Map coordinates

After learning about map scale, the next logical thing to learn is to read map coordinates.  Tiger read the following book for introduction to the topic:

As an introductory exericse, Tiger worked through a page to identify the points on a grid map with numbers on the x-axis and alphabets on the y-axis.  This was very straightforward because Tiger is already familiar with reading maps with such coordinate points.

Next, I introduced Tiger to another way to represent coordinate points -- using numbers in both the x and y axes.  This was slightly confusing because now Tiger had to figure out which axis was represented by the respective numbers.

For this exercise, I had Tiger draw out the X-axis and Y-axis, then he was to list the coordinates of the points that I put on the grid.

This was followed by applying our understanding of coordinates to drawing, first by linking various pre-set coordinates into straight lines and forming a shape on paper.

Next Tiger got to apply what he had learnt so far onto graph papers.  He was to identify various points on the graph paper based on a set of coordinates that I verbally read out to him.

These form the smaller shape on the paper.  Once the original, smaller shape was drawn, I gave him a multiple which he was to use to draw the bigger shape.

Here is another application of scaling up:

The next application was slightly more complicated than the ones before.  Here, Tiger had to:
1) plot the points on the paper;
2) reflect the figure on the y-axis;
3) learn that the equation for a straight line between two given points and which goes through the point (0,0) is y = -x.
4) apply his knowledge of rotational symmetry to plot the points of the final figure which was symmetrical to the original figure on the line y = -x.

Tiger played the following games to conclude his study of the coordinates:

1. Archery
2. Lost
3. Cops and Robbers

The lessons come from the following books:

This post is linked up to:
1) Look What We Did!
2) History and Geography Meme #69
5) Homeschool Mother's Journal: April 12, 2013
6) Hobbies and Handicrafts - April 12
7) Collage Friday - Part Time Unschoolers?
8) Homeschool Review
9) Weekly Wrap-Up: The One with the 2:1 Conference 2013
10) Math Monday Blog Hop #95
11) Hip Homeschool Hop - 4/16/13

Translation, Reflection, and Rotation

As a follow up to learning about symmetry, we looked at a very similar and much related concept of translation, reflection, and rotation.  Afterall, there are three basic types of symmetry: horizontal, vertical, and rotational.

The concept is easily shown by taking a half-photo of anything.  In our case, I have Tiger trace out three copies of the half-photo of a lion.

Then place the traced images next to the original half-photos to show the three concepts.  We also did a short quiz to make sure Tiger has understood the concept.

We played a simple game of writing in different ways using a mirror, testing out the concepts we just learnt.

The final application of the concept was more complicated, as Tiger was tasked to apply all that he has learnt to copy the original design from one quadrant to three other quadrants.  That took a bit more time.

The ideas for the lessons come from the following books:

After the book lessons, Tiger hopped onto the computer and tried his hands at the following games:

1. Putting Two and Two Together
2. Nine-pin Triangles
3. Transformation Tease 

This post is linked up to:
1) Hearts for Home Blog Hop #6
2) Homeschool Mother's Journal: March 1, 2013
3) Hobbies and Handicrafts - March 1
4) Collage Friday - Sharks, Titanic, and Handel
5) TGIF Linky Party #65
6) It's a Wrap
7) Creative Learning Link Up #4
8) Weekly Wrap-Up: The Strangely Bittersweet One
9) Share it Saturday - Dr. Seuss Features
10) The Sunday Showcase - 3/2/13
11) Math Monday Blog Hop #89
12) Hip Homeschool Hop - 3/5/13
13) Look What We Did!

It is featured on Look What We Did! 10 Great Resources: Math, Science, History, and Art.

Snowflake maths

Just for the records, we have had non-stop snowing over the weekend, so it looks like we are not going anywhere far for a while.

With the examination of the properties of snowflakes from our previous science lesson on snowflakes, we followed naturally onto the mathematical aspects of this interesting phenomenom: symmetry.

We have previously touched upon the idea of symmetry so we did a quick revision with a ruler and the snow crystal prints to determine the number and types of symmetrical lines we could find in each snowflake print.

Using a protractor, we explored a little about the 60-degree angle that were very prominent in the snowflakes we examined.

Once Tiger grasped the basic understanding of the protractor and angles, he used it to mark the location of the lines of symmetry in a circle before cutting it into a hexogonal snowflake.

Next, we learned about three types of symmetries: vertical, horizontal, and rotational.

There was a lot of cutting involved in this series of lessons, as we learned about different ways to fold and cut our papers to achieve design we wanted.

One way to think of the line of symmetry is to regard it as the line where a mirror would be placed. With that in mind, we used a mirror to prove that the reflection in the mirror was the same as the symmetrical pattern we made.

Still working along the concept of the mirror-image/reflected image, Tiger did more excises which comprised of:
1) cutting out letters that can be formed from mirror images (capital letters A, C, E, H)

2) drawing a symmetrical figure

3) constructing symmetrical figures using T-square and different-angled triangles, then colour them in.

The ideas for this lesson come from these books:

Besides the hands-on activities, we also watched a clip about the application of symmetry:

This post is linked up to:
1) Look What We Did: January Link-Up
2) All Year Round Blog Carnival: Winter
3) Share it Saturday
4) The Sunday Showcase 1/19/13
5) Math Monday Blog Hop #83
6) Hip Homeschool Hop - 1/22/13
7) Hearts for Home Blog Hop
8) Weekly Wrap-Up: The One with the Renewed Motivation
9) Homeschool Mother's Journal: January 25, 2013
10) Collage Friday - Feeling Like a New Person
11) It's a Wrap
12) Hobbies and Handicrafts - Jan 25
13) TGIF Linky Party #60