The term 2 math exam will take place on Wednesday June 19th:
Students should begin reviewing the following (Will be updated as we return to these topics in class)
FRACTIONS:
-Equivalent fractions: Lowest common denominator, factors/multiples, mixed numbers vs. improper fractions
-Conversions: Fractions, decimals, percentages, ratios
-Fraction operations: Addition and subtraction (LCD and/or butterfly method), multiplication, division (multiply the reciprocal)
-Problem solving with fractions
--> The total (totale ou la somme) = addition
--> How much less? The difference (la différence) = subtraction
--> a fraction OF something (e.g. 20% DE ___) = multiplication (e.g. price x 0.2 or 1/5 = discount of 20%)
TRANSFORMATIONS
-Translation vectors [-5, + 2]: x = movement left or right, y = movement up or down (e.g. move left 5 and up 2)
-Reflections: Along x-axix = keep x the same, y flips; along y-axis = keep y the same, x flips
-Rotations:
If 90 or 270, flip the numbers for x and y, signs are given based on the quadrant you end up in
If 180, flip the signs e.g. (3,4) --> (-3, -4)
ALGEBRA
y = mx + b
m = the multiplier, how your equation changes
b = the y-intercept, where your equation starts
For example, the graph below could represent earnings from a lemonade stand. If I spend $8 on supplies, but charge $1/lemonade, my multiplier (m) is 1 because I make $1 every time I sell a lemonade. However, my graph STARTS at -8 because I am out $8 based on what I spent on supplies. I would need to sell 8 lemonades BEFORE I can begin actually MAKING money. Anything I sell after 8 lemonades is positive income.
Solving equations:
Step 1) simplify:
-combine like terms or distributive property
Step 2) isolate for the variable by moving terms across the equal sign using inverse operations
Step 3) Solve --> make sure your variable value is evident and makes sense, you can check using LS = RS
SA AND VOLUME:
We will begin by reviewing basic formulas for areas and apply these formulas to the calculation of surface area. Students will be encouraged to use nets (unfolded 3D shapes) to ensure they find the area for each face.
Students should begin reviewing the following (Will be updated as we return to these topics in class)
FRACTIONS:
-Equivalent fractions: Lowest common denominator, factors/multiples, mixed numbers vs. improper fractions
-Conversions: Fractions, decimals, percentages, ratios
-Fraction operations: Addition and subtraction (LCD and/or butterfly method), multiplication, division (multiply the reciprocal)
-Problem solving with fractions
--> The total (totale ou la somme) = addition
--> How much less? The difference (la différence) = subtraction
--> a fraction OF something (e.g. 20% DE ___) = multiplication (e.g. price x 0.2 or 1/5 = discount of 20%)
TRANSFORMATIONS
-Translation vectors [-5, + 2]: x = movement left or right, y = movement up or down (e.g. move left 5 and up 2)
-Reflections: Along x-axix = keep x the same, y flips; along y-axis = keep y the same, x flips
-Rotations:
If 90 or 270, flip the numbers for x and y, signs are given based on the quadrant you end up in
If 180, flip the signs e.g. (3,4) --> (-3, -4)
ALGEBRA
y = mx + b
m = the multiplier, how your equation changes
b = the y-intercept, where your equation starts
For example, the graph below could represent earnings from a lemonade stand. If I spend $8 on supplies, but charge $1/lemonade, my multiplier (m) is 1 because I make $1 every time I sell a lemonade. However, my graph STARTS at -8 because I am out $8 based on what I spent on supplies. I would need to sell 8 lemonades BEFORE I can begin actually MAKING money. Anything I sell after 8 lemonades is positive income.
Solving equations:
Step 1) simplify:
-combine like terms or distributive property
Step 2) isolate for the variable by moving terms across the equal sign using inverse operations
Step 3) Solve --> make sure your variable value is evident and makes sense, you can check using LS = RS
SA AND VOLUME:
We will begin by reviewing basic formulas for areas and apply these formulas to the calculation of surface area. Students will be encouraged to use nets (unfolded 3D shapes) to ensure they find the area for each face.
Next, students will move onto volume. grade 7s will work with square based or rectangular prisms while Grade 8s will extend to cylinders. Regardless of shape, the general formula for volume of a prism is:
V = Area of base x height
V = A x h
Students must sub in the necessary formula for A (area) depending on what the BASE FACE is for their prism.
Cylinders:
V = Area of base x height
V = A x h
Students must sub in the necessary formula for A (area) depending on what the BASE FACE is for their prism.
Cylinders:
Notice, in the above image:
A = 2(area of the circles) + (C x h) A = 2(πr^2) + (2πr x h) Remember, your formula for AREA of circles is the only formula which includes a "squared" or exponent 2. You must do the exponent first (PEDMAS), then times your answer by π (3.14), THEN times by 2 as you have TWO circular faces. The pink part is referring to the circumference; depending on whether or not you have been given the radius or the diameter, you can use C = 2πr OR C = πd |
Notice, in the above image:
V = A x h (reminder Area of a circle is π r^2) So as it is with any prism, volume is equal to the area of the base (in this case a circle), times the height. |
February
This week, students will explore algebraic expressions. We will begin with study of SIMPLIFYING expressions in order to make them easier to solve.
For example: 7x + 9 - 5 + 2x
Step 1: Combine LIKE terms (x's go together, numbers go together)
7x + 9 - 5 + 2x
Step 2: Re-write the equation with like terms together. Don't forget to look at the sign IN FRONT of your term.
7x + 2x + 9 - 5
In this case, 7x is the same as +7x and the 2x is being added.
9 is a positive integer or +9, and 5 is a negative integer. More simply I can say 5 is being subtracted.
Step 3: Complete the simple math. I know you can do it!
7x + 2x + 9 - 5
9x + 4
Later in the week, we will move to the DISTRIBUTIVE PROPERTY.
This principle allows us to make expressions easier to solve as it eliminates brackets. By using multiplication from the beginning, we end up with terms we can then simplify to make it easier to isolate for variables.
In the final example in the bottom right, a will multiply with both b and c making the final simplified expression ab - ac.
Feb 4-8
Following our study of cartesian planes, students will be expanding on their knowledge of growing patterns in the form
y = mx + b on a graph.
Reminders:
y = mx + b
m = multiplier (what the pattern CHANGES by)
b = constant (where the pattern starts, what stays the same)
On a diagram, your b represents where the number crosses the y axis making it your y-intercept.
We know this, because b is found on a table of values for term 0, meaning your point is (x, y) --> (0, y)
When solving for unknowns in the form y = mx + b, make sure you remind yourself of what your table of values would look like x = input or term number, while y = output, what's changing, number of tiles etc.
Following our study of cartesian planes, students will be expanding on their knowledge of growing patterns in the form
y = mx + b on a graph.
Reminders:
y = mx + b
m = multiplier (what the pattern CHANGES by)
b = constant (where the pattern starts, what stays the same)
On a diagram, your b represents where the number crosses the y axis making it your y-intercept.
We know this, because b is found on a table of values for term 0, meaning your point is (x, y) --> (0, y)
When solving for unknowns in the form y = mx + b, make sure you remind yourself of what your table of values would look like x = input or term number, while y = output, what's changing, number of tiles etc.
January 28th- Feb 1st:
This week, students will explore rotations along a Cartesian plane (about the origin, or about different points).
We will begin our study with the mathematical rules for rotating objects around the origin (0,0)
In this case, a few simple steps should be followed:
1) Determine direction and how many quadrants you are moving
SAM = sens avec l'aiguille des minutes = clockwise = sens horaire (with the minute hand)
SCAM = sens Contre l'aiguille des minutes = COUNTER clockwise = sens antihoraire (against the minute hand)
If you move 90 degrees, you move ONE quadrant over,
If you move 180 degrees, you move TWO quadrants over
If you move 270 degrees, you move THREE quadrants over
2) Based on which quadrant you will end up in, you now know the signs of your x and y
e.g. Point A ( 3, 2 ) rotating 90 degrees counter clockwise will end up in quadrant 2 (-,+)
3) Flip your x and y --> ensure you use the proper signs (Voila, you're done!)
A ( +3, +2 ) --> A' (-2, +3)
Watch the video below for help with rotating along any point:
January 21-25th:
This week, students will begin review of cartesian planes (les plans cartésiens) and transformations of coordinates and shapes.
Students will be expected to understand and work with the following transformations: Translations: Any movement left (-) or right (+) along the x axis or Any movement down (-) or up (+) along the y axis *Picture looks the same, but has moved within the quadrants) (x, y) --> (x + a, y + b) where a is movement left (-) or right (+) and b is movement down (-) or up (+) |
Reflections:
The symmetrical reflection of a shape along ...
-The x axis (x coordinate stays the same, y flips signs)
(+2, +3) --> (+2, -3)
-The y axis (y coordinate stays the same, x flips signs)
(+2, +3) --> (-2, +3)
-A diagonal: BOTH x and y coordinates flip signs
(+2, +3) --> (-2, +3)
Réflexion selon l'axe des x Réflexion selon l'axe des y Réflexion selon un diagonale
The symmetrical reflection of a shape along ...
-The x axis (x coordinate stays the same, y flips signs)
(+2, +3) --> (+2, -3)
-The y axis (y coordinate stays the same, x flips signs)
(+2, +3) --> (-2, +3)
-A diagonal: BOTH x and y coordinates flip signs
(+2, +3) --> (-2, +3)
Réflexion selon l'axe des x Réflexion selon l'axe des y Réflexion selon un diagonale
_____les_transformations -_student.docx | |
File Size: | 784 kb |
File Type: | docx |
January 2019:
Following the Christmas break, we will complete a short review of fractions and converting to ratios, decimals and percents as well as looking at equivalent, improper and mixed fractions. Next week, we will explore operations with fractions (Please see below for support).
Adding and Subtracting Fractions:
Step 1: Find a common denominator
Step 2: Add or subtract the numerator, denominator does not change
Step 3: Simplify as necessary
Following the Christmas break, we will complete a short review of fractions and converting to ratios, decimals and percents as well as looking at equivalent, improper and mixed fractions. Next week, we will explore operations with fractions (Please see below for support).
Adding and Subtracting Fractions:
Step 1: Find a common denominator
Step 2: Add or subtract the numerator, denominator does not change
Step 3: Simplify as necessary
Alternative Method: Butterfly *Be sure to pay attention to the sign, beware silly mistakes
Multiplication of Fractions: le produit
Step 1: Convert to improper fractions if necessary
Step 2: Multiply the numerators, multiply the denominators
Step 3: Simplify as necessary
*Les questions vous demande de trouvez un fraction DE quelque chose (If you are asked to find a fraction OF a fraction, you are multiplying two fractions together e.g. (what is 1/2 of 2/3 --> 1/2 x 2/3 = 2/6 or 1/3)
Step 1: Convert to improper fractions if necessary
Step 2: Multiply the numerators, multiply the denominators
Step 3: Simplify as necessary
*Les questions vous demande de trouvez un fraction DE quelque chose (If you are asked to find a fraction OF a fraction, you are multiplying two fractions together e.g. (what is 1/2 of 2/3 --> 1/2 x 2/3 = 2/6 or 1/3)
Division of Fractions: le quotient
Step 1: Convert to improper fractions if necessary
Step 2: Flip the SECOND FRACTION and change the sign to multiplication
Step 3: Multiply the fractions
Step 4: Simplify as necessary
Step 1: Convert to improper fractions if necessary
Step 2: Flip the SECOND FRACTION and change the sign to multiplication
Step 3: Multiply the fractions
Step 4: Simplify as necessary
Students are currently preparing for their exam on December 12th
In preparation for the exam, students should begin reviewing the following:
(YOU MUST BE LOGGED INTO A GOOGLE GMAIL ACCOUNT TO VIEW)
https://docs.google.com/presentation/d/1TO5Ibwg4hJdgiheMe8wh_WNa7o055WHQ5LUQLP2H-_I/edit?usp=sharing
Révision
Traitement des données
-7e: p. 97 #2, p. 104 # 3-6, 11
-8e: p. 110 # 4, 7,9
Facteurs et Multiples:
-7e: p. 21 #2, p. 2, 5, 6, 11
-8e: p. 41 # 1, 3, 4 p. 14 # 4, 6, 9, 10, 12
PEDMAS:
-7e: p. 28 # 6-8, 19, p. 33 # 10-11
-8e: p. 41 #1, 3, 4 p. 37 # 4, 6, 10
Nombres entiers (Integers):
-7e: p. 188 # 8, 10 p. 205 # 2-6
-8e: p. 196 # 1-10, p. 206 # 4-7
-Data management (Traitement des données)
--> Primary vs. secondary data (les données primaires et secondaires)
Les données primaires sont collectionner par TOI MÊME.
--> Census vs. sample (Échantillon et recensement)
Pour un recensement, tu dois demander a CHAQUE PERSONNE dans la population, pour un ÉCHANTILLON tu demanderas seulement aux quelques personnes dans une manière qui pourra éviter du biais.
--> Les diagrammes (Circulaire, Bandes)
-how to make one, how to interpret
-N'oublie pas un titre, les étiquettes, les axes (x,y), une légende
--> Mean, Median, Mode, Range (Moyenne, Médiane, Mode, Étendue)-
-how to calculate, how to interpret
--> Bias (le biais)
Week 14: December 3rd-7th
This week, students will finish up their unit on Area (writing a quiz on Wednesday) and begin reviewing for our exam next week.
Week 13: November 26-30
This week, students will explore various problems and solve for the area of geometric figures (squares, rectangles, triangles, trapezoids). Grade 8 students will move one step further and calculate area of a circle.
Week 12: November 19-23
This week, students will continue exploration of triangles and angles. Grade 8 students will begin working with the Pythagorean Theorem.
For practice with angles, triangles and the Pythagorean theorem, please complete Chapter 10 Lessons here:
http://www.nelson.com/school/elementary/mathK8/math8/studentcentre/studtryout.html#ch10
Week 11: November 12-15
This week students will finish up study of unit rate and conversion and begin our study of triangles.
For extra support with the French terminology of triangles and geometry, please see the powerpoint below:
Traitement des données
-7e: p. 97 #2, p. 104 # 3-6, 11
-8e: p. 110 # 4, 7,9
Facteurs et Multiples:
-7e: p. 21 #2, p. 2, 5, 6, 11
-8e: p. 41 # 1, 3, 4 p. 14 # 4, 6, 9, 10, 12
PEDMAS:
-7e: p. 28 # 6-8, 19, p. 33 # 10-11
-8e: p. 41 #1, 3, 4 p. 37 # 4, 6, 10
Nombres entiers (Integers):
-7e: p. 188 # 8, 10 p. 205 # 2-6
-8e: p. 196 # 1-10, p. 206 # 4-7
-Data management (Traitement des données)
--> Primary vs. secondary data (les données primaires et secondaires)
Les données primaires sont collectionner par TOI MÊME.
--> Census vs. sample (Échantillon et recensement)
Pour un recensement, tu dois demander a CHAQUE PERSONNE dans la population, pour un ÉCHANTILLON tu demanderas seulement aux quelques personnes dans une manière qui pourra éviter du biais.
--> Les diagrammes (Circulaire, Bandes)
-how to make one, how to interpret
-N'oublie pas un titre, les étiquettes, les axes (x,y), une légende
--> Mean, Median, Mode, Range (Moyenne, Médiane, Mode, Étendue)-
-how to calculate, how to interpret
--> Bias (le biais)
Week 14: December 3rd-7th
This week, students will finish up their unit on Area (writing a quiz on Wednesday) and begin reviewing for our exam next week.
Week 13: November 26-30
This week, students will explore various problems and solve for the area of geometric figures (squares, rectangles, triangles, trapezoids). Grade 8 students will move one step further and calculate area of a circle.
Week 12: November 19-23
This week, students will continue exploration of triangles and angles. Grade 8 students will begin working with the Pythagorean Theorem.
For practice with angles, triangles and the Pythagorean theorem, please complete Chapter 10 Lessons here:
http://www.nelson.com/school/elementary/mathK8/math8/studentcentre/studtryout.html#ch10
Week 11: November 12-15
This week students will finish up study of unit rate and conversion and begin our study of triangles.
For extra support with the French terminology of triangles and geometry, please see the powerpoint below:
géométrie-_angles_triangles_lignes.pptx | |
File Size: | 9874 kb |
File Type: | pptx |
Week 10: November 5-9:
This week, students will begin exploring mean, median and mode as they relate to sets of numbers. Students will also continue exploring the conversion of numbers and unit rate.
Mean = moyenne = average = total sum of all data/number of answers
Median = médiane = middle number, if a set of numbers includes and even number of responses, you need to find the average of the two middle numbers
Mode = mode = the most common, most popular number in a set (if one number does not appear more frequently than another, or if there is a tie, there is no mode)
Range = étendue = the amount of space between the highest and lowest number (highest - lowest = range)
Example: For the following set of data:
52%, 94%, 58%, 77%, 100%, 88%, 100%, 100%, 76 %, 74%
Step 1: Place all numbers in order from smallest to largest
52%, 58%, 74%, 76%, 77%, 88%, 94%, 100%, 100%, 100%
Mean = (52 + 58 + 74 + 76 + 77 + 88 + 94 + 100 + 100 + 100) / 10
= 81.9 %
Median = 77 + 88 / 2 (Because there are 10 total numbers in the set, there is no exact middle, so you find the average)
= 82.5 %
Mode = 100% (3 people got perfect on the test, making it the most common score)
Range = 100 - 52
= 48 (all students scored within 48 points of one another, everyone passed)
In this case, the mean and median are somewhat close to one another so either are a good indicator of how the class did. Because multiple people got 100%, 100 is not an outlier, though it will still influence the average and bring it up a bit. 52% does not appear to be an outlier either, as another person finished in the 50s as well. The median eliminates all the people who did very well, or more poorly, so it is probably the best indicator of how the class did as a whole.
Week 9: October 29th-Nov 2nd
This week we will primarily focus on operations involving decimals (addition, subtraction, multiplication and division). Students will review place value in an attempt to develop flexibility of numbers (e.g. comparing whole numbers, decimal numbers and fractions). Students will be asked to consider how to break down numbers (decompose) into it's building blocks to compare the value of numbers (<,>,=). For extra help, please see the images and videos below, and complete extra practice worksheets:
Multiplication Review (with decimals) Long Division Review (with remainders as decimals)
|
|
Week 8: October 22-26th
This week, students will review basic multiplication and division facts (with and without the use of a calculator) in preparation for our next Number Sense unit using decimals.
Week 7: October 15-19
This week students will be introduced to integers (postive and negative numbers), and the addition, subtraction, multiplication and division of these numbers. For extra support, please download the "cheat sheets" below.
integers_note__french___english_.pdf | |
File Size: | 33 kb |
File Type: |
add_subtract_integers_fact_sheet.pdf | |
File Size: | 59 kb |
File Type: |
multiply_divide_integers_fact_sheet.pdf | |
File Size: | 57 kb |
File Type: |
Week 6:
This week, students will begin exploring growing patterns and algebraic expressions (y = mx + b) using a variety of strategies and tools. For example, students explored the following example: You are ordering poutine from Skip the Dishes. Each poutine costs $4 and the company always charges a 7$ delivery fee. a) write an expression for the total cost of x number of poutines (y = mx + b) Step 1: What stays the same? (b = your constant) b = $7, no matter how many poutines I order, I will ALWAYS be charged a $7 delivery fee Step 2: What is changing? What is your multiplier? m = 4, for each poutine I order, the total cost increases by $4 Step 3: Write your expression, by subbing in values for variables y = 4x + 7 b) how much will it cost for you and a friend to order poutine for yourselves? Solve for y, when x = 2 y = 4(2) + 7 y = 8 + 7 y = 15 Therefore, it will cost $15 to order poutine for myself and a friend. c) how many poutines can you buy with $27 Solve for x when you know y. 27 = 4x + 7 (to isolate for x, move the 7 across the equal sign using the inverse operation, subtract 7 from 27) 20 = 4x (to isolate for x, move the 4 being multiplied across the equal sign using the inverse operation, divide 20 by 4) 5 = x Therefore, I can order 5 poutines with 27$, 20$ is how much it costs for the poutines, plus the $7 delivery fee. |
Week 5: October 1st-5th
This week students will continue exploration of number relationships and the order of operations in algebraic expressions. Students will explore the solving of equations with variables when given the value of variables, and begin solving for unknown variables by using inverse operations across the equal sign.
Weeks 3&4: September 17-27
Over the course of two weeks, students will be working with numbers and operations while developing the following skills
-Factors (PGFC)
-Multiples (PPCM)
-Prime Factorization
-Exponents
-Square Roots
-Order of Operations (BEDMAS)
Weeks 1-2: September 4-14th
Students will begin the school year with Data Management via exploration of surveys and graphs. Students will be conducting a survey to address issues in our school community while considering bias and sample size and presenting their findings in a relevant manner.
Critères de succès: Je peux
- Recueillir des données
- Organiser et présenter les données de la façon appropriée
- Évaluer les représentations des données
Important French math terminology.