This Is What We Have Learned 2

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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Extra information is information that is not needed.

Missing information does not complete the information.

It takes 4 hours to drive from Boston to New York. Jordan has a meeting in New York at 2:00 P.M. Can she arrive at her meeting on time?

Missing information: what time did she leave

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Line the numbers up by place value.Multiply the bottom number by each digit of the top number.

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A percent is a special kind of ratio in which the first term is compared to 100. The percent is the number of hundredths that represents the part of whole.

A percent represents a part of a whole, just like a fraction and a decimal.

when you estimate sums or differences it means that you round to the nearest number the number you’re gonna add or subtract

6,000 2,000 = ~400 5,602 - 2,344

2,000 700 = ~2,700 2,314 + 671

7 + 3 + 10 = ~20 7.4 + 3.1 + 9.8

A translation moves a figure in a straight direction.

A translation 4 units left and 3 units up

Integers name distance and direction from zero.

The magnitute of -3 is 3. The direction is negative.

Integers are the whole numbers and their opposites; 0 is its own opposite

The magnitude of 115 is 115. The direction is positive.

Numbers that are opposites of each other have the same&nbsp;distance from zero.

Example: Temperature below 10 degrees. What this problem says is that theirs 10 degrees below zero, meaning it is an integer. You can use a number line to help you, in a number line, ten units away from 0 to the left is -10, the answer is -10 degrees.

Ordered pairs are coordinates on a coordinate plane. A coordinate plane is made up of a x axis and a y axis. Coordinate planes can also have integers in them like the one you have to the right.

Examples of ordered pairs are: (-4, 3), (3, 5) which can be placed on the coordinate plane.

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❖the difference between a number n and 3 ❖3 less than a number n ❖a number n decreased by 3 ❖3 fewer than a number n ❖a number n minus 3

❖the product of a number n and 3 ❖3 times a number n ❖a number n multiplied by 3 ❖3 of a number n

Distance between points on a coordinate plane.

Each square on a coordinate plane is 1 unit long, so you can have distance between points on a coordinate plane measured in units.

To measure a distance between points you first need the points on a coordinate plane. Then you count the space between each point, one square is one unit.

There is 16 units between point A and point B in this example

2 Digit quotient is the same as the 1 digit quotient but instead of 1digit are 2 digits.

An outcome is the result of an action.

An event is a collection of possible outcomes. You can use a formula to find the theoretical probability.

Ruled paper

•When you divide decimals by 10, 100 and 1,000 you just need to move the decimal point to the left depending on how many zeros there are.

•When you divide a decimal by a whole number you first move the decimal point up and forget about it, and then you just start to divide as usual.

This chart says how the number is said, it is said one hundred twenty three billion, seven hundred eighty one million, two hundred forty five thousand, six hundred thirty two

On this type of table, there is y and x, both can have different values and a different equation.

Like find the value of x if y is 4, 6, 9 and then it appeares y times 3 equals x. So what you have to do next is to put the y values on the right, the equation of y x 2 = x, and then the value of x on the left.

Making graphs are to separate data by percent and numbers

This can be applied to Addition and Multiplication 

When you use mental math you use Properties of Operations

The order of the addends does not affect the sum

addends may group differently, but the sum is the same.

The sum of any number and zero is the same number

Hi Click the arrow to see the hole presentation.

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In this picture the answers are the half of each number like: the half of 12 is 6 and the half of 6 is 3 

Try to Look for a pattern means to look for things that can be the double the half 

Estimating quotients with 2 digit divisors

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This lesson is about how to solve Multiple-Step Problems.

Example: If 40% is 60 out of 100 then the fraction would be 

If only 5 blocks are painted out of 100 then it’s 

On some problems, they won’t tell you what was the start of something like the time, they will just tell you the end or a part and say things like:

-How much they added -If they take something off -How much it taked to do something

After filling her bird feeders, Barbara has 3 1/2 cups of mixed birdseed left. The two feeders in the front yard took 4 1/2 c each.&nbsp;The two feeders in the backyard each took 2 3/4 c.&nbsp;The&nbsp;two feeders next to the living room window each took 3 1/4 c.&nbsp;How much mixed birdseed did Barbara have before filling the feeders?

So, in this example, you need to work backwards since the question is how much does she had in the start. The question gives us different numbers of how much she put on each, so we need to add that numbers to how much she had after filling the bird feeders. After we do that, we have the answer which is 24 1/2 cups.

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In December the snowfall was 0.03 in. and in January it was&nbsp; 2.1 in. Which was the total snowfall?

Miami’s annual precipitation in 2000 was 60.93 in. Albany’s&nbsp; was 40.82 in. How much greater was Miami’s precipitation&nbsp; than Albany’s?

A bar graph uses bars to show data that can be&nbsp; counted.&nbsp; A double-bar graph uses two different-colored&nbsp; bars to compare two similar sets of data that can&nbsp; be counted. Bar graphs may show data vertically or&nbsp; horizontally.

A pictograph uses pictures or symbols to show&nbsp; data.

When you need to find the percentage you can find it in different ways for example when you have decimal point you need to know the value. for example 0.85 will be 85/100=85%. If you have a fraction you divide the numerator and denominator for example 1/4 = 0.25 = 25% when you need to the percentage of a number you just divide

an expression is a mathematical phrase containing numbers, variables, and at least one operation

An expression DOES NOT have an equal sign, and is solved downwards

36+23 58-15 15 x 9 39 ÷ 13 m+18 a-44 26 x b w ÷ 5

Congruency happens when two figures are the same shape or size. It doesn’t matter if the two shapes were translated, rotated, reflected, because if they are still the same size and shape, they will always be congruent

• Estimation: Decimals Divided by Whole Numbers For example: If we had 535.6 divided by 35 and then you estimate 535.6 to 520 and 35 to 40 in this case we estimate by using compatible numbers and the answer would be about 13.

• When dividing a decimal by a decimal you have to move the decimal point the times that you need to make the divisor a whole number and also move the decimal point of the dividend the same amount of times.

A graph in the shape of a circle that shows how a&nbsp; whole is broken into parts is a circle graph.

Estimate each quotient.Tell which method you used.

First, write the problem.&nbsp;Line the numbers up by place value.

There are several ways that you can add and subtract numbers mentally to solve a problem.

Commutative Property of Addition You can add two numbers in any order. 15 + 27 = 27 + 15

Associative Property of Addition You can change the groupings of addends. 17 + (13 + 10) = (17 + 13) + 10

Compatible numbers are numbers that are easy to compute mentally. 25 + 93 + 75 25 and 75 are compatible because they are easy to add. 25 + 93 + 75 + (25 + 75) + 93

With compensation, you adjust one number to make computations easier and compensate by changing the other number. 320 - 190 +10 +10 &nbsp;⇓ 330 - 200 = 130

•Multiplying decimals by 10, 100, 1,000 is very easy, because you just have to move the decimal point the right by the amounts of zeros.

•When you multiply a decimal by a whole number you just multiply as always and the answer you will move the decimal point to the left by the number of times a number is after the decimal point.

By Mateo Villarreal Miranda Herreara Regina Rodrigues

Symmetry is when you divide a shape and the sides that are divided are the same shape and size. However, Rotational Symmetry happens when you rotate a figure and it’s still the same as the original state of the figure

➢A pentomino is an arrangement of 5 identical squares, each having a&nbsp; &nbsp;common side with at least one other square.&nbsp; ➢There are 12 possible pentominoes.

The 1 digit quotient is the  hole number of the answer of the division.

You can solve a problem by making easier problems.

Calculate Figure It Out GIF by Hey Arnold

Rafael has 5 apples he lends 2 to Denisse and 1 to Santiago how many apples does he have left?

First you can subtract 5-2 and that gives you 3 then que can subtract 3-1 and it gives you 2 so the apples that he is going to have left are to apples.

A ratio is a comparison of two quantities. You can write a ratio in three ways:

A stem-and-leaf plot is a graph that uses the digits&nbsp; of each number to show the data distribution.&nbsp; Each data value is broken into a stem (digit or digits&nbsp; on the left) and a leaf or leaves (digit or digits on&nbsp; the right).

A histogram is a bar graph with no spaces&nbsp; between the bars. The height of each bar shows&nbsp; the frequency of data within the interval. The&nbsp; intervals of a histogram are of equal size and do&nbsp; not overlap.&nbsp; It is used to show the frequency of equal ranges&nbsp; or groups of data.

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Dayana picked apples for 2 hours. She picked 28 apples&nbsp; in the first hour, and at the end of two hours, she had 49.&nbsp; How many apples did she pick during the second hour?&nbsp;

Dixon bought a pack of pencils and then gave 12 away.&nbsp; He now has 24 left. How many pencils were in the pack&nbsp; of pencils that Dixon bought?

Estimating Quotients with 2-Digit Divisor

To Estimate the 2-digit divisor if the number is below 5 you estimated to the to the nearest 10 below the 5 but when the number 5 or more you estimated to the nearest 10 over the 5.

You can also write probabilty as a fraction for example:

You have this spinner what is the probability that the spinner will land in red?

The answer will be 25% but a percent is also a fraction so 25% is 1/4 of 100%  so it is 1/4

Light wood

Find each quotient.Check your answers by multiplying

In surveys you normally use graphs to understand it. 

With the data of the image, if the entire class responded to the survey how many students are in the class?

What is the information is collected about the music?

How many and what kind of CDs were bought.

An exponent tells how many times the base will be used as a factors

{The Distributive Property says that multiplying a sum&nbsp; by a number is the same as multiplying each&nbsp; addend by the number and then adding the&nbsp; products.}

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

Theater tickets for children cost $5. Adult tickets cost $3 more.&nbsp; If 2 adults and 2 children buy theater tickets, what is the total cost?

Luis has a $10 bill and three $5 bills. He spends $12.75 on the&nbsp; entrance fee to an amusement park and $8.50 on snacks.&nbsp; How much money does he have left?

• Estimating the product of a decimal and a whole number it’s easy. For example, if you have 0.33 x 104 you estimate the 0.33 to 0.3 and 104 to 100 and now you multiply and it give you about 30.

• When multiplying two decimals you forget about the decimal point and you just multiply as always and depending on how many numbers are after the decimal point is the times that you are gonna move it to the left.

You can use the number line below to help you round 8,237,650 to the nearest million. Is 8,237,650 closer to 8,000,000 or 9,000,000?

8,237,650 is less than halfway to 9,000,000. 8,237,650 is closer to 8,000,000

❖the quotient of a number n and 3&nbsp; ❖a number n divided by 3 ❖a number n divided into 3 ❖the ratio of a number n and 3

Expressions• 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 downwards and does NOT have an equal sign

• Expressions are solved following Order of Operations (PEMDAS) and always in this way:&nbsp;

To estimate the product firsts do the problem then when you finish the problem estimate the product to the nearest 10 100 or were they tell you.

The Range of the data is the length of the least number and the grates number.

The median is the number of the middle like 1,2,3,4,5 and median is the 3 because is the is not the least but no the grates

The mode is the most numbers that are repeated like 1,1,4,5,3,8,6,1 the mode is the 1 because is numbers that most repeats.

Draw a&nbsp; Picture and Write an Equation

When Mary was born, she weighed 8 pounds. When she was&nbsp; 10 years old, she weighed 10 times as much. How much did&nbsp; she weigh when she was 10 years old?

To drive from New York City, NY, to&nbsp; Los Angeles, CA, you must drive about 2,779 miles. If you drive 60 miles per&nbsp; hour without stopping, about&nbsp; how many hours do you have to drive?

How to get the mean first you add all the numbers then divide the sum by the total of numbers.

Line graphs show changes over time. Some line graphs may show a trend in the data.

In one building there is 7 stories. If there are 21 stories in all, how many buildings are there?

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