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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In this lesson we will learn how to fit an equation into each pattern in each table

Here we need to find the rule then make an equation the rule with be add 5 and the equation will be y= x + 5

First we need to find the rule so we see that the numbers go from greater to least so we can say the rule could be divide or subtract so division can’t be so it is subtraction the rule with be subtract 8 and the equation will be y= x - 8

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In this lesson we will learn how to complete the table with the equation

Here there are giving us the values of x to find the values of y so y=  2(0)+4 so 2 x 0 equals 0 + 4 equals 4 so the first value is 4 then we do this again but with the other x values y = 2 (1) + 4 so it will be 6 and then y = 2 (2) + 4 and it will be 8 then we do it again y = 2 (3) + 4 and it is 10

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Topic 14-7 Problem Solving: Reasonableness 

So on this lesson we need to do what we were doing in the past few lessons, multiply. We need to multiply because we need to check if the problems they will give us are right or if they are wrong. For example: this image that is below the text.

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Adding integers and subtracting integers!!

When adding integers adding negative numbers is like subtracting with positive numbers

When subtracting integers subtracting negative numbers is like adding positive numbers

Topic 14-3 continuation Percentages Greater Than 100% and Less Than 1%

Now less than 1%. We can find this by obviously finding the percentage then dividing the percentage by 100 like we do to find the decimal. Then we need to find the fraction like I showed in the chart soma pages before this one.

By doing this we need to estimate the percentage of the numbers to make the numbers easy to multiply, like for example if someone is telling you to estimate 69% of 798 you will need to say 0.7 x 800. And the answer for that is 560.

To measure angles or draw them you need a protractor.

Graphing equations with more than one operation

In here we have to make an table for the equation so we gave the values to x then you subtract 0 - 3 = -3 then 1 - 3 = -2 and 3 - 3 = 0 and then we graph it

Here we multiply 3 (-1) - 5 = -8 and than 3 (0) - 5 = -5  then 3 (1) - 5 = -2 and then we need to graph it

Making tables or pictures help get the ratio of something 

Rates tell for example how many miles can a car run in 1 hour

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Table of contents: Topic 14 -Page 2 Topic 14-1 -Page 3 Topic 14-2, Topic 14-3 -Page 4 Topic 14-3, Topic 14-4 -Page 5 Topic 14-5, Topic 14-6 -Page 6 Topic 14-7 Topic 15 -Page 8 Topic 15-1 -Page 9 Topic 15-2 -Page 10 Topic 15-3 -Page 11 Topic 15-4, 15-5 -Page 12 Topic 15-6

When placing integers that are negative they ALWAYS go before 0, and positive integers ALWAYS go after 0.

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In order to solve multi-step problems, you need to do several operations in order to solve one problem. And also you have to find the hidden question in order to solve the problem.

Lesson 9-1: Understanding Division of Fractions

To find the answer for division of fractions, you need to multiply.

You need to multiply the numerator of the first fraction by the denominator of the second fraction. Then multiply the denominator of the first fraction by the numerator of the second fraction. If there is a whole number make it into a fraction by adding a one as a denominator. Simplify if you can.

The steps for an equation are do the reverse operation on both sides of the equal sign. Now  inverse operations undo each other. After that just write x=random number and then check by substituting.

A ratio is a comparison of 2 quantities. You can write a ratio in 3 ways:

A proportion is an equation with 2 equal ratios.

A ratio can compare a part to a whole, a part to another part of the whole, or the whole to a part.

Parts of circles are chord, radius, diameter, arc, and more.

A function is a relation in which there is only one y- value for each x-value you can also write a rule and an equation that tells how to find one value of the function when the other value is known. Also tables and graphs can represent relations

Topic 14-5 Find the Percentage of a Number

Topic 14-6 Tips, Taxes, Discount, and Simple Interest

In here we mostly need to convert things into decimals and then multiplying them, for example 5.6% of 425, we make the 5.6% into a decimal, so we divide it by 100. It’s now 0.056 x 425 which it’s equal to 23.8

So here you will need to add or subtract the percent depending on what you need to do, taxes=add discount=subtract tip=add.

By: William Zhou, Gilberto Cavazos, and Andrea Arteaga

To estimate quotients you only need to make the fraction into a whole number. Then, you need to divide normally.

To divide a mixed number you need to make the first fraction into an improper fraction. then, you need to make the second fraction also into an improper fraction, the difference is that the numerator of the second fraction will be the denominator of that same fraction. Finally you only need to multiply both improper fractions and get the answer. Simplify if possible

Lesson 9-2: Dividing a Whole Number by a Fraction

In order to divide a whole number by a fraction, you need to find the reciprocal of the second fraction. The reciprocal is the inverse of a fraction. For example 2/3 its reciprocal is 3/2. After finding the reciprocal, you have to make the whole number into a fraction, in order to do that just add a one as the denominator. Then simplify both the numerators and the denominators, in order to do that, simplify horizontally, (both fractions if you can). Now multiply the numerator by the numerator and the denominator by the denominator. Simplify if you can.

In order to divide fractions, you need to find the reciprocal of the second fraction. Then, you need to see if you can simplify horizontally, and finally you just need to multiply the numerator by the numerator and the denominator by the denominator. Simplify if possible.

Multiplying a Fraction and a Whole Number

To multiply a fraction and a whole number you need to make the whole number into a fraction. To do this simply put a 1 in the denominator. For example 16 turns into 16/1. And now you need to multiply horizontally, simplify if possible.

To estimate a product you need to round your fractions to the nearest half, fourth, etc. And to round your mixed numbers you need to round them to the nearest whole.

In this lesson we will learn how to solve equations with more than one operation

One example with be this you apply inverse operation of adding is subtracting then inverse operations undo each other then you subtract 19 - 7 4x equals 12 than you apply inverse operation of dividing is multiplying so inverse operations undo each other you divide 12 divide by 4 equals 3 so x=3 then finally check by substituting.

When multiplying or dividing with two numbers that are both negative or both positive the answer is always positive

When multiplying or dividing integers that are 1 negative 1 positive the product or quotient will always be negative 

Here’s a chart for you to know the most common percentages.

Topic 14-1 Understanding Percent

In this lesson we will learn on how to get the percent of shapes. For example this circle is 3/4 shaded so it’s 75%.

This square is 6/25 shaded so it’s equivalent to 24/100 which is 24%.

<a href="bookcreator://page/SAK2CXZcTJWN9PiDoiffuw">Topics 8 &amp; 9</a>

<a href="bookcreator://page/QJl764UGTF24S368f9UKRA">Topic 10</a>

<a href="bookcreator://page/hdRc36dHTUGf2gOQCLHmAQ">Topic 11</a>

<a href="bookcreator://page/333s_MVZTEGPLHROA7JJ2A">Topics 12 &amp; 13</a>

<a href="bookcreator://page/kuXP_j8ZSymM7aaGyg1rkg">Topic 14</a>

<a href="bookcreator://page/21jnP-m0Q3mlwBl8TwpQQw">Topic 15</a>

Symmetry is when you cut something in half and both sides are the same

Transformations is like when something moves like translation or rotation or reflection

To solve an equation you need first to identify the operation applied to the variable, then state the inverse operation, so if the equation is adding you subtract, if the equation is multiply you divide. Then you need to apply the inverse operation on both sides of the equal sign. After that you solve the equation. Finally you check by substituting.

To find the patter you only need to find the missing numbers and then describe the pattern.

A ratio table is a table that shows the ratios of different thing for example number of hops and number of jumps.

Unit Rates Help you know how many of a thing you can do during time,or quantity.

The number of hops with 15 jumps will be 9 hops.

This will be 30ft per 6 hours ,or also 5ft per hour.

To multiply a fraction you just need to multiply horizontally and if it is posible simplify.

To find the product of mixed numbers you need to make the mixed numbers into improper fractions, and multiply. As always, you need to check if you can simplify. And turn your answer back into a mixed number.

Topic 14-2 Fractions, Decimals, and Percents

Topic 14-3 Percentages Greater Than 100 and Less Than 1

Now we learn how to find the percent but also the fraction and the decimal too. For example:

Now we have percentages that are greater than 100% and less than 1%, first I will explain the greater than 100%. So here it will just be normal but instead of 100% you will put like 105% instead of 1 you will put 1 5/100 and instead of 1 you will put 1.05, example:

As we know this circle is 2/4 shaded, which it’s equal to 50% and 0.5. We can get the decimal point by dividing the percentage into 100, so you will move it twice to the left.

You can use cross multiplication to solve proportions.

You Can write to explain a ratio, unit rate, etc

Write a proportion. Use a variable for the number you don't know. Cross multiply, and then solve.

In the example, they will need to raise 625 dollars

In this lesson you will learn about lines, line segments, rays, perpendicular lines, and more!

Maps and scales help get the unit rate of a place, person, animal, or thing

Line JL is 77.5, Line KL 65 in so the measure of angle K and triangle JKL is 100°.

Rates can be wrote in words. Ex: 5 miles per hour

Comparing rates is easy but you need to have an equal object to make an equal rate

Unit rates have real-life units or items like miles, hours, etc.

In the example above, we can see that gallons have different quantities, but we can solve that

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