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"BOO" to Fractions? Recognizing Equivalent Fractions, Reducing Fractions

Here is a Halloween riddle: Which building does Dracula like to visit in New York City? Give up? It's
the Vampire State Building!! (Ha! Ha!) Here is another riddle. What do ghosts eat for breakfast? Scream of Wheat and Ghost Toasties!

Okay, so what do these riddles have to do with teaching math? I have been attempting to come up with ways for my students to recognize fractional parts in lowest terms. As you know from this blog, I have used Pattern Sticks, the Divisibility Rules, and finding Digital Root. These are all strategies my students like and use, but to be a good mathematician requires practice - something most of my students dread doing. I can find many "drill and kill" activities, but they tend to do just that, drill those who don't need it and kill those who already know how to do it. So to drill and "thrill", I created fractional word puzzles for specific times of the year.

The one for October is Halloween Fraction Riddles. It contains eight riddles that the students must discover by correctly identifying fractional parts of words. For instance, my first clue might be:

The first 2/3's of WILLOW. The word WILLOW contains six letters. It takes two letters to make 1/3; therefore, the first 2/3's would be the word WILL. This causes the students to group the letters (in this case 4/6), and then to reduce the fraction to lowest terms. The letters are a visual aid for those students who are still having difficulty, and I observe many actually drawing lines between the letters to create groups of two. 

At first, I thought my students would breeze through the activities, but to my surprise, they proved to be challenging as well as somewhat tricky - just perfect for a Trick or Treat holiday. Maybe this is an activity you would like to try with your intermediate or middle school students. Just click on this link: Halloween Fraction Riddles.

A Go Figure Debut for A Canadian who is new! Plus she teaches high school science!

Jacqueline is from Alberta, Canada and she has been teaching high school science for six years. Like so many of us, her favorite aspect of teaching is building relationships with her students. Jacqueline says her classroom always had a relaxed vibe because she always wanted her students to feel welcome and at peace. She wanted her classroom to be a place where students felt comfortable coming at lunchtime or after school or to just hangout.

Jacqueline also loves creating resources. She was always interested in graphic design growing up and loved how she could implement that into little things like making her lesson slides and notes. This year she took a break from teaching to go back to school for a one-year graphic design program. So far, she has been loving it and is looking forward to implementing her new knowledge into her future classes and lesson creations.

In her spare time, Jacqueline enjoys kayaking, playing squash, and playing board and card games. Often her family gets together and plays games together. Jacqueline has always loved the logic and strategy element of games and she thinks that is one of the reasons she was so interested in teaching science.

Jacqueline creates notes that she hopes students will find aesthetically pleasing and fun to fill out - things like having bubble letters and diagrams to color in. In addition, she has Google slides in her store that go along with the notes so teachers can project those and have students follow along. One thing that is really important to Jacqueline when teaching is making sure her students are actually understanding the information, and not just memorizing it (which she feels happens all too often in biology). She really tries to emphasize developing understanding with her notes and not merely presenting the information.

Jacqueline currently has 72 products in her store, four of which are free. Her featured FREE resource is entitled Planets of our Solar System Notes and Crossword. This nine page resource includes student notes, a teacher key, and slides for teaching. It is notes about the planets of our solar system and includes a review crossword puzzle. This resource can be used by students on Google Drive or Google Classroom. It follows the Alberta Science 9 Unit E (Space) Curriculum.

Jacqueline's' paid resource is over electricity. It is called Circuits and Schematics Notes and Practice and includes student notes, a teacher key, and slides for teaching. The notes are about how to draw circuit schematics with a practice at the end. This resource contains 19 pages.  Five are students note pages; five are key pages and nine are Google slides. It follows the Alberta Science 9 Unit D (Electricity) Curriculum.

If you teach junior high or high school science, you will discover some or many of Jacqueline's resources are a perfect supplement to what you are doing. Check out her store, and definitely download her free resource.

October - Is It "Fall" or "Autumn"? Doing Science Investigations Using Leaves

October has finally arrived.  October means football (Ohio State, of course), cooler weather, and gorgeous leaves. (It is also the month my husband and I were married.) In October, we see the leaves turning colors, and the deciduous trees shedding their leaves.

Another name for fall is autumn, a rather strange name to me. Through research, I discovered that the word autumn is from the Old French autumpne, automne, which came from the Latin autumnus. Autumn has been in general use since the 1960's and means the season that follows summer and comes before winter.
Fall is the most common usage among those in the United States; however, the word autumn is often interchanged with fall in many countries including the U.S.A. It marks the transition from summer into winter, in September if you live in the Northern Hemisphere or in March if you live in the Southern Hemisphere.  It also denotes when the days are noticeably shorter and the temperatures finally start to cool off. In North America, autumn is considered to officially start with the September equinox. This year it was on September 23rd.
With all of that said, the leaves in our neighbor's yard have already begun to fall into ours which aggravates my husband because he is the one who gets to rake them. Maybe focusing on some activities using leaves will divert his attention away from the thought of raking leaves to science investigations.  
Remember ironing leaves between wax paper?  We did that in school when I was a little girl (eons and eons ago).  Here is how to do it.
  1. Find different sizes and colors of leaves.
  2. Tear off two sheets about the same size of waxed paper.
  3. Set the iron on "dry".  No water or steam here!
  4. The heat level of the iron should be medium.
  5. Place leaves on one piece of the waxed paper.
  6. Lay the other piece on top.
  7. Iron away!
You can also use this activity to identify leaves.  According to my husband who knows trees, leaves and birds from his college studies, we "waxed" a maple leaf, sweet gum leaf, elm leaf, cottonwood leaf (the state tree of Kansas - they are everywhere), and two he doesn't recognize because they come from some unknown ornamental shrubs.

Maybe you would like to use leaves as a science investigation in your classroom.  I have one in my Teacher Pay Teachers store that is a six lesson science performance demonstration for grades K-2. The inquiry guides the primary student through the scientific method and includes: 
  1. Exploration time
  2. Writing a good investigative question
  3. Making a prediction
  4. Designing a plan
  5. Gathering the data
  6. Writing a conclusion based on the data. 
Be"leaf" me, your students will have fun!

Terrible at Factoring Trinomials (Polynomials) in Algebra? Try This Method that NEVER Fails!

I spent the summer months tutoring a high school girl who was getting ready to take Algebra II.  She didn't do very well in Algebra I and with geometry between the two classes, she was lost. Since she is a very concrete, visual person, I knew I needed to come up with different algebraic methods so she could succeed. 

When we got to to factoring trinomials, she really needed help as most of the methods were too abstract for her. For those of you who have forgotten, a trinomial is a polynomial that has three terms. Most likely, students start learning how to factor trinomials written in the form ax2 + bx + c

There are several different methods that can be used to factor trinomials.  The first is guess and check using ac and grouping. Find two numbers that ADD up to b and MULTIPLY to get ac in ax2 + bx + c. The second approach is the box method. You write the equation in a two-by-two box. This method is more thoroughly explained on You Tube. Look up factoring trinomials using the box method.  There is also the method of slide and divide which again you can look up on You Tube to see exactly how that works. Grouping is another method. Students need to choose which method they understand and which one works best for them. With continual practice, they will get better and faster at using it.

My favorite method is the one most students understand and grasp. It builds on the ac method, but takes it takes it one step further. It made sense to my student, and she was easily factoring trinomials after only two tutoring sessions.

Because it worked so well, I developed a new math resource. It is a step-by-step guide that teaches how to factor quadratic equations in a straightforward and uncomplicated way. It includes polynomials with common monomial factors, and trinomials with and without 1 as the leading coefficient. Some answers are prime. This simple method does not treat trinomials when a =1 differently since those problems are incorporated with “when a is greater than 1” problems.

Following each explanation (five total) are a set of six practice problems that replicate the method introduced. You might familiarize the students with the method, then assign the problems to practice, OR you might present all four explanations, and then assign the practice problems to review. Some students will catch on rapidly and will not need to go through all of the steps while others will need more repetition and practice. Differentiate your instruction accordingly. Try working in pairs or small groups since students tend to learn from each other.


Included in this resource are the following:
  • A detailed explanation of this factoring method.
  • Five variations when using this method
  • Five sets of practice problems – 30 in total
  • Two sets of review problems – 12 total
  • Answers Keys with the complete problem-solving process