6th grade students in the Advanced Math Program at Latin American School in Monterrey, Mexico share what they have learned in the first trimester of the school year 2022-2023.

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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A relationship between two expressions or values that are not equal to each other.

if the numbers that go in are greater, we use &gt; but when they aren’t, we use &lt;.

Graphing inequalities is the process of showing what part of the number line contains values that will "satisfy" the given inequality.&nbsp;

Solving an inequality it’s like solving an equation, the process is similar and it has the same dynamic as it. We did the normal inequality and then we added the opposite operation at the end ( -10 ≥ n-4 +4 )

Graphing inequalities by multiplying or dividing it’s actually very simple. It may look hard but when you learn by heart the process of graphing and solving inequalities of + and -. You’ll master this.

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For comparing and ordering fractions you need to fin the LCM of all the numbers in the list. For finding the LCM you need to make a table in which you are going to put the original numbers and the numbers they can be divided by. Once you are done dividing, multiply all the numbers you got and the product will be the LCM ( Least Common Multiple ). Now just multiply the numerator by the same number you multiplied the denominator to get to the LCM.

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When you add numbers with the same sign add the absolute values and give the same sign.

When you add integers with different signs find the difference of their absolute values and give the sign of the integer with the greater value.

When you multiplying integers when they are the same sign the answer is positive and with different signs the answer is negative. You just need to multiply as always. Positive x Negative = Negative Negative x Negative= Positive Positive x Positive = Positive Negative x Positive = Negative

Subtracting Integers is the same as adding it’s opposite.

Dividing integers just divide normal and use the rule of multiplying integers.

By : Iker Freites Pollonais, Juan Felipe Borbón Salazar, Rogelio Francisco Rodriguez Lopez, Regina Calvillo Padilla

When you estimate you round up or down, but how to know when you should round it up or down? Well if the number is 5 or above you round up, and when the number is 4 or below you round down.

Now what if you use decimals? Well the same rules apply. For example 3.2 does it go up or down? Down because 2 is less than 4.

For example number 47 is it round up or down. Up because 7 is bigger than 5.

Adding and subtracting is quite easy, but adding and subtracting with decimals have some extra rules. For example when you add and subtract you have to a line the decimal point if not your answer can be wrong.

After that is just like normal adding and subtracting.

In order to simplify, fractions we need to get the GCF ( Greatest Common Factor ) of the numerator and the denominator. For us to be able to get the GCF we need to make the prime factorization of both numbers. And the PRIME numbers they have in common will be multiplied and the number you get will be the greatest number both numbers can be divided by. Now just divide by the GCF on both numbers and that should be the simplest form.

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By: Santiago, Mateo P, José Humberto, Rodrigo Daniel

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Multiplying decimals may seem quite hard, but it is actually easy! I’ll show you.

In this example, we are going to multiply normally, and then add the decimal point, since there are two decimals, (one for each number) we will put the decimal point before the last two digits. (It is not necessary to add the zero).

When we are talking about money, it is necessary to have just two decimals, but the process is the same.

Page 1. Cover Page 2. Index Page 3. Exponents and Order of Operations Page 4. Prime Factorization Page 5. Simplifying Fractions Page 6. Comparing and Ordering Fractions Page 7. Mixed numbers and Improper Fractions Page 8. Fractions and Decimals Page 9. Rational Numbers Page 10. Scientific Notation

The first thing you have to do is take out the decimal points, then make a little house, like the one to your left, then see how many times the number fits.

Decimal points Decimal points are things you have to take out when dividing, the number of times you make the decimal point go right, the more digits before it, if there are no digits left, add zeros. There needs to be no decimal points left, so when dividing a number with two decimals with a one with three add a zero, four decimals, two zeros, and so on.

A fraction is a part of a whole. Meanwhile a decimal is a number that is less than one ( Tenths, Hundredths, Thousandths, etc. ). To convert a fraction into a decimal you divide the numerator by the denominator, and to make a decimal into a fraction you write the number with the denominator being 10,100,1000 or any other number according to the place value of the decimal and you write the decimal as the numerator. Now you get the simplest form of it and thats the fraction.

Integers that are less than zero are negative integer and integers greater than zero are positive integers.

So when you compare and order integers you need to check if they are positive or negative and after that you just check which one has a greater value.

In this one both are negative but -3 is farther to 0.

In this one 4 is greater because it is positive and -4 is negative

You can also see this when you compare, this means absolute value is the highest value a number has without changing its digits. When you see this in a negative number change it to a positive number.

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Lessons 1, 2, and 3 Pages 4 and 5 Lessons 4, 5, and 6 - Pages 6, 7, 8 and 9 Lessons 7, 8, and 9 - Pages 10 and 11 Conclusion - Page 12 Credits - Page 13

By: Jimena Martínez, Rodrigo Raúl, Alyssa Garcia

1-9: Order of Operations and Distributive Property

An improper fraction is a fraction that its numerator is greater than is denominator. For example 19/5, the numerator is 19 and the denominator is 5. For a improper fraction to become a mixed number you will need to see how much times 5 fits into 19 which is 3 and the remaining 4 will be on the fraction which is 3 and 4/5. Now to convert a mixed number into an improper fraction you need to multiply the whole number times the denominator ( 3 x 5 ) and add the numerator ( 4 ). A mixed number is a mix of a whole number and a fraction.

Precision is saying the best metric unit for something.

For example, if someone asks you which measurement is more precise, you need to say the lowest measurement 

Also you can measure in decimal. The more decimals a measurement has, the more precise it is

To add or subtract fractions first you need to find a common denominator between the two fractions and then multiply the numerator by the times the denominator needs to be added to get to that number

If needed, when you finish the addition or subtraction  of fractions, you simplify them to their simplest form

Multiplying and dividing fractions and mixed numbers 

Fractions and Mixed numbers can also be divided or multiplied.

by multiplying you can simplify the fractions in diagonal.

When you divide fractions you need to convert the division into a multiplication using the reciprocal of the divisor

When you divide or multiply mixed numbers you need to convert them into improper fractions 

Adding and subtracting mixed numbers is almost the same as adding and subtracting fractions. Adding and subtracting mixed numbers include whole numbers.

To add mixed numbers, First you need to add the whole numbers, then you need to find a common denominator, after that, you need to multiply the numerator by the times it takes for the denominator to get to the compatible number, and finally you add the 2 numerator and you get another mixed number.

To subtract mixed numbers, first you find a common denominator, then you convert the numerator so it’s compatible with the new denominator, and then you subtract the whole numbers and the fractions. If the fraction on the top cannot be subtracted by the fraction on the bottom, you take 1 from the whole number and add to the numerator.

The customary system is divided into 4 sets:

1 ft. = 12 in. 1 yd. = 3 ft. 1 mi. = 5280 ft. 1 mi. = 1760 yd.

3 tsp. = 1 tbsp. 2 tbsp. = 1 oz. 1 c. = 8 oz. 1 pt. = 2 c. 1 qt. = 2 pt. 1 gal. = 4 qt.

1 min. = 60 sec. 1 hr. = 60 min. 1 day = 24 hr. 1 week = 7 days 1 yr. = 52 weeks 1 yr. = 12 months 1 yr. = 365 days

Prime factorization or factor tree shows the numbers a number can be divided by ending on prime numbers. For example 36 can be divided by 2 and 18 , but 2 is prime so we stop there. We can still continue with 18 which is 9 and 2 and we stop in 2. Lastly 9 can be divided by 3 and 3 and those numbers are prime so we are done.You can continue with the tree until you get 2 PRIME numbers like in the example below.

A used system in which numbers are expressed as products consisting of a number between 1 and 10 multiplied by an appropriate power of 10

Order Of Operations &amp; The Distributive Property 

The Distributive Property is multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together.

Mean: the sum of all the values in a set of data Median: the value separating the higher half from the lower half of a data sample ( the middle number) Mode: the number in a set of numbers that appears the most often Range: the difference between the largest and smallest numbers

Order Of Operations P arenthesis E xponent M ultiplication D ivision A ddition S ubtraction

This process is followed when performing an operation,for example 4x5-3, what would you perform first? Well,multiply 4x5 and then subtract 3 so, 17

Here we have a video explaining what we do when solving a mean median mode and range question.

Lesson 3: Solving equations by adding or subtracting 

Lesson 1: Evaluating Algebraic Expressions

Finding the value of an expression when a given number is used to replace a variable is known as evaluating an expression. You must substitute a number for each variable and carry out the operations in order to evaluate an algebraic expression. Here are some examples:

Number sense is&nbsp;a good intuition about numbers. So, you could easily answer any given question. For example, 2+w =4. Knowing number sense will help you understand the answer without having to do all the boring process.

Inverse operations include addition and subtraction. If an equation contains addition, remove the addition by solving from both sides. Likewise, if an equation contains subtraction, add to both sides of the equation to reverse the subtraction.

Lesson 2: Solving equations using number sense

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Solving equations is one of the most difficult lessons for a 6th grader, but if you pay attention to the process you will never worry about not knowing how to solve it 

The first thing we have to do is to get the variable alone but this is a two step operation so we’ll have a few mira steps until we get the variable alone

We’ll start with the last thing you would do in a normal math problem, the last thing you would do in a normal math problem would be add 4, so now we start by subtracting 4 on both sides of the equal sign, opposites undo each other, the multiply 10 on both sides, opposites undo each other, so now we have “ r = 10”

And finally check by substituting the variable with your answer and if it does not give you the answer of the original problem you did something wrong and you need to try again 

Two step expressions are really simple, you just have to identify the operation, see the values and numbers they give you for the variables and replace them, and solve the expression 

When estimating with fractions, you can use benchmarks. You can estimate to 0, 1/2, or 1.

Also, when estimating mixed numbers you need to round them to the nearest whole number

Page 6 :Multiplying and dividing fractions and mixed numbers

Page 7 : Changing Units in the Customary System

Page 4 : Adding and Subtracting fractions

Page 5 :Adding and subtracting mixed numbers

In this cases we’ll divide by 1,000, because as you can see in the chart, there are units between them.

Remember… Divide by ten if you want to get a smaller unit of measurement, multiply by ten if you want to get a bigger unit of measurement. Move the decimal point to the right if dividing, move it to the left if multiplying.

0.3L to ml, divided by 1,000 we’ll move the decimal three spaces to the right, making 300ml. 22.4km to m, we’ll also divide by 1,000, we’ll move the decimal point three spaces to the right and we get 22,400m.

Solve equations by multiplying or dividing

Solving equations is not that simple but if you understand the process you could do it in your sleep! Let me give you an example to help you:

First we need to get the variable alone so we do the opposite operation that’s performed on the variable to have the variable alone, in this case it’s multiplying 8 so we will divide by 8 on both sides of the equal sign

So the 8 disappears on the variables side because opposites undo each other, but now you have to perform the operation of dividing by eight in the other side 

So 64 divided by eight equals 8, and because the variable was alone we can say that “n equals 8” 

And it would be exactly the same with division just that you would have to multiply on both sides instead of dividing

A rational number is an integer, fraction, decimal, whole number that terminates. A irrational number is a number that never ends and repeats.

The order of operations is the order in which all operations need to be solved in an equation or expression.

An exponent shows the number of times a number is multiplied by itself. When an expression is inside parenthesis and the exponent is outside of the parenthesis it means that the number you will get will be multiplied by itself N number of times.

Parenthesis Exponents Multiplication Division from left to right Addition Subtraction from left to right.

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