5th 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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Read and understand Choose a variable for the unknown. The unknown is the total number of monkeys at the zoo. Draw a picture to show that the total number of monkeys is divided into4 equal sections of 23 monkeys. PLAN AND SOLVE Write an equation using the variable and the picture.

She should have divided it into 3 pieces of 4 in long.

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Making a table to solve a problem can help you to visualize the information and organize it in a way that the problem is easier to solve.

Joshua’s burgers charge $5 for a cheeseburger and $1 extra for each extra topping. How much will it cost to have 3,5 or 9 toppings in your burger?

Multiple step problems contain hidden questions, some times you can’t answer the problem until you answer the questions that are hidden

Example: James and Raul designed and printed T-shirts for school spirit week. James had 35 T-shirts printed and Raul had 3 times that number printed. It costs $3.25 each to print the T-shirts. How much did it cost altogether for James and Raul to print the T-shirts? In this case the hidden question is: how many T-shirts did Raul have printed?, first solve the problem, than you will have your answer.

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Topic 4-2 Adding and subtracting equations

Solve 27+x=30 To get the “x” alone undo the adding 27 by subtracting 27 on both sides of the equal sign 27+x-27=30-27 x=30-27 x=3 Then check by substituting 27+x=30 27+3=30 30=30

Solve x-32=32 To get the “x” alone undo the subtracting 32 by adding 32 on both sides of the equal sign x-32+32=32+32 x=32+32 x=64 Then check by substituting x-32=32 64-32=32 32=32

Multiplying by 10, 100, and 1,000 Move the decimal point the same number of places to the right as there are zeros. Annex zeros if you need to. 1.12 × 10 = 11.2 The decimal point moves 1 place to the right. 0.2 × 100 = 20 The decimal point moves 2 places to the right. 0.006 × 1,000 = 6 The decimal point moves 3 places to the right.

Dividing by 10, 100, and 1,000 Move the decimal point the same number of places to the left as there are zeros. Annex zeros if you need to. 0.2 ÷ 10 = 0.02 The decimal point moves 1 place to the left. 1.08 ÷ 100 = 0.0108 The decimal point moves 2 places to the left. 170 ÷ 1,000 = 0.17 The decimal point moves 3 places to the left.

Step 1: Find the LCM of the denominators to find a common denominator. Step 2: Add or Subtract. Simplify if it’s possible.

Adding and Subtracting: Unlike Denominators

Topic 6: Fractions, Decimals, and Mixed Numbers

Miss Marce is building a totem for the Book Fair.It includes all of the teachers’ names. On Monday 15, Miss Marce had 3/21 of all the teachers, on Tuesday 16 she had 6/21. On Wednesday 17 she had 9/21. If there are 21 teachers in all, when will Miss Marce finish the totem? 

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Normally we use scientific notation in very large number, scientific notation is to make a number shorter, by turning it into a decimal, the greatest digit will be the whole number and the other ones will be decimals, and we multiply it by the power of 10 depending on how far you have to move the decimal point to get back to it original number.

Using divisibilty rules is an easy way to identify whether the given number is divided by a fixed divisor without actually performing the division process.

You can tell that 28 is a number that can be divided by 2 because it is an even number

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Topic 4-4 Solving Multiplication and Division Equations

To solve an equation make the two sides of the equation equal with the variable alone on one side. And you can use inverse operations and properties of equality.

Inverse operations: undo each other

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

Use division to undo multiplication

Use multiplication to undo division

Equations can be with algebra or numbers.

m x 9 = 54 m x 9 divided by 9 = 54 divided by 9 m=6

3 x 6 =18 3 x 6 divided by 6 = 18 divided by 6 3=3

Here are some videos that explain how you can add and subtract fractions 

The same as fractions and divisions, fractions and decimals are the same, because fractions can turn into decimals and decimals into fractions. So to write a decimal as a fraction correctly, the ones place turns into the denominator and the tenths or hundredths place into the numerator. Examples:

Also, when turning decimal into fractions, we can also simplify to have an equivalent fraction 

= 0.6, 6 — 10

0.28, 28 — 100

0.5 = 5 — 10

0.3 = 3 — 10

0.06 = 6 — 100

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

• A variable is a letter or symbol that stands for a certain value within an expression

• An expression is solved downwards and does NOT have an equal sign

• Expressions are solved following Order of Operations (PEMDAS) and always in this way:

1. Expression 2. Substitution 3. Solution

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In this example the 2 is in the ten thousands place

In this example the 8 is in the millions place

The prime factorization is used when you want to know what numbers you need to multiply to get the number

To get the prime factorization you need to do the factor tree

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Author:Mateo Villarreal Ilustrator:Santiago Salazar

For 4 and 8, order the numbers from least to greatest.

5)  472,315,000; 471,278,000; 477,515,000

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If you have a multiplication like so: 8x8x8; you can use an exponent

A exponent tells how times the base will used as a factor

To write a product in exponential form: 4x4x4x4x4x4x4 First write the base: 4 Count the number of times the base is used as a factor. This is the exponent. 4 7

To convert an improper fraction into a mixed number you need to divide the numerator by the denominator, the quotient is the whole number, the remainder is the numerator, and the denominator stays the same as it was on the original fraction. Here’s an example:

To convert a mixed number into an improper fraction you need to first multiply the whole number by the denominator and add the product to the numerator and the denominator stays the same. Then you can show the equality by turning the improper fraction into a mixed number. Here’s an example:

The Distributive Property says that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.

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

One way to get the GCF of to numbers is with prime factorization

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The first step to estimate a sum or a difference is to round to the nearest whole numbers.

Like 4.38 + 9.179, we round 4.38 to 4  and 9.179 we round it to 9, then just add 4+9. So the estimate answer will be 9+4 ≈ 13.

Like 14.25-5.14. We round 14.25 to 14, and 5.14 we round it to 5. Then we subtract 14-5≈9

To divide a whole number by a decimal, you first need to multiply both of the numbers by the power of 10 so that it makes the divisor a whole number.

Divide 138 divided by 0.04, first multiply by 100 to make 0.04 a whole number. Always remember to multiply 138 by 100 too, after that use long division to find the quotient, so your answer will be 3,450

I M P O R T A N T

Example: We need to find the Least Common Multiple (LCM) of 6 and 7. We can divide six by 2 so we put a 2 in the side and we put 3 below the 6 because that’s the answer, but because 3 is a prime number 3 is only divisible by itself so we put a 3 on the side and a 1 below the 3. 7 is also a prime number so we put a 7 on the side and a 1 below the 7.

Example: We are going to find the Least Common Denominator or (LCM) of 4 and 5. First we need to do a table. Then we are going to list our numbers an we are going to divide them by 2. Like 2 is not divisible by 5 we are going to put a. Then we divide the 2 by 2 so it is going to be 1 and that’s it.

3-1 Estimating sum and differences 3-2 Adding and Subtracting 3-3 Estimating Products and Quotients 3-4 Multiplying Decimals 3-5 Dividing by a whole number 3-6 Dividing a whole number by a decimal 3-7 Dividing Decimals 3-8 Evaluating Expressions 3-9 Scientific Notation 3-10 Multi-Step Problems

Sometimes making an organized list helps you to solve a problem easier.

Jose, Sumi, and Tina need to stand in a straight line in the school cafeteria. In how many different ways can they stand in the line?

Read and Understand Step 1: What do you know? Jose, Sumi, and Tina need to be in a straight line.

When writing a number line, it needs to have a start, and an end. So, if the end of a  number line ends in a specific number, the numbers that the number line will have, need to be divisible by the number the number line ends. Examples

There are speed bumps in a neighborhood every 0.25 miles, use the number line to show where there’s a speedbump.

In order to use this number line you need to divide the number line into fourths or into 25 hundredths like this:

Now with this number line you can show where there is a bump in the neighborhood.

Multiply 0.72 x 23, First ignore the decimal points, then multiply like if your multiplying two whole numbers. Count the number of decimal places in both of the factors, Last use that number of decimal places to write the answer. It’s the same as 0.45 x 0.8 for example they’re  the same steps.

Step 2: What are you trying to find? How many different ways can the three friends stand in the line?

Answer: Jose, Sumi, and Tina can stand in the line in 6 different ways.

Plan and Solve Step 3: Make an organized list to find the different ways Jose, Sumi, and Tina can stand in the line.

Decimal forms of Fractions and Mixed Numbers 

Fractions and Mixed Numbers can be turn into decimals, but there’s different ways of turning fractions and mixed numbers into decimals. So when turning a fraction into a decimal, we first turn the fraction into a division so we can divide, and the quotient will be the decimal form of the fraction. But, if a number of the quotient is repeating, we call it a repeating decimal, or also a non-terminating decimal. Example:

When turning a decimal into a mixed number, we first have to have a decimal with a number ending in the tenths or hundredths place, and then turning the decimal into a fraction with the denominator being one hundred or one thousand, and divide them to get the simplest form, and then we add a whole number to make it into a mixed number. Example:

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First you have to rewrite the dividend for it to be a whole number, you do that by moving the decimal point to the right until you have a whole number then start dividing.

Example: 0.2 divided by 1.5, first move the decimal point 1 space to the right, so it will be 2 divide by 15 then start dividing  how many times does 2 fit into 15, it fits 7 times so we multiply 7 times 2= 14 -15 1 so how many times does 1 fit into 2 it fits 2 times. Then you keep dividing until you get 0

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Find 1.093 + 41.6, round 1.093 to 1 and 41.6 to 42, after that, make sure you line up the decimal points, add the numbers, regroup if is necessary. Write the decimal point in you answer.

Find 18.5 - 7.82, round 7.82 to 8, then, line up the decimal points, and as same as addition, subtract the numbers and then write the decimal point in your answer.

A decimal is a number that uses a decimal point. Each digit in a decimal number has a place and value. You can use a place-value chart to determine a digit’s place and value. The decimal point is read “and”.

The 8 is in the thousandths place. Its value is 8 thousandths, or 0.008. The standard form of the number is 5.2684.

The word form is five and two thousand, six hundred eighty-four ten-thousandths.

By: Regina Rodriguez, Miranda Herrera, and Denisse Bruner 

Equivalent fractions are easy.The only thing to do it correct you multiply the denominator and the numerator by the same number to do it easier multiply by a small number.

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By: Santiago Salazar And Mateo Villarreal

Estimating  Sums and difference of Mixed Numbers

If you want to round to the nearest whole number you just need to see if the fraction is close to the total or it isn’t for example: 8 6/7 we will round up the fraction to a 1 because 6/7 is close to 7/7 and we will add 8 to the 1 so our estimated answer is 9.

when you want to sum or subtract the fractions you will just see if the fraction is close to the total and if not you leave the number as it was and if it’s close you will round up by 1 more so if you have 7 3/4 your answer would be 8

The property of equality is that everything you do in one side of the equal sign you need to do it in the other for the equation to be equal

No because on one side you add 1 more, than on the other side

No because on one side you are adding 2 more, than on the other side 

To understand fractions in shapes number lines and so more.There are question like what is the shaded part of the shape you need to count hominy shaded parts are and then count that are in different color.

Find 196 divided by 32, first put the decimal point in the dividend, then divide, put the decimal in the quotient above the decimal in the dividend, then add a zero after the decimal point in the dividend, then bring the zero down, after that divide, then add and add zeros until there’s no remainder.

Topic 4-3 Problem solving: Draw a picture and solve an equation 

Juan spent $29.32 at the grocery store. Now he has $2.31 left. How much did Juan have before he went to the grocery store.

What do you know? Juan has $2.31 now, he spent $29.32 What do you need to find out? How much Juan had before entering the store.

1. Assign a variable. X=how much Juan had before entering the store 2. Draw a picture. 3. Write and solve an equation. $29.32+2.31=x $31.63=x 4. Answer the question. Juan had $31.63 before entering the store

Fractions and Divison and Fractions and Decimals

Fractions and divisions are the same, because unlike the other operations,  we can convert a division into a fraction and fractions into a division. Examples:

To convert a fraction into a decimal properly, the denominator turns into the divisor and numerator into the dividend.

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You need to make sure that your fractions have the same denominator and if not you have to find the Least Common Denominator(LCD)

A conjecture is a generalization that you make and think it is true

The difference between to even number will always be a even number It is reasonable because if you subtract 24 from 30 the difference will be 6.

when evaluating an expression, you have to follow. Pemdas P is for parenthesis E is for exponents, M is for multiplication, D is for division,A is for addition and S is for subtraction

Example: [(4.2 times 3.4) - 9.28], first we solve the parenthesis in the parenthesis 4.2 times 3.4 = 14.28 then we subtract [14.28- 9.28] = 5

Step 1: Add the whole numbers. Step 2: Add the fractions.

To do a fraction in simplest form first find the greatest common factor of the denominator and the numerator then dived by GCF and that is all.I’m going to put an example.

•Translating Words Into Expressions •Properties of Operations •Order of Operations •The Distributive Property •Expressions •Make a Table

The order of the factors does not affect the product. 

Factors may be grouped differently, but the product is the same.

4 × 6 × 8 = (4 × 6) × 8 = 4 × (6 × 8)

The product of any number and zero is zero. 

The product of any number and one is the same number.

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Find 3.73 times 8.16. First you need to round 3.73 to 4 and 8.16 to 8. After you get the whole numbers multiply them, so it can give you the answer.

Find 34.518 divided by 9.272. First find the compatible numbers in this case it will be 34.518 make it to 35 and 9.272 make it to 9, after that divide the two numbers, so that you can get the answer.

The order of addends does not affect the sum.

Addends may be grouped differently, but the sum is the same.

The sum of any number and zero is the same number.

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