This book was created by 5th 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

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A prime number has exactly two factors, 1 and itself, and a composite number has more than two factors. One way to find if a number is prime or composite is by doing prime factorization.

Prime factorization is when you are writing a composite number as the product of its prime factors.

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Steps: <ol><li>make the addition horizontally </li><li>Add first the whole number then the fraction</li><li>If it gives you an improper franction make it as a mixed number </li><li>simplify if it is possible </li></ol>

Solving Multiplication and Division Equations

We already know that to solve an equation, we have to make the two sides of the equation equal with a variable alone on one side. We can use inverse operations and properties of equality

Remember: Inverse operations “undo” each other. Because of Properties of Equality you can multiply or divide both sides of an equation by the same number and the two sides of the equation remain equal.

A machine can wrap a package in 5.22 seconds. If Josh has 4 packages to wrap, how many seconds does it take? Solve the equation t = 5.22(4) to the find the total time.

t= 5.22 (4) 5.22 ° 4 = t 5.22 ° 4 = 20.88 t = 20.88 so Josh is going to stay 20.88 seconds so he can wrap the package

7-1 Adding and Subtracting: Like Denominators 7-2 Least Common Multiple 7-3 Adding and Subtracting: Unlike Denominators 7-4 Estimating Sums and Differences of Mixed Numbers 7-5 Adding Mixed Numbers 7-6 Subtracting Mixed Numbers 7-7 Problem Solving: Make a Table

First, we need to know what’s the LCM(Least Common Multiple). The LCM is, like the name says, the smallest common multiple that two or more number can be multiplied for them to be alike.

For finding the LCM for the numbers, you need to do this process:

Steps: 1.- List the prime factors of each number. 2.- Circle the greatest number of times each different factor appears. 3.- Find the product of the factors you circled.

By Diego Villarreal Cantú and Santiago Ortiz Antunes

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The multiple-step problems often have hidden questions that you cannot answer the question until had founded 

Mau do 8 hours of training Wednesday, Thursday and Friday in all.and he has 2 games of 50 min each how many mau did train or play in all

Like this question, you want to know how many Mau did play or train but, there a question that is hidden that is know how many hours Mau play  , and then do the sum of when he play and when he train

Solving Additions and Subtracting Equations

You can use inverse relationships and the properties of equality to get the variable alone to solve an equation.

To get c alone, undo adding 5 by subtracting 5 from both sides 

Remember that you need to do the same thing to both sides of the equation to keep the equation equal.

for this topic we are going to use a table like this: 

The library sells pen sets. Mariam sold 8 sets for a total of $100 in sales. Find an equation that can be used to find s, of the cost of each set?

First: What do we know? Mariam sold 8 pen sets for $100 Second: What do you need to find out? the value of S Assign a variable: S= how much is each set Draw a picture 100 Solve the equation 8s = 100 Answer the question each set cost $20 dollars

Estimate:7.54+3.36 1.Round each decimal to the nearest whole number 2.Add to estimate

Rounding: Round each factor to the nearest whole number and multiply.

Ignore the decimal point first multiplied like  normally 

Compatible numbers: Find compatible numbers and divide.

And then add the decimal point to the place's,and you need to put the decimal point in the places it is before Example: if is    0.34 x 19 the product you need to put the decimals in two places because 0.34 has 2 decimals places

We use &lt; or &gt; to compare two numbers

We start with the greatest place, if the numbers are different one should be greater than the other.

Because 6 is greater than 4 6,371 is greater

We order the numbers from least to greatest or from greatest to least. We know that by finding the different number when you are compering you will know which one is greater or less.

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By: Roberto Sánchez Tamez and Ulrich Sebastian González Lopez 

A fraction is a part of a whole.fractions are used to show part of a set.

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In this lesson you will learn how to convert an improper fraction into a Mixed number and the other way around

When the Numerator is GREATER than the Denominator the fraction is called an improper fraction. To simplify it you will need to see how many times does the numerator fit in the denominator and put a Whole number besides the fraction to show how many times does it fit and there you have the mixed number 

To convert the mixed number into an improper fraction you will have to multiply the WHOLE NUMBER times the denominator and then add the numerator 

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5-1:Factors, Multiples, and Divisibility 

In this lesson you need to tell if a number is divisible by another number. And how will you know this? By applying the divisibility rules!

The divisibility rules are rules that a number has to know if that number is a divisible by another number 

3 : the sum of the digits in the number is divisible by 3

7 : the last digit of the number is doubled and the difference between that and the remaining digits is 0 or a multiple of 7

4 : the las two digits of the number are divisible by 4

8 : the last three digits of the number are divisible by 8

9 : the sum of the digits in the number is divisible by 9

6 : the number is divisible by both 2 and 3

The 8 is in the hundredths place as a decimal is 0.08

Seven and four thousand, eight hundred thirteen ten-thousandths.

The place of the underlined digit is ten-thousandths 

The place of the underlined digit is the ones

The number 64,729,831,500,400 and other numbers can be written in different ways.

Sixty-four trillion, seven hundred  twenty-nine billion, eight hundred thirty-one millions, five hundred thousands and four hundred 

60,000,000,000,000 + 4,000,000,000,000 + 700,000,000,000 + 20,000,000,000 + 9,000,000,000 + 800,000,000 + 30,000,000 + 1,000,000 +500,000 + 400

The underlined digit is in the hundred millions place. 700,000,000

Solving Multiplications and Divisions  Equations 

To solve an equation, make the two sides of the equation equal with the variable alone one one side.

You can use inverse operation and properties of equality.

say  that you can multiply or divide both sides of the equation by the same number and the two sides of the equation remain equal.

Properties of Equality

use division to “undo”multiplication.

Use multiplication to “undo” division.

Peter solved an equation r ÷ 14 = 19 and be got 266 is his answer correct?

Yes, because he did apply correct the inverse operation on both sides.

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Jake earns 8 points for every dollar he spends at the supermarket. Which value completes this table?

First for this we will need to use pemdas this is the clue  for what do first

So first the exponents then the multiplication next the division and finally the sum

In this lesson you will learn how to make decimals and fractions have the same value 

Method 1: write a equivalent fraction that has a power of 10

First you write the number with any power of 10. 0.125= 125/1000

Method 2: Divide the Numerator by the Denominator

You have completed this lesson

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You can add or multiply numbers in any order and the sum or product will be the same.

You can group numbers differently. It will not affect the sum or product

You can add zero to a number or multiply it by 1 and not change the value of the number.

Multiplication Property of Zero If you multiply a number by zero the product will always be zero.

★Topic 4 ★

1- Properties of Equality 2-Solving Addition and Subtraction Equations 3- Draw a Picture and Write an Equation 4-Solving Multiplication and Division Equations 5- Draw a Picture and Write an Equation

Made by: Alexa Vergara and Andrea Villarreal

To have an equation balanced, you need to apply the same operation on both sides. but how do we do it? both sides need to be equal; for example:

Steps: 1- Add the same number to each side 2- Subtract the same number from each side 3- Multiply each side by the same number 4-Divide each side by the same number

Equation = Equation EQUAL

Another example: b+5 = 35 and that is equal to: 30-5= 30 but why subtract?? Because inverse operation undo each other And the example is TRUE because the same operation was applied on both sides

Step 1 Put the decimal point in the dividend.Divide put the decimal in the quotient right above the decimal in the dividend

First to divide a decimal you need to make the decimal a whole number 

Step 2 Add a zero after the decimal point in the dividend. Bring down the zero and divide.

Step 3 Repeat step 2 until you have no remainder.

Then let’s find 0.7÷84 ,because you need to make 0.7  a whole number you will  move the decimal point 1place to the right on both sides 

The first thing is that subtracting mixed number is the opposite of adding them but the process is different. If the number is subtracted from is a whole number; you need to rename it for it to be a mixed number, if the number that subtracts is a whole number; you only subtract the whole number of the subtractor and the fractional part stays the same, if it all the numbers have like denominators you only rename if the subtracted’s fractional part is less than the subtractor’s, and if they have unlike denominators you find the LCM, if the subtracted’s fractional parts is less than the subtractor’s you rename it again and when all is done you subtract. Simplify if asked and possible.

In this lesson you will learn how to convert fractions to a division and the other way around 

For example the fraction 1/4 as a fraction would be 1 divided by 4. To make a fraction to a division you will transform the numerator into the divisor and the denominator into the dividend and the other way around

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In this problem solving lesson you need to draw a table(like the title says) for organizing the information in a way that you can see the sequence that gave you in a variables like: days and points, each day you win 50 points more than the day before and you got 100 in the first day. How many points you got in 1 week?

d stands for the day, and p stands for the points. You add 50 points to the winning o the last day so in day 1 you got 100, you add 50 to the points won in the day before and add those points to the day 1’s points and you got day 2 points.

Problem Solving: Make an Organized List

Zoe, Connie, Jane, and Sofi are playing a game were they need to be in a  zigzag. In how many different ways can they be in the zigzag?

We solve it by seeing all of the options we have without repeating them.

 Zoe, Connie, Jane, and Sofi can be in a zigzag 16 different ways.

Multiplying and Dividing by 10, 100, and 1,000

You can use place value to multiply or divide by 10, 100, 1,00

If we multiply we need to move the decimal point to the right the times of how many zeros there  are.

If we are dividing we need to move the decimal point to the left the same times of zeros there are.

In this lesson you are trying that a fraction can not be divided any more this is known as Fractions in simplest form

The fractions in simplest form are fractions that cannot be divided any more. And how do you convert a fraction into its simplest form? By dividing the numerator and the denominator by the same number until they one of the numbers is prime 

Step 1:Estimate using compatible numbers step 2:Make the divisor a whole number.Multiply the divisor and the dividend the same power of 10.Place the decimal in the quotient. Step 3:Divide as you would with whole number.Remember that sometimes you may need to add zeros to complete the division. Step 4:Compare the quotient with your estimate.

Equivalent fractions are the same fractions but expressed in other form.

You can use division or multiplication  to find equivalent fractions.

Equivalent fractions name the same amount.

Problem Solving : Draw a Picture and Write an Equation 

Zoo keepers divided some land into 4 sections for the monkeys at the zoo. Each section has 23 monkeys. How many monkeys are at the zoo.

Choose a variable for the unknown. The unknowns is the total of monkeys  at the zoo.

Draw a picture to show the total number of monkeys is divided into 4 equal sections of 23 monkeys.

Write an equation using a variable and the picture 

In this lesson you will have to draw pictures to answer the questions

A street has bumps every 0.25 mile. How many bumps will there be in 2 miles?

By:Jose Eugenio Padilla Hernandez and Dante Arteaga Torres

Problem Solving:Make and Test Conjectures

A conjecture is a generalization that you think is true.A Conjecture can be proven true or false.

An exponent tells how many times the base is going to multiply.

Remember: is not 4x6 is 4x4x4x4x4x4

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Commutative Property: The order in which numbers are added or multiplied does not affect the sum or product. Associative Property: The way in which numbers are grouped to be added or multiplied does not affect the sum or product

Adding and Subtracting:Unlike Denominators

If you are gonna add or subtract with unliked denominator;you need to make the LCM.

Steps: <ol><li> identify the denominators </li><li>find the LCM of the denominators </li><li>multiply your numerator times the number you multiply the denominator to get the LCM</li><li>add or subtract </li><li>simplify if it is possible</li></ol>

We use &gt;, &lt; or = to compare two numbers.

We compare decimals by using place value.

The digit in the tenths place tells us which one is greater. 7 is greater than 3.

We know that when we find the numbers that are different when we are Compering we know which one is greater.

Adding and Subtracting: Like Denominators

When a fraction have the same denominator you only add or subtract the numerator.

Steps: <ol><li>Identify the denominator </li><li>then add or subtract the numerator </li><li>simplify if it is possible</li></ol>

The greatest number that divides into two numbers is the greatest common factor(GCF)of the two numbers.

A way to find the greatest common factor is to do a factor tree.

In a factor tree we find the factors of a number.Commonly in a factor tree to find the GCF we have to find the common factors of both numbers.And multiply them.

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6-4 Decimal forms of fractions and mixed numbers 

In this lesson you will learn how to convert fractions to decimals, decimals to fractions and how to write whole numbers with decimals 

How to convert fractions to decimals

How to convert decimals to fractions

Write 13/16 as a decimal

Write 0.85 as a fraction 0.85= 85 hundredths= 85/100

Divide the numerator by the denominator. Add zeros if necessary 

Write 85/100 in simplest form

If the decimal repeats place a bar above the number for example: 0.3333 = 0.3̄

Write 6.450 as a mixed number

Congratulations you have Completed this lesson

Estimating Sums and Differences of Mixed Numbers

This is relatively easy,  you need to round the fractional part of the mixed number up if it is one half or greater or down if it’s less than one half. Then, we add the all-ready rounded numbers.

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