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

Lesson 1: Estimating with Fractions and Mixed Numbers; Page 3

Lesson 2:  Adding and Subtracting Factions; Page 4

Lesson 3: Adding and Subtracting Mixed Numbers; Page 5

Lesson 4: Multiplying Fractions and Mixed Numbers; Page 6

Lesson 5: Dividing Fractions and Mixed Numbers; Page 7

Lesson 6: Changing Units in the Customary System; Page 8

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P2-4 Comparing and Ordering Fractions

P2-5 Mixed Numbers and Improper Fractions

1. Find the Least Common Multiple (LCM) of the denominators.

2. Find equivalent fractions by multiplying the numerator and the denominator by the same number.

Mixed number- a number that includes a whole number and a fraction Improper fraction- a fraction in which the numerator is greater than or equal to the denominator

2. Compare the new fractions.

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-4 x 5= -20 5 x 5= 25 -60 x -3= 180

22 -2 = -11 -52 -4 = 13 -9 -3 = 3

What you need to do to solve 1-step equations for additions you have to subtract the number that you are adding in both sides of the equal sign and to find the answer you just subtract the number that you were adding from the sum of the equation.

An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

1-step equations with subtractions are the opposite of 1-step equations because you need to ADD the number that you were subtracting to the difference of the equation

An inequality is , a statement of an order relationship; greater than, greater than or equal to, less than, or less than or equal to; between two numbers or algebraic expressions.

1-step equations with multiplication you need to do the same from the other to but you need to divide the number that you were multiplying in both sides of the equation that means that you need to divide the number that you are multiplying from the product of the equation and that is your answer

1-step equations with division are the opposite of 1-step equations with multiplication because you need to multiply the number that you are dividing in both sides of the equation so that means that you need to multiply the number that you were dividing to the product of the equation

By: Pablo Leal, Valeria Maldonado, and Renata Martinez

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We place the decimal point so that there are 3 decimal places

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<a href="bookcreator://page/cci5LHfFQEC3jNNhR9JggQ">Chapter 1</a>

<a href="bookcreator://page/T2UwmBfgQd-1pOwEw3PIUA">Chapter 2</a>

<a href="bookcreator://page/wbGgeA1GR-21gI9tfobywg">Chapter 3</a>

<a href="bookcreator://page/yNMFwsBFSlmFUZfR5BLtNA">Chapter 4</a>

Chapter 2 Exponents, Factors, and Fractions

By: Esteban Rodriguez, José Fernando Viggiano, and Rocío Villegas 

The Metric System of measurements uses prefixes to describe amounts that are much larger or smaller than the base unit. The base units for measuring length, mass, and volume are shown in the table below.

Order of Operations and the Distributive Property

P arentheses E xponents M ultiplication D ivision A ddition S ubtraction

7 x 38 7 x (30 + 8) (7 x 30) + (7 x 8) 210 + 56 266

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.

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By: Bárbara Rivas, Diego Javier and Ximena Olivares

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P2-1 Exponents and Order of Operations

<a href="bookcreator://page/eYilFv77QcSDe_Bd0ZPDJQ">P2-1 Exponents and Order of Operations</a> <a href="bookcreator://page/oU4PakHwQEWsfANLYwk4ow">P2-2 Prime Factorization</a> <a href="bookcreator://page/oU4PakHwQEWsfANLYwk4ow">P2-3 Simplifying Fractions</a> <a href="bookcreator://page/1imrR5gPQW-uXahroJ5CrQ">P2-4 Comparing and Ordering Fractions</a> <a href="bookcreator://page/1imrR5gPQW-uXahroJ5CrQ">P2-5 Mixed Numbers and Improper Fractions</a> <a href="bookcreator://page/kujYwHynQoiDBCOOg8qgag">P2-6 Fractions and Decimals</a> <a href="bookcreator://page/kujYwHynQoiDBCOOg8qgag">P2-7 Rational Numbers</a> <a href="bookcreator://page/h5Kdi_V6Tl6WU3bnS-vvcg">P2-8 Scientific Notation</a> <a href="bookcreator://page/h5Kdi_V6Tl6WU3bnS-vvcg">Video Links</a>

An exponent tells us how many times the base will be multiplied by itself. For example: 3^5 will be 3 multiplied by itself 5 times which is 3x3x3x3x3. They’re the second thing we do in the order of operations or PEMDAS. Now, it gets tricky for negatives. If we have -4^3 the number 4 is the base, not -4. To add an exponent to a negative number, we need to write it between parenthesis. So, now, if we write (-4)^3 -4 is the base. Finally, as we said earlier, exponents are the second thing we do in the order of operations. Check the operation below. We start with our parenthesis (3+7) so 10. Next our exponent 4^2 which is 16. Now multiplication and division are done from left to right (same for addition and subtraction!) so 3x10 which is 30. Now 16/2 is 8. Finally out subtraction: 30-8 which is 22 and that’s our answer.

A number is written in scientific notation when there is a number greater than or equal to 1 but less than&nbsp;10 multiplied by a power of&nbsp;10.

YouTube links: P2-1: <a href="https://youtu.be/xLcgug8iEYY">https://youtu.be/xLcgug8iEY</a> P2-1: <a href="https://youtu.be/ZKKDTfHcsG0">https://youtu.be/ZKKDTfHcsG0</a> P2-3:<a href="https://youtu.be/AtBUQH8Tkqc">https://youtu.be/AtBUQH8Tkqc</a> P2-4: <a href="https://youtu.be/N8dIOmk_lHs">https://youtu.be/N8dIOmk_lHs</a> P2-5: <a href="https://youtu.be/1xuf6ZKF1_I">https://youtu.be/1xuf6ZKF1_I</a> P2-6: <a href="https://youtu.be/Gn2pdkvdbGQ">https://youtu.be/Gn2pdkvdbGQ</a> P2-7: <a href="https://youtu.be/cLP7INqs3JM">https://youtu.be/cLP7INqs3JM</a> P2-8: <a href="https://youtu.be/trdbaV4TaAo">https://youtu.be/trdbaV4TaAo</a>

A Fractions represent&nbsp;equal parts&nbsp;of a whole or a collection.&nbsp;

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero

In algebra, a decimal number can be defined as a number whose&nbsp;whole number&nbsp;part and the fractional part is separated by a decimal point. The dot in a decimal number is called a&nbsp;decimal point. The digits following the decimal point show a value smaller than one.

Any repeating or terminating decimal represents a rational number

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Prime factorization, as its name implies, divides numbers by their prime factors until they reach one. When you reach one, you’ll have the prime factorization of the number. You’ll mostly use prime factorization to figure out the Lowest Common multiple (LCM), or the Greatest Common Factor (GCF) of two or more numbers. You can write it in one of two ways. Either by a “factor tree” or a table.

When we simplify a fraction, we divide both the numerator and the denominator by their GCF (Greatest Common Factor), and effectively finding “simplest” version of the fraction. Now, you can usually find the GCF mentally if the numbers are not that big. If you’re having difficulty, just use the table method, and the last two numbers will be your fraction in simplest form. Let’s use 32 and 48 once more.

Let’s find the LCM of 32 and 48. We’ll use the table method. To do this, find the prime factorization of both numbers. Common prime multiples of the two numbers divide both of them at the same time. Once you have the prime factorization, just multiply and that’s the LCM.

Now we multiply 2x2x2x2x2x3 or 2^5x3, which is 96. That’s our LCM.

Now for the GCF we’ll only use common prime factors, until there are none. Once you find all of them just multiply and that’ll be your answer. Let’s try to find the GCF of the same numbers, 32 and 48. We can now see that the GCF is 16.

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An inequality uses greater than, less than; or greater than or equal to, and less than or equal to.

An inequality looks like this: 6 + d &lt; 8

Inequalities can be of one step, or two step, but they are solved the same way as equations you need to add or subtract, multiply or divide, on both sides of the inequality like this: 6+d - 6 &lt; 8 - 6, inverse operations undo each other, and d &lt; 2.

Inequalities can also be graphed on number lines as shown below, when it’s less then the arrow goes left and viceversa, when the symbol is &lt; or &gt; the circle will be open like this ⭕️ , and when the symbol is like this ≥ or ≤ the circle will be closed like this 🔴.

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RULES FOR ADDING INTEGERS: Adding integers with the same sign: * Add the absolute values. * Give the same sign. Adding integers with different signs: * Find the difference of the absolute values. * Give the sign of the integer with the greatest absolute value.

RULES FOR SUBTRACTING INTEGERS: Subtracting an integer is the same as adding its opposite.

ADDITION (-34) + 50 50 - 34 = 16 (-34) + 50 = 16 (-10) + (-7) 10 + 7 = 17 (-10) + (-7) = -17 SUBTRACTION (-8) - (-6) 8 - 6 = 2 (-8) - (-6) = -2 (-38) - 30 38 + 30 = 68 (-38) - 30 = -68

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Its almost the same thing as solving 1-step-equations, but here you need to get rid of the number that’s farthest from the variable.

x-7+1=2 x-7+1-1=2-1 x-7=1 x-7+7=1+7 x=8 8-7+1=2 2=2

First you subtract 1 on both sides of the equal sign (inverse operations) Then you are left with

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