Creative Math: lesson on Squares

Our lesson in squares was one I had been looking forward to teaching for awhile having gleaned some lovely ideas from many creative mums! Today's lesson was inspired mostly by Child's Play. She blogs about their creative math club and the ideas are wonderful.
I managed to purchase a whole bunch of these square papers from Popular bookstore but you could probably cut your own supply easily enough with a good quality paper cutter. I let the girls play the squares for a while and then we chatted about what they understood about the properties of a square.

These were the points that were made:

- they have four straight sides
- they are equal in length
- they have four right angles

I then introduced the term Quadrilateral. What is that? A four sided shape with four vertices or corners. The square is a regular quadrilateral where all the sides and angles are equal.

This led to a discussion about other quadrilaterals like a parallelogram, trapezium, rhombus and rectangle. This site has some nice simple definitions of each of these. I then pointed out that the square was cool because it could be lots of other things too like a parallelogram, a rectangle, a rhombus and a trapezium. We went through the properties of each of these shapes to understand how that would be the case.

With their paper squares, I asked them to make the smallest square they could. They made it with 1 square. Then I asked them to make the next smallest square, they used 4 squares to make that. I pointed out that numbers that can form a square when put together in a grid are "square numbers". We followed this thought with the next two set of squares. 9 Squares and 16 squares.

I then pointed out looking at the grid of squares, that in order to make a square of 4, you needed 2 squares x 2 squares. With a square of 9, you needed 3 squares x 3 squares and with 16 squares, you needed 4 squares x 4 squares. I showed them that they could write it as 1², 2², 3²  and so on. This was the short way of say 1x1, 2x2 and 3x3. 

At this point I introduced the concept of square roots. I asked them to look at the side of square of 4 and see how many square there were - there are two. Then as I drew the diagram  and I explained that this diagram was asking the question “what is the side of a square of four?” They gave me the answer "2". "Let's try that with the other numbers. What is the square root of 9?" - 3 "And the square root of 16?" - 4. At that point they got it. 

I had them write the notation down by each square as seen in the picture above. 

Take the square of 4 for example.

• How many squares are there? - 4
• How many squares across and down? - 2x2
• What is another way to write this? - 2²
• What is 2 the square root of? -   

I then had them write a number line from 1 to 10 and then square the numbers.

After they had done this, I set them the task of finding a sequence of 3 numbers where the square of that number plus the square of the next number equals the next number squared. They took a little time and came up with 3,4 and 5 as the only sequential numbers that would add up.

I then gave them 3 squares cut to exact size - 3inches, 4 inches and 5 inches and told them to construct a triangle with those pieces of paper. It was a right triangle.

It was at this point, to my absolute delight, my oldest went "Oh I know what this is, it is Pythagoras' triangle!" How did she know this? The day before, in preparation for the lesson  I had read "What's your angle Pythagoras?" by Julie Ellis and she had made the connection from what we had read about his discovery and the exercise we were doing. She had discovered the concept! 

So we were able to see that whenever we have a right angled triangle, we can always apply the Pythagorean theorem which was the sum of the areas of a and b (in their diagram above) was the sum of the area of c or more commonly written as   . 

We finished off with the visual aid of a 12 foot string which was marked off at every foot. I asked how we could make a right angled triangle and they divided the rope into 3 feet, 4 feet and 5 feet and then joined it and voila! We had a right angled triangle!

I ended our lesson by watching this video from How Stuff Works. Some of the Math was beyond them (and me!) but it was helpful to see how this formula might be used in real life scenarios.

Next time we'll tackle Geometrical Solids.

Egyptian Day

These last two years, we have been working through our Tapestry of Grace (TOG) Year 1 curriculum for our Humanities studies. The focus has been on the Ancient world and we have just loved it! I never covered this in school so I was learning right alongside my girls. I plan to post about each of our individual study units in time.

One of the things that is recommended by TOG is the End of Unit Celebration. It is an opportunity to show off all the projects and work the children have accomplished over the months they have worked on a Unit. My approach to this has been to have a special day set aside where we have an "Ancient day". So, in the past two years we have had an Ancient Egyptian day, Ancient Civilisations day (which included the Ancient Americas, Ancient China and the Indus Valley), Ancient Greek and Ancient Roman days. We also celebrated our study of the Israelites with as Seder/Passover meal.

I love these and so do my children. They won't let me get away with not having a special celebration at the end of a unit now. It is a great way to review and enjoy all that they have learnt in a relaxed and fun way. It doesn't take a lot of effort but it does remain in the memory for a long time!

As it was our first celebration since we started homeschooling, I definitely went all out, making costumes and planning a really full on day. The costumes were kept simple and I've been able to reuse it for both our Greek and Roman days. I got a cheap white cotton sheet and folded it into the right length, cut a hole at the fold for the head and sewed up the sides. I also found a filmy pleated material which they wrapped around their waists. I also had some shiny gold cloth which I sewed onto one costume - you'll see my sewing skills are pretty limited hence the poor workmanship! They then adorned themselves appropriately with headbands and jewellery.

You can download the Egyptian jewellery template from Danielle's Place. I thought it worked really well! They enjoyed having the opportunity for the liberal use of black eyeliner as well. Of course, mummy and baby had to be dressed as well - since Egyptian children were usually naked, we let Adventure-man wander around in his nappy covered by a white towel. : )

We started the day with a quiz which acted as a review of the things they had learnt over the Unit. They had to start at the end of the room and for every correct answer, they got to advance one square floor tile and when they were at the other end of the room, we got into an imaginary Time Machine and travelled back to Ancient Egypt. They were able to call out famous sights and structures as we flew by them (imaginary of course!).

On our arrival, we tackled some Eyptian Math. These are a few sites that explain how they counted and calculated and it also provides some worksheets.

http://www.eyelid.co.uk/numbers.htm

http://webinstituteforteachers.org/99/teams/egyptmath/mathproblems.htm

http://letsplaymath.net/2007/08/11/egyptian-math-puzzles/

http://www.associatedcontent.com/article/736149/mathematics_lesson_plan_egyptian_math.html?cat=25

We then finished off a colouring book project about the 10 Plagues found here.

During our Egyptian studies they made an Egyptian hunting snake-heard throwing stick by painting a wooden spoon. We used the Hands and Hearts Discovery Kit for many of the crafts we did for this unit - it includes the kit and instructions on how to make a paddle doll, Senet (an Egyptian boardgame), how to mummify an orange, how to make your own paint like the Egyptians and it also contains a CD with lovely notebooking pages. 

We learnt that children would practice their hunting throwing skills with a stick like this so I set up a line of soft toys on the top of our chair and the girls practiced their throwing skills. We then played a game of Senet on their homemade boards.You can find out more about Senet here and play online too.

After Senet, we had a go at some of these online games about Ancient Egypt:

Egyptian Tomb Adventure

Death in Sakkara 

The Jeweller of Memphis

During lunch we stopped to watch one of our documentaries on Ancient Egypt from the Discovery Channel. After it was over, we had a look at some Egyptian recipes and decided what we would like to cook for dinner. I took the girls shopping and they helped put the meal together.

We used the following recipes:

Ancient Egyptian Marinade

Ingredients
1/2 cup olive oil
2 tablespoons ground cumin
1 tablespoon ground coriander
1 onion, grated
3 cloves garlic, finely minced
1 teaspoon cayenne pepper

salt and freshly ground pepper to taste

We marinated Chicken thighs for about 40 minutes and then grilled them in the oven, they were delicious!

Korrat (Leeks)

Ingredients
2 lbs. leeks
3 garlic cloves, crushed
1 Tbsp sugar
4 Tbsp vegetable oil or extra-virgin olive oil
lemon juice
salt
Slice the leeks into 2 inch pieces. Fry the garlic and sugar in hot oil until the sugar becomes slightly carmelized. Lower the heat and add the leeks, until they are slightly coloured. Sprinkle with lemon juice and salt. Barely cover the leeks with water and cook until tender and the liquid is reduced. 

Egyptian Potatoes

20 medium red potatoes, peeled and sliced 4 cups thinly sliced onions 3/4 cup (1-1/2 sticks) butter, cut into small cubes Salt to taste Pepper to taste 6 cups tomato sauce Preheat the oven to 200C. Prepare the potatoes and set them aside in a bowl of lightly salted water. Lightly grease a large casserole dish with butter or vegetable oil. Spread out potatoes in a layer, then make a thin layer of onions, dot with cubes of butter, and sprinkle with salt and pepper to taste. Make another layer of potatoes, onions, and butter cubes, season the layer, and continue until you have used up your ingredients, finishing with a layer of potatoes. Pour the tomato sauce over all, cover the casserole with aluminium foil and bake for an hour. Remove the foil and bake for another half hour. Allow to rest for 10 minutes before serving.

We finished off our meal with fresh figs and a date cake that we purchased. I found the first two recipes at Counter-cultural School and the potato recipe here.

Everyone dressed up for the feast including dad and we had a great time! It was a lovely memory to make a big effort and it is one the kids remember well.

There are many other activities one might do on a day like this - you could make a sugar lump pyramid, write your name in Hieroglyphics and make a cartouche, draw like and Egyptian, or mummify an orange. As we took about three weeks to complete our studies, we spread our hands-on activities out over those three weeks.

Enjoy!

Being consistent with memory work

When I started homeschooling, one of the things I definitely wanted my kids to be doing was memorising verses and poems. The problem with this was how to incorporate into our day in a consistent way that wasn't stressful!

I came across a wonderful idea a few years ago which has worked really well for us. (I can't remember where I stumbled across the idea and so can't acknowledge the creator but will gladly rectify that omission if I can).

We use an Index Card holder as seen above to store all our verses and poems. I usually get them to copy out the verse for the week on index cards or if it is a long poem, I will print it out for them to stick onto their cards. 

On each dividing tab, I have written the following:

Daily 

Even

Odd

Days of the week: Monday to Friday

Days of the month: 1-31 

When I give my girls a new verse or poem, we read it aloud, often create some actions or songs to go with it and then they file it in the Daily tab. Every day, they will review or recite to me whatever verses or poems they have in the Daily tab.

If I think they have mastered it to some extent, they can move their card to either the Odd or Even tab (depending on whether the date is an odd or even date). They will then have to review these cards once every two days.

If they have it down, they get to move their cards up to one of the days of the week, so if it is Monday when they have mastered the verse and I tell them to move it up, they will file the card behind the Monday tab. This will ensure that they review the verse once a week.

Finally, once they know the verses inside out, I will allow them to move it to the days of the month tabs. So for example, if they've learnt the verses on the 22nd day of the month and I've told them to move it up, they will file it behind the 22nd tab. This will mean that they will review this verse once a month.

With this method, they aren't overloaded with too many things to review in one day but it also ensures we don't forget to do it!

After a long holiday, we begin to forget what we've learnt. At that point, when we start back at school, I have them collect all the verses and poems and put it randomly in the days of the week tabs so that they can review them and then pop them back in the monthly tabs if they know them still. If they have trouble remembering the verses, they go back in the Daily tab again.

And that is how we make sure we are consistently learning and reviewing our memory work. Simple but effective.

A typical day?

I've been asked by a few people now what our typical day looks like - the truth is there is no real typical day for Adventure-man who fits into the routine of the two older girls.

The plan is that we wake up somewhere between 7.30 - 8am and find our way to breakfast. During this time, if I've had a reasonable amount of sleep, I'll start singing the verses that we are learning together with Adventure-man. My two girls have their separate memory work which they attend to later in the morning but they learn too as they sing along.

After breakfast, we all get changed and ready. The girls have their usual chores of making their beds and emptying out their laundry baskets. We meet for family devotions on the sofa sometime between 8.30 and 9am (closer to 8.30 if  I am on their case reminding them of the time and more like 9am if I decide to take the relaxed approach).

During that time, we worship along to our favourite worship CDs or sing worship songs together (or do "boogie worship" when requested by Adventure-man or the girls - this consists of energetic dancing, jumping, waving of flags or shaking a variety of toddler noisemakers!). Some mornings, we take the more contemplative approach and just "soak" in the Lord's presence as we play the CDs. They will then record in their journals verses, thoughts and anything they feel the Lord is saying to them at the time.

Over the past year we have been using Character Building For Families Vol 1. I really like it because it is short, involves no preparation and there is no written work. Each day you look at bible verses around a character value like Obedience, Servanthood, Gratitude or Contentment and discuss a variety of questions and it always leads on to how to apply what we have learnt. Each Character study lasts about two weeks.

During Lent in the run up to Easter this year, we followed a different set of bible readings and devotions - The Lenten Tree: Devotions for Children and Adults by Dean Lambert Smith

I liked this very much because it had readings and devotional thoughts for both adults and kids and it also had various ideas of hands-on activities that you could do to make the Lenten period more meaningful. I'll definitely use it again next year.

With our Year 1 Tapestry of Grace History studies we had the opportunity to read through huge chunks of the bible from Genesis to Malachi (sometimes using the bible and at other times using Catherine Vos' Child's Story Bible for the more obscure parts of scripture or for when we needed a "child-friendly" telling of events). Now, this year, I am looking for something they can interact with actively and have just purchased  The Bible Study Guide For All Ages and so far they quite like having material to interact with as we read from the bible. 

After reading the bible and discussing the passages, we end with prayer. With devotions done, the girls go off and do their memory work. We have a particular system for this which I will write a more detailed post about soon. During this time, Adventure-man is free to join us in much as he wants to and if he gets a little too boisterous, the trains come out. We often will finish our devotions with a round of kids praise songs just for him.

While the girls are reviewing their memory work, I play with Adventure-man. I'll spend some time on the Calendar with him and we'll play with the activities I have set up for him the night before. This is what his shelf looks like in his room with different activities laid out.

I have to admit that his letter related activities probably only get rotated twice a week on his shelves at the moment and the rest of the week we'll do free play, drawing, crafts, tracing, using scissors and other activities like that. As I am now actively trying to include him more in our homeschool day, I will have to be a bit more organised about this.

The longer we homeschool, the more flexible I am becoming and I feel less and less bound by our schedule. This is a HUGE change for me as a Type A Scheduler! I am becoming as concerned about the quality of their learning experience as I am the quantity we cover in a day. However, if I was to come up with a general  picture of what goes on, this would be it:

Memory work (either personal review or recite to mum)

Math 

Break (outdoor) and snack (often I'll read a poem to them or we'll do a picture study while they snack)

Language Arts

Piano Practice/Typing

Lunch

Scheduled Independent reading

tapestry of Grace work which includes History/Literature/Geography/ or we may do Science/Art/ Music Appreciation - one of these in some form

Playdate or scheduled activities (this term: Sewing, Skating, Musical Theatre, Ballet)

On any given day, this will change but it is what I have in mind to achieve during the day. One morning a week they have Mandarin and Piano lessons. Adventure-Man's afternoons will usually consist of a struggle between  myself and him to get an early afternoon nap in and if he doesn't sleep, then as far as possible I try and direct him to independent play while I teach the girls. 

Of course, the beauty of homeschooling is that you can switch things around according to their interests and your time. Being freed from the need to tick off everything on my list has led me into some wonderful avenues of learning with the girls. As usual, I am learning as much as they are. 

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!