Working with rates

For our athlete comparison project we will need to do a lot of calculations involving logic, and our understanding of rates and proportions.  Below are the steps we would take to solve a problem involving speed.  Remember the steps are the same no matter what rate you are working with.

Rates, Ratios, and Proportions

We've been exploring multiplicative thinking by exploring rates/ratios and proportions.

Below are some definitions of key words:

Ratio:  A comparison between numbers.  

If we had 10 kids in a group, and 4 had glasses:

We could write this as a part to part ratio:  4 glasses: 6 no glasses

Or it might be part to whole:  4 glass: 10 kids total.  

If we write a ratio as part:whole we can also represent it as a fraction:

4

10 

Kids have glasses

Rate:  A comparison (type of ratio) when we have 2 different units.  The most common of these is speed, which shows a comparison between time and distance.

Other rates include hourly pay ($/hr), bulk food prices ($/kg), or gas mileage (L/km).  

With every rate there are 2 units so there are always 2 unit rates.  

Proportions:  Two ratios that are equivalent are said to be proportional.  This means they are related by multiplication and division.

So for our glasses example if the whole school is in the same proportion as the group 2 out of every 5 kids would wear glasses.  

If there were 500 kids, 200 would wear glasses.

Science

We've been working on a number of tasks as we start to explore the Biology of Cells and Systems

Here's what we've been doing:


1) Adaptation task.  This is a non-research based task that should take a total of 30 -40 min

Identify a need (food, movement, breathing, protection).  Identify at least 3 different organisms.

For each organism, provide a general description (e.g.  where does it live?  What specific challenges would it have meeting this need? )

Identify specific adaptations that the organism has made in order to meet the need they identified

Analyze the similarities and difference between the different ways of meeting the needs between their 3 organisms. 

2) Is it alive.  We've spent a couple of class periods on this.  You should have it finished in your book by the end of next week.

Choose “something” that doesn’t fit nicely into the classifications of living or nonliving.  Possible examples include:

• The Earth
• Viruses
• Artificial Intelligence
• Fire

Your job is to provide: 

At least 3 arguments explaining why your organism is “living”

At least 3 arguments explaining why your organism is “non-living”

This part can be done at 6 detailed point form sentences.  Give your reason, and then explain it.

A final decision

After analyzing your reasons come to a final determination whether your topic should be considered living or nonliving.  Make sure you support your decision with specific reasons. Your final argument needs to be based on the defined characteristics of life.  You can also include your own ideas about what it means to be alive.

3) Biomimicry. This is a task where we will have one or two more classes to work on:

Your challenge:

Brainstorm at least 3 different possible ideas.

On your own or in groups of 2-3 create your own proposal for Biomimicry technology based on 1 of these ideas.

Your technology proposal should include:

- What 'biology' your technology is based on.

- How it works in nature.  Be specific describe the mechanism.  

- The biological purpose it serves.  Think about how it 'elegantly' serves a purpose.  Be specific

- How you would apply the biology into technology.

4)  Finally we are now exploring a task that focuses on Body Systems.  The task sheet will be shared with you next week.

- What problems would it solve

- What advantages would it have

- Why it would be better than a 'traditional' technology.

Average Athlete

We are going to be exploring proportions and ratio by using speed to create projects that try to give an audience a sense of how fast great athletes really are.

Here is the task:

You’ve been hired by TSN to create a visual, that could either be put on the website, or shown on TV, that effectively and clearly compares a rate or speed of a professional or Olympic athlete with an “average” person (you get to choose how to define average).

We started by watching some examples of videos that tried to provide a sense of speed as inspiration and a starting point:

In order to start the project you need to:

1) Identify your "athlete of excellence" - This can be any professional or world record holder.  The project does need to be based on a speed or rate.

Once you've identified your 'athlete of excellence' you need their speed that you will use as your comparison.  For example Usain Bolt's world record 100m time is 9.58second.

2) Identify who or what you will be comparing your athlete to in order to help show how fast your athlete of excellence is.

This can be one person (yourself, your friend, your Mom), multiple people, or an average of people.

Once you've identified your comparison you need to get a speed.  This means you need to find out how fast your average athlete did your identified task.  This might be as simple as finding how fast your run 100m (or using your last years track time) or you might need someone help you measure how fast you can shoot a puck, or throw a ball. 

You will need your data by the end of the week to avoid falling behind.  If you can't choose an athlete or task Mr. Hassett can give you an athlete and sample times.

What Does it Mean to be Alive

As we start to our explore biology we have had some fascinating conversations about what makes something alive.

Here is a video we watched on some of the complexity of defining life.

Watch and think about how you would define life.

What characteristics/qualities would something have to have in order to be considered alive?



We also watched this video on the characteristics of living things:

Now choose “something” that doesn’t fit nicely into the classifications of living or nonliving.  Possible examples include:

• The Earth
• Viruses
• Artificial Intelligence
• Fire
• Someone on Life support

Your job is to provide: 

At least 3 arguments explaining why your organism is “living”

At least 3 arguments explaining why your organism is “non-living”

This part can be done at 6 detailed point form sentences.  Give your reason, and then explain it.

A final decision

After analyzing your reasons come to a final determination whether your topic should be considered living or nonliving.  Make sure you support your decision with specific reasons. Your final argument needs to be based on the defined characteristics of life.  You can also include your own ideas about what it means to be alive.

You need to create a short convincing argument that you will present to your peers (small or large group), that convinces them of your decision.  Be prepared to present this argument to the class.

You will have a more class time to work on this and we will pick a day that you will share.

Similar Shapes

We have shifted our focus towards working with proportions, ratios, and rates. 

Proportional relationships are ones where numbers are related by multiplication and/or division.


To start we looked at 'similar shapes' or shapes that have the same angles, and the same proportions of sides. 

We explored similar shapes, created our own, and used a variety of strategies to identify whether shapes were similar to each other.

In your book you should have the following finished:

1) Using the similar triangle page draw a triangle that is similar to the 4 on the page.  How do you know its similar

2) On graph paper draw your own set of 4 shapes that are 'similar'.  In your book make sure you've proven their similar

- Do they have the same angles?

- Are the side lengths in proportion?

3) Solve the find the fakes sheet.  Record your thinking in your book. 

Biomimicry

We're going to be exploring what we can learn from nature, or the wisdom that nature holds.

As a starting point we are exploring Biomimicry, or technologies that mimic natural forms and process'.

Here are a couple of videos and links with some great examples.






https://synapse.bio/blog/10-biomimicry-examples


Your job is to pick 2-3 examples


For each:

Brief 2-3 sentence explanation of your example.  Make sure to include what problem it is solving.

Is it mimicking: Form, Process or ecosystem

Think about:

What are the advantages of the natural way of solving the problem? 

What can we learn from the natural way of problem solving?

Linear Equations

We've been working on linear equations in the form ax + b = c.  We will do a check in on these equations after the Family Day long weekend.

This week we've started to look at equations that involve division.  No matter what the equation the following strategies always apply:

- The goal is always to isolate x, or get x all by itself on one side of the equation

- You always deal with the constant value with addition or subtraction, before you start multiplying or dividing,

- You can simplify equations by using inverse operations.  For example you can simplify + 8 by using subtraction or 3x (3 times x) by using division.

- An equation is only solvable if it remains balanced.  This means that we need to preserve equality by doing the same operations to both sides of an equation.

Below is a list of steps with an example.  We will be dealing with the first step (brackets) later in the year.

Lab analysis

Both classes have had the chance to have a peer review of their analysis for their labs.  Labs are due next Monday, there will be a folder on Google docs that the lab can be placed in.

Make sure to use the feedback to improve your work.  If you want more feedback share your work with someone whose opinion you trust at home.  They can use the checklist and the exemplar that are shared with you to read your work and provide some suggestions to write the best analysis you can.

Science Labs

We have been working hard at creating our own focused lab reports and analysis. 

The focus for this report is on:

Clear testable problems
Well organized, easy to understand observations
Detailed, specific, accurate and concise analysis.


All students have access to a checklist that will be used to assess their final lab report, including 2 exemplars of an excellent analysis they can use to help them write their own.  It is shared on Google Drive.

We will be doing peer assessment of the analysis early next week.  104 needs to have a rough draft finished by Monday, and 108 will be doing it on Tuesday.  Due to the band concert 108 will have some time on Monday morning to work on their analysis in class.

Translating practical situations into Mathematical language

We continue to explore algebraic relationships and equations.

Below are a list of learning intentions or things that you should understand and continue to practice:


1) Operations with integers.  This includes multiplication/division as well as subtraction/addition

2) Solving for x in an equation.  This includes when there is a negative coefficient beside x (For example -4x - 6 = 14).

We are spending some time looking at how we can take real life situations and translate them into mathematical language.

Here are the examples we started in class.  We will be working on them again tomorrow and then they are homework.

Working with negative X

Based on feedback from exit slips we identified that the biggest challenge students were having involved solving problems that had a negative coefficient for X.

Below are some problems to practice this skill.  Remember, you can solve by using algebra tiles, drawing pictures, or by recording your steps mathematically.  Even if you don't use the tiles create a mental picture of whether your tiles would be positive or negative to help you organize your thinking.

Remember the learning intentions:

- Be able to model how to solve linear equations with algebra tiles
- Be able to find x for a given equation

Your final answer should be in the form of a mixed number.  Remember be careful to watch your signs (is x positive or negative)

Questions:

From class:

7 - 2x = 9                4 - 8x = -23            6 - 5x = 18          -9 - 8x = -47              -3 - 4x = 76


14 - 12x = 107                   -7 - 3x = 4


Some extra questions:

5 - 3x = -7                 -4 - 5x = 16          7 - 4x = 28            5 - 6x = 41            10 - 3x  =   -11


5 - 4x = 21                7 - 3x =  -33         8 - 4x = 55            3 - 7x = -34             9 - 4x = -55

Mix and Flow experiment

In Science we are creating our second lab.  Based on how our first labs turned out we are focusing on 3 main components:

Creating an experiment focus:

Questions: Testable and specific (focused)

Usually centred on a theory about a relationship:

How does ______ impact _____

Is there are a relationship between ____ and _____

Observations (Measurements):
Specific and Precise

Organized and easy to read  - tables, charts, graphs

Focused on the question

Analysis:  (Conclusion)

- Detailed and thorough (See checklist)

At home share what your problem is and what you've discovered so far. 

This week we're going to make sure that we've presented our results/observations in a clear and easy to read manner.  Feel free to share your results to someone at home and ask them:

- Do the results match the lab question?

- Are the results organized and easy to find?

- Can you easily find the important information?

- Could I look at the results and easily see the difference between each variable?

We're also going to be looking at two key concepts/calculation:

Density and Concentration.  Can you define each word?

Finding the Unknown

We've been exploring how we can use algebra tiles to find unknown numbers in linear equations.

So far we've been working with questions in the form of:

Ax + B= C

For example:   5X - 3 = 12

Can you model how you'd solve that problem using tiles.

Below are a list of questions we've been working on in class.  The left side is a little easier.  You should be able to do at least 10 of these questions.  You can finish them all if you need a little more practice.

Integers

We've spent time exploring how to multiply and divide with negative numbers.

The learning intention is to both:

- Be able to model how to multiply and divide integers (negative numbers) accurately using a number line

- Be able to efficiently calculate multiplication and division of negative numbers based on patterns (e.g. A negative times a negative will be a positive product)

Below are the questions we started in class (apologies about the messy writing) . You need to model at least 1 multiplication and 1 division using a number line.

You need to find the product or quotient to all of them (not necessarily with a number line)

Welcome back

Welcome back

It's been a great start. Here's an update of some of the stuff we're working on:


Math:

We've been exploring how to represent the relationship between numbers in t-charts, equations, and graphs.  Looking a the list of numbers below:

Can you write the equation?
What do you know about the graph?

                       X                                Y
                       0                                -4
                       1                                 4
                       2                                12
                       3                                20


You will need to do a graph to show the relationship between the figure number and the number of shapes for your final visual pattern assignment.

The final visual pattern assignment is due on Monday the 13th.  The checklist for what you need is shared on Google Drive.


Science:

We've been talking about what makes an excellent or 4 scientific discussion or conclusion.  We've created checklists that will be used to assess your ongoing conclusions.

There is a different one for 104 and 108, but both are very similar.

108

- Explanation that includes WHY!!!!

- Clear diagrams that support your explanation.

- All the information is useful -  concise

- Scientific vocabulary

- Accurate 

- Detailed

- Well organized and easy to understand

104

The explanation is detailed - includes as much information as you can

- Constantly ask and answer :   "WHY!!!!"

Labels

Visuals support the explanation

Explanation is concise - to the point

Use accurate vocabulary

Makes sense

Accurate based on correct scientific information.