Creative Math: Lesson on Triangles

I need to say right off, that these lessons are not original and borrowed in part or in entirety from other blogs and websites!

The main resources for this lesson came from: 

Illuminations  - this is a fabulous resource for Math lessons done in a hands on and creative way.

Jimmiescollage  - lots of fantastic ideas for everything, she has put together the Shakespeare Lens as well as the Transitioning to Living Math lens in Squidoo that I mentioned in previous posts.

Daily Life of a Mom - excellent lapbooking ideas for a study on Triangles.

Below is a snapshot of how we used their ideas in our lesson.

We started off using the lesson plan from Illuminations where I asked them questions about what a triangle is, what properties they have like how many sides and angles.

We then took time to build different shapes using triangles based on this worksheet. They built squares, bigger triangles and parallelograms. We also used pattern blocks to see the different ways one could build a triangle. Again, just a fun way to interact with the shapes.

After reviewing what we have discovered about the properties of a triangle, we proceeded to talk about angles and they marked out the angles on the triangle.

They then drew a circle and divided it into quarters and I showed them that they made right angles. Then we looked at a straight line and worked out it was 180 degrees (90+90) and then they worked out that a circle had 360 degrees (180+180) - which they already knew from their previous lesson.

I cut out a variety of triangles in different sizes and had them measure the angles of each triangle with a protractor (acknowledgements to Jimmiescollage for this idea). From this exercise, they discovered that the angles on a triangle are always 180 degrees! They then cut the angles out of a triangle and lay them next to each other to form a straight line! It was cool to see it visually even if they knew it in theory.

We moved onto discussing the different types of triangles.

We talked about the properties of a right angled triangle, equilateral triangles and Isosceles triangles using lapbook pieces from Daily Life of a Mom. I liked that they discovered the properties rather than just being what they are.

In our next activity, I asked them the question if any three lengths could equal the sides of a triangle. I gave them this sheet where they investigated this statement. A list of different lengths were given to them and they had to guess what kind of triangle it would make. The girls then cut the specified lengths out of centimetre grid paper and tried to make the triangles. They found that in some instances they couldn't make a triangle when the sum of the lengths of the two shorter sides were not greater than the length of the longest side. This exercise helped them to understand more clearly the properties necessary to make either an equilateral, isosceles, right angle or scalene triangle.

It was a simple lesson that reinforced what my elder daughter had learnt before while teaching my younger daughter some new terms. As usual Creative Math day was a big hit. Next come the Squares!

Creative Math: Lesson on Circles

So this was our first go at a creative Math class which was a big success in terms of enjoyment and I think also in terms of learning. It was simple, hands on and quite effective.

What is a creative Math class? It is my attempt to make Math hands-on fun for my kids to help them overcome any negativity about the subject. It is about taking a different approach to the subject to enhance their learning by allowing them to discover Math concepts for themselves rather than just telling them the solution or formula.

The following is an account of how our morning went.

First, I had them perform a warm up activity where they had to find as many circles and spheres in the house in 30 seconds. Each item got a point and creativity was rewarded with extra points. A little scrambling around the house is always useful to wake them up!

We then started with the basics:

1) Points, Line and Plane 

I instructed them to draw on their small white boards the following:

- a point (a dot), label it capital A, draw another point and label it capital B

- draw a line between A and B. This is a line – it has only 1 dimension, that dimension is length.

It is a set of points in a straight line.

- look at a sheet of paper (it is flat)– this is a plane – a plane is infinitely wide and long – it has NO thickness.

- I then had them draw a circle.

- All 2 dimensional shapes like circles exist in a plane.

2) What is a circle?

The next activity was an outdoor activity (I had photos but they somehow have managed to disappear :( ).

I had the girls hold each end of a skipping rope. The one in the centre was stationary and the other walked around her. I asked them what shape they made? (A circle - yay good!) Then, at every step, I had them make a point and then they had to join all the points together. (Look you've made a circle!) –I have to admit that it was not a perfect circle so we had to improvise a little but since this was really just basic geometry, they had no problems making the adjustments. When they were done, I gave them the definition below:

A circle is a set of all points in a plane that are the same distance from a given point. (the centre child is the given point)

Then we worked through these questions:

(i) What do you call this point? the centre – mark it O

(ii) Draw a line from the centre to any point along the circle – what is this called? – Radius

Is there just one radius? – no there are many Radii. (e.g the spokes of a bicycle wheel) Can you see that the rope represents the radius of the path formed by you walking around?

A radius is a line segment – it has two endpoints.

(iii) Mark the centre O and 2 points on the circle (A and B)

Does the length of the Radius change at all? No – they are all the same length. So OA and OB are the same length.

(iv) Now draw a line from one point of the circle to another point on the circle

This is called a chord.

Draw a chord near the centre of the circle and one further away – which is longer?- The one closer to the centre.

The farther away the chord is from the centre, the shorter it is.

(v) Can you draw the longest chord?

Do you know the special name of this chord? – Diameter.

Not only is it the longest chord, what else does it do? It divides the circle into 2 equal parts called a semi-circle.

(vi) Measure the radius of the circle and then the diameter? What figures do we have? (again, since our circle was a little wonky the figures were not very accurate but we adjusted)

What do you notice about the diameter? the diameter of a circle is twice the length of it’s radius.

3) Circumference

Having covered the basics, we talked about perimeter and circumference. We talked about how the path around any geometric shape is called a perimeter. Then I had them walk around the edge of the circle and I asked them if they knew the special name for this perimeter? - It is a circumference. It is the distance around the circle.

I mentioned 2 other terms to them:

A tangent - a straight line or plane that touches a curve or curved surface at a point but does not intersect it at that point.

A secant - a straight line that intersects a curve at two or more points.(is it the same as a chord?)- a chord is the bit of a secant that lies within the circle.

We then played Simon Says around the circle (I got this idea from this fantastic blog which has lots of ideas for teaching math creatively). I would shout the following:

Simon says, jump on the circumference/ put your elbow on the centre/ put a toe on the secant/ run around a half circle/Put a toe on the chord and an elbow at the centre/Everyone form a diameter across the circle/Make a radius with your body/Make a tangent.

4) Learning about Pi

After cooling down, we continued with some table work.

They had to measure three different circles (we used a plate, coaster and a magic tape roll) with a string. They recorded it in their Math books and then measured the diameter of each circle. I had them compare the length of their string with the length of the diameter and they noticed (Hurray) that in every instance, despite the different sizes of the circle - the circumference was always 3 times (and a bit) longer than the diameter.

measuring circles to find their circumference and diameter

A table to compare their results and work out Pi

My mathy husband happened to be around so he talked to them about ratios and showed them how to work out the diameter, circumference and radius and discussed Pi with them, which was great because I don't think I could have explained it as well as he did.

This is what they learnt from this exercise:

The circumference is always a little more than 3 times longer than the diameter.

This type of comparison is called a ratio.

This can be written like a fraction C/d.

And it will ALWAYS BE THE SAME NUMBER.

This is called Pi – it is a very long number but it is about equal to 3.146.

The symbol for pi is 

We then watched a really fun video of a song about Pi.

This lens also has great ideas for teaching Pi in creative ways. Did you know there is a Pi day? It is March 14 (3.14) :).

The session was finished with the story of Archimedes from Mathematicians are People Too.This is a great book with biographies of people like Thales, Archimedes, Pythagoras, Galileo and Pascal to name a few. It makes for an excellent living link to Math concepts and History. We also read Sir Cumference And The Dragon Of Pi which is part of a highly enjoyable series teaching numerous geometrical concepts.

 

The girls made a paperchain out of pi numbers as they were listening and memorised quite a few of the numbers in the process.

If we had more time I could have used copywork quotes and Notebook pages from here to extend the learning but even I know when to stop!

It took us all morning but they really responded well to subject which was my goal and I am hoping that it will begin to break down the barriers of resistance to Math as they have more fun with it.

There will definitely be more lessons like this.

Learning to be creative with Math

Math is not my strong point. Numbers cause my brain to fizzle and explode. Sadly, I think I may have passed this on to my eldest daughter who has declared on numerous occasions ” I hate Math!”. And while I am a self-confessed Math-phobic, my heart sinks, because my goal for my children to be fearless in the face of any challenge.

So, once again I am presented another opportunity for some self-reflection and growth. I know I could easily spend hours planning and thinking about subjects I love like History, but with Math, I was content to hand the workbooks to my kids and lett them get on with it after some explanation. I realised that I needed to spend more time on this particular subject especially since I didn’t feel confident about it. Afterall, I wanted to make it fun and undaunting for them so they could flourish rather than have to carry all my hang ups about the subject.

We had started off with Right Start Math which was great in theory but unfortunately, in practice, I found it so teacher intensive that I let it fall by the wayside. The curriculum is great but my implementation was poor! I started to use the local Singapore Math course and workbooks (why not since Singapore Math is so highly regarded in Homeschooling circles). It worked fine but I got lazy and just let them work through the books.

Occasionally, when I saw them struggling with a topic, I supplemented with Mammoth Math having tried a free sample from Currclick.com. I used their workbook on Time which set a firm foundation for my younger daughter and I used their workbook on Fractions with my eldest. She didn’t love it but got through it and came out with a fairly good understanding. It was logical and thorough in its approach.

I also purchased Life Of Fred (Fractions) for her – she loved the stories but was not enamoured with the review questions at the end of each chapter. I like its unusual approach to teaching Math and we will probably come back to it later on. I have heard that Life Of Fred works better as a review once the child has mastered or at least got some grasp of the subject.

I used (to great effect) Times Tales to help solidify and teach the multiplication tables to them. It uses stories and mnemonics to help kids memorise their times tables.It worked really well and my oldest, who was struggling to remember her tables, just got it. My other daughter who hadn’t even started working on learning her tables now knew all her upper multiplication facts (i.e.3×6, 3×7, 3×8, 3×9, 4×6, 4×7, 4×8, 4×9, 6×6, 6×7, 6×8, 6×9, 7×7, 7×8, 7×9 ,8×8, 8×9,9×9). It took us about 10 days to accomplish this! Such a relief after months of slogging away with drills, learning wrap-ups, computer games, memorisation. I think it would work particularly well for visual learners.

More recently, for fun, I introduced them to a few fun ways to “see” their times tables. One was the Multiplication Clock (an idea garnered from this site). A combination of Art and Math!

copyright 2007 Robinsunne

I also discovered a wonderful site called Right Brained Math which has some great videos and activities that help kids have fun with the times tables by seeing the patterns and playing with puzzles. This is one of the videos from the site.

In search of more ideas and a curriculum that would work for us, I did my usual l trawl of the internet and stumbled upon this intriguing website called Living Math – a holistic non-traditional approach to Math. It has a fantastic reading list for Math related literature which covers history, science and many Mathematical concepts.

What I am doing now:

First, I switched curriculums after hearing about this fascinating programme called the Mathematical Enhancement Programme (MEP). It is a full downloadable curriculum that is free online! It is a curriculum that draws its teaching strategies and methods from the Hungarian system. It adopts a rigorous spiral approach and is very interactive. I understand that it is on a trial run in UK schools at the moment. The best step by step explanation of this programme can be found on this blog.

Highlights of the program, according to the CIMT:

• High expectations of students and teachers
• Mathematics taught as an integrated subject
• Continual review of facts and concepts
• Interactive lessons
• Stress on the logical foundations of mathematics
• Use of models and manipulatives to help students visualize concepts
• Encourages creative thinking and problem-solving

It is teacher intensive but I guess I am in a different frame of mind now and have managed to work it into our schedule so that I work separately with each of my girls. After using this for the first time, both girls declared that they love it! They also have interactive workbook pages on their website which allows kids to work online and they can check their work themselves. My routine now consists of my teaching one child one to one following the MEP lesson plan while the other does the interactive pages online or works on some other aspect of Math, reads a living Math book or does some puzzle/logic type exercises.

Secondly, I decided that I would use a combination of ideas that I had gleaned from the Living Math site as well as from the blogs of families who have implemented this style of “doing Math” into their routines. I thought that I would have at least 1 “creative math” day in our household where we would give plenty of time to the subject, reading related literature, using crafty hands on projects and learning tools and PLAYING GAMES! I will be posting more specifically on these Math days soon.

This link will take you a great introduction to implementing Living Math into your homeschool . Love it!

So I’m hopeful for the future and we shall see how it goes!