Another Internet Resource

 I was out looking for additional information on using project based learning in Math because that is apparently one of the goals of the school.  In the process, I stumbled across the K-12 Internet resource center site. 

According to the website, it has over 3500 web and video resources along with over 240 lesson plans which sounds quite impressive.  So I checked the lesson plans.  They have the lesson plans subdivided into English, math, science, history, and other subjects. So of course, the first one I looked at was math.

The math lesson plans offer me the opportunity to drill down even further by grade levels. If you don't filter before going further, you are taken to a page with the filters across the top and a list of places with grade levels and if there are lesson plans or videos associated with the place.

After checking out several sites are actually sites that have some free materials but may ask one to subscribe to get all the benefits. However, many sites are totally free with worksheets, videos, and activities.  There are quite a few nice resources to get ideas, find lessons, etc.

I also did a general search on math to see what that brought up. The first couple or three listings were sites to show how certain math words are used in real life.  Many of the words are associated with physics but there was also a link for words used in geometry. Then I came across a nice place for math worksheets but they offer both lessons and practice so that makes it nice if you have a student who is a bit more advanced and needs work beyond the others in your class.  They can read the lesson that has a couple of problems and the problems are explained with quite a bit of detail. 

One interesting link was to the Math Learning Center which has lots of free materials including books, worksheets, and so much more.  The one thing that caught my eye was two books on algebra through visual patterns.  I checkout the free downloadable pdf and liked the way every lesson is detailed with every step you need.  I've often wondered about how to present certain concepts and this offers some different ways.  I like it.  This site has materials for grades K to 12 and it is well worth checking out.

There is even a link for a math dictionary for the younger children.  I will say that the definitions listed are not always easy to read for the really young children, it would be nice for older kids.  In addition, there is a link to a place with all sorts of math posters that could be downloaded and used in the classroom.  

This is a site well worth checking out because it has math resources that I've never seen before.  There are just too many to talk about here in my blog so check them out yourself and see if you find activities and such that you can use yourself.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

 If you laid all the iPhones and iPads end to end that are sold in one year, they will cover half the circumference of the earth.  So if the circumference is about 25,000 miles, how long would the line of iPhones and iPads be in kilometers?

Warm-up

 If an Olympic swimming pool is 164 feet long and a beaver can swim the length 16 times without taking a breath, how far can he swim in miles before taking another breath.

Ways To Improve Student Engagement.

 Sorry about yesterday.  I live in a small place in Alaska that has at best 2G phone service and internet that can be problematic.  It went down after I'd gotten my first entry for the week and went down right after so I couldn't do anything, even at work. So I am back and on time with my Friday entry. Today, I'm revisiting student engagement since that seems to be an ongoing struggle.

Fortunately, there are some things teachers can do to engage students so they are more involved with our lessons. One of the easiest things is to use manipulatives either virtual or physical.  Don't be afraid to use manipulatives in middle or high school since they can be used for multiple situations. 

For instance, grab some of those manipulatives that are small cubes, strips of 10, and squares of 100.  Instead, use the small cubes to represent numbers, the strips represent the x's and squares to be x^2.  You can use them to teach binomial multiplication and trinomial factoring.  You can also use them to teach combining like terms in algebra.  If you have two different colored sets, one set represents positive and the other negative.  I've have also used these for x^3 by combining x^2 with a single x to make x^3.   This type of manipulative can also be used to help students visualize properties of exponents, the distributive property, and even basic fractions.

In addition, it is important to provide differentiated instruction since most of us have students at a variety of levels even though they are in the same class. Sometimes, it can be instruction so one starts with the basics for those who need it, moving up to the more complex application of the same concept for those who are more advanced.

Don't forget to include math games.  When students are having fun, they really enjoy themselves.  One can use Kahoot, Quizlet, or other type of online game.  One can also arrange scavenger hunts, gallery walks, and so much more. 

Furthermore, take time to show how math is related to the real world.  Let students do activities where they are involved and consider assigning project based learning to have them more involved.  Due to a Covid outbreak, I have less than half of my normal number of students, so I am having them take recipes, enlarge them, calculate ingredients in cups, pounds, gallons, and quarts as if they are a real bakery.  Once they figure out what they need each day to bake 1025 loaves of banana bread, they will calculate the cost of purchasing the supplies needed to make that.

Finally, provide opportunities for students to explain their thinking to others. When you use word problems, substitute names of students so it is more relatable and use places they know.  When I have automobile problems, I usually have to rewrite them to use things like snow machines or boats since that is the preferred method of transport in places I work.

Give it some thought as to how you can get students more involved.  Let me know what you think, I'd love to hear.  Have a great weekend.

Ways To Teach Fractions In Middle School.

 

One quick way to find out if you middle school and high school students know fractions is to ask them to make a square that is 3.5 by 3.5.  I did that for art and a few of my students didn't know they should start at zero.  They ran their lines from one to three and something.  Others weren't sure where the 1/2 mark was, if there was no 1/2 written.  This showed me they didn't have a firm grasp of relating fractions to a ruler which acts as a number line.

Although, many of the methods mentioned are used in elementary school, they can be used in middle or high school with a bit of modification.  It is still highly recommended that students connect from concrete, to visual, to abstract for the best way to fully understand the topic.  We know that when students use physical and visual representations, it helps them build fluency.

One thing we often forget when teaching fractions is that in addition to being part of a whole, they are also units in and of themselves.  So the denominator is the unit and the numerator is the number of units. So when we see 3/2, it means three units that are say 1/2 inch wide.  It is also 1 1/2 or one whole and half of a whole so many fractions have multiple identities. The reason to show fractions on a number line is that it shows they can be counted.  It is important for students to understand that 1/denominator is the basic unit for this fraction.

Furthermore, it is important students understand equivalent fractions for instance, if you fold a paper in half and color in the half, it is the same area as if you folded a paper in four and colored in two of the squares, or folded it in eight and colored in four.  Although they look different, they are really the same amount.  In addition, this shows that there are multiple representations of the same number which is important for changing fractions so they have the same denominator.

Many of these activities can be done via paper folding, tape diagrams and circles, area models, and number lines so students see fractions as units and numbers, as equivalent fractions so they see that one fraction can be represented in more than one way, and then add, subtract, multiply, or divide fractions.  When I researched this, I ended up with some great ideas to help me provide scaffolded instruction for a young man who seems to have to idea on how to do fractions without a calculator.  So I will be applying them. Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

 

In 2010, a study was done to see who texted more, girls or boys?  They found that girls texted about 80 messages per day while the boys only texted 30 per day.  What percent of the girls texting rate did the boys text.  

Warm-up

 If there are 27 bones in each hand, including those in the wrist and there are 206 bones in the body, what percent of the bones are found in the hands?