Measuring in a Different Way

In class last night, we measured without a ruler or yardstick. We took our hands, feet, forearm, fingers, and arms to measure objects in the room. While several measurements were close (those that chose the same form of measuremen), they were not exactly the same and the measurements were not exact. This is an interesting approach when teaching the importance of proper measurements. The thought processes behind the differences of proper and improper measurement. Below is a link where a teacher has his students completing this activity.



Measuring with Non--Standard Units

A New Way to See Shapes

Creating Stories

This is a great little video (click the header above) about a different way to use Tanagrams. Usually, these objects are used with seeing shapes differently, how shapes can be made, what fits in an area, etc.

In this video, the students are creating their own mythological story. The students need to keep along the lines of Greek mythology, but other than that, they can make up their creature (it can be a cross between two creatures, or a new god) and create it with Tanagrams. This is seeing shapes differently in a more fun and engaging way. I love this idea.

Practical Tips for Fractions

Learning to Teach

Doug M. Clarke, Anne Roche, and Annie Mitchell wrote the article, "10 Practical Tips for Making Fractions Come Alive and Make Sense." This is an article that can come in use for both new and seasoned teachers. As new teachers, we do not know everything that is out there. We have not experienced much, and our first couple of years are spent learning what and how we need to teach. Seasoned teachers have experienced a lot. These teachers have their groove and feel that they know best. In a lot of ways they do, however, even seasoned teachers can update their teaching methods. The information that we teach is always changing, why shouldn't the way we teach?

10 Tips

1. Give a greater emphasis to the meaning of fractions than on procedures for manipulating them--We need to not worry about "meeting the standards" as much as we need to worry about whether our students are truly understanding what fractions are, what their purpose is, and how to use them.
2. Develop a generalizable rule for explaining the numerator and denominator of a fraction--We introduce telling students that the denominator represents the "whole" and the numerator is the equal parts that fit in. While this may work for smaller fractions that are less that 1, it does not work for fractions that are larger than 1. Instead, the new definition that is suggested is "In the fraction a/b, b is the name or size of the part (e.g., fifths have this name because 5 equal parts can fill a whole), and a is the number of parts of that name or size. If we have 7/3, the 3 tells the name or size of the parts (thirds) and the 7 tells us that we have 7 of those thirds (or 2 1/3)."
3. Emphasize that fractions are numbers, making extensive use of number lines in representing fractions and decimals--number lines allow students to see all the variations that fractions can take, and see how fractions can compare to decimals and whole numbers.
4. Take opportunities early to focus on improper fractions and equivalences--If students are understanding fractions, they can move on to improper fractions. The students who are struggling can sometimes pick up faster by playing games and watching their classmates.
5. Provide a variety of models to represent fractions--Manipulatives, manipulatives, manipulatives.
6. Link fractions to key benchmarks, and encourage estimation--This helps students to learn residual thinking and understand the meaning behind fractions.
7. Give emphasis to fractions as division--I look at figuring out fractions by division sometimes.
8. Link fractions, decimals, and percents wherever possible--These are in everything: clothes sales, gas prices, etc. Linking these items to as much stuff as possible lets kids know that it is something that is important in their life.
9. Take the opportunity to interview several students one on one on the kinds of tasks discussed in this article to gain awareness of their thinking and strategies--Always keep communication open with your students, not only with math strategies (new and old), but with learning strategies for every subject.
10. Look for examples and activities that can engage students in thinking about fractions in particular and rational number ideas in general--Keep it interesting, but, informational.

Manipulatives

How kids can use manipulatives.

https://www.teachingchannel.org/videos/teaching-fractions

Take a look at this video above. Fran Dickinson does a good job explaining how beneficial manipulatives can be. Manipulatives can be used to break down a whole and see the little parts that make it up.

Dickinson taught his lesson in a very confident format, which helped his students have confidence. Fractions are a topic that most people like to run from, including teachers. When we have this aura about us on a certain topic students can sense it. We need to be comfortable with teaching this category so that we can exude that comfort onto the students.

Technology Manipulatives

• ThinkCentral

Why Use Manipulatives?

Why should we have kids use manipulatives?

We do this because it allows students to VISUALIZE a problem and see multiple ways that the problem can be solved. If a student is confused about how fractions work, manipulatives break down the fraction so that they can see all the parts. Fractions are part of a whole, manipulatives can show students all the part that make it up.

13 Rules that Expire

Expiring Words?

The deeper I get into the education field, the more I realize that I have more to learn. Learning how to teach new math concepts is actually a little confusing for me. I grew up with it one way. Now that I'm an adult and about to teach myself, I'm learning that they way I learned is actually not the best. Education is an ever growing and ever changing field.

13 Rules

A breakdown of the 13 Rules:

1. When you multiply a number by ten, just add a zero to the end of the number---while this is true quite often, and can simplify many problems, this particular rule is talking about exceptions, like with fractions/decimals. This is definitely not a rule we can follow when addressing these problems.
2. Use keywords to solve word problems---students need to be sure to look at the entire problems. Key words can be helpful, but they must pay attention to the entire problem.
3. You cannot take a bigger number from a smaller number---kids learn later in their education that this is actually true. So while we teach whole number subtraction in elementary school, we cannot make a blanket statement like this.
4. Addition and multiplication make numbers bigger---This is another thing that coincides with decimals and fractions. Multiplication and addition may just do the reverse.
5. Subtraction and division make numbers smaller---This is not true when dividing negatives, and sometimes with fractions. Numbers can actually come out quite larger.
6. You always divide the larger number by the smaller number---This is just completely false, and students don't even realize they do this regularly because it is not presented as a mathematical problem.
7. Two negatives make a positive---integers can throw this rule through the loop.
8. Multiply everything inside the parentheses by the number outside the parentheses---PEMDAS. If the numbers within the parentheses are being added then this statement is true. However, when the numbers are being multiplied in the parentheses, then they must be multiplied first with each other, and then multiplied by the outside number.
9. Improper fractions should always be written as a mixed number---"This rule can certainly help students understand that positive mixed numbers can represent a value greater than one whole, but it can be troublesome when students are working within a specific mathematical context or real-world situation that requires them to use improper fractions."
10. The number you say first in counting is always less than the number that comes next---When we put a relationship with that number, it could be quite the opposite, like "three dozen eggs is more than eight eggs, and three feet is more than eight inches."
11. The longer the number, the larger the number---0.12345 is much smaller that 0.6. Negative numbers, even in the thousands, will always be smaller than 1. The length of the number has no real bearing on it's size.
12. Please Excuse My Dear Aunt Sally---In a way, order matters. Parentheses, exponents, multiplication, division, addition, and subtraction. However, multiplication and division hold the same weight, as does addition and subtraction. There are problems where both are present and you can take different routes to anser WITHOUT it effecting the outcome. For example, 3^2 – 4(2 + 7) + 8 ÷ 4. This problem can be addressed first by solving the exponents, the addition problem within the parentheses, or simplifying the division section. This problem cannot continue, though, until 2+7 has been solved and that has been multiplied by 4.
13. The equal sign means Find the answer or Write the answer---The equal sign means that both sides are equivalent. 3+4=7 means that 3+4 is the same as 7.

Expired Language

Reasoning About Division

The Old Way

Every week I continue to learn just how much everything has changed since I was a kid in grade school. Growing up, we did math in the standard formats. For me, there was only one way that a problem could be solved. Luckily, that method worked for me and I never questioned it. However, now there are several approaches to take for solving a division problem. The first three that will be talked about are similar. There are only slight changes among them.

Standard Division

This method is what I grew up with. To me, it's common knowledge. Now that I have heard what my teacher has said I can understand why some of my students in the afterschool program I used to work for struggled with this. We teach our students in addition, subtraction, and multiplication to work from the right to left. When it comes to long division, we change direction; we move left to right. Again, this worked for me, and still does. I never questioned with it, and it is a little hard for me to SEE the problems, although I can understand the thought processes behind them.

Greenwood Method

This method seems a little easier to work with. The students do not need to necessarily work the problem out exactly. They make close estimations and work the problems out that way.

Pyramid Model

This is very similar to the previous model, except that the numbers are stacked on top and added together, rather than on the side.

Know, know, know

As is usual, when it comes to teaching, you need to know yourself and your students. Knowing your students is the most important factor in all of this. You need to know how to teach multiple methods of learning because there will be a few students who need a different method. You just have to be comfortable with teaching these methods.

Multiplication Song

2x Table Rap

• Antenna Rap

  I like this video because students love rap. This kind of music always gets kids up dancing and involved. The catchy tune can be easily memorized and they also match the numbers with something that helps to keep it memorized, "jumping 4," "bowling 10," etc.

3x Table Jam

• Jammin' Song

  I like the way this song says the equation, "two 3's is 6." It says that for each part, so students can better understand and visualize what 2x3 actually is.

5x Table Pop

5x Table Song

• This song is made similarly to a singer that kids love. While her actions and songs may not always be the most appropriate for young ears, Miley Cyrus is VERY popular among the little ones. This song, however, introduces more skip counting. They begin the song by including multiplication, but it quickly turns into skip counting by 5's. This is not a song to play at the beginning of the learning segment, however, later it can be introduced and students can have some fun.

Times Tables

Each of these videos has something interesting and unique to the way that they can reach kids and teach multiplication. You have to know your students, though; you have to know where they are in the learning sequence and be careful about what you show.