable that is +24 and then we do the inverse operation that is -24 on both sides of the equal sign. Then the inverse operations undo each other and we have. 12a= 24 then we need to find the inverse operation of (12) that is /12 on both sides of the equal sign. Then the inverse operations undo each other and the answer is a=2

Any set of ordered pairs is a relation.&nbsp; A function is a relation in which there is only one y-value for each&nbsp; x-value

An arc is part of a circle connecting two points of the circle. An arc that&nbsp; connects the endpoints if a diameter is a semicircle. A sector is a region bounded by two radii and an arc

Two intersecting diameters form 4 central angles. The sum of the adjacent central angles of any circle is 360 degrees.

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Graphing equations with more than one operation

This topic is basically the same than the last one but with more than one operation

In this equation we need to give value for X and then do the equation and get the value of Y and then pass it to a graph.

Angle pairs are&nbsp;angles that appear in twos to display a certain geometrical property. Some of the angle pairs include: Complementary angles. Supplementary angles.&nbsp;

14-6: Tips, Taxes, Discount, and Simple Interest

-A tip is a percent of the bill that you give to the waitress. -Taxes are 10% of the price of the object you buy , this percent is added when you are paying. -A discount is when a object’s price is lowered in order to sell more products.

A figure has reflection symmetry if it can be reflected onto itself. The line of reflection is a line of symmetry. Some figures have more than one line of symmetry.

When a figure rotates onto itself in less than a full turn, the figure has rotational symmetry.

1. Subtract 3 1/5 on both sides of the equation. 2. Inverse operations undo each other. 3. Solve. 4. Check by substituting.

 Look for a rule or a pattern that is made on each number so it is reasonable.

Fractions, Decimals and percent are all part of a whole: -Fractions are parts of a whole which have denominators and numerators Example: 1/2 -Decimals are also parts of wholes but they are shown as a number and has a decimal point after the zero Example: 0.54 -Percents are the same as decimals but you move the decimal to the right and put a percent sign Example: 74%

Integers name distance and direction from zero

Integers are the whole numbers and their opposites, the negatives; 0 is its own opposite

Negative numbers are number below zero for example the point we graphed at the left of the number line.Positive numbers are numbers with a bigger value than zero like the point we graphed at the right of the number line.

Ratios

Multiplying a fraction and a whole number

You can’t multiply a fraction and a whole number so you have to turn the whole number into the number and the 1 as denominator, and then you check the cross products to see if you can simplify and then you multiply Numerator x Numerator and Denominator x Denominator

An improper fraction is whose numerator is equal to or larger than the denominator

To estimate a product with fractions and whole numbers or whatever first estimate to numbers that can be easily divided because multiplying a fraction is the same as dividing it so in this example where 4 5/8 x 1/3 and here 1/3 and for that the best estimate for 4 5/8 is 6 so now multiply it and it is equal to about 2

To multiply mixed numbers you have to make the mixed numbers a improper fraction and then make crossed products to simplify if posible and then multiply it and simplify if possible

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First multiply 60x15 Then divide by 45 and get your anwser

Draw a rectangle that is similar to a rectangle with the sides:15l and 9w (also explain why they are similar)

They are similar because they’re corresponding sides are proportional 

The scale of a map is the ratio of a distance on the map to the corresponding distance on the ground.&nbsp;

A map is a diagram representing  an area of land or sea showing physical features, cities, roads, etc.

We need a rule. And a way to find it is to find the  operation that is reasonable with all the table like in this pattern the most reasonable operation is add 5

Then we can do an equation to prove that the rule applies to all the table. And for that we need to substitute the values of X and Y

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When you multiply integers: -If it’s negative and negative the answer will be positive -If it’s positive and negative the answer will be negative -If it’s positive and positive the answer will be positive

Right Acute Obtuse equiangular

Point: An exact location in space. Line: A straight path of points that goes on forever in two directions. Ray: Part of a line with one endpoint, extending forever in one direction. Line segment: Part of a line with two endpoints. Midpoint: The point halfway between the endpoints of a line segment. Congruent line segments: Line segments with the same length. Plane: A flat surface that extends forever in all directions. Intersecting lines: Lines that pass through the same point. Parallel lines: Lines that are in the same plane but do not intersect. Perpendicular lines: Lines that are intersecting lines that form right angles (square corners). Skew lines: Lines that lie in different planes. They do not intersect and are not parallel.

Congruent Figures have the same size and shape

A translation moves a figure in a straight direction A reflection of a figure gives it a mirror image over a line. A glide reflection is a translation followed by a reflection. A rotation moves a figure about a point. A figure has reflection symmetry if it can be reflected onto itself. The line of reflection is a line of symmetry. Some figures have more than one line of symmetry. When a figure rotates onto itself in less than a full turn, the figure has rotational symmetry.

Topic 10-2: Comparing and Ordering Integers

When you compare negative numbers is not the same as positive numbers, -5 is not bigger than -2 because -2 is nearest to 0 than -5 to 0.

When you compares positive and negative numbers the positive number will always be bigger.

A pattern is the repeating of a group of shapes,numbers,letters or pictures.

In this topic we need to get the values of the variables in the equation and then pass it into a graph

In this equation we have Y and X and we need to substitute them with a value like -4 = -1 - 3 -4 = -4 and then get -4 and -1 into a graph

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TOPIC 8 Lesson 8-1 Multiplying a fraction and a whole number- 3 Lesson 8-2 Estimating products - 4 Lesson 8-3 Multiplying fractions - 5 Lesson 8-4 Multiplying mixed numbers - 6 Lesson 8-5 Multiple-step problems - 7 TOPIC 12 Lesson 12-1 understanding ratios - 9 Lesson 12-2 equal ratios and proportion - 10 Lesson 12-3 Understanding rates and unit rates - 11 Lesson 12-4 Comparing Rates - 12 Lesson 12-5 Distance, Rate, and time - 13 Lesson 12-6 Draw a picture - 14

On Multiple step problems you will need to find 2 problems when you are only given 1 to get the full answer and you need to find what is next to get your answer Example : Tina spent 1 1/2 hours setting up her computer. It took her 3 times as long to install the software. How long did it take Tina to set up the computer and install software? and here you have to find the HIDDEN question to get the answer so in this case the question we are given is so we are multiplying 1 1/2 times 3 but we need something else to get it and the hidden question is: How long did it took Tina to download the software?

14-3: Percents Greater than 100 and Less than 1

Angles are measured by a tool called protractor

Topic 13-1 &amp; 13-2: Using Ratio Tables &amp; Unit Rates

A ratio table is a structured list of equivalent (equal value) ratios that helps us understand the relationship between the ratios and the numbers. A unit rate means&nbsp;a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second

There are 3 hops / 5 jumps. How many hops will be in 15 jumps?

make 60c/12tsp to 5/1 and multiply 5x20 (cross products) d=100c

d c /20tsp. 60c/12tsp what equals to d?

To do work backwards you need to identify the operation according to what is telling the question

Dividing Integers like multiplying you only need to do the equation, and if there is one negative number the answer will be negative but if there are two negative the answer will be positive.

Percents are like fractions or decimals, part of a whole, in this case the whole is 100% and as in fractions and decimals, the percents are part of 100%.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

1 : 3 (for every one boy there are 3 girls)

Equal Ratios are the same as a proportion. A proportion is the same as a ratio but with a higher rate but it is still equal like 5 gallons/ hour and a proportion will be 20 gallons/ 4 hours

A unit rate means a rate for one of something

Rate: 40 steps per 4 sec Unit Rate: 10 steps per 1 sec

To compare rates you must get the Ratio of it and you get it by dividing it and then comparing both ratios

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By: Alyssa Garcia, Iker Freites, Rodrigo Garcia

As in 10-5 you need to divide the percent divided by 100 and the multiply it by the whole number.

To solve an equation with integers means that the variable can be either a positive or a negative number.

When you estimate a percent you will round the whole number to a number that is easier to divide sometimes you also estimate the percent.

For example: 35% of 102 0.35x100 35% of 102 is about 35

Topic 10-3: Rational Numbers in a Number Lines

When you use a number line with integers the negative numbers are on the left of zero and the positive numbers to the right of zero.

When you add integers with same signs: -Add the absolute values -Give the same sign When you add integers with different signs: -Find the difference of the absolute values -Give the sign of the integer with the greatest absolute value

Dividing two fractions is the same as&nbsp;multiplying the first fraction by the reciprocal of the second fraction. The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators.

Flip the divisor into a reciprocal. Change the division sign into a multiplication sign and multiply. Simplify if possible.

when it’s a mixed number what you gotta do is round up the fraction. For example 1 1/3 would be rounded up to 1.

10-9: Graphing Point on a Coordinate Plane

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

A diameter is any line segment through the center that connects two&nbsp; points in a circle. A radius (plural, radii) is any line segment that connects the center to a&nbsp; point on the circle A chord is any line segment that connects two points in the circle A central angle is an angle whose vertex is the center of the angle

To find the percent of a number you need to multiply the percent as the denominator of 100 times the number that is the whole of that percent.

1. Change to improper fractions 2. Change to multiplication with the reciprocal of the divisor 3. Simplify 4. Solve

1. Keep the whole number the same. 2. Change the division sign into a multiplication sign. 3. Flip the fraction you are dividing by. 4. Multiply the one on the top left with bottom right and multiply top right with bottom left 5. Simplify

Topic 9-2 and 9-5: Dividing Mixed Numbers and dividing a whole number by a fraction.

14-3:Percents greater than 100 and less than 1

Some percents are less than 1 while others are more than a hundred for example:145% &amp; 0.33%

Distance, Rate, Time                       

To get the Rate you have to divide Distance divided by Time r= d/t To get the Time you have to divide Distance divided by Rate t=d/r To get the Distance you have to multiply time by rate d=t x r So with this formulas you can find the time, distance, and rate of anything 15 mi time = 2h rate = ? So we divide 15 by 2 and get 7.5 which is the rate

Pamela walks 1 mile and runs 4 miles in her daily workout 

What is the ratio of miles walked to miles ran during each of workouts?

10-9: Graphing Points on a Coordinate Plane

When you graph points on a coordinate plane the first number is x and the second number is y

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