Ms. Bearse's Site

We have some sprouts!  We now will start measuring their growth each day and then we can figure out the growth rate.

We have been practicing representing expressions with algebra tiles.  We are getting pretty good at it.  Now that weare solving equations, these representations are becoming useful yet again.  We put a popsicle stick as the equal sign, and have to do the same thing on each side, always.  We can add blue or red tiles to make zeros, or divide up both sides into groups to simplify equations.  
This is 2x=8. To simplify it, we can divide each side in two groups and we can see that 1x=4.

Here we have variables on both sides of the equal sign.  Our goals are as follows

1. Get all variables on one side
2. Eliminate the constant that is on the same side as the variable
3. Eliminate the coefficient beside the variable.

So this equation is 5x=3x-2

We can simplify by either removing 3 red rectangles (3x) from each side, or by placing 3 blue rectangles (-3x) on each side.

This will leave us with 2x=-2 and we split each side up into 2 groups to see that x=-1

Using algebra tiles helps us see what we are doing, and helps us understand.

Lots of assessments happening in room 208 these days.  We’re using our resources, and working hard to communicate what we understand.

The next test is Friday.  Here are the things you’ll need to know.

We are working on surface area and volume formulae for various solids.  Today we looked at spheres and pyramids.

To calculate the volume of a sphere, we used displacement.  We submerged a tennis ball in a displacement tank.  The water displaced overflowed into a juice concentrate container that has been cut so that the height and diameter are equal.  The juice concentrate container was selected as it has the same diameter as the tennis ball.  We can substitute 2r in the place of h in the formula for the volume of a cylinder.

Since the displaced water (the volume of the sphere) is 2/3 the volume of the cylinder, through a bit of calculating we can derive the formula for the volume of a sphere.

We also looked at the area of a sphere.  We used an orange to help us.

The diameter of the orange is close to 8cm.

We then peeled the orange and put the peels into a rectangle.  We know how to calculate the area of a rectangle.

The next step is to make a relationship between the area calculated, and the diameter squared.  We have to compare square units to square units.

The factor we found was always around 3.  This value should be pi.  Since the sphere is not exact, and neither is the rectangle, we don’t expect our pi approximation to be exact either.

We then used some algebra and exponents to derive the formula for the surface of the sphere.

Our pyramid exploration was open ended.  The restrictions were that they needed a square base, and the height needed to be exactly 8 cm.

In order to make the pyramid actually 8cm tall we need to calculate how tall each triangle face should be.  We use the pythagorean theorem to do this.

After a tough quiz today we spent some time working on some puzzles.

We are exploring exponents and algebraic expressions.  We are looking at what an exponent means, and how coefficients change expressions, and how important brackets are.  We are representing coefficients here.  The corfficient shows how many of someing there are.The next set show what thee exponent 2 means.  It makes the model a square.  The coefficient, not in brackets, indicates how many squares we need.

Here is another example.

When the coefficient is a fraction, we need a fraction of the square.
An expression with a coefficient in brackets, and an exponent outside changes things.  The base of the exponent 2 in this case is 2x.  This means the side length of the square is 2x.  You will notice that this is equivalent to 4 x squared.

A similar relationship extends to the following…

An exponent of 3 makes the model a cube.

A coefficient outside brackets shows how many cubes to make.

And if the coefficient is in the brackets it shows the side length of the cube.  Here 8 x cubes could fit inside this bigger cube.

We are attempting to build (3x)^3 here, it’s a big challenge!  We need to make 27 cubes all linked up to make a big cube

Here is a tiny cube, one eigth of the x cube.  Note how (0.5)^3 is equal to 1/8.

We need to remember to pay close attention to the power, the coefficient, and whether there are brackets!

We unwrapped our beans today and were thrilled to see so many roots.  

We planted the beans in soil, marking the type of bean on a popsicle stick.

We have a windowsill garden now.  We are watering each day, and will keep track of the growth when we see it.  The goal is to determine the growth rate of each type of bean, and compare them.

We experimented today with algebra tiles.  The goal was to make squares.

We are connecting the dimension of the square with the polynomial that represents the area.  We talked about perfect squares and difference of squares today.