Intermediate II number sense (5-6 new curriculum) Carte 19, Intermédiaire II sens du nombre (5-6 nouveau programme) Flashcards
If you have a number expressed with more decimal places, is it more or less precise than a number with less decimal places?
Un nombre exprimé avec plus de décimales est-il plus ou moins précis qu’un nombre avec moins de décimales ?
It is more precise.
Il est plus précis.
Does a zero in the rightmost place of a decimal number change the value of the number?
Un zéro à l’extrême droite d’un nombre décimal change-t-il la valeur du nombre ?
No, it does not.
Non, ce n’est pas le cas.
How many decimal numbers can fit between any two decimal numbers?
Combien de nombres décimaux peuvent s’insérer entre deux nombres décimaux ?
infinitely many
un nombre infini
What is place value symmetry?
Qu’est-ce que la symétrie des valeurs de position ?
This states that the left and right of the ones place mirror each other. One over is tens and tenths, two over is hundreds and hundredths and so on infinitely.
Cela signifie que la gauche et la droite de la place du 1 se reflètent l’une l’autre. Un au-dessus correspond aux dizaines et aux dixièmes, deux au-dessus aux centaines et aux centièmes, et ainsi de suite à l’infini.
You need to be able to place any decimal number on a number line.
Place a decimal number on a number line of your choosing or do the question your teacher gives you.
Vous devez être capable de placer n’importe quel nombre décimal sur une droite numérique.
Placez un nombre décimal sur une droite numérique de votre choix ou répondez à la question posée par votre professeur.
Answers vary.
Concepts explored here are to be able to divide into tenths on the number line and follow the tenths place in the decimal to locate where to place the number. Of course, you will need to find the ones place first and then look at the tenths.
Les réponses varient.
Les concepts explorés ici sont la capacité à diviser en dixièmes sur la droite numérique et à suivre la position des dixièmes dans la décimale pour savoir où placer le nombre. Bien sûr, vous devrez d’abord trouver la place des uns, puis regarder les dixièmes.
You need to be able to round any decimal number to any place.
Round a sample number of your choosing or do the question your teacher gives you.
Vous devez être capable d’arrondir n’importe quel nombre décimal à n’importe quelle position.
Arrondissez un nombre échantillon de votre choix ou répondez à la question posée par votre professeur.
Answers vary.
Concepts explored here are that you must look one place over to the right of where you intend to round. If that number is 0, 1, 2, 3, or 4, then you remove that number and anything to the right. BUT if the number is 5, 6, 7, 8, or 9, then you must add one to the place to the left of that large number, and then remove the large number and anything to the right.
Les réponses varient.
Les concepts explorés ici sont les suivants : il faut regarder un chiffre à droite de l’endroit où l’on a l’intention d’arrondir. Si ce nombre est 0, 1, 2, 3 ou 4, vous enlevez ce nombre et tout ce qui se trouve à droite. MAIS si le nombre est 5, 6, 7, 8 ou 9, vous devez ajouter un à l’endroit situé à gauche de ce grand nombre, puis enlever le grand nombre et tout ce qui se trouve à droite.
Where are negative numbers placed on the number line?
What is the symbol to represent a negative number?
What are some real-life contexts of negative numbers?
Où sont placés les nombres négatifs sur la droite numérique ?
Quel est le symbole représentant un nombre négatif ?
Quels sont les contextes réels des nombres négatifs ?
To the left of zero if it is horizontal. Below zero if it is vertical.
negative sign -
temperature
debt
elevation
À gauche de zéro s’il est horizontal. En dessous de zéro s’il est vertical.
signe négatif -
température
dette
élévation
Is zero positive?
Le zéro est-il positif ?
no
non
Is zero negative?
Le zéro est-il négatif ?
no
non
What is magnitude?
Qu’est-ce que la magnitude ?
The distance from zero.
Magnitude will not be negative because it is a distance. So the magnitude of -6 is just 6.
Every positive number has an opposite negative number with the same magnitude.
No direction is given if you have just magnitude. You cannot tell where to go, just the distance.
La distance par rapport à zéro.
La magnitude ne sera pas négative car il s’agit d’une distance. Ainsi, la magnitude de -6 est juste 6.
Chaque nombre positif a un nombre négatif opposé avec la même magnitude.
Aucune direction n’est donnée si l’on ne dispose que de la magnitude. On ne peut pas dire où aller, il suffit d’indiquer la distance.
What is an additive inverse?
Qu’est-ce qu’un inverse additif ?
A number and its opposite are called additive inverses.
For example 6 and -6 are additive inverses.
If you add them together they make 0.
They have the same magnitude.
Un nombre et son opposé sont appelés inverses additifs.
Par exemple, 6 et -6 sont des inverses additifs.
Si vous les additionnez, vous obtenez 0.
Ils ont la même valeur.
What signs are used to indicate direction?
Quels sont les signes utilisés pour indiquer la direction ?
positive and negative
+ -
Negative is the opposite direction as positive.
positif et négatif
+ -
Le négatif est la direction opposée au positif.
Which number is larger?
7 or -8?
Quel est le nombre le plus grand ?
7 ou -8 ?
7
Which number has a larger magnitude?
7 or -8?
Quel est le nombre qui a la plus grande magnitude ?
7 ou -8 ?
-8 has a larger magnitude. Its magnitude is 8.
-8 a une plus grande magnitude. Sa magnitude est de 8.
What is an integer?
Qu’est-ce qu’un nombre entier ?
all natural numbers, their additive inverses, and zero
…-3, -2, -1, 0, 1, 2, 3, …
tous les nombres naturels, leurs inverses additifs et le zéro
…-3, -2, -1, 0, 1, 2, 3, …
Is the sum of two positive numbers positive or negative?
La somme de deux nombres positifs est-elle positive ou négative ?
positive
positif
Is the sum of two negative numbers positive or negative?
La somme de deux nombres négatifs est-elle positive ou négative ?
negative
négatif
What is the same as adding an additive inverse?
Qu’est-ce que l’addition d’un inverse additif ?
subtracting a number
for example adding -8 is the same as subtracting 8
la soustraction d’un nombre
par exemple, ajouter -8 revient à soustraire 8
You need to be able to add any two integers. This explores if you are able to express a difference as a sum. Model this on a number line.
Make up a question or use the one your teacher provides.
Make sure to practice four types of questions: - two positives
- two negatives
- one positive that is greater in magnitude to one negative
- one positive that is smaller in magnitude to one negative.
Vous devez être capable d’additionner deux nombres entiers quelconques. Ceci explore si vous êtes capable d’exprimer une différence sous la forme d’une somme. Modélisez ceci sur une droite numérique.
Inventez une question ou utilisez celle fournie par votre professeur.
Veillez à vous entraîner à quatre types de questions : - deux positifs
- deux négatifs
- un positif plus grand qu’un négatif
- un positif plus petit qu’un négatif.
Answers vary.
Concepts needed here are how to plot on an number line, as well as addition means to go to the right, and subtraction means to go to the left. If you add a negative number, you will go to the right a negative amount, which really just means to go in the opposite direction, so you will go to the left.
Les réponses varient.
Les concepts nécessaires ici sont la façon de tracer une droite numérique, ainsi que le fait que l’addition signifie aller vers la droite, et la soustraction signifie aller vers la gauche. Si vous ajoutez un nombre négatif, vous irez vers la droite d’une quantité négative, ce qui signifie simplement que vous irez dans la direction opposée, donc vers la gauche.
What is an algorithm?
A process you can follow to more efficiently solve a problem. Someone else proved that it works, so you can use it even if you don’t quite understand how it works.
For example I use this algorithm to solve a certain step in the rubix cube:
R’DRD’
R = turn the right side clockwise
D = turn the down side clockwise
R’ = turn the right side counterclockwise
There are many algorithms that people use such as the addition, subtraction, multiplication, and division algorithms when working with two digit numbers.
Add two numbers (mininum two-digit) together using the addition algorithm. Come up with a question or use one provided by your teacher.
Answers vary.
Make sure to line up the numbers by place value. When you get more than 9 as an answer, add one or more to the place to the left, depending on the number in the tens column in your answer.
What is a divisibility test?
A method to determine the factors of a natural number.
Is it possible to divide by 0?
no
If a number is divisible by another number and you divide it by that number, what is the remainder?
0
What is the divisibility test for 2?
If it ends in either 0, 2, 4, 6, or 8, then it is divisible by 2.
What is the divisibility test for 3?
If you add up all the digits in the number and if the sum is divisible by 3, then the original number is also divisible by 3.
Keep in mind that with a number like this: 3966633933
It is possible to just make sure that every digit is divisible by 3 instead of adding them all together first. But, every single one of them must be divisible by 3!
What is the divisibility test for 5?
If the number ends in 5 or 0 then it is divisible by 5.
Be able to determine the factors of any natural number. Pick a natural number and determine all its factors, or have your teacher give you a number.
Answers vary.
The main concept here is that you should be able to split the number by two factors and then continue to make a prime factorization tree by further splitting each number into two factors.
For example:
18 = 9 x 2
But 9 = 3 x 3
So 18 = 3 x 3 x 2
This is usually shown more easily in a tree diagram.
Associative Property for multiplication
The order in which three or more numbers are multiplied does not affect the product.
2 x 5 x 3 = 2 x 3 x 5
What is a composite number?
A number that can be expressed as a product of smaller numbers other than itself and one.
Usually we talk about different natural numbers and we determine if they are prime or composite. 0 and 1 are neither prime nor composite.
What is prime factorization?
A number represented as a product of prime numbers.
How can you find a composite factor of a number?
If a number does have a composite factor, you can get this by mulitiplying the prime factors together of that number in various combinations.
What is a power? (What is exponentiation)
The symbolic representation of repeated multiplication of identical factors.
What is a base?
The bottom number of the power, that represents the repeated factor.
What is an exponent?
This indicates the quantity of identical factors that are repeatedly multiplied.
Is a power divisible by its base?
yes
Complete the prime factorization of a composite number of your choice. Express your final answer in order of lowest to greatest prime and use exponents to represent your final answer.
Answers vary.
Try to learn to check for divisibility by 2, 3, 5, and 10 as this is the most efficient way. Then divide the number as you go to see what is left. Then check divisibility by other prime numbers such as 7, 11, 13, 17, 19 etc. You should have only prime numbers in your final answer.
Use the standard algorithm for multiplication to multiply a three-digit number by a two digit number.
Answers vary.
Make sure that you remember to erase carried numbers between each of the bottom numbers so that you don’t double-count something from a previous process.
Your teacher will show you this on paper since it must be seen in real-time.
Use the standard algorithm for division to divide a three digit number by a two digit number.
Answers vary.
Make sure that you are fluent in regular multiplication and division first, and then try this with the help of a teacher. It is important to know how to express the remainder if the number does not divide evenly.
Can a fraction represent quantities greater than 1?
yes
What is an improper fraction?
The numerator is greater than the denominator.
How can you express a natural number as a fraction?
Use the natural number as the numerator, and 1 as the denominator.
Anything divided by 1 is just itself, so this means that this new representation is equal in value to the old representation.
Can an improper fraction be represented in a different way? What way?
Yes, a mixed number in the form of A b/c where A is the number of wholes, and b/c is the fractional remainder or fractional part.
Why do we need fractions?
They allow counting and measuring between whole quantities.
Be able to compare fractions to benchmarks of 0, 1/2, and 1. Pick a fraction (including mixed, and improper) and plot it on a number line.
Answers vary. Make sure that you are thinking about what the fraction would be if it were over 10 or some other divisor that you can see on your number line. This will help you to more accurately plot your point.
What is a fraction?
Numerator is the quantity to be shared.
Denominator is the number of shares or number of groups.
Numerator / Denominator
Convert from a fraction to a decimal. Choose fractions that are mixed and improper as well.
Answers vary. Have your teacher help you to find a denominator of 10, 100, or 1000 to help convert the fractional part.
Before adding or subtracting fractions, what must you do?
Find a common denominator by finding the least common multiple between the two denominators present. Alternatively you can just multiply the two denominators together and the product will be your new common denominator.
The denominators must be the same before you can add or subtract. If they are already the same, you do not need to find a LCM or change the denominators to match.
What is a LCM?
Least Common Multiple
Given two or more numbers, you can determine the least common multiple by skip counting by the number itself, and recognizing when one of those results matches the other set.
For example: 6 and 8
6: 6, 12, 18, 24, 30, 36, 42, 48, ….
8: 8, 16, 24, 32, 40, 48, ….
You can see that 24 is the LCM here since it is the lowest of the common numbers between the two sets. 48 is just a common multiple and is higher than required.
When finding a LCM it is important to find the smallest solution so that the subsequent math steps are easier.
Be able to add mixed number fractions together. Ask your teacher to give you a question, or make one up yourself.
Answers vary.
You can add the fractional parts first, and then remember to carry any wholes to your whole addition.
Be able to reduce fractions and also be able to make equivalent fractions. Make up a question or ask your teacher for a question.
Answers vary. If you know your divisibility tests the process of reducing a fraction is much easier.
What does “related denominator” mean?
If one denominator is a multiple of the other, then the two denominators are related.
It is useful to recognize when denominators are related since if they are related, you can just use the higher denominator as your common denominator. This is used when adding or subtracting fractions.
Using 2, 3, and their additive inverses, make four addition problems and find their sums.
a) (+2) + (+3) = 5
b) (+2) + (-3) = -1
c) (-2) + (+3) = 1
d) (-2) + (-3) = -5
Using 2, 3, and their additive inverses, make eight subtraction problems and find their differences.
a) (+2) - (+3) = -1
b) (+2) - (-3) = 5
c) (-2) - (+3) = -5
d) (-2) - (-3) = 1
e) (+3) - (+2) = 1
f) (+3) - (-2) = 5
g) (-3) - (+2) = -5
h) (-3) - (-2) = -1
