Warm-up

The smaller elephant is about five and a half feet tall. Estimate the height of the tree in inches.

Warm-up

How high do you think the arch is in dolphins?  How wide is the base?

Place Based Math

 

The other day, I attended the third webinar in a series on teaching math via distance or hybrid because there is always the possibility that our school district could end up going red. The class addressed turning math problems into open ended problems but at the very end, the instructor mentioned place based math.

By definition, place based math activities are activities that use local history, culture, economy, arts, or literature to help students learn more about math.

The instructor indicated that one needs to create situations that are based on local knowledge and understanding.  For instance, here in Alaska, I might post a picture of someone standing under a pair of bones that form a parabolic shape.  Based on what they see, you might ask students to estimate the height of the bones, or ask them to create a quadratic equation for the parabolic shape.  

In another place such as in Colorado, it might be looking at pictures of signs showing the grade of a mountain road with the numbers blacked out and asking students to come up with the grade or perhaps asking them to explain what a 6 percent grade represents in terms of the mountain.  Take it a step further by asking them to decide what grade is too steep for a fully loaded truck going uphill.

Something like that wouldn't work well where I live because the only local roads go a few miles inland and there are barely any speed limit signs and no grade signs for certain.  But if I asked my students to tell me how long it takes to get to the next town by boat or by snow machine which opens up the possibility of  having students create their own word problems.  

Another possibility down in the area of the Gulf would be showing a shrimping boat and asking students to estimate the amount of shrimp the boat could hold and what the load could sell for.  Up here, it would be taking a picture of a local fishing boat and asking students about the number of salmon it could hold in pounds.

One of my favorite activities for locally based math is to have students recreate a cross section of the local landforms from a topographic map so they can see an outline of something they are familiar with.  Once they have the cross-section completed, I ask them to calculate the slope or grade of a few different points on the cross-section.  

There are also wonderful mathematical exercises one can do with the differences in daily highs or daily lows over the period of a month for the area.  If it's in a colder place, some of the math would involve negatives from start to finish. There is also the possibility of having students calculate the daily average temperature for the month based on data collected by the students every day.

A couple of my freshmen argued they didn't need math at all.  I said they did and they should name something that didn't require any math.  They promptly suggested they didn't need to know math for when they went out hunting with their guns.  This lead to pointing out that they use an intuitive math they've developed over time based on the experience of learning to shoot.  I also took time to explain that the calculational math we do in class is what we use to explain how the bullet moves through the air, it's speed, it's trajectory.  In other words, we can use mathematical equations to explain the actual firing of a gun. 

Again it was something the boys could relate to and introduced the topic of mathematical modeling to explain how things work.   I'll take this a step further later but in the next week, I've got some ideas for locally based math to use as warm-ups. Let me know what you think, I'd love to hear.  Have a great day.

The Importance of Number Sense.

We talk about number sense in regard to our students but I can tell you with absolute certainty, that too many students arrive in high school with little to no number sense.  Unfortunately, the lack of number sense creates some problems of its own.  

Students who have a well developed number sense tend to do better in math because a good number sense encourages them to think flexibly while feeling more confident. 

In addition, if students do not develop a strong number sense early on, they will have difficulty developing the foundational knowledge to do even simple arithmetic and certainly will struggle with performing more complex mathematics. A study of seventh graders was conducted back in 2013 lead researchers to conclude that the students who struggled at this age were the same ones who had the least amount of number sense in first grade.

Students can develop number sense by visualizing numbers in a variety of different contexts, exploring numbers, and relating to numbers in different ways but it takes time.  One way to help students develop a better number sense is to show there are multiple ways to complete a problem.  Ask students for suggestions on how to solve it and write the suggestions on the board.  This gives students a chance to see different strategies.

Another suggestion is to ask students to calculate certain problems in their head because when students perform mental math it helps them build their knowledge of numbers and their relationships.  When the numbers get a bit too large or does not work with the memorized steps they need to learn to be flexible with ways to solve these problems.

In addition, teachers should have students participate in classroom discussions where they talk about different strategies that could be used to solve various problems.  This helps students clarify their thinking while developing the ability to critical think about other peoples strategies.  It is important to note the strategies on the board so students can see a relationship between their mathematical thinking and symbolic representation.

Take a moment to embed estimation and rounding activities into various situations as it is something that textbooks do not cover as well.  Furthermore, the teacher should ask them about their numerical thinking for both correct and incorrect answers because it shows you value their thinking and it has to make sense to them.  Finally, take time to pose questions which have more than one answer such as two numbers added together make 35.  What two numbers might they be? or Suggest three sets of numbers that add up to 35.

So it is important to work with students on developing number sense, even if they are in high school.  Let me know what you think, I'd love to hear.  I do plan to revisit this. Have a great day. 

Estimation and High School Students.

I've discovered that most of my students have trouble with estimation.  In fact, they often equate estimation with making guesses rather than using certain strategies to come up with a reasonable answer.  I'm not sure how much instruction they get in the earlier grades but I do know that estimation is an important skill to have.

First of all, estimation is a higher level skill requiring  students to understands the concepts and carry out mental math manipulation.  They have to look at the numbers in a problem, decide if they should round up or down while keeping a running total.  

Basically, it is important to help students develop the ability to estimate because it shows how well a student understands the concept and the reasoning behind it when they are not relying on the standard step by step procedures.  In addition, it helps students develop strategies which in turn strengthens their problem solving skills and logic and as stated before, it helps develop their number sense.  It is also a great skill to have when planning for things such as a Thanksgiving dinner.

Furthermore, the ability to estimate helps students develop number sense so they know if their answer is reasonable.  Without a developed number sense or ability to know if their answers are reasonable, it is much easier for students to make computational errors.  The other day, I discovered my highest level students in Math didn't seem to grasp that when they are due to get a raise every year, their salaries should be going up.  Over half the class had a decreasing amount earned.  This tells me they lack certain skills.

Second, estimation allows students to carry out mental math faster because they can round numbers to come up with ball park figures. This is an important skill in business where people look at the estimated costs for upcoming projects.  Someone who is good at estimation can look at the numbers, do some quick calculations in their head and come up with an estimated cost for the whole thing.  They rely on spread sheets to do the actual calculations.  

In addition, to estimating using addition, subtraction, multiplication, and division, students also need to be able to estimate how long it might take to do something, or how long it might take to travel from point A to point B or even how many calories in the cookie they are eating.  

It is worth taking time to discuss why estimations are important in real life and the type of estimations one runs into.  There are general estimations such as why the local football field might want to estimate the number of people who are planning to attend the next football game?  Aside from an approximation of the amount of take at the gate, the concession stands have to know so they have enough food or souvenirs available to sell.

Or if you need to have something fixed, most people get estimations before they agree to have the work done so they can plan for the output.  Although the estimation is usually a specific amount such as $3967.28 for redoing the plumbing in the bathroom, or $256.98 to have the breaks redone, we rely on that as being the largest amount we pay.  

Unfortunately, the math books I use at school do not really address estimation.  That is a shame because estimation is such an important skill.  I'm working on figuring out how to integrate it into my classes so students get better at it.  I'll talk more about it another time. Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

 

If an African Elephant weighs between 5000 and 14,000 lbs depending on it's size, what do you think would be an average weight for one?  Explain your thinking.

Happy Halloween

Don't forget to turn your clocks back one hour tonight!