This book was created by 6th grade students in the Advanced Math Program at Latin American School, in Monterrey, México.


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

An exponent tells how many times the base will be used as a factor.

base

product of factors

value of the expression or standard form

<ul><li>P arenthesis</li><li>E xponents</li><li>M ultiplication</li><li>D ivision</li><li>A ddition</li><li>S ubtraction</li></ul>

(12 - 4) 2 + (14 ÷ 7) (82 + 2) 64 + 2 66

(64 - 42) ÷ (-3 + 5) (64 - 16) ÷ 2 48 ÷ 2 24

An equation is a mathematical sentence stating that 2 expressions are equal 

Solving Equations require to follow this steps:

IDENTIFY the operation applied to the variable.

APPLY the inverse operation on both sides of the equal sign.

To multiply fractions, you first check if you can simplify, this can be done by checking if the numerator of the first number and the denominator of the other number (or viceversa) are multiples of a number. For example, in the multiplication of ¼ x 16, 4 and 16 (denominator and numerator) are both a multiple of 4, so you divide both of them by 4. 

Then, to multiply the fraction and the whole number you have to multiply the numerator times the numerator and the denominator times the denominator. To help you see which one is the denominator of the whole number, you can put the whole number divided by 1 (something like this: x/1 where x is your whole number). Now you can multiply the numerator times the numerator and the denominator times the denominator. Here’s and example:

Now lastly, you have to simplify. To simplify an improper fraction, you divide the numerator by the denominator. The quotient would be the whole number and the remainder would be the numerator of the fraction (the denominator is the divisor of the fraction we did earlier). Then to simplify fractions, you need to get the GCF of both numbers and divide both of them by the GCF. Here’s and example:

Solving equations by multiplying or dividing

To solve equation by multiplying or dividing you need to add the inverse operation undo each other and check by substituting.

To solve two-step equations you need to firs identify the first inverse operation, like in the equation 3a+5=20 first you subtract 5 on both sides then, it should give you 3a=15 you divide by 3 on both sides and then you check by substituting and that’s how you solve two-step equations.

Rules: 1.Add from right to left 2.Subtract from right to left

By: Miranda Herrrea, Eugenia Lozano, Regina Gallaga and Elisa Miranda

Precision is to be able to identify the best unit to use depending on its capacity

For example: What measure will fit better for a flagpole? Yards Miles

The correct answer is yards because a flagpole its more probable to measure yards than miles.

To be able to identify the most accurate answer you will need to know the value of each unit. Here is a table that will help you.

Converting Improper Fractions to Mixed Numbers

how to convert an improper fraction into a mixed number!

<ol><li>divide the numerator bu the denominator n÷d</li><li>put the result in the whole numbers place W n/d</li><li>The reminder put it in the numerator</li></ol>

how to convert a mixed number into an improper fraction!

<ol><li>multiply the whole number by the denominator</li><li>add the product to the numerator</li></ol>

………………………………………………………………………………………………………………………………..

Multiplying decimals can be really easy, when you multiply decimals you have to make a specific process so that you can get to your answer.

First, you have to multiply the numbers as whole numbers, completely ignoring the decimal point.

Then, after you do that you go down to the next row and skip a number and start multiplying in this case with the 4.

After that, you just keep doing the same process until you have finished with the final number.

Finally, you will add all your numbers to the final product, and add the decimal point in this case 4 times to the left.

Rational Numbers are any finite number, and any number with a whole as a square root.

These are rational, because they are finite and they have a whole as a square root.

These are irrational, because they are infinite and the square root is not a whole number.

Prime factorization is the process of expressing a number as the product of its prime factors. Prime factors are the prime numbers that multiply together to give  the original number. For example, the prime factorization of 12 is 2 x 2 x 3, as 2 and 3 are prime factors of 12.

Writing a composite number as the product of its prime factors shows its prime factorization. You can use a factor tree to find the prime factors:

When multiplying or dividing two integers, if both have the same sign (positive or negative) the result will be positive.

When multiplying or dividing two integers with different signs the result will always be negative

To divide fractions and whole numbers, you need to get the reciprocal of the divisor. Next, you have to change the division sign into a multiplication sign. Then multiply normally.

Rules: 1.You can use rounding and compatible numbers to estimate with decimals. 2.Round each number to the nearest whole number, then add. 3.When dividing use compatible numbers.

Solving equations by adding and subtracting 

Here are some example of equations with addition and subtraction.

Remember: you will apply the same rules mentioned previously as to multiplying and dividing 

Chapter 2 Merry Mathmas!

Scientific Notation is a way of writing numbers that are too big or too small.

To solve you need to count the number of times you move a decimal point until you end up with one whole number and (if it has more than one number) a decimal.

3-1

Estimating with Fractions and adding and subtracting 

Fractions are more commonly to be estimated by using benchmarks. A benchmark is 0 1/2 or 1. When a fraction is closest to one of those three numbers it is rounded to either 0 1/2 or 1.

Some examples may be: 4/5 is closest to 1 2/5 is closest to 1/2 1/9 is closest to 0

To subtract or add first we gotta have the same denominator. We can find it by finding the least common multiple and that’s our denominator. After we do that we subtract or add the numerators of both fractions, the denominator doesn’t change. Examples: 1/4 + 1/2 , first we turn the denominator to be the same denominator. 1/4+ 2/4 , Now we add normally; 3/4 is our answer. Now Lets try subtracting. Examples: 2/5 - 3/10 , First we have to find the LCM which is 10. So 4/10 - 3/10, Now we just subtract normally so the answers is 1/10.

This is a video of how it should be done.

2.- move the decimal point until you have a whole number

Converting Between Percents, Decimals, and Fractions

Convert fractions into decimals <ol><li>turn the denominator into any power of 10 (ex. 13/100)</li><li>turn the fraction into a decimal by putting 0. And the amount of zeros the power of 10 has</li><li>put the number in the numerator in the decimal(ex. 0.13) </li></ol>

Convert decimals into fractions lets say we hace the decimal 19.89 and we want to convert that into a fraction <ol><li>because the 19 is a whole number it goes on the side(19 n/d)</li><li>Then count how many places are in the decimal</li><li>put a 1 and add the amount 0 for the amount of decimal places (89/100)</li><li>simplify if possible</li></ol>

Solving inequalities by multiplying and dividing

If you divide both sides of an inequality by a positive number, the symbol will stay the same. If you divide both sides of an inequality by a negative number, the symbol gets reversed.

If you multiply each side of an inequality by the same positive number, the symbol remains the same. If you multiply each side of an inequality by the same negative number, the symbol gets reversed.

To change the units in the customary system you will need to know if you need to divide or multiply.

Here is a chart that will help you solve the problem.

Example: pints to quarts divide

From a smaller to a larger unit, divide. From a greater to a smaller unit, multiply.

Example: gallons to pints multiply

Expressions, Equations, and Inequalities 

By Mateo Villarreal,Leonardo Alibani, Rafael Mercado,

To graph an equation, you first need to analyze it. If the variable is greater, you make an open circle on where the other number would go on the graph, and draw an arrow pointing to the right. If the variable is less than the other number, draw an arrow to the left. If the variable is greater than or equal to the other number, make a closed circle, and an arrow pointing to the right. If the variable is less than or equal to, make a closed circle, and an arrow pointing to the left.

Adding and subtracting integers is just about learning the Integer Rules.

Rules for adding integers with the same sign:

• add the absolute values • give the same sign

Rules for adding integers with a different sign:

• find the difference of the absolute values • give the sign of the integer with the greatest absolute value

• Subtracting an integer is the same as adding its opposite

An expression is a mathematical phrase containing numbers, variables and at least one operation.

A variable is letter or symbol that represents a specific value within an expression.

Any expression requires to be solved downwards and DOES NOT have an equal sign.

Expressions need to be solved following the Order of Operations (PEMDAS) and always in this way:

1. 2. 3.

Lesson 1, Estimating with fractions and adding and subtracting. Page 3 Lesson 2, Adding and subtracting mixed numbers. Page 4 Lesson 3, Multiplying fractions and whole numbers. Page 5 Lesson 4, Dividing fractions and whole numbers. Page 6 Lesson 5, Changing units in the customary system. Page 7 Lesson 6, Precision. Page 8

First we analyze the problem we know we have to get the LCD to get the fractions in order from least to greatest 

So we make the fractions to the fractions with 30 as denominator and we order them from Least to Greatest

now we have the fractions in order from least to greatest 

Comparing Fractions

Compare fractions write &gt;, &lt;, or =

First we analyze the problem we know we have to get the LCD

To get the numerator we get what 16 times what is 80 so 16 times 5 is 80 so 10 times 5 is 50 and the same on 6 so 10 times 8 is 80 so the numerator will be 48

And there we know 10/16 is greater than 6/10

Bright ideas border

By: Ignacio Ostos, Santiago Salazar, and Sofia Cantú

Now we are going to add or subtract mixed fraction, it is really similar to adding or subtracting normal fractions. It is a little different. This are the steps: First turn the mixed fractions into improper fractions, you do that by multiplying the whole number by the denominator and add it to the numerator. Then you gotta have the same denominator, to find it you’re gonna have to find the LCM and that will be your denominator. Now you just add or subtract normally. Examples: 3⅔+ 4¼, First you have to make then to an improper fraction, which is 11/3 + 17/ 4. Then you have to get the same denominator, which is 44/12 + 51/12= 95/12. Now we turn it to a mixed number and that’s our answer 7 11/12. Example: 2¾ - 6½, First you have to turn it not an improper fraction which is 13/2 - 11/4. Then you have to get the same denominator, which is 26/4 - 11/4 = 15/4. Now we turn it to a mixed number and that’s our answer 3 ¾

Three times a number minus ten is twenty.

Five times a number minus seven is thirty-three

Four times a number plus four is twenty four

The MEAN is the sum of the data divided by the number of data items

3 5 5 8 8 9 9 9 = 7 56 divided by 8 =7

The MEDIAN of a data set is the middle value when the data are arranged in numerical order. The MEDIAN of a set always separates the data into two groups of equal size. The MEDIAN for an even number of data items is the mean of the two middle values

The MODE of a data set is the item that occurs with the greatest frequency. A set of data may have more than one MODE. There is no MODE when all the data items occur the same number of times.

The RANGE of a data set is the difference between the greatest and the least values. You can find the RANGE by subtracting the least value from the greatest value

3 5 5 8 8 9 9 9 = 6 3 - 9 = 6

Example: Label these integers on the number line: -6, 8, -9, 0, 2, -2

Ordering integers is really easy, you just have to memorize where are the numbers placed and located. On a number line, positive integers are located on the right side of zero, and the negative integers are located on the left side of zero.

“&lt;“- less than ”&gt;”- greater than ”=“- equal to

Solving Inequalities by Adding and Subtracting 

In adding and subtracting inequalities, we will use a variable to show the value that is missing, and so to solve a problem like adding and subtracting inequalities, you’ll have to see if the symbol is pointing less or greater than, if the symbol is pointing less, the variable would be less than the value, and vice versa. Also, like an equation, the operation will be solved downwards 

Simplifying Fractions

Reduce the Fractions to its Lowest Terms

Find divisible number for numerator an denominator 

We can divide by 2, 5, and 10 will divide by 10 because is the greatest

And we have 7/10 in simplest form

Name

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