This book was created by 3rd 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

for answering two problem questions you first need to read the text very closely to see what questions you need to answer.

Liliana gave 3 pencils to each of the 12 students in her class. How many pencils did she give out?

The first question can be a multiplication or anything .

Each pencil had 3 cute school stickers next to it. How many school stickers did she give out?

Use the answer from problem 1 to answer problem 2.

12 pencils x 3 school stickers = 36 pencils . Liliana gave out 36 pencils. 36 pencils x 3 school stickers = 108 school stickers. Liliana gave out 108 school stickers.

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A thousand is a 4 digit number to a 6 digit number.

Thousands can also be represented in blocks.

Thousands can also be represented in words called word form:

The last number a thousand can reach is 999,999 or nine hundred ninety-nine thousand, nine hundred ninety-nine.

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Problem Solving Missing or Extra Information

Krista can type 60 words per minute. She wrote an essay by hand in 5 hours, and it is now 4 pages long. She wants to type her essay. How many words can she type in 45 minutes.

The sentence  “she wrote an essay by hand in 5 hours, and it is now 4 pages long are extra information

And the solving sentence are “can type 60 words per minute, how many words can she type in 45 minutes”

Lesson 1 Using Mental Math To Multiply 2-Digit Numbers

You can multiply with mental math by using facts and patterns.

The product has the zeros that the factors had.

Example: 2x4=8 2x40=80

To find 50 x 500 , multiply 5 x 5 and then write 3 zeros at the end.

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You can’t subtract 6-7, so the 6 becomes a 16

Now the next digit, 0 - 7 can’t subtract, so the 0 becomes a 10. And the 7 becomes a 8

You can subtract 6 - 3 but the 3 changes from a 4

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Giant coronal mass ejection in an active star

Made by : Ángela Chuy Leo

<ol><li>Made by: Ángela Chuy Leo</li></ol>

Warp blue

#24 Dizzying space travel - "Inktober2019"

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Problem solving:draw a picture and write an equation

Understand when to choose a particular operation can help you solve problems.

A goldfish lived from 1956 to 1999.How many years did it live?

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Problem Solving: Draw a Picture and Write an Equation

Here are some things that will help you with this lesson.

Step 1: Read/Understand • Find the information the problem gives you.

• Find the information the problem wants you to figure out.

• Figure out which operation you need to use.

Step 2: Plan and Solve • Draw a picture to help you visualize the problem.

Step 3: Check • Check your answer by using the inverse operation.

Rafael has two dollars and he wants to buy magnets that say Germany for his friends . Each magnet costs 50 cents. How many magnets can he buy?

The question tells you that Rafael has two dollars and the magnets cost 50 cents each.

The question is asking you to find how many magnets Rafael can buy.

Too  find the answers is easy you can add you can subtract there are more tricks 

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Lesson 4: Rounding Whole Numbers

Round whole numbers is when you round specific numbers either up or down.When do you know when to round up or down? Easy!,if the number is 5 or greater round up and if it’s 4 or less round down. Example:

1,643 if you want to round the 1,000 you check the number to the RIGHT and since it’s 6 your round up (cuz it’s greater than 5) but if you want to round 40 u always round the number next to it (on the right) no matter if it’s a 0 or any number (unless it’s the last one..which is impossible to round)

Remember that you can also use a number line to help.

You can use the Properties of Multiplication to help you find products. Commutative Property of Multiplication: You can multiply any two numbers in any order. 2 3 3 2 Identity Property of Multiplication When you multiply any number by 1, the product is that number. 7 1 7 Zero Property of Multiplication When you multiply any number by 0, the product is also 0.

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Problem Solving: Use Objects and Reasoning

Andrea made a design with the figures shown at the right. She placed all the figures in a row. No figure was next to a figure with the same number of sides as itself. No two shaded figures or unshaded figures were next to each other. The first figure in the design was a trapezoid.

How did Andrea arrange the rest of her design?

You need to find the order of the figures in the design.

You can use the clues you have to place the figures. Draw a picture to help.

You know the trapezoid is first. It has 4 sides and is shaded.

The next figure cannot have 4 sides or be shaded. The triangle is second. It has 3 sides and is unshaded.

The next figure cannot have 3 sides or be unshaded. The pentagon is third. It has 5 sides and is shaded.

The next figure cannot have 5 sides or be shaded. The square is fourth. It is the only figure left. It has 4 sides and is unshaded.

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By Julian McKinnis and Melisa Sifuentes Acosta

Illustrated by Julian McKinnis and Melisa Sifuentes Acosta

Associative Property (Grouping)

The order of the factors does not affect the product

Factors may be grouped differently but the product is the same

The product of any number and zero is zero

3 times 7 times 8 = (3 times 7) times 8 = 3

The product of any number and one is the same number

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Estimating Sums and Differences of Whole Numbers

Estimate to the nearest hundreds, thousands 

By: Julia Perales Chapa

How do you use expressions containing variables ? To use an expression with a variable, replace the variable with a value and compute. 

  Imagine that we are adding 42 + M .Suppose M=2 . Substitute 2 for M . Then add 42 + 2 .

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You can use array of place-value blocks to multiply.

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Thanks for reading our book see you next time!

4x6 is the same as 8x3 if you don’t know the 6x5 but you know all the time table of 3  you can multiply 3x10= 30

There are more tricks too multiply  and one is when you don’t know 4x6 but you know 4x5you can add 4

<ul><li>THANKS FOR READING THIS BOOK!!</li></ul>

Remember that some of the rules in division is that you can not divide by zero because zero is nothing. For this lesson you can remember that every time that you multiply by zero the product is zero because every time you divide you multiply etc. the product or the quotient is gonna be zero.

Special Rule: You cannot divide a number by zero.

45÷0 cannot be done.                 7÷0 cannot be done.

You can divide zero by another number except zero.

Examples that can be done.

0 ÷ 1,476 = 0 0 ÷ 35 = 0 0 ÷ 567 = 0

Multiplying 2-digit numbers by multiples of ten

To find the product of 60 and 26, you can use breaking apart.

Mark of a section of the grid to show 60 x 26. 

draw a line to separate the factor 26 into the tens place and the one place so show 26 as 20 + 6.

There are 2 section 60 x 20 and the other section 60 X 6 .

So now multiply to find the products. 60 rows of 20 and 60 rows of 6

Use the first digit  to add which is the ones place

If it’s more than nine you have to carry in the tens place

6x2=12 60x2=120 600x2=1,200 600x20=12,000

And another way to do this is by adding the zeros from the factors so because there is 3 zeros in the factors just add 3 zeros to 6x2 which is 12 just add the 3 zeros and the product is 12,000.

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How do you find a rule to write an expression ?

To find a rule and write an expression, look at the numbers being compared. Which is the greater number ?

Consider 57 and 50 , 57 is greater than 50 so cross out addition.

Find how much greater 57 is than 50 . 57 is 7 more than 50, so the rule must involve subtraction.

Look at the other 2 columns of numbers and compare them . The top number is 7 more than the bottom number. The rule is subtract 7 so the expression is v - 7.

Using Multiplication Facts to Find Division Facts

You can always use fact families for these lesson they can always help a lot. Some examples are: 

8 x 4 = 32 4 x 8 = 32 32 ÷ 8 = 4 32 ÷ 4 = 8

7 x 6 = 42 6 x 7 = 42 42 ÷ 7 = 6 42 ÷ 6 = 7

Using Money to Understand Decimals

Fact:Reading decimals and money are very similar for example “$4.32” is read as “four dollars and thirty-two cents”.And 4.32 written as a decimal is four and thirty tenths and two hundredths.

dollars (ones)

dimes (tenths)

pennies (hundredths)

So it would be: Money: 4 dollars+3 dimes+2 pennies Decimal: 4 ones+3 tenths+2 hundredths

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By Nicolas Wilson Zhou Liu            and          By Julia Perales Chapa

First multiply the ones but regroup if necessary.

The we multiply the tens and again regroup if necessary.

Lastly we add the partial products and that leaves us with 24 x 13 which equals 312.

And that is how to multiply 2-digit by 2-digit numbers.

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To multiply we need to repeat the number 2 times like 7x2 we need to sum 2+2+2+2+2+2+2 or 7x2=14

Multiplication and division are the opposite the same as addition and subtraction are the opposite.

You can use fact families with multiplication and division which is the same with addition and subtraction.

And remember that every time you divide or multiply by zero the product or the quotient will be zero because zero is nothing, is like multiplying or dividing 6 times nothing or 8 divided by nothing because zero is nothing.

0 - 7 = 0 0 - 75 = 0 0 - 120 = 0 0 - 56 = 0

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You can multiply mentally by using  compatible numbers or breaking apart numbers.

Patterns can help you multiply by numbers  that are multiples of 10 or 100.

By Luis Enrique Treviño Cantú and Olivia Díaz González Bustamante 

Arrays and an Expanded Algorithm

Here is how to find the product of 16 x 44 using an array.

Draw a rectangle 16 units long and by 44 units wide.

Divide a rectangle by tens and ones for each factor.Find the number of squares in each smaller square.

Then add the squares in the four rectangles: 400 + 80 + 120 + 24 So, 16 x 44 = 624

When you divide, you separate things into equal groups.

You can find the quotient of 42÷7 by multiplying 7 x ?= 42. The quotient is 6.

Remember that multiplication and division are the opposite.

You need to put 18 cups in 3 boxes. How many cups will be in each box? 18 ÷ 3 = 6

Example:

You cannot subtract 8 from 5, so you make it a 15. Now you have to subtract 6 from 4, but that is not possible either. Besides, you had borrowed 1 ten, wich you now have to give it back… The 6 becomes a 7 and the 4, a 14. Now you need to subtract 3 from 4, but you had borrowed 1 from the hundreds, so you have to give it back. Now take away 4 from 4, and finish finding the difference.

Properties of Operation

Commutative Property (Order)

Addens may be grouped differently, but the sum is the same

Example:

The sum of any number and zero is the same number

Example:

In this topic you will learn how to divide in many different ways. Including dividing by zeros.

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Here is how to multiply a 2-digit number by a 1-digit number using paper and pencil.

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You can use rounding or compatible numbers to estimate products.

Meanings of multiplication and parents for facts

Multiplication is a multiplication sentence

Write an addition sentence and a multiplication sentence

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Multiplying 3-Digit by a 1- Digit Numbers.

Lesson 2 :Millions

Definition: Millions are 7 digit numbers and can reach up to 9 digits.

20,000,000+1,000,000+900,000+30,000=21,930,000

In word form is any number + million at the end for example: one hundred million ,twelve million.

roughly calculating or judging a number or value

Using rounding

Estimating is when you roughly round a number to the closest tens, hundreds,etc.

Lesson 7: Problem Solving Making an Organized List

Chuy,Sergio, Luis,nico and Leo are brothers.Two of the five brothers must help their father at his business each Suturday.How many combinations of two brothers are possible?

LOWPOLY CITY STREET PACK BUILDINGS STYLIZED

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We hope you enjoyed with Chuy, Angela, and Leo, and we hope that you enjoy 3rd and all the topics. Bye.

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Problem Solving: Draw a Picture and Write an Equation

Steps:

<ul><li>Step 1: Wich information are you given?</li><li>Step 2: What information do you need to figure out?</li><li>Step 3: Draw a Picture.</li><li>Step 4: Choose the operation and write the equiation.</li><li>Step 5: Solve the equation!</li></ul>

Olivia is reading a book that is 68 pages. She has read 24 pages so far. How many more pages does she have to read to finish her book?

Problem solving: Draw a picture and write an  Equation

To draw a picture is very easy you need too read the problem subtract or add and find answer

July has a fish in 2023 when July go too buy the fish they say to July the fish can live 40 years at what year the fish they die?

Thank you for see this I thing you learn about this see you soon goodbye 👍

Find a rule and write an expression using multiplication and division.

To find a rule and write an expression, look at the numbers being compared. Which is the greater number?

Consider 3 and 24. 24 is greater than 3, so rule out subtraction and division.

Find how much greater 24 is than 3. 24 is 8 times more than 3, so the rule must involve multiplication.

Look at the other two columns of numbers and compare them. The bottom number is 8 times more than the top number.

The rule is multiply by 8, so the expression is 8 x b.

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 backwards 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.

Thank you for reading our book see you next time!

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