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

The area of a figure is the amount of surface it covers. 

This is the process for getting  the area of this figure.

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To show how you can share items, you can divide to find a fraction of the total. Four people shared two submarine sandwiches equally. What fraction of the sandwiches did each person receive? Divide each sandwich into 4 equal parts. Each part is 1-4 or 1/4 Each person received one equal slice from each sandwich for a total of 2 slices. There are 8 slices altogether, so each person got 2/8 of the shared sandwich.

<a href="bookcreator://page/DqEXBhlCShKXcrWHLSw83A">Topics 8 &amp; 9</a>

<a href="bookcreator://page/Nd3Zs_qnTG23_bIMHkEjAA">Topic 10</a>

<a href="bookcreator://page/ud0FjmSOStiT1czjdYUwwg">Topic 11</a>

<a href="bookcreator://page/nukewPO8RseWfttGd5c2mA">Topics 12 &amp; 13</a>

<a href="bookcreator://page/h7SmexLJQ1Wmh9-HqfA1rw">Topic 14</a>

<a href="bookcreator://page/eFcBKU5gRYaUuycsvrVVqw">Topic 15</a>

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Factors are the numbers that we use to multiply and are before the product

Chapter 1: Using mental math to divide, Estimating quotients, and Dividing with remainders

We need to have at least one factor with at least 1 zero because to use mental math we take out all zeros

Take out the zeros, then multiply the factors and last add zeros

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To measure angles we need a protractor, this is a protractor:

Leanne wanted to compare4/6 and 3/4.She used fraction strips to help.

She compared the amounts that were shaded in each picture.Because the amount shaded in 3 is more than the amount shaded in 4/6, she knew that 3/4 is greater than 4/6. So 3/4 &gt; 4/6.

Solid figures are three - dimensional figures. 

This rectangular pyramid has,5 faces,8 edges, and 6 vertices.

This square has 6 faces,8 edges, and 12 vertices.

This triangular pyramid has,4 faces,6 edges,and 4 vertices

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Adding and Subtracting Decimals

You can use a grid to add or subtract decimals. 

You can also add and subtract decimals this way. Make sure you align the decimal points. 

Example 2: 14.01 +56.21 70.22

Intersecting lines pass through the same point Perpendicular lines are like intersecting lines, but when they cross they make a right angle

You already see lines, but you don’t see line segments, rays, and angles A ray is a like one line but it only extends from one of the two sides A line segment is a part of a line with two endpoints An angle is formed by two rays that have the same endpoint, we measure angles in degree(°)

3rd grade Topic 8 and topic 9 Factors and Basic geometric ideas

By Ignacio Ostos Aponte and Ana Regina Gallaga

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Rounding Decimals

To round to the nearest whole number, you need to see which is the number after the decimal point and you round to it. If the number is 4 or less, the whole number remains the same. If the number is 5 or more, round up the whole number and add 1.

Example: 4.3 is rounded to 4. 7.9 rounded to 8.

Sometimes when you are dividing with “the process” (page 4) the first factor is less than the divisor, if this happens, you need to go to the next digit including the first one an example is:

If you see the 2 is less than the divisor so you go to the 3 and see how many times it fits, then you do the rest of the steps and it ends something like this:

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To show 0.30 you would shade 30 out of the 100 parts. One part of the hundreths grid can be compared to a penny, since a penny is equal to 0.01. And one part of the grid is equal to 0.01.

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By: Regina Rodríguez Contreras and Sofía Cantú Martínez.

You can use fraction strips to write a mixed number as an improper fraction. &nbsp;3_1 of the model below is shaded.

Into how many parts is each strip divided? 2 This is your denominator. Count the shaded halves. There are 7. This your numerator. 3 1/2 is the same as the improper fraction 7/2

Estimating Sums and Differences of Decimals

To estimate sums and differences of decimals, first  round each decimal to the nearest whole number. After that you can add or subtract the estimated numbers. 

Example: 4.61 + 5.12 10 11.21 - 7.66 3

A prime number is a number that only has two factors (1 and itself) and a composite number has more than two factors Example: 81 is a composite number because it has more than 2 factors

To estimate quotients we need to round the first factor to the nearest ten, five, hundred, or thousand

When we divide with remainders we have two factors and when we divide them they don’t have all the same amount

Why R? Because R stands for remainder and to know how many remainders we have in a division we first need to turn the division like this:

Then we do the process to divide like this:

Then maybe you are wondering... what is that 3 doing there?🤔

A quadrilateral is a polygon with four sides, there are regular quadrilaterals and irregular quadrilaterals this is a regular:

Regular quadrilaterals are this ones A parallelogram: four-sided polygon with two pairs of parallel and equal sides A rectangle: rectangle is a parallelogram with 4 right angles A square: square is a rectangle with four equal sides A rhombus: rhombus is a parallelogram with 4 equal sides A trapezoid: trapezoid is a quadrilateral with only one pair of parallel sides

A grid can be used to show tenths and hundredths.To show 3 hundredths, you would shade 3 of the 100 parts.

The perimeter is the distance around a polygon.

The perimeter of a polygon is the sum of the lengths of its sides

The top number, the numerator, tells the number of equal parts described. The bottom number, the denominator, tells how many equal parts there are in all.

2/3 Numerator: 2 parts are shaded. Denominator: There are 3 parts total.

To use a protractor we need to put the point of the angle in the point at the bottom of the protractor then we align the straight line with the zero like this:

Finally we check what is it’s measure, in this example the measure is about 140° so it’s an obtuse angle. we can do this with all angles so try it yourself

Chapter 4: polygons, triangles, and quadrilaterals

A polygon is a figure with two dimensions (length and width) that doesn’t has open spaces or/and curved sides Example: this figure is not a polygon because because it has curved sides

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Chapter 3: lines, points, and planes, line segments, rays, and angles, and measuring angles

A line is a straight path of points that goes on forever in only one direction A point is an exact location in space A planes is a flat surface that extends forever in all directions

Let’s make a little test what is this:

And you will do the same when you subtract!

Volume is the capacity that a container can hold.

multiply the 3 measures lenght × width×height to get the volume of the figure.

That 3 is the remainder! If you some time you don’t know how to get a remainder, you can make a photo, an example is this one:

Chapter 2: dividing 2-digit by 1-digit numbers, deciding where to start dividing, factors, prime and composite numbers

To divide two digits by 1 digit you need to start making it from left to right, first you check how many times does the divisor fit in the first factor of the dividend, then put the number of times it fit and put the remainder at the bottom then put the next number at the right of that number then see how many times does the divisor fit in the number that the two factors create, put the number of times it fit at the top then you put the remainder at the bottom.

Multiplying and Dividing Decimals

Multiply a whole number by a decimal the same way you multiply two whole numbers and put the decimal point in the product. Divide a decimal by a whole number like you divide two whole numbers and put decimal point in the product.

Examples: 1.3 12.5 5= 2.5 x 4 5.2

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Here is a video for you to know how to subtract fractions with unlike denominators.

<a href="https://youtu.be/RunORqzH_90">https://youtu.be/RunORqzH_90</a>

<a href="https://youtu.be/IPzE0Z5h-fU">https://youtu.be/IPzE0Z5h-fU</a>

When you add fractions with unlike denominators, you need to change the fractions to equivalent fractions so they have a common denominator.

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To make fractions in simplest form you need to divide both the numerator and the denominator by the same number and here we have an example below.

And remember the fractures in simplest form always go inside a box.

Triangles are polygons with three sides, a triangle has 7 forms to classify them that split in two categories, the categories are: By sides: Equilateral triangle: 3 sides equal Isosceles triangle: 2 sides equal Scalene triangle: no sides equal By angles: Right triangle: one angle exactly 90° Equiangular triangle: 3 angles equal Acute triangle: all 3 angles less than 90° Obtuse triangle: One angle more than 90°

Benchmark fractions are fractions that are commonly used, such as 1/4 1/3 1/2 2/3 and 3/4.They are useful when you estimate fractional parts.

The factors are the numbers that we use to multiply together to get another number example: 2 and 3 are factors of 6, because 2 x 3 = 6 A number can have MANY factors!

To know all the factors of a number we need to use divisibility rules this are the rules: For 1: always! For 2: if the last digit is 0, 2, 4, 6 or 8 For 3: if the sum of the digits is a multiple of 3 For 4: if the number formed by the last two digits is a multiple of 4 For 5: if the last digit is 0 or 5 For 6: if it’s divisible by 2 and 3 For 7: if double the last digit subtracted from the number form by the rest of the digits is 0 or a multiple of 7 For 8: if the last three digits of the number are divisible by 8 For 9: if the sum of the digits in the number is divisible by 9 For 10: if the number ends in 0

Then we start checking if it’s divisible by that numbers, if a number is divisible by one of the rules, then divide that number of the rules by the number you want to get the factors Example: the factors of 54 are 1,2,3,6,9,18,27,54 to know what is the factor of the other one you can make a T table like this:

To round to the nearest tenth, you need to see the number in the hundredths place and you round to it. If the number in the hundredths place is 4 or less, remove the hundredths place. If the number in the hundredths place is 5 or more, add 1 to the tenths place and remove the hundredths place.

Example: 1.13 is rounded to 1.1 17.48 rounded to 17.5

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