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

Brackets and parentheses are both used to show groupings. Brackets are used to avoid double parentheses. Use [( instead of ((.

Scientific Notation is used to write very large and very small numbers more easily.

Evaluate expressions according to the order of operations.

To write a number in scientific notation in standard form, move the decimal point the number of places shown by the exponent of 10.

1. Evaluate inside parentheses, then evaluate inside brackets.

40² ÷ [9.6 - (8 x 0.2)] + 6 40² ÷ [9.6 - 1.6] + 6 40² ÷ 8 + 6

For a positive exponent, move the decimal point to the right.

For a negative exponent, move the decimal point to the left.

Write each number in scientific notation.

3. Multiply and divide from left to right. 

1600 ÷ 8 +6 200+6

<a href="https://youtu.be/NqX5cDidMQY">https://youtu.be/NqX5cDidMQY</a>

<a href="https://youtu.be/Q_klLmTSyyw">https://youtu.be/Q_klLmTSyyw</a>

Using expressions to describe patterns is a way for you to understand a pattern no matter how complex or simple. Let's say that the input is 8 and the output is 2, and another one is 12 and 3. You can easily guess this pattern is x/4, so we just made an expressions to describe this simple pattern.

Making a table can help you knowing the operation. How? Well let’s say that our x or input is 4 then to the other side we put 7. And again on the x we put 8 and on the output we put 5. This is a way to get organized, and it will be easier than just putting it in a random order, that will just get you confused.

How to add and subtract like denominators

To add and subtract like denominators you only need two steps

To find the least common multiple of 2 numbers you need to do 3 steps

Don’t add the denominator because if you add the denominator it will not be the correct answer

To simplify you need to divide it by the same number. If you don’t divide it by the same number the simplification will not be correct

The same you need to do with subtraction with like denominators

3.Check what common multiple is the least

1. 7 x 0.5 = 3.5 2. 12 x 0.08 = 0.96 3. 24 x 0.17 = 4.08 4. 0.4 x 0.17 =0.068 5. 1.9 x 0.46 = 0.874 6. 3.42 x 5.15 = 17.6130

Multiply 0.72 x 23 Ignore the decimal points. Multiply as you would with two whole numbers. Count the number of the decimal places in both factors. Use that number of decimal places to write the answer.

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

2. Add a zero after the decimal point in the dividend. Bring down the zero. Divide. Subtract.

<a href="https://youtu.be/dSFja7Jsg6c">https://youtu.be/dSFja7Jsg6c</a>

<a href="https://youtu.be/U3KoxaJer70">https://youtu.be/U3KoxaJer70</a>

3. Repeat step 2 until there is no remainder.

Remember, you can always use estimation to see if your answer is reasonable. 180 ÷ 30 = 6. You can check your answer using multiplication. 32 x 6.125 = 196

The dot in a decimal number is called a decimal point. The digits following the decimal point show a value smaller than one. Here's an example of a decimal number 17.48, in which 17 is the whole number, while 48 is the decimal part. ... Here's an example of how the fractional part can be converted into decimals.

Adding and subtracting fractions and mixed numbers

By Nicolás Ponce Morales and Pablo Leal Saldaña 

By Renata Martínez Martínez And Ximena Recio Tovar

Here's an example showing the relationship between the place or position and the place value of the digits in a number. In 14,769. 1 is in ten thousands place and its place value is 10,000. 3 is in thousands place and its place value is 3,000. 9 is in ones place and its place value is 9.

Adding and subtracting unlike denominators

Estimating sums and Differences of mixed numbers 

To add and subtract unlike denominators you need 3 steps

1. Use the least common multiple to find a common denominator

3. Add and subtract and simplify if possible

Now multiplication: 1) Commutative Property: the order of the factors does not affect the product. 2) Associative Property: Factors may be grouped differently but the product stays the same. 3) Zero property: every number multiplied by 0 is 0. 4) Identity property: every number multiplied by 1 is the same number.

Remember: EXPRESSIONS ARE NOT EQUATIONS. That means that expressions do not have an equal sign. That is one of the most common mistake when solving expressions, so here is how you solve them correctly. Let’s say that n=6 and we want to solve 3n. One thing you should remember is “substitution then solution” which means we substitute the value and then we solve. Now 3*6 18.

Divisibility Rules................Page 3 Prime Factorization...........Page 4 Greatest Common Factor.........Page 5 Fractions in Simplest Form.........Page 6

<a href="https://m.youtube.com/watch?v=ZKKDTfHcsG0">https://m.youtube.com/watch?v=ZKKDTfHcsG0</a>

<a href="https://m.youtube.com/watch?v=jFd-6EPfnec&amp;t=4s">https://m.youtube.com/watch?v=jFd-6EPfnec&amp;t=4s</a>

<a href="https://m.youtube.com/watch?v=S9X9PaN8obg">https://m.youtube.com/watch?v=S9X9PaN8obg</a>

An&nbsp;exponent&nbsp;refers to the number of times a number is multiplied by itself. For&nbsp;example, 2 to the 3rd means: 2 x 2 x 2 = 8.

A multiple of a number is the product of that number and any nonzero whole number

Writing a composite number as the product of its prime factors shows its prime factorization

This product is unique except for the order of the factors

You can use a factor tree to find prime factors

To add and subtract decimals, you must line up the decimal points.

You can use rounding or compatible numbers to estimate sums and quotients.

1. Write the Numbers, lining up the decimal points. Annex zeros so all numbers have the same number of decimal places. 2. Add the numbers. Regroup if necessary. Write the decimal point in your answer

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

Video about estimating products and quotients:

<a href="https://youtu.be/GSgM9HMcxO0">https://youtu.be/GSgM9HMcxO0</a>

______ 12, so 4.287 x 2.804 ≈ 12

42.693 is close to 43, so the answer is reasonable

1. 45.6 + 26.3 = 71.9 2. 14.25 - 5.14 = 9.11 3. 17.2 + 6.08 = 23.28 4. 24.84 - 22.7 = 2.14 5. 13.64 - 8.3 = 5.34 6. 0.214 + 15.9 = 16.114 7. 3.652 - 1.41 = 2.242 8. 18.06 + 9.798 = 27.858 9. 8.006 - 6.38 = 2.626

Compatible Numbers: Find compatible numbers and divide. 16.173 ÷ 2.45 | | v v 15 ÷ 3 = 5, so 16.173 ÷ 2.45 ≈ 5

Video about adding and subtracting decimals:

<a href="https://youtu.be/gD-h0HGurg8">https://youtu.be/gD-h0HGurg8</a>

1. 3.73 x 8.16 2. 35.518 ÷ 9.272 3. 7.349 x 5.62 | | | | | | v v v v v v 4 x 8 ≈ 32 36 ÷ 9 ≈ 4 7 x 6 ≈ 42

Write the fractions so they both have the same denominator then add the whole numbers at last add the fractions and you get your answer. ( simplify if you can )

To subtract mixed numbers. First, the fractional parts must have the same denominator. Then you subtract the whole number then you subtract both numerators but if the one on the bottom is bigger you have to borrow one from your whole number and then subtract.  ( Simplify if you can ) 

A&nbsp;fraction&nbsp;is in&nbsp;simplest form&nbsp;when the top and bottom cannot be any smaller, while still being whole numbers. To simplify a&nbsp;fraction: divide the top and bottom by the greatest number that will divide both numbers exactly (they must stay whole numbers).

Topic 2: Variables, Expressions, and Properties

To break apart the number is to separate the tens place and the ones place for easier numbers to compute. Let's say the number you have is 1284 so you separate the numbers into 1,000, 200, 80, 4. When you multiply or add compute every one of those number by the same factor or addend. This can also work with subtraction.

2——- the number is even 3——- the sum of the digits in the number is divisible by 3 4——-the last two digits of the number are divisible by 4 5——-The number ends in 5 or 0 6——-The number is divisible by both 2 and 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 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 10——The number ends in 0

Table of Contents: Estimating Sums and Differences (P. 2) Adding and Subtracting (P. 3) Estimating Products and Quotients (P. 3) Multiplying Decimals (P. 4) Dividing by a Whole Number (P. 4) Dividing a Whole Number by a Decimal (P. 5) Dividing Decimals (P. 5) Evaluating Expressions (P. 6) Scientific Notation (P. 6) Multiple-Step Problems (P. 7)

Estimate: 7.382+4.97 1.Round each number to the nearest whole number. 7.383+4.97 | | V V 7 + 5

Video about estimating sums and differences:

2. Add to Estimate: 7 + 5 = 12 7.382 + 4.97 ≈ 12

<a href="https://youtu.be/FpIsHEGEaHk">https://youtu.be/FpIsHEGEaHk</a>

You can also round the number to any decimal place Estimate the sum. Round to the nearest tenth.

3.947 + 11.286 | | v v 3.9 + 11.3 = 15.2, so 3.947 + 11.286 ≈ 15.2

Round each number to the nearest whole number to estimate the answer.

1. 4.38 + 9.179 ≈ 13 2. 62.873 - 12.7 ≈50 3. 52.83 + 97.288 ≈ 150 4. 131.049 - 82.604 ≈ 48 5. 79.14 + 32.546 ≈ 112 6. 48.486 + 63.029 ≈ 111 7. 112.658 - 81.903 ≈ 31 8. 586.735 - 204.63 ≈ 382 9. 107.139 + 90.621 ≈ 198

Using Variables to Write Expressions

Sometimes you might encounter a sentence which you can translate into an expression “like the sum of a number n and 3” which you can translate into n+3, or “the quotient of n and 3” which means n/3. There is a lot of sentences that can be translated into expressions so here is some of the most common ones.

Addition and multiplication have different properties for you to remember and make easier to solve. Let’s start with addition: 1) Commutative property: the order of the addends does not affect the sum. 2) Associative Property (Grouping): addends may be grouped differently by the sum will always be the same. 3) Identity property: the sum of any number and zero is the same number 

Fraction- a part of a whole number

Mixed number- a number with both a whole number and a fraction

Decimal- a number that has digits to the right of the decimal point

Denominator- the number below the fraction bar in a fraction

Improper fraction- a fraction in which the numerator is greater than or equal to its denominator

Numerator- the number above the fraction bar in a fraction; the number of objects or equal parts being considered

Now this is very important. Expressions may have multiple operations and it's not like you can do whichever one you want. That is why we have PEMDAS which is an acronym for parenthesis, exponent, multiplication, division, addition and subtraction. When you are doing multiplication or division then do it from left to right, and addition and subtraction as well. You can remember this acronym with “please excuse my dear aunt sally”.

Now this are some more ways to use expressions

Congratulations you can now solve expressions!!!

Multiple-step problems often contain hidden questions. Sometimes you can’t answer the problem until you have answered those hidden questions.

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?

Book by: José Manuel Hernández Rodríguez and Carlos Antonio Edén Wynter Guerrero

Hidden question: How many T-shirts did Raul print? 35 x 3 = 105 T-shirts

Solve the problem: 35 + 105 = 140 140 x $3.25 = $455

<a href="https://youtu.be/9wc1TrzVBTM">https://youtu.be/9wc1TrzVBTM</a>

Answer: It cost $455 to print all the T-shirts.

When you divide by a decimal, you need to rewrite the dividend and the divisor so that you are dividing it by a whole number.

<a href="https://youtu.be/cfr-yZxTH8Y">https://youtu.be/cfr-yZxTH8Y</a>

1. Estimate. Use compatible numbers. 2. Make the divisor a whole number. Multiply the divisor and the dividend by the same power of 10. Place the decimal in the quotient. 3. Divide as you would with whole numbers. Remember that sometimes you may need to annex zeros to complete your division.

Move the decimal point 1 space to the right

Video about dividing a whole number by a decimal:

<a href="https://youtu.be/7JPIX3odZrY">https://youtu.be/7JPIX3odZrY</a>

<a href="bookcreator://page/BDo4nzAoTA-1VHf13D2nDA">Topic 1</a>

<a href="bookcreator://page/XRhfX4jTTre6CRgQFoBd8w">Topic 2</a>

<a href="bookcreator://page/Vl_JI8q5SayCI_ByvJ56Bg">Topic 3</a>

<a href="bookcreator://page/bhwl9fZqQVW_CMvQ7N1z5Q">Topic 4</a>

<a href="bookcreator://page/rhIXli0ITbqbqCX2bCi5pA">Topic 5</a>

<a href="bookcreator://page/HHepEam4Rh2Fd6e730BBdw">Topic 6</a>

<a href="bookcreator://page/53ALciFmSpW0B-uxO33Pdg">Topic 7</a>

By Diego Javier González Campos and José Fernando Viggiano Pérez

How to find the greatest common factor of two numbers

Name

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