Converting fractions into...Decimals!

For this week’s post, I wanted to explore fractions again, but this time converting them not into percentages, but into decimals.

To convert a fraction into a decimal, you take the numerator of the fraction and divide it by the denominator.

It might help to review or have a visual aid (like Trenice referenced in one of her blog posts) that reminds students that the denominator is the bottom number of the fraction and the numerator is the number on top.

When converting a fraction to a decimal the fraction bar is the same as a division sign:

a/b   =   a ÷ b 

On https://www.math-salamanders.com I found these terrific fraction information cards that I will definitely be using in my classroom and to brush up on y understanding of the topic. What I really liked about these cards is that they have multiple representations of the same value. This can help students connect the relationship between, for example, 3/10 equalling 0.33 and 30%

Fraction	Equivalent to	Decimal	Percent
1/2 2/2 1/3 2/3 3/3 1/4 2/4 3/4 4/4 1/5 2/5 3/5 4/5 5/5 1/6 2/6 3/6 4/6 5/6 6/6 1/8 2/8 3/8 4/8 5/8 6/8 7/8 8/8 1/10 2/10 3/10 4/10 5/10 6/10 7/10 8/10 9/10 10/10	1/2 1 1/3 2/3 1 1/4 1/2 3/4 1 1/5 2/5 3/5 4/5 5/5 1/6 1/3 1/2 2/3 5/6 1 1/8 1/4 3/8 1/2 5/8 3/4 7/8 1 1/10 1/5 3/10 2/5 1/2 3/5 7/10 4/5 9/10 1	0.5 1.0 0.333 0.666 1.0 0.25 0.5 0.75 1.0 0.2 0.4 0.6 0.8 1.0 0.166 0.333 0.5 0.666 0.833 1.0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0	50% 100% 33.3% 66.6% 100% 25% 50% 75% 100% 20% 40% 60% 80% 100% 16.6% 33.3% 50% 66.6% 83.3% 100% 12.5% 25% 37.5% 50% 62.5% 75% 87.5% 100% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Math Joke of the week:

What did one decimal say to the other?

Answer: Did you get my point?

Perspective time.....I've been writing and thinking a lot about shapes, volume, the Golden Mean...these are elements of art and how math shapes the world around us. With them, we can create on a flat 2-dimensional piece of paper something that comes to life and has depth.

Aside from shadowing and light what helps our eyes and brain see 3d forms on flat paper is perspective. I haven't been able to try this yet, but, as I was thinking about perspective and prospective students I wondered if this might be another way to help students who don't think they can be good at math. A student can observe that an object that is farther away looks smaller. They can observe the shape of the object in relation to itself and the objects around it. There is familiarity in these observations because we observe them without realizing it every day. It's really an easy way to have the students connect that their visual art brain has been working the math brain all along.



Perspective can be found by using the X Y Z axis. While it is important for the student to be able to plot a point on a graph, it's also equally important to show them how math is working all around them.

A cute saying I ran across on www.gradeamathhelp.com that might help the students remember which axis is which was x to the left and y to the sky. It might lack a little directionality, but it can help them get started.

The x y axis is also known as the coordinate plane or cartesian coordinate system. Every point in space, on earth or in your room, has two coordinates which place it uniquely in that spot. When we look at google maps to find the location of the new trampoline park we sometimes see a string of weird numbers with an N or W appended to them. These are the coordinates of the trampoline park's location on earth's x y axis that defines it as being in your town rather than on an island in the South Pacific. Pretty cool, huh? Starting simple is always good. 

A popular technique to learn how to use the x y axis is to draw and number it and then count up the y axis, mark it and then count over on the x axis and bring your finger up till it meets the line that marks the y coordinate. 

Math Joke of the Week:

Q.What do you say when you see an empty parrot cage? 

A. Polygon.

Last post I talked about shapes. In this post, I want to explore volume. This was a topic that was difficult for me as a student so I really wanted to review it and spent quite a bit of time reading and practicing. I found a few really great resources to help explain how to find the volume of an object.
From what I read, starting with a cube makes it easier for the students to associate the shape to the equation. I think it would be helpful to also have manipulatives for them to build and measure. One page had an example of using sugar cubes...though I'm sure students would love that...I think that having a class that energized would be a unique experience I'm not sure I want to have!

How to find the volume of a cube or a rectangular box of tissues

Volume of a Box 



 

Volume= l x w x h

When trying to find the volume of a box we have to multiply length x width x height
So if our box of tissues was 10 inches long, 4 inches wide and 3 inches wide we would have the equation 10x4x3=120. For the area of a box, it doesn't matter what number is multiplied first, the sum will be the same.

Volume of a Cylinder 

Volume = πr²h

The formula to find the volume of a cylinder is similar to that of a cube because you are using multiplication. The big difference is that you are using the radius squared as well as π, two numbers that students might be less familiar or apprehensive using. 

The equation we would use is 3.14 x radius x radius x height so if our cylinder has a radius of 4 inches and a height of 6 inches we would have the equation 3.14 x 4 x 4 x 6= 301.44.

Volume of a Cone

Volume = 1/3πr²h

Now, we have to change things up a bit when we get to the volume of a cone and do some division! We also can use the Pythagorean Therum to find the slant, pretty cool stuff! The equation we would use is very similar to the one we used to find the volume of a cylinder with the important addition of division, 3.14 x radius x radius x height÷3

Math Joke of the Week: 

Q: How do you make one vanish? 
A: Add a 'g' to the beginning and it's gone!

I thought it would be interesting to follow the idea of math and how it applies to the world around the students. One assignment that my sons loved was finding shapes hidden around the house. This was like a really fun treasure hunt for them. For them, the assignment was done almost too quickly and their papers were filled with all the places they found circles, triangles, rectangles, and squares. The assignment reinforced the shapes they had already learned and it helped connect the idea that the world is made up of shapes. Further, this activity also began to show that shapes can make up 3-dimensional objects that they would learn about later. 

In looking for other activities to help students solidify their understanding of shapes I ran across this neat worksheet:

What I liked about this worksheet was that it engages the student to use their higher cognitive thinking skills rather than just identifying what shape is presented and could be used as a check in to see that the students have a concrete understanding of shapes.

Math Joke of the Week: 

What kind of tree does a math teacher climb? Geometry.