# January 26th to January 30th

No, you are not receiving this email a day too early:),  it is a short week here at Duffield School.  On Thursday many of our junior high students enjoyed a wonderful day on the ski hill in Marmot – what a fantastic opportunity for those that enjoy the thrill of the slopes.

A huge thank you is sent out to Mrs. Petterson who did all of the work to organize the day!!  Also, to Mrs. Satermo and Mr. Olson who joined the group as supervisors even with the EARLY morning wake up call required.  Remember, there is no school tomorrow (Friday, January 30th) as it is a PD Day for staff.  As for the highlights, here we go:).

In Grade 7 we spent the week reviewing the order of operations with decimal numbers.  We did not spend a lot of time on this as many of us are quite good at this already.  Understanding the order of operations is a very important skill for students in order to continue to be successful in mathematics as they will encounter it MANY more times throughout their years.  Also, we spent time converting between fractions, decimals, and percents.  We took some notes on these processes, which I have uploaded to the blog if you would like to have a look, and then completed some practice questions.  To end the week we wrote our quiz on this lesson, as well as began to look at word problems that involve percents.  In this lesson students will be asked to calculate percents of a number.  For example, what is 15% of 60.  To do this students translate the word “of” to mean multiply.  We will continue to work on this next week, as well as prepare for our unit 3 exam coming VERY soon.

In Grade 8 we finished our study of the surface area of triangular prisms and moved on to look at the surface area of cylinders.  To begin we completed an Investigate Task where we calculated the surface area of an empty glowstick tube.  Through this investigation students came to realize a few things.  1.  A cylinder has 3 faces – 1 rectangle and 2 congruent circles.  2.  The one dimension of the rectangle is equivalent to the circumference of the circles.  3.  We only require 2 pieces of information to calculate the surface area – the height (or length depending on orientation) of the cylinder and either the radius or diameter of the circles.  Our biggest challenge so far has been to remember the difference between the formula for circumference (pi x diameter OR 2 x pi x radius) and the formula for area (pi x radius squared).  We have also begun to create our own formula sheets that we will be permitted to use on all quizzes and exams.  Students have been strongly encouraged to take the time to create a personal formula sheet as I will not be providing them with one should they choose not to make their own, as well as to use pictures, words, and symbols to help them.  Next week we will finish our study of surface area, write lesson quizzes, and begin to look at volume.

In Grade 9 we spent time this week reviewing how we work with equations as many of us are struggling with the concept of performing inverse operations in order to isolate the variable in the equation.  I do think the review time was valuable and some have now got the idea of performing inverse operations to BOTH SIDES of an equation.  We also reviewed the following:

1.  If we only see an x in an equation it will graph as a vertical line.  We will sometimes have to isolate the variable first, then verify our solution through substitution.

2.  If we only see a y in an equation it will graph as a horizontal line.  Again, we will sometimes have to isolate the variable first, then verify our solution through substitution.

3.  If we see an x and a y in an equation it will graph as an oblique line (diagonally).  With these equations we find it help to create a table of values, assign our own values for x, and then substitute in to solve for the equivalent y value.

To end the week we began to match equations with lines, and lines with equations.  Next week we will begin to interpolate and extrapolate, as well as begin to prepare for our upcoming unit exam.

Some reminders:

1.  The grade 9 class is selling Little Caesars pizza kits.  These orders are due back to the school by February 13th.  Please support their efforts to fundraise for their year end trip to Jasper.  Thanks:).

2.  Next Thursday and Friday are Teachers’ Convention – no school on either of those dates.

3.  Interim Report Cards go home on Wednesday of next week.  Please review your child’s with them and then sign and return them to the homeroom teacher ASAP.

Until next week:)

# January 19th to January 23rd

Another week of 2015 has come and gone already.  Many of us had the pleasure of spending Tuesday on the ski hill – and what a beautiful day it was to be on the slopes from what I was told.  THANK YOU, Mrs. Leavell for doing all of the work to organize that for our students.  As for the math highlights, here we go as usual:).

In grade 7 we began the week by mastering the fine art of dividing with decimal numbers.  As usual, we started by modelling this with base ten blocks, then moved to drawing it in grid paper, and finally completed questions with math symbols.  Again, with the models and the pictures we used the area of a rectangle as our model.  The area represents the dividend, the one dimension represent the divisor, and the second dimension (the one we create in order to get the required area using the provided dimension) is the quotient.  We also realized that, if we multiply or divide the dividend and the divisor by the same power of 10, the quotient will remain the same.  For example, we know that 30 ÷ 6 = 5.  If we multiply or divide 30 and 6 by the same power of ten, the quotient will remain 5.  So, 300 ÷ 60 = 5, 3 ÷ 0.6 = 5, 3000 ÷ 600 = 5, etc.  This helps us when we divide by decimal numbers because we can “dump the decimal” once again, and, as long as we maintain the proportion, the quotient will not change.  The following are pictures of notes that we took to help us with this concept.

Once we were done with division we moved on to solving order of operations questions with decimal numbers.  For these questions we were permitted to use our calculators for single operations, but not the entire question.  This meant that we needed to know that we solve all operations within brackets first, then multiply and / or divide left to right, and end with adding and / or subtracting left to right.  Next week we will begin to look at how fractions, decimals, and percents relate to one another.  I would anticipate a unit exam on lessons 3.4 to 3.8 before we break for teachers’ convention.

In grade 8 we began the week by reviewing our research project.  The notes that students created will benefit them MANY times throughout this unit.  They can also find the “answer key” on this blog site under grade 8 resources for unit 4.  We started to look at the surface area of rectangle prisms by calculating the surface area of this cereal box.

The above picture is of the task, while the picture below is of the various strategies that the students used when they determined that the surface area of this prism to be 1591.5 cm squared.

As you can see, students came up with more than one way to solve this problem, but all required them to see that a rectangular prism is made up of 6 rectangular faces and the total surface area is the combined sum of those 6 faces.  We completed some independent practice questions on this concept and then began to look at the total surface area of triangular prisms.  For this scenario we used a Toblerone Chocolate Bar box as our model that we needed to calculate the surface area of.  as you can see below, students had some fun calculating the surface area.  After, we talked about how the object has 5 faces, 3 rectangles and 2 congruent triangles.  This is helpful information as the total surface area will be the combined sum of those 5 faces.  We need to remember that the base and height of a triangle form a 90 degree angle (and are not always 2 of the 3 sides of the triangle).  Also, we need to remember that the formula for finding the area of a triangle has us dividing by 2 as a last step (we often forget to do this).Next week we will do more with the triangular prisms, as well as calculate the surface area of cylinders.

In grade 9 we continue to look at linear relations.  We began the week by completing our quizzes on the first 2 lessons of the unit.  After that we completed an Investigate activity to help us to see that, sometimes, both x and y will be on the same side of an equation.  For example, x + y = 20.  To help us we can create a table of values and substitute a value for x in order to determine y.  If I substitute 5 in for x, then y must be 15 in order to make 20.  We also discovered that some relations only have one variable.  After graphing a few of these we came to see that, if x is our only variable, the graph will be a straight line that travels vertically.  If y is our only variable, then our graph will be a straight line that travels horizontally.  To help us to remember this, we have to think that the x line travels in the opposite direction of the x axis, and the y line travels in the opposite direction of the y axis.  When we have both an  x and a y, the graph that we create will be a straight line that we call oblique.  Next week we will write / finish our Lesson 4.3 quizzes and then begin to match equations with graphs, as well as interpolate and extrapolate.  Should be LOTS of fun!!

Until next week:)!!

P.S.  Don’t forget that next Friday is a PD Day – no school for students.  Also, Thursday is the Marmot trip for those students that have registered for it.

# January 12th to January 16th

Another busy week has come and gone.  Students seem to have settled back into the routine and are engaged in learning the various concepts taught at each grade level.  On Tuesday the grade 6-9 students were entertained by Robb Nash and his band.  This was an EXCELLENT presentation from what I have heard (I really wish I could have been there but was at a PD session at the time).  The message he shared was definitely a positive one that students identified with on some level.  A HUGE thanks to Mr. Mireault for arranging that for us!!!

In grade 7 the week was spent on practicing our skills with multiplying decimal numbers.  We had our quiz on this on Wednesday.  For the most part we understand the movement of the decimal point when we “dump it” and then “get back together”.  On Wednesday we also began to work on dividing with decimal numbers.  This is always a challenging concept for students as many of them have forgotten a strategy to divide with larger numbers (such as long division).  As with multiplication, we began to look at division with base ten blocks and grid paper.  I have attached a picture of our investigate question for you to have a look at.

When we multiplied our factors combined to create a rectangle with an area equal to the product.  Since division and multiplication are inverse, we can use this same area model to help us.  The area has now become our dividend, the one factor is now our divisor, and the second factor will be our quotient (Dividend divided by divisor equals quotient).  We completed some practice of this on Friday, as well as looked at patterns to see how we can divide decimal numbers without the use of models.  Next week we will look at Order of Operations with decimal numbers, as well as complete a mid-unit review.

In grade 8 we continued to look at objects and nets.  We can now name objects according to the faces that make them.  Also, when we name them, we can classify them as either a prism or a pyramid.  When we have a prism we know that we will see rectangles and 2 congruent polygons.  For example, a hexagonal prism will have 6 rectangles and 2 congruent hexagons.  When we have a pyramid we will see triangles and a single polygon for the base.  For example, a hexagonal pyramid will have 6 triangles and 1 hexagon.  We also know that the term “regular”, when used to name a polygon, tells us that all of the sides are the same length.  For example, an octagon has 8 sides, while a regular octagon has 8 sides that are all of equal length (like a stop sign).  On Friday we used our time to work on our research task that is due on Monday.  The task is intended for students to see the connection between the net, the formulas, and the total surface area of an object.  Truly, the extension from grade 7 is simply the addition of multiple faces together.  We already know how to find the area of a rectangle and a triangle.  Since a triangular prism is the combination of 3 rectangles and 2 triangles, we simply find each individual  area and then find their sum.  We will begin to look at calculating the total surface area of a cube and a rectangular prism next week.  Over the weekend, I encourage you to ask your child about the nets they created, and in some instances, the creative names they gave them, such as Nicholas’ Cage:).

In grade 9 we continued to look at linear relations.  We now know multiple ways to represent a relation – words, pictures, graphs, expressions/equations, and a table of values.  The attached picture is of our Investigate question that asked about a cellphone bill that was \$20 + \$0.10/text message sent – sorry it is a bit blurry.  Students were asked to represent to relation in as many ways as possible.  These were our suggestions.

We also determined how we can tell if our relation will be linear or not.  We have 2 strategies.  If we have our graph, we know we will see a straight line (this can be a set of dots that extends in a linear pattern).  A straight line can be horizontal, vertical, or oblique  So far all of our graphs have been oblique.  We will see next week why that is.  If we have a table of values, we will see a constant change in our (our independent variable) and a constant change in our Y (our dependent variable).  Students really need to ask themselves what is staying the same, what is changing, and how is it changing.  Also, we are all quite good at substituting in our independent variables to determine our dependent variable, but struggle a bit when we are determining the independent variable when we know the dependent.  For example, we can work with the equation 5X= Y, and substitute in values for X to calculate the corresponding Y.  Where we struggle is when we know Y and have to solve for X.  Such as 5X = 20.  We have to show that, when solving, we must divide BOTH SIDES by 5 to determine X to be 4.  We will continue to work on isolating our variable next week.

Good luck to both of the Senior Spartan Basketball teams this weekend who are playing in Ponoka!!

**Please note, the next round of hot lunch order forms are due next week.  Also, some students will be away on on a ski trip on Tuesday.  Those students need to check with their teachers to see what they will be responsible for and, if they had ordered hot lunch before knowing about the trip, be sure to cancel.

Until next week:)!!

# January 5th to January 9th

Welcome back, Everyone!!  I hope that your break was a memorable one spent with family and friends.  Although the 2 weeks seemed to fly by, I managed to fit in time with all of my loved ones, as well as some quiet time with a good book or funny movie, and completed some school work that required my attention.  As for our first week back, here are the highlights.

All classes began the week by doing a little self reflection.  The new calendar year seemed like a good time to sit back and assess what we can be super proud of, as well as determine any areas for growth.  Students were asked to assess themselves, as honestly as possible, on areas relating to being successful in mathematics class.  I hope that you all had an opportunity to sit with your child to honour the things that they wanted to share as their strengths, as well as help them to determine a strategy to reach their goals.  If you have not yet seen your child’s please ask them for it and return it to the school as soon as possible.  Thanks:).

In Grade 7 we spent the week looking at how we multiply decimal numbers.  We have used base ten materials and grid paper to help us with this.  In the past, the flat represented 100, the rod represented 10, and the small cube represented 1.  Now, with decimal numbers, we will let the flat represent 1, the rod represent 0.1, and the small cube will represent 0.01.  These materials help us as we think of the multiplication question as if it were a question relating to the area of a rectangle (length (factor #1) x width (factor#2) = area (product)).  Grid paper helps us draw the picture of what we created with the base ten materials.  The following is a picture for you to see how base ten can model our multiplication.

We also learned a strategy to multiply decimal numbers without models.  In this strategy we “dump the decimal” and multiply with the related whole numbers, and then estimate a logical place to return the decimal when we have finished.  For example, 2.3 x 4.2 would become 23 x 42.  This has a product of 966.  Now, we can use front end estimation to place the decimal back in where it makes sense.  In this example 2 x 4 is 8 so our product of 2.3 x 4.2 should be about 8.  This tells me that a logical solution to my original question is 9.66.  We completed practice questions for Friday and reviewed them together as a class.  We will be quizzed on this on Monday and then begin to look at the inverse operation; division.  I suggest each student take time to quickly review how to long divide if they have a few minutes this weekend.

In Grade 8 we spent the early part of the week working on a chapter #1-#3 cumulative review.  The reason for the review is to refresh our memory on what we have already learned so far this year, as our final exam will also be cumulative.  Also, it is a nice, easy way to get back into the groove of mathematics after a 2 week break:).  After our review we completed an activating prior knowledge task together as a class.  The purpose was to recall the formulas we already know for area of a square, rectangle, triangle, and circle, as well as the formulas for calculating the circumference of a circle, as these will be pivotal in success in our new unit.  We also looked at the key vocabulary that we will be expected to use accurately in this unit.  We ended the week by looking at our first lesson, Exploring Nets.  A net is a diagram, made of shapes, that can be folded to make an object.  Also, we looked at how we construct and classify prisms and pyramids.  We will continue to do more of this next week, as well as begin to look at the surface area of right rectangular prisms.  Note:  Students have been given a research project on the subject of area and surface area to do over the next week on their own time.  The purpose is for them to see the connection between the net and the process used when calculating the surface area of an object.  It will be due On January 19th.

Here are some examples of nets for you to see:

In Grade 9, just as with the grade 8’s, we spent the early part of the week working on a chapter #1-#3 cumulative review.  Again, the intention was to refresh what we have already learned, as September seems like so long ago, and our June PAT exam will be an assessment of all the concepts taught.  As well, it helps to alleviate the shock to the system that might occur if we jumped right back into the thick of things right after the break.  After that, we completed a Unit 4 activating prior knowledge task together as a class.  For this task we needed to recall how to solve an equation by isolating the variable, and then verify our solution through substitution,  The key here is to always remember that, what you do to one side of an equation you MUST do the same to the other.  This is because an equal sign is like a balance scale, it communicates that what we have on the right hand side is equal to what we have on the left hand side.  To end the week we began Lesson 4.1 by completing an investigation task relating to tables and the number of people we can fit at the tables.  I encourage you to ask your child about the 3 ways we have learned to represent a linear relation.  Also, have them show you how they can create both the expression and the equation from a diagram or table of values. Next week we will complete some practice questions on Monday, write a quiz on the lesson on Tuesday, and then look at what makes a relation linear and analyze their graphs.

A reminder to grade 9 parents that we have the bottle depot account in Stony Plain under the name Duffield School Grade 9 Trip.  Thank you to those families that have already taken advantage of this!!  Also, our Christmas Dance concession profit was an astounding \$170.85!!  Great job, Mrs. Amanda Smith and her helpers!!

Finally, please check that your child still has a functionally scientific calculator that they bring to class.  There seems to be a large number of students in each class that need to borrow technology on a daily basis, and I only have a few to spare.

Until next week:).