Making Math Matter: Using Other Subjects to Build Meaningful Mathematical Connections

One of the most effective ways to engage students in mathematics is to show them that math is not an isolated subject. Every school day, students move from science to history, language arts, and social studies, yet they often fail to see how these subjects connect. By intentionally incorporating ideas from other disciplines, teachers can transform mathematics into a powerful tool for understanding the world.

Science provides countless opportunities for mathematical exploration. One fascinating example comes from astronomy. Students studying the solar system often learn that planets do not travel in perfect circles. Instead, their orbits are ellipses. In analytic geometry, an ellipse can be modeled by the equation:

X^2/a^2 + Y^2/b^2 = 1

Since a represents the semi-major axis and the b represents the semi-minor axis, students begin by looking up the major and minor axis of each planet in the solar system.  Then they determine the an and b for each planet before actually calculating the orbit. In addition, they can compare the nearly circular orbit of Earth to the more elongated paths of other planets. This exercise can be done with scientific notation so students can see when scientific notation is used.  Suddenly, students see the way our solar system works.

History offers equally meaningful mathematical applications. Rather than simply memorizing dates and events, students can analyze historical data using percentages and ratios. Consider the impact of World War I or World War II. Students can calculate what percentage of a country's population served in the military, what percentage volunteered before conscription, or what percentage of soldiers lost their lives during the conflict.

To introduce the activity, students can practice on hypothetical situations. For example, if a nation had a population of 50 million people and 5 million served in the military, students can calculate that 10% of the population served. If 400,000 soldiers were killed, students can determine that 8% of those who served lost their lives. Then students could look up the actual information for their country be it the United States, Australia, New Zealand, or the UK. 

Once they've researched the numbers, they can calculate the statistics for the number who served in the military versus the percent who died.  In addition, teachers  can also ask students to compare casualty rates between countries or between different wars, encouraging thoughtful discussions about the human cost of conflict while reinforcing proportional reasoning and percent calculations.

These lessons also strengthen students' data literacy. Students learn that statistics tell stories, but only when interpreted carefully. They begin asking deeper questions: Why were casualty rates different? How did population size influence military service? What factors affected survival? Mathematics becomes a tool for historical investigation rather than just computation. Another possibility for history is having students calculate how fast the Japanese balloons traveled to Oregon or Alaska from Japan, or how long it took the mini submarines travel to Pearl Harbor. 

Connections extend well beyond science and history. In geography, students calculate map scales and distances. In economics, they examine inflation, taxes, and compound interest. Physical education provides opportunities to analyze heart rate, speed, and averages. Art introduces symmetry, tessellations, proportion, and geometric design. Even literature can include graphing character relationships or analyzing patterns in poetry.

These interdisciplinary experiences help students understand that mathematics is the language used to describe patterns, solve problems, and make informed decisions across nearly every field of study.

When students recognize these connections, engagement increases because the mathematics has a purpose. Instead of asking, "When will I ever use this?" they begin asking, "What can this math help me discover?" That shift in thinking is one of the greatest rewards of cross-curricular teaching. By building bridges between mathematics and other subjects, teachers help students see that math is not just another class—it is a way of understanding the world around them. Let me know what you think, I'd love to hear.  Have a great day.

Making Connections.

  We all know how important it is for students to make connections to prior knowledge, to life and the world around them.  The other day, I realized I have to teach my students to learn to connect seemingly different things. 

The idea came from two sources.  The first is a book I'm reading called "Writing on the classroom wall" by Steve Wynborny who also does those Splat activities.  He said "Learning is about making connections." The other is my mother who talks about relatives and always includes the information of how they are related.  Always.

So I realized I needed to start getting my students thinking in terms of connections but that isn't easy because they've never had to think much in math till they got to my class.

I started this past Monday.  I wrote Steve's sentence on the board and explained we were going to spend the week tackling this.  So I used the warm-up for introducing this.  I love that it causes them to really think about what they are doing and I suspect they are doing some higher level, critical thinking.

This past Monday, I asked them to find the connection between two drawings.  They gave the surface answers like "It has a bunch of lines."  or  "They are both purple.".  I told them that is not a connection, that is a physical description.  After letting them struggle for a bit, I asked questions and got them to the solution of they are connected because of multiplication. 

The next day I asked them to explain how the moon and the oceans are connected. Many  of them googled it before writing down a complex answer on gravitational pull, etc.  Some discussed the size, some said I don't know.  I told them they are over thinking it.  One simple connection is all they need. Finally someone called out "tides".  I pumped my fist.  That was the break through point.  They started to look beyond the surface.  Some even started looking deeper.

Another time, I asked for a connection between music and cooking.  In addition to fractions, I got things like improvisation.  In jazz and in cooking you create your own "recipes" for the final product.  You have the guidelines to do it but you adjust and create something new within that frame work.

I had a few things like the tower of pisa and a can of coke.  They took to the internet to look up pictures so they could compare the two.  The universal conclusion was they are connected by their cylindrical shape.  Another was a clown and Rudolph.  Most everyone said the red nose but one girl said she was looking for a different connection.

This has been a great week doing it because my students are talking more, checking out the internet, and looking for those connections.  The next step is to start asking for connections in regard to the math I teach.  This is going to be much harder but it will happen if I take them through it a step at a time. 

It is going well and I like this better than my usual warm-ups because they are more involved and really thinking.  Let me know what you think.

Revelation

  Today, I started teaching function notation to my Algebra I classes.  They got as far as learning to take the value given and substituting it into the equation to get an answer.

After class, I realized I need to take this one step further by having students connect the input and output as giving a location on a line.

I fear I am guilty of teaching functions, function notation and linear equations as separate entities rather than showing their relationships.

I found a wonderful chart, I wish I had to introduce functions. It gives examples such as selecting K on a snack machine after putting money into it (input), the machine processes the information, and a Twix candy bar comes out. (output) or A zero on the phone is pushed (input), the phone sends a signal to a receiver (process), and the operator answers (output).  Practical examples of input, process, and output.

By introducing the topic this way, it identifies prior knowledge that can be built up.  It is easy to relate this to the value for x being the input, substituting the value for x and doing the math in the equation, with the output being the answer.  Once students learn function notation, the next step would be to relate this to a graph. 

Since functions and graphs are related it is important students be taught the two together so they get a chance to understand the connection.  In addition, its nice to relate function notation with an actual value representing a point on the graph to that point. 

When I went through my teacher training program, the world still treated this topics as separate topics.  In fact, most of the math I taught was taught in isolation from other mathematical topics.  So as I read, think, and reflect, I find more and more connections I try to share with my students.

Once I get students used to thinking in terms of function notations, functions, and graphs, I want to take them to the next step showing the four ways points can be represented but I hope to do it so they see the representations are related. 

I'll let you know how this goes.  I'd love to hear your thoughts.  I'm off.  Have a great day.

Connections in Math

  I'm currently reading a book "Writing on the Classroom Wall" by Steve Wyborney which is filled with big ideas that apply to learning.

The first one is "Learning is about Making Connections".  Making connections is one thing my students struggle with daily.  They approach each topic as if it is totally isolated.

I constantly struggle with trying to help them make connections.  Steve includes some great examples, including ones I can use in my lowest level math.  I like the ideas he presents but the review of the book is for another day. 

The first big idea brought up the need for students to connect ideas together in math.  I came across an article from the National Council of Mathematics discussing this very topic.  The example the author provided gave me an "aha" moment because I've never seen the connection.  At some point in elementary, middle or high school, teachers cover multiplication, division, multiples and factors.  When the class used manipulatives to find the area of various polygons, a student pointed out this was just like using factors and multiples from earlier in the year.  Give it some thought and that student is absolutely correct.

Too many times, both students and teachers rely on tricks or procedures without going any deeper?  My students cannot explain why when dividing fractions, they have to flip the bottom fraction and multiply.  I've covered it in high school math because my students have never seen the explanation.

The NCTM states all students should:
1. Recognize and use connections among mathematical ideas.
2. Understand how mathematical ideas connect and build upon one another to build a coherent whole.
3. Recognize and apply mathematics in situations outside of mathematics.

This article actually reinforces the idea of showing all the steps even if the students are not thrilled with all the micro steps because they are so used to using shortcuts and tricks. 

This spring, I started looking at reorganizing all my math classes so I group similar processes together to see if I can help students see connectivity.  For instance, review exponents and rules of exponents before going on to rational exponents, logs, natural logs etc which all use the same rules rather than teaching them at various points throughout the course.

I'm thinking of reviewing regular fractions and teaming it up with algebraic fractions since the process is the same for both.  I'm hoping by starting with the simpler review, students will have a chance of extending their understanding that one situation is actually a more complex application of the other.

In the past I've reviewed the lattice method of multiplying whole numbers before showing students how its used to multiply binomials.  The process is the same.  I also have used drawings of the same type to show both the multiplication of numbers and binomials. 

I'm hoping to utilize the concept of Big Ideas next year to show the umbrella idea applies to more than the one thing they've concentrated on the past. 

I'd love to hear what you think about this.  I appreciate when I hear from readers.  Have a great week.

Connectivity

  I've been teaching math for a fairly long time and the way its presented has changed so much since I received my credentials.  Recently with the change of focus, I've realized that I should be teaching solving multiple step equations just before I teach slope and graphing.  Technically, if you put y = instead of a constant = you'd have a linear equation.

So I think next year, I'm going to teach solving one, two, and multi-step equations first then move to teaching linear equations as they are so closely related.  This year, I'm slowly realizing I need to connect with certain topics with other topics so students begin to see the relationships with in Math.

So the order I"m looking at for teaching this grouping is as follows.
1. Solving one step equations.
2. Introduce the idea of x and y values as coordinates and or points
3. Solving two step equations.
4. Introduce linear form, function, equations and connect with points
5 Solving multi-step equations with variables on each side.
6. Solving multi-step equations that require combining like terms or distributive property.
7. Identify m and b of  the linear equation.
8. Introduce graphing using m and b. 
9.  Show finding slope from graph using triangles and finding the b.
10. Finding the slope mathematically.

This is a big change for me because I'm so used to teaching solving one and two step equations in one unit.  Later on, I teach linear equations as if they are completely different and isolated.  I've been wondering if that is one reason my students have trouble transferring the knowledge.  Do they see these topics as completely unrelated and therefore must be treated as different topics?

I'm looking for ways to teach certain topics so they make more sense to my students.  So far my teaching factoring of quadratics is going well.
1. Factoring GCF out of the trinomial.
2. Teach the Diamond method of finding the factors.
3. Take those results to be used to factor the quadratic with a leading coefficient of 1.
4. Teach the Diamond method to find factors for a quadratic with a leading coefficient of a so a is not equal to 1.
5.  Have students use the factors to rewrite the trinomial into four terms.  They will practice taking it this far.
6. Complete the factoring from # 5.
7. Introduce the quadratic formula for equations that cannot easily be factored.

I'm only up to step 3 but I had a student who looked at what we were doing and said "UnFOILing the equation."  First time, I've ever heard a student make a direct connection.  It was cool.  I'll get back to this when I'm finished with this part of the unit.