This book was created by 6th grade students in the Advanced Math Program at Latin American School in Monterrey, Mexico.

This is What We have Learned 3

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

To find the slope of a diagonal line you have to:

First you choose a point in the grid then you count the vertical squares until you hit the line if it’s going up it’s positive, if it’s going down it’s negative

Then you go back to the point and count horizontally until you hit the line, it doesn’t matter which way it’s going it’s positive

In form of a fraction the vertical number goes on the top and the horizontal on the bottom, finally you convert it into a decimal

The scale is&nbsp;the ratio that defines the relation between the actual figure and its model. A interval is a set of numbers that contains all numbers lying between any two numbers of the set.

Having a scale break on a graph can be very helpful especially when working with bigger numbers. For example if you were to start with 0 but wanted to go all the way to 647 it’s better to start at a much smaller number.

For example, in this graph there is a scale break because only the most important part of the data is shown.

In this graph, finding the interval is easy since it has simpler numbers,it’s 100. 

Mateo Yolanda Ximena Alyssa

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To use a stem-and-leaf plot you need to separate the first digit(s) from the last digit from a number, you list all the first digits from your list from least to greatest from top to bottom, and those are gonna be your stems, then separate with a line and at the right of its stem put it’s leaves (only separated by a line) which would be the last digits that have the first digits in common, and list them from left to right from least to greatest, and like that you repeat it with all the stems until you have written down all your numbers.

Stem-and-leaf plots are&nbsp;useful for displaying the relative density and shape of the data, giving the reader a quick overview of the distribution.

Generally, simple interest is an annual payment based on a percentage of the saved or borrowed amount, also called the annual interest rate. Compound interest is interest earned not just based on the saved or borrowed  amount, but also on the interest already earned so far.

$1,240 at 8% compounded annually for 2 years

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Spreadsheets are programs used for organizing different sections of a table.

Remember, a spreadsheet always needs a title!

The A1, B1, C1, say what the rest is mostly about 

For example, if you are asked for A2. You just go down A and match with 2! This spreadsheets are usually seen is programs like Excel, Numbers, Google Spreadsheets, etc…

Formulas are being used in many math apps. It is often helpful to transform such a formula to express a particular variable in terms of the other variables.&nbsp;

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Red zig-zag pattern

Hope you enjoyed and learned something!

Page 3 Page 4-5 Page 6 Page 7 Page 8 Page 9 Page 10

Frequency Tables and Line Plots Spreadsheets and Data Displays Stem-and-Leaf plots Random Samples and Surveys Estimating Population Size Using Data to Persuade Scatter Plots

A number sequence is&nbsp;a list of numbers that are linked by a rule.&nbsp;

An arithmetic sequence is&nbsp;an ordered set of numbers that have a common difference between each consecutive term.&nbsp;

A geometric sequence is&nbsp;a sequence in which each term is found by multiplying the preceding term by the same value.

 To find the next numbers in the sequence, you need to first get the rule, and just apply it to the last numbers of your sequence.

Subtract the first term from the second term&nbsp;to find the common difference. On this example, the answer is 7

When you translate shapes they tell you to where to translate it and also how many units. There could also appear a case in which the shape is already translated and you need to know how many units it translated and into which side. This is done by checking both shapes and then check how many they translated.

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Random samples and surveys are used to get information of many kinds. This surveys and samples can be biased or unbiased. One way a sample could be biased is if you want to know the best ice cream shop in town and only ask costumers that are in one specific ice cream store. And a survey could be biased in the way that you use the adjectives, for example: "Would you rather delicious creamy chocolate ice cream or vanilla." Here you are persuading people's minds into thinking that chocolate is better.

A survey asks the best place to buy shopping goods. You ask all the people coming out of H-E-B. Biased or Unbiased.

You want to know what is the best movie to watch in theaters. You ask 100 people for their opinion in the supermarket. Is it biased or unbiased?

Biased, because people coming out of H-E-B might prefer to buy there instead of other shops.

Unbiased, because people at the supermarket may watch a lot of movies, watch not a lot so it could be very random.

Probability and Experimental Probability 

The best way to see the probability of something is by putting the things as a fraction. For example: The probability to have a 2 in a dice is 1/6. The probability of choosing a king on a deck of cards is 1/13.

The experimental probability is almost the same as probability. To see the experimental probability you need to try the experiment so you can see the probability. For example: You want to see the experimental probability of having a 2 in a dice. So you throw it 6 times. The number were 4,6,1,2,3,2. So the experimental probability will be 2/6 or 1/3.

25/100 = x/300 x=25 x 300 / 100 x= 75

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P10-4 Graphing Nonlinear Relationships

Linear functions have graphs that are straight lines. The rate of change between any two points is constant. Nonlinear functions are functions whose rates of change are NOT constant - their graphs are not straight lines. We can determine if a function is linear or nonlinear by inspecting a table of values, a graph, and/or the equation.

Graphing data shows if a relationship exists between two quantities (also called variables). If two variables show a linear relationship, they are directly proportional to each other, however, not all relationships between variables are linear. Some are curves which show a squared or square root relationship.

A relation is a set of ordered pairs (x, y).

A relation is a function if each x-value has only one y-value.

What can you do to 2 to get 8? Add 6 or multiply by 4.

What can you do to 3 to get 12? Add 9 or multiply by 4.

What can you do to 4 to get 16? Add 12 or multiply by 4.

What can you do to 5 to get 20? Add 15 or multiply by 4.

You can multiply each x-value by 4 to get its y-value.

A pattern rule tells you how to make a pattern. For some patterns, you can make a pattern rule by saying: • how to start the pattern and • how to get each term from the term before it.

For Example, Start at 8 and multiply by 2 each time: 8,16,32,64, and so on.

You can use tables to determine the data for a certain graph:

You apply a table to distribute the data and then find a formula for the number of moons there is for one sun.

Graphing Points in Four Quadrants——— pg.4-5 Graphing Linear Equations——— pg.6-7 Finding the Slope of a Line——— pg.8-9 Graphing Nonlinear Relationships——— pg.10-11 Translations of Shapes——— pg.12-13 Line Symmetry and Reflections——— pg.14-15 Rotational Symmetry and Rotations——— pg.16-17

A representation, usually as a table or graph, used to explore, summarise and communicate features of data.

Data Displays, usually represent their name. So, if a line display obviously has lines. There are also Double Displays. Which have 2 of the same display. It is mostly shown in line displays. There are multiple displays. The most common are; Circle, Bar, Line. Double Line and Bar Graphs also exist. 

Estimating population size is something usually done by scientists when wanting to get a estimate of the actual number of animals of a certain species. Usually what's done is, first they capture and tag 100 monkeys, after a year, they captured and released 100 monkeys which 40 are tagged. This means that we will need to make a proportion which will be 40/100 = 100/x now we will apply the 3 rule ( (100 x 100)/40) which will be a estimate of the population of monkeys which is 250 on the area.

A group of scientists tagged a group of 20 sharks. One year later, they found 35 sharks of which only 13 were tagged. So we have to get the estimate of the population of sharks.

Here you would round up because you can't have part of a shark so the population size would be about 54 sharks.

12-1: probability 12-2: experimental probability 12-3: sample space 12-4: compound events 12-5: permutations 12-6: combinations

A sample space is the set of all possible outcomes in an experiment. Example: We tossed two coins. To represent the sample space for this experiment we are making a list, a table, and a tree diagram that are the most common sample spaces.

To interpret a graph,&nbsp;read the title or labels. The title tells what information is shown . Then, study the graph to know what it shows. 

In this example, the movement of the story shows that it flew into the air and lowered down onto the water. That is what is represented on our graph, an increase when it started flying, a decrease when it started falling back down.

A frequency table is a three column table which outlines the possible outcomes and the frequencies observed in a sample. You can draw a Line Plot to demonstrate the information in the frequency table.

A scatter plot is a graph that relates two sets of data. To make a scatter plot, graph the two sets of data as ordered pairs. A scatter plot can show a relationship, or trend.

As on set of values increases, the other set tends to increase.

As one set of values increases, the other set tends to decrease.

When you graph points in four quadrants you need to check the numbers you are given. The first number you are given is x and the second one y. It could be (2,5). X is the vertical axis and y is the horizontal axis. When there is a positive number in x the points need to be at the right of zero and if x is a negative number it will be graphed to the left of zero. When y is a positive number it is on top of zero and if y is a negative number it is below zero.

There are four quadrants in a coordinate plane. The quadrants can be identified as quadrants 1, 2, 3, 4. When a point is in quadrant 1, both x and y are positive. When it is in quadrant 2, x is positive but y is negative. When it is quadrant 3, both x and y are negative. When it is in quadrant 4, x is positive but y is negative. There could be times that the point lands on the x or y axis

A function rule is&nbsp;the relationship between the dependent and independent variables in the form of an equation. The function rule of a specific function, explains how to find the value of the dependent variable y, with the independent variable x.

This one is an easy one to solve, the answer is divide by 9. To find the function rule look for any compatible numbers like 72 and 8, then just add, subtract, multiply or divide.

If a vertical line drawn anywhere on the graph of a relation only intersects the graph at one point, then that graph represents a function. If a vertical line can intersect the graph at two or more points, then the graph does not represent a function

P10-7 Rotational symmetry and rotations

If a figure can be rotated 180° or less and match the original figure, it has rotational symmetry. The number a figure rotates is the angle of rotation. When a figure has rotational symmetry, the angle measure the figure must rotate to match the original figure.

A rotation is a transformation that turns a figure about a fixed point called the center of rotation. You describe a rotation by its angle measure and its direction. The direction of a rotation can be clockwise or counterclockwise. 

What and how do I graph a linear equation?

A linear equation is&nbsp;a set of points in the coordinate plane that all are solutions to the equation. If all variables represent real numbers one can graph the equation by plotting enough points to recognize a pattern and then connect the points to include all points.

To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.

Sometimes, someone can exaggerate on a graph to persuade someone of something by using an interval very small and it looks like the changes are very big while using a greater interval the differences look much smaller.

A compound event is an event that has more than one possible outcome. There are Independent events and Dependent events.

Example of Independent event: You draw a card from a deck of cards and replace it. Then draw a second card.

Example of Dependent event: You draw a blue marble from a bag. Without replacing it, you take another blue marble.

This is a pentagon and it has 5 lines of symmetry 

Name

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