Inductive vs. Deductive Reasoning

One of my favorite Geometry lessons is the one introducing inductive and deductive reasoning. It’s fun and engaging. I like to open the lesson by showing the students a YouTube video: Monty Python Deductive Reasoning (Should be called Inductive Reasoning, but oh well!)

This lesson has many opportunities for discussions on how people reason and come to the wrong conclusions. You can bring up the media, social media, racism and many topics where people might come to the wrong conclusions. I also like to talk about predicting weather. The topics are endless.

My lesson from Teachers Pay Teachers has several handouts that can be added to the student’s interactive notebook. One of the activities is to have students cut out the examples seen below and place them with the correct headings: Deductive or Inductive.

The lesson also includes some 12 task cards. I like to group the students into fours and have them turn their desks together. They put the task cards in the middle of the tables and select a card, answer it on an answer document and then place the card back into the middle of the pile. Here’s a sample:

Finally, the lesson has a short 3 question worksheet that I like to use as a group quiz. I have the students work together through the quiz. They all have to write on their own paper. I assign each person a letter and they put it beside their name. After about 15 minutes or less, I spin a spinner that has A, B, C, or D on it. The person with the letter I land on, puts their paper on top and that is the one I grade for the group. I tell them this ahead of time. This gives them incentive to work and make sure everyone is participating.

Here is a copy of the resource that I have on TpT. Take a look. It’s also a part of a unit as well as in my Geometry Curriculum.

Study Guides for Math Portions of College Entrance Exams and College Readiness Exams

When you think of college entrance exams, I’m sure the SAT, PSAT and ACT come to mind. More high schools are offering these tests during school. Some students will take these tests 2 or 3 times or more. Why? Because they need a certain score to gain entrance into a school or to apply for a scholarship. The PSAT is a nice warm up to help students know where they stand before they take the real thing.

Every October, schools offer the PSAT/NMSQT to their juniors. Although sophomores can also take it , only the junior scores count toward the National Merit Scholarship competition. Schools are also starting to offer the PSAT 8/9 (for 8th and 9th graders) and PSAT 10 (this is the regular PSAT, but does not qualify for the National Merit Scholarship competition).

It’s good that schools are offering these tests to their students so they can see the format of this test and the way questions are asked. The SAT is a very important test for students planning on going to college. Colleges use the SAT (and/or ACT) to make admission decisions which makes these tests very important for students that want to go to a certain school.

The ACT is another college entrance exam. Some schools are offering this test during the school year to their juniors. The ACT is different and has a science section where the SAT does not. Again, this test requires practice and there is no pre-test like the SAT.

There are a couple of more tests worth mentioning. Nowadays, colleges want students to take a college readiness test to see if students have the skills to start taking college courses. The ACCUPLACER is used by many states. Texas has their own college readiness test called the TSI. Both the ACCUPLACER and TSI are similar. Students scores will determine if they are able to start their English and Math courses on level or if they will need to take some remedial classes first. The ACCUPLACER and the TSI can be taken as early as the 9th grade and in some cases, earlier. Early College High Schools have their students take the college ready tests the summer before their 9th grade year to give them plenty of time to retake them until they pass.

I’ve been teaching high school math for 30+ years, and it was not until I became a teacher at an Early College High School that I became fully aware of all the tests students take. I realized that I needed to be the one to help them get to where they need to be. I know how important it is for high school teachers to help incorporate college entrance and college readiness practice into their curriculum, especially math teachers. I’ve spent a lot of time creating many resources to do just this.

Below, you will find links that will take you to my Teachers Pay Teachers Store where I sell these resources. There are many options, but the option that I recommend if you are planning on doing a ton of review is the Math Test Prep Bundle for College Entrance. It contains the SAT Bundle, ACT Bundle and a TSI/ACCUPLACER Bundle that you see below:

College Readiness and College Entrance Exam Bundle
ACT Math Prep

3 Reviews – 86 Questions

SAT/PSAT Math Prep

6 Reviews – Worksheets, Bellringers and a 5 Week PSAT Plan.


7 Reviews!

I’ve recently started a digital version of the TSI/ACCUPLACER College Readiness Bundle (this is the exact same, but for a digital classroom setting). It is incomplete, but will be finished by the start of the next school year.

It is so important that math teachers take the time to prepare students for their future. Start making a plan now on how to meet the needs of your students. We all have different situations, but I’m sure you can find a way to include study material that will increase your students’ chances of success on college entrance exams and college readiness exams. Good Luck!

Quadrilateral Unit

Quadrilaterals are a big topic in geometry. There are so many things to know that it tends to get confusing for students. Students have misconceptions from their middle school math classes that are hard to overcome such as that a square is a square and only a square. A square is no way, no how a RECTANGLE! OH My!

I created a quadrilateral unit where I begin with a card sort activity. The cards have different shapes on them and the students are asked to separate them into parallelograms, trapezoids and other major shapes. This year, I decided that they should have a “for sure” pile and also make a “not sure” pile. I love listening to the conversations. Below is a pic of some slides I show:

The next thing that I like to do is discuss the Venn Diagram for Quadrilaterals. For some students, this is a breeze but for others, they are totally confused on why I’m using ovals in a diagram to represent groups of quadrilaterals. It’s best to make sure your students remember what a Venn Diagram is. I like to give an example of a region with math students overlapping a region of biology students to show that the overlap means all students taking both math and biology. Look at the Venn Diagram below. Can you figure out what quadrilaterals go in each region? Can some go in more than one spot?

This unit is the best place to use always, sometimes and never questions and if the students understand the Venn Diagram, then the always, sometimes and never questions are pretty obvious. It’s also a good time to talk about what does opposite and consecutive mean? Many of the definitions and properties use this terminology, so I spend time helping them understand where opposite sides and angles are versus consecutive sides and angles.

I like to get the kite and trapezoid out of the way first, so I can spend most of my time on the parallelograms. Students are not familiar with the kite, so this is usually a brand new topic for them. They think they know what a kite is but usually they are getting a rhombus confused with a kite. Each time I present a new quadrilateral, I give the definition and then we try to find other things that are always true about the shape. This is cool, because you get to talk about the diagonals and how they create congruent triangles. I also try to put proofs into the lesson as much as possible.

During the trapezoid part of the lesson, there is a discussion on isosceles trapezoids, midsegments of triangles and medians of trapezoids. A good reminder at this time is how trapezoids are related to parallel lines cut by a transversal, so that they can understand that there are some same side interiors that will be supplementary. Again, there is so much information, that its hard to know when to stop. Trapezoids could be a two week lesson if you let it, but I keep it to two pages. After the trapezoid lesson and the kite lesson, I give the students some practice on finding various parts of the shapes.

The rest of this unit is spent on parallelograms. Each time that I get to a new shape, I call it a “Parallelogram Study” or “Rectangle Study” etc. I let the students work through the definitions, properties and proofs. The other aspect of this lesson is discussing the coverses of the definitions and properties. This helps the students realize that if you see a shape and you are not sure what it is, then what is the least information you need to decide it is a rectangle for example.

The lesson concludes with practice on the parallelograms. There is a page of work where some major algebra topics are practiced. For instance, there is a rectangle problem where the students have to set up and solve a system. There is a rhombus problem where the students have to solve a quadratic. There is a square where the students find the length of the diagonal using the variable “s” for a side. This problem is a lead up to 45-45-90 triangles. I usually have to help the students with this whole page, but I don’t mind. Since I’m an Algebra II teacher as well, I like my geometry students to see as much algebra as time allows.

There is a set of task cards that act as a review for the Quadrilateral Test at the end of the unit. The test is only two pages long, but it is pretty involved. There is a major problem where the students have to find quite a few things. The picture of the problem is seen below:

Finally, there is another quick assessment that I use as a retest. All answer keys are included. It usually takes me about two weeks to get through all the work plus a couple of extra days to review and take the test. I love this unit. The information is extensive and I love how it hits on previous geometry and algebra topics. If you are interested, please check it out in my store. Click the pic below to go see the Quadrilateral Unit. If you would like to read more about my geometry curriculum, I have a blog post that you can read here: Geometry Curriculum for the Year.