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.