This blog post represents what I have learned in this similarity unit.
What is an Enlargement and a Reduction?
- An enlargement is to make an original object bigger and a reduction is to make an original object smaller.
- We use multiplication to create an enlargement or reduction for an object.
- Examples of enlargements: Any numbers over 1, impropre fractions, percentages over 100%
- Examples of reductions: Any numbers under 1, propre fractions, percentages under 100%
- If the scale is 1 or 100%, that means that is not an enlargement nor a reduction and actually stays the same.
What is a Scale Factor?
- It is a ration that demonstrates two corresponding lengths in two figures.
- For the scale factor, the original length goes on the bottom and the length in the original goes on the top.
Equations with Scale Factors:
- Here is an example of a question including a scale factor.
- What is the actual length of an object if the scale is 1:10 and the length of the object in the diagram in 4?
- Similar triangles are triangles with equal corresponding angles and proportionate sides.
- To figure out if two triangles are similar, you have to create ratios that correspond to the sides. If they equal the same number, they are similar but if they do not, then they are not similar.
- To figure out a missing side length from a similar triangle, you have to use the butterfly technique (multiplying the information in a cross like formation).
- To figure out how to measure and object is taller than you are, you can use this technique by using a mirror.
- You place a mirror on the ground and measure how tall you are from your eyes, the distance between where you are standing and the mirror and the distance between the mirror and the object.
I chose to measure one of the walls from the outside of my house.
Person’s Height: My height is roughly 5’4.5, which the same as saying 163.83cm
The Distance Between the Mirror and I: The distance between where I was standing and where the mirror was placed was 35cm.
The Distance Between the Mirror and the Wall: The distance between where the mirror was placed and the wall was 105cm.
Here is a diagram I created to show my information..
If I look at the middle table, my enlargement is a scale factor of 2. To enlarge my image, I multiplied the given information by two.
My reduction was a scale factor of 0.5. I reduced the given information my multiplying by 0.5.
What is a Linear Inequality?
- A linear inequality is an equation that involves linear functions. An equation also includes one symbol of inequality:
- < is less than
- > is greater than
- ≤ is less than or equal to
- ≥ is greater than or equal to
- ≠ is not equal to
- = is equal to
- A linear inequality ressembles just like the linear equations from the last unit, except with an inequality symbol to replace the equal sign.
What do these Equations Mean?
- If we were to write “x<4”, that would be that a number is less than four. Same goes for “x>4”, which would mean that a number is greater than four.
- If we write “x≤4” that would mean that a number is less or equal to four. Same goes for “x≥4”, which would mean that a number is greater or equal to four.
How do you Graph a Linear Inequality?
- When graphing linear inequalities on number lines, we use different types of dots to identify the inequality sign. if it’s an open dot, we use those for equations that contain less or greater signs. If it’s a closed dot, we use those for equations that contain less or equal to, and greater or equal to signs.
Here are some examples of linear inequalities plotted onto graphs:
(Graph 1: x<-2, Graph 2: x≤-2, Graph 3: x>-2, Graph 4: x≥-2)
How do you Solve Linear Inequalities?
- Solving linear inequality equations is just like solving normal linear equations,
- One thing that always helps me is to remember is
These will help you remember what to do first when you are solving your equation.
- Here is an example of the steps of solving the linear inequality equation “2x+4>3x+1”..
- If an answer to an inequality equation is negative, you have to switch the sign to the opposite sign.
What is a Linear Equation?
- A linear equation is an equation between two variables that gives a straight line when plotted on a graph.
- Here are 2 simple examples of linear equations: 5x=6+3y or y=2x+1
- Here is an example of a linear equation that has been plotted on a graph:
- Linear equations can contain variables that are whole numbers, integers, decimals and fractions. When dealing with linear equations that have fractions, the best way to solve it is to find a common denominator.
How can Equations be Modelled Using Algebra Tiles?
If you don’t have algebra tiles you can always draw out and solve the equation by drawing the tiles on paper. I did not have tiles so below I visually represented how I solved the linear equation.
- When using algebra tiles, coloured tiles are positive integers and non-coloured tiles (white tiles) are negative integers.
- Larger coloured rectangular tiles are used as 1x and the smaller coloured squares are used for 1.
- Larger non-coloured rectangular tiles are used as negative 1x and the smaller non-coloured squares are used for negative 1.
- See photo below:
This is an example of how I visually solved the equation below. I drew it out using algebra tiles.
How to Solve Equations Algebraically?
To solve the following simple algebraic equation I have get x all by itself. We call that isolating the variable.
If you have the equation: 2x+3=7
- I want to get x alone. The first step would be to get rid of the +3 by subtracting 3 (this cancels each other out). I remember that what I do to one side of the equation, I have to do to other so I subtract 3 from 7. Now, I’m left with 2x= 4
- to isolate the x I divide 2 by 2 to cancel each other out (which leaves me with x on its’ own). What I do to one side, I do to the other so I divide 4 by 2 and I get the answer x=2
French Immersion Teacher – Grade 5/6
I chose to interview Natasha because she works with my mom at her school. Ever since I was little, I have always wanted to become a teacher when I grew up. I love working with children and think that teaching would be the best choice for me. I would like to work at the elementary level and even become a French immersion teacher.
I have learned from this interview that this is a job that requires a lot of responsibility and patience, but is a beautiful career because you get to make connections with your students and are able watch your students grow and become amazing people in the future.
- I am passionate about being a teacher because I love being a part of child’s growth and success. I love learning myself, and being a teacher is all about learning new things all of the time.
2.It takes a lot of schooling and post secondary education to become a teacher. I spent time being a TOC before I landed a full time position and the first few years of being a teacher is not easy. There is a lot time spent planning, prepping, assessing, conferencing, organizing, collaborating and providing feedback. Some years are harder than others.
- For someone who is interested in becoming a teacher I would tell them that they are choosing a profession that doesn’t allow for you to clock out when the workday is done. Be prepared to work very hard! However, it’s also the most rewarding profession to be in. You get to work with other awesome teachers and the best part is making connections with your students. There is nothing better than seeing your students grow and learn.
- Yes I would be open to further contact.
(own question) What is your favourite part of the job? I have a few favourite parts. I love working with other teachers. The teachers at my school are great and we collaborate a lot on ideas. I love it when my ex students come back to see me! There’s no better feeling when they come for a visit and to say they enjoyed my class. And obviously my favourite part of the job is having a close connection with my students.
(own question) How many years does it take to become a teacher?
I did the PDP program at SFU after I got my degree. I also went back to university to get my 2 year 5+15 graduate diploma. Some people go to UBC to do their teacher training, others have gone to UVIC.
Sites for pictures: