Boom cards

It was the end of February when we were told that schools would close and that we should invent a new way to teach overnight.

After two months I’m still struggling. I love technology and I think it has great potential, but most of us made a mistake. We thought that we could continue teaching in the old way, only behind a screen instead of in class, but kids get bored. Sometimes I get this  feeling that all my students are sleeping, and there is nothing I can do about it…almost.

A few days ago, I ran into boom cards www.boomlearning.com.

It allows you to create interactive lessons and do everything you want: drag and drop, fill in the blanks, multiple choice.

There are thousands of decks already created by other teachers, some are free others you have to pay for, but they are beautiful, engaging, and fun and you can create your own decks, so you can decide the level perfect for your class.

Another bright side of it is that you can sell the decks that you create.

I teach middle and high school and from what I understand boom cards are not so common to be used for older students while they are really popular for elementary school.

Boom Cards are the perfect combination of engagement and efficiency for elementary teachers. The platform provides a unique digital experience for the students as it presents content in perfect bite-sized pieces. Bright visuals guide the students through essential learning tasks one question at a time and the students feel like they’re playing the latest app. The entire process is streamlined with the ability for students to input their responses instantaneously. 

The very fact that kids aren’t overwhelmed with a list of questions or associated information is one of the reasons educators are flocking towards the cards.

The control that Boom provides teachers is unprecedented as the cards guide your students through your learning objectives and records all responses creating feedback opportunities and usable data for assessment.

For students learning in a digital environment it is an absolutely vital tool and as they re-enter the classroom it will remain a staple of the modern elementary classroom. 

Come and see:


Thanks to Kenny’s classroom for his help:



Online teaching

That’s it. We are at home; we can’t go outside (I live in Italy) unless we have to buy groceries or medicines.

School are being closed since the beginning of March, and we don’t know when and if will open again.

I’m locked at my place and I’m scared, I have to admit. I’m afraid for my family, my parents are not so young and I have some health issues: due to brest cancer three years ago I did chemo, two years ago I was hit by a landslide and spent a couple of weeks more dead than alive, in November I fell and broke my shoulder; I feel all the symptoms at least ten times per day.

I’m afraid for my country, what will happen to us when things will go back to normal?

I’m afraid for my students. They are all enough to understand what is happening, but maybe not old enough to fully understand.

As a teacher and as a mother I feel that we can’t abandon them. We need to be by their side and help them, but in order to do that we have to change.

We need to let the kids learn in a different way. I do believe that is more difficult for us than for them. They are a connected generation, they know how to use pcs, smartphones and tablets better than us, so we don’t need to let the kids learn in a different way, but we need to learn how to teach them in a different way.

I took one of my resources and recorded a video for my students.

You can do the same, sending them the Power Point presentation or adding voice and comment, as I did.

Take a look here:

To do that I prepared a lesson about linear equations using Power Point, than I used Screenocast, it is free if you record 15 minutes video, and I added voice and hand written notations.

If you need a quick tutorial about how to use screenocast, you can find it here:

It was not so easy for me to record the voice, mostly because I’m Italian and, besides my funny accent I mispronounced few words, so I had to do it again, but at the end I did it.

If you are not online with your students, I would say this is a good solution, but if you have the chance it’s better an online lesson.

You can use the Power Point presentation and interact with the kids, explain and write on the presentation.

I use zoom https://zoom.us/, it’s free and easy, you also have the possibility to record your session, so if a student is absent you can send the lesson to him.

I prepare the Power Point and send to them, asking to study and solve some easy exercises, then I see them online, I explain the topic and we move to more challenging exercises.

I’m doing lessons with my classes and I have to say, I like it. My students seem to be engaged, they participate and follow, I can can mute them all, so they can’t interrupt an explanations asking if yesterday I went to the hair dresser (hair dresser are closed right now, by the way), but they listen till the end, and then questions are smart.

I also created a google form where they can ask questions, so if it’s something that might concern everybody I answer during the lesson, if not I simply send a message to the kid who asked the question. in this way they are not afraid to ask, I like it and they seem to like it too.

A problem I’m struggling with is testing the students. I’m trying to see if I can find a way to test them, I created some tests using google form and I’ll try with my students. I’ll write something about it as soon as I have done it.

You can find my test here,


I like it, but I’m struggling to find a way for the kids not to cheat. I also found a bunch of websites that offer tests online.

I’m going to take a look at them, and then I’ll let you know, in the next post.

I know it’s a difficult time, and I wish we can get back to normal as soon as possible, but I also think that we all should try to make the best of this period, and possibly try to find something good.

I hope that you all are safe at home.


Valentine’s day – Fractions activity

Do you need a fun activity for Valentine’s day?



No prep, ready to print activity for Valentine’s day, including colouring activity with equivalent fractions and additions and subtactions.

Copyright © 2020 Matemaths

All rights reserved by author.

Permission to copy for single classroom use only

Not for public display.

If you are looking for other Valentine’s activities:




if you need to teach fractions look for:





Please feel free to contact me anytime!

Email: matemaths@libero.it

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Not only math, English activity by Mr Forman from ELA in Middle School

Normally I do math, but in this period of distance learning I had also to help homeschool my son. Luckily, because I found an amzing person and a wonderful teacher.

Here is what I think about his product.

Why do I love boom cards?

Because are amazing, and because when you look you can find amazing jobs.

I’m a math teacher, so I don’t usually look for anything else than math.

This time I needed something for my son’s English lesson.

Mr Forman is a Middle school ELA teacher, and I feel so lucky I’ve found him.

The deck I’m talking is composed by 50 cards on Figurative Language.

The first part explain simile, metaphor, onomatopoeia, imagery, allusion, alliteration and personification.

The explanation is clear and easy, and you feel like “of course! it so easy, why didn’t I understand before?”

Then you can find a set of exercise where you have to find the right figurative language. Examples once again are clear and beautiful to read. You get to master the topic with very little effort, and most of all without getting bored.

My son is not English mother tongue, but he immediately understood and begged me for more boom cards from Mr. Forman.

Take the time to step by Tpt, Boom cards, The Wheel or Ampedup and take a look at his products, You will enjoy them, I promise.


Mardi gras

Mardi Gras has origins in medieval Europe, it comes from French and means Fat Tuesday, it’s the day for eating a lot and unhealthy food before the traditional forty days of fasting during the season of Lent in the Catholic faith.

This feast was common, during the medieval times in Europe, specially in Italy and France. This tradition found it’s way to the New World.

The first celebration of Mardi Gras in US is dated 1699, in a place 60 miles near the city that woul have become New Orleans.

Over time this celebration grew, with parades and street parties.

When the spanish arrived in New Orleans, in the 1760s, they tried to shut down this celebration. The restriction continued till the early 1800s, when this celebration was recognised but not encouraged.

The first official mardi Gras’ parade took place in 1837.

Do you celebrate Mardi Gras and need a theemed math activity for your students?



Monomials part 2

Multiplying Monomials

When you multiply monomials, you will need to perform two steps:

Multiply the coefficients (constants)

Multiply the variables, using the famous laws of indices!

For example

For example

Dividing Monomials

Let’s start by taking a look at a few problems in “expanded form”. Once you examine these examples, you’ll discover the rule on your own!

Both numerator and denominator get raised to the third power. We have to apply the Power of a Power Property and multiply the exponents. Then you subtract the exponents for the final division expression.


Monomials part 1


monomial is an algebraic expression that consists of only one term. (A term is a numerical or literal expression with its own sign.) For instance, 9x , -4a², and  3mpx³ are all monomials. The number in front of the variable is called the numerical coefficient. In -9xy, -9 is the coefficient.

Adding and subtracting monomials

To add or subtract monomials, follow the same rules as with signed numbers, provided that the terms are like. Like terms have the same pronumeral part, i.e. the same letters. E.g.,  and , but  and  are not like. Notice that you add or subtract the coefficients only, and leave the variables as they are.

For example

When terms or monomials contain the same variable and same exponent, they are like terms. Addition of monomials is done by adding the coefficients, without changing the variables nor the exponents.

x + 2 x = (3+2)x = 5 x

8y + 3y = (8 + 3)y = 11y

4np3 + 8np3 = (4 + 8)np= 12 np3

7 + 7x + 13x = 7 + (7 + 13)x = 20x + 7

For example

To subtract monomials, follow the same rules as with numbers, provided that the terms are like.

Let us subtract 12x from 10x
Given monomials are, 12x and 10x
12x-10x = (12-10)x = 2x


The letters and exponents never change; only the numbers out front change.

Whatever letters are in the problem are the same in the answer.



Relative numbers (part 2)

Multiplying Positive and Negatives numbers

We can only do arithmetic in the usual way.

To calculate 5(−2), we have to do 5· 2 = 10 — and then decide on the sign.

Is it +10 or −10?

For the answer, we have the following Rule of Signs.

Rules of signs

Like signs produce a positive number;

unlike signs, a negative number..

if the value of x is positive, then the value of −x must be negative, and vice-versa.

Since we call the positive or negative value of a number its sign, then we can state the following principle:

A minus sign changes the sign of a number.

On the number line, a minus sign reflects a number symmetrically about 0. You can observe it in the following picture:

segni opposti

When you multiply:

+ times + two positives make a positive:+ 3∙2=6

– times – two negatives make a positive: + (-3)∙(-2)=6

– times + a negative and a positive make anegative: (-3)∙(2)=-6

+ times – a positive and a negative make a negative: 3∙(-2)=-6

Formal rule:

A formal rule is simply a rule we write with letters. We write it with letters because we want it to apply to any numbers:

formal rule

Rule for 0:

Any number, multiplied by 0, gives 0 as a result.


Dividing Positive and negative numbers

Reciprocal: two numbers are reciprocals if their product is 1:


A division is a multiplication by the reciprocal:


When you divide, the rule is the same as for multiplication!

+ divided by + two positives make a positive: + 6÷2=3

– divided by- two negatives make a positive: + (-6)÷(-2)=3

– divided by+ a negative and a positive make a negative: (-6)÷(2)=-3

+ divided by- a positive and a negative make a negative: 6÷(-2)=-3

Exercises: (solutions at the end)



Relative numbers (part 1)

Addition and subtraction

We can count forwards: 1, 2, 3, 4, …and the question is: if you can go in one way, can you go the opposite way? The answer is: negative numbers

number line

Now we can go forwards and backwards as far as we want.

+ is the positive sign

– Is the negative sign

No sign means positive

What you see above is called the number line.  The negative numbers fall to the left of 0.  (We say that a negative number is less than 0.) The positive numbers fall to the right.  (We say that a positive number is greater than 0.)

We imagine every number to be on the number line.  And so the fraction ½ will fall between 0 and 1; the fraction −½ is between 0 and −1; and so on.

IN ARITHMETICS we cannot subtract a larger number from a smaller:

2 − 3.

But in algebra we can.  And to do it, we invent “negative” numbers.

2 − 3 = −1  (“Minus 1” or “Negative 1”).

What are the two parts of a signed number?

Its algebraic sign, + or − , and its absolute value, which is simply the arithmetical value, that is, the number without its sign.

The algebraic sign of +3 (“plus 3” or “positive 3”) is + , and its absolute value is 3.

The algebraic sign of −3 (“negative 3” or “minus 3”) is − .  The absolute value of  −3 is also 3.

If a number has no written sign it means that is positive.

Positive numbers start from zero and go to the right, negative numbers start from zero and go to the left.

Adding positive numbers

In algebra we speak of “adding,” even though there are minus signs.

Considering that positive numbers start at zero and go to the right and negative numbers start at zero and go to the left, if you want to add 5+(-9) you start from zero and go five “steps” to the right, from that point you jump nine steps to the left.

Look at the number line below:

number line somma

The answer is -4.

Adding negative numbers works like a “regular” addition, but in the opposite direction: instead of going to the right you jump to the left.

Look at the number line to see how -2+(-3) is calculated:

number line somma neg

The answer is -5.

  • If the terms have the same sign, add their absolute values, and keep that same sign.

2 + 3 = 5.                 −2 + (−3) = −5.              −2 − 3 = −5.

  • If the terms have opposite signs, subtract the smaller in absolute value from the larger, and keep the sign of the larger.

2 + (−3) = −1.            −2 + 3 = 1.

Algebra, after all, imitates arithmetic, and it is easy to justify these rules by considering money coming in or going out.  For example, if you borrow $10 and then pay back $4, we express that algebraically as
−10 + 4 = −6.
You now owe $6.

Subtracting positive numbers

What sense can we make of

2 − (−5) ?

Remember that every number has a negative. For example the negative of 5 is -5…..and the negative of -5 is –(-5) that is 5. This rule will be true for any number.



The first term does not change. Changes only the second!

For example:+6-(+3)=+3   but careful:

So Positive minus Positive gives you:

POSITIVE if the first number is bigger, but NEGATIVE if the first is smaller!


Here is a fundamental rule for 0:

Adding 0 to any term  does not change it.

  1. a) 0 + 6 = 6 b)      0 + (−6) = −6
  1. c) 0 − 6 = −6               d)  −6 + 0 = −6

Positive and negative together


Two like signs become a positive sign

+(+)=+         3+(+2)=3+2=5

-(-)=+          6-(-3)=6+3=9


Two unlike signs become a negative sign

+(-)=-          7+(-2)=7-2=5

-(+)=-          8-(+2)=8-2=6

If you liked it here you can find the PowerPoint presentation about this topic (click on the image):

signed numbers

And if you are in need of activities, check these boom cards:


Exercises (solutions at the end)



Ex 1

Ex 2

Ex 3


sphere is the set of all points, in three-dimensional space, which are equidistant from a point. The radius has one endpoint on the sphere and the other endpoint at the center of that sphere. The diameter of a sphere must contain the center and touch two points of the sphere.


The largest circular cross-section in a sphere is a great circle. The circumference of a sphere is the circumference of a great circle. Every great circle divides a sphere into two congruent hemispheres (half a sphere).


Surface area of a sphere

Surface area of a sphere is the two-dimensional measurement that includes the total area of all surfaces that bound the sphere. The basic unit of area is the square unit.

The formula to calculate the total surface of a sphere is:

sup sfera

Inversae formula:

sup sfera inv

Volume of a sphere

To find the volume of a sphere you must figure out how much space it occupies. The basic unit of volume is the cubic unit.

The formula to calculate the volume of a sphere is:

vol sfera

Inversae formula

vol sfera inv


  1. Find the surface area of the sphere whose radius is 4 cm.
  2. What is the diameter of the sphere, if the surface area of the sphere is 576π cm2.
  3. What is the diameter of the sphere, if the surface area of the sphere is 784π cm2.
  4. The volume of a sphere divided by its surface area is 9 cm. What is the radius of the sphere?
  5. The volume of a sphere divided by its surface area is 7 cm. What is the radius of the sphere?
  6. What is the volume of the hemisphere, if the diameter of the hemisphere is 7.2 cm.
  7. Find the surface area of the earth assuming the earth to be a sphere of radius 6369 km.
  8. Find the sum of the volume of a cone with radius 1 cm and height 5 cm and the volume of a sphere of radius 1 cm.
  9. An adhesive compound in liquid form is prepared in a container of hemispherical shape having a radius of 180 cm.This compound is to be packed in cylindrical bottles of radius 1 cm and height of 4 cm. How many bottles are needed if the liquid prepared exactly fills the container?


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