Apr. 12, 2006 Teaching Multiplication
When I was a child, I was taught that 3 x 3 = 9. I don't remember ever being taught what that meant. I just had a multiplication table to memorize and it gave me fits. Multiplication can be taught as a series of addition (three sets of three equals nine). But we're going about it a little different.
The thing I like most about the Singapore math program is how it goes from the concrete to the pictorial and then to the abstract with every concept. This isn't from my Singapore materials, but it does follow the format. Here, we are practicing in the concrete with blocks to map out the area of our garden. Later, we will use graphing paper to do this in pictures and, when she is ready, she will move to figuring these papers out abstractly using only numerals.
The thing I like about the Biblical Principle Approach is how it all begins with scripture and illustrates how mathematics reflects God's nature and how we can use mathematics to "subdue" the Earth.
Yesterday, I introduced the concept of area in connection with our gardening unit and gave my daughter several problems to figure out. Then she got to make up her own problems which she always looks forward to.
For this, you need square tiles and paper. The back of my hundreds chart worked wonderfully because its blocks are each one inch square, just like our square tiles.
We started with our small garden which is 4 ft by 4 ft. I had her line up four blocks across to represent the width and four down to represent the length. She then filled in the rest and counted up the blocks to find the area of the garden. She wrote the multiplication problem on her work surface in a way that helped her see the relationship between the blocks and the problem and then copied it on her paper in the more traditional format. Here is a picture of one problem:
6 x 3 = 18 Yeah! She did several problems and got them all right!
The principle we are working with is Christian Self-Government and how we can use mathematics to fulfill our obligations. Is that a principle? I guess it is now!
teaching math, math, homeschooling, home school, multiplication
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Feb. 14, 2006 Back to School
Math has been interesting. We finished up our unit in measurement and found an interesting connection to Christ. I cannot remember what Little Mouse's original question was, but it had something to do with relativism. We talked about non-standard measurement and the difficulty of using your hands and other body parts to measure. Then we talked about standards in our own lives.
What happens when everyone does "what is right in his own eyes?" Well, we know from scripture it does not turn out well. But we keep trying it. Yes! magazine, in an article entitled, Why America needs a spiritual progressive Left, states we are in "a real spiritual crisis in America." Of course, they propose "a universal spirituality and values not tied to any particular religion but foundational to all religions..." The article has some interesting views on Christianity. There is a whole movement calling for a "higher spiritual and ethical standard."
Any standard but Christ, obviously. And any standard that applies to anyone but me. Meausring morality in cubits and spans as we each construct our own little domicile of spirtism. Yeah, that'll work.
There is a higher standard. A perfect one, in fact. Like that little standard inch protected in some government vault somewhere (or is it on display in the Smithsonian?) Except our standard is not hidden away. It has been revealed in scripture. Our standard is Christ, and whether you believe in Him or not, it is the standard against which each of us will be measured. It makes no sense to rebel against the inch, saying "I'll create my own unit of measurement, one that reflects my values, my aspirations and one that is personal to me." And yet it seems the majority of our world seems to think that makes perfect sense in morality.
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Jan. 26, 2006 Teaching Measurement
We are learning about measurement. The following actually encompasses what we will be doing for this unit of mathematics and is not a single lesson plan.
Thou shalt not have in thine house divers measures, a great and a small.
Deu 25:14
Principle: God requires us to be fair in all our dealings.
Leading Idea: Standardized measurements ensure accuracy in measuring, and promote fair trade.
Background: Look at the history of measurement. Measurement was once not very accurate. The cubit of the bible was the distance from the tip of the elbow to the tip of the middle finger. These kinds of measurement worked fine when one craftsman was doing the measuring. But think about how big the ark would have been if it were measured by Shaq's cubit as compared to your child's cubit.
Activity: To illustrate this, you will need more than one person and some different things to measure. Measure items using your cubit, hand and foot. How many hands across is the window when your youngest measures it? Your oldest? You? What would happen if you needed to replace the window? If dad measrued the window with his hand and then sent Jr. to the store with directions to buy a window five hands wide and 10 hands tall, how likely would it be that the clerk would get the right size order?
Reasoning: Assist the child in reasoning out the necessity of a standard and devise different methods of obtaining a standard. One method is to designate one person's hand the standard hand, etc. But whose hand? And how will others be able to measure accordingly? King Edward I of England had a similar problem. In the thirteenth century, he designated the iron ulna (after the name of the bone in the forearm) as the standard measure of one yard. The foot was to be one third of that and the inch one 66th.
Illustration: Introduce standard measurement as it exists today. Look at tools we use to measure, including a balance, a scale, a ruler, a yardstick and measuring cups. Talk about how the standard helps us to measure accurately and consistently for baking, sewing and for trade. Ask the child which of the systems God had in mind when He said we should not have divers measures.
Application: Do something requiring measurement...sewing, baking, a craft project...whatever you and your child enjoy doing together. Ask questions about measurement as you complete the project and help her to reason and apply the information.
This can be tied easily to history (the above site provides a lot of historical information about the development of our modern standards) and scripture when talking about godly dealings with men. The above verse is directly relavent, but think also of James chapter 2 and how that relates. What is God's standard of measurement for our lives?
If you have posted lesson plans or lesson ideas today, leave me a comment and I'll post the link here for others to find your post. If you would like more lesson ideas, peruse the list which will hopefully develop, or browse through my blogroll under "Friday Favorites." These are other bloggers who have indicated that they would participate on a regular basis. If you would like to be added to this list, let me know and I'll add you and help you through getting the blogroll in your sidebar.
Happy Blogging!
Dana
Today is Mozart's birthday...and National Chocolate Cake Day. Find out mor over at Janne's place!
And Miiko has some great lesons for teaching scripture and from scripture. She is logging her lessons as she works through the Judah Bible Curriculum. Mine is on its way!!!!
Here is a post I stumbled across that is worth reading: The Engish Blog
And one more...for those of you interested in teaching reasoning and encouraging children to reason more, this is an excellent example of teaching through questioning.
lesson plans, lesson planning, teaching math
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Jan. 20, 2006 Interesting insights from a 7 year old
First off, I just wanted to share this picture because it is so adorable...Baby Bug with our puppy, Holden:
She is so proud to be able to pull herself up on that table and walk back forth along it! Her little eyes shine and her face just beams with delight.
Second, to end our week's discussion of the attributes of shapes, my daughter got to play with her pattern blocks. Since I could not get the scanner to work, she just did some free play. Tomorrow, she'll make some figures out of Pattern Animals: Puzzles for Pattern Blocks.
This is one of the things she made. By itself, it may not seem that impressive. She made one mistake, too. But that is not why I took a picture of it. It is what she said in describing what she did and why. I wondered if the Holy Spirit coud speak directly through my seven year old daughter because I could not quite believe that she grasped exactly what she was saying. She said this was her picture of the bible.
The triangle represents the written word, the law we have to follow.
The bottom is the peace that comes from reading God's Word and following His law.
The top represents beauty. When we are filled with His peace, we can see all the beauty of His purpose.
I cannot really add to that, so I'll just leave that as my stunning moment for the week.
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Jan. 5, 2006 Friday, Again
After my muffed math lesson, I returned to some thinking on the general topic. We're working on shapes and unfortunately, this is not terribly well defined. I did not line out a clear principle, although there is one. Well, a principle at least. It is a bit vague. We did some reasoning and here are more or less the steps we took:
God created everything.
He made everything a certain way for a certain purpose.
He gave everything certain characteristics or attributes to fulfill His purpose.
Things can be described by their attributes.
Christians have certain attributes.
Here is the work she did (keep in mind she has visual problems and her handwriting is atrocious...and now that I'm thinking of it, keep her in your prayers. She is going to see a neuro-opthamologist week-after-next).
Here are the attributes we will be covering regarding shapes:
Whether they slide on an inclined plane.
Whether they roll on an inclined plane.
Whether they can be stacked.
How many faces they have.
How many points they have.
After she can rightfully identify each of the solids we are working with by sight, we will begin simple "riddles." "I have six faces. All of my faces are the same size. I slide and stack but do not roll. What am I?" (a cube)
Then we will go back to the attributes of Chirstians and show how we can recognize Christians by their attributes (essentially the fruits of the spirit). I love this because it ties in directly with the study of the Sermon on the Mount we did before Christmas.
Here are some of the attributes of Christians we may be covering (one per day until we finish this section. Right now I'm unsure of how many we will get to.)
1) "...they know his voice." John 10:4
2) " ...blameless and harmless, the sons of God, without rebuke, in the midst of a crooked and perverse nation..." Phillipians 2:15
3) "...the righteous are bold as a lion." Proverbs 28:1
4) "... clothed with humility..." 1Peter 5:5
5) " He is ever merciful..." Psalms 37:26
6) "...the stedfastness of your faith in Christ." Colossians 2:5
7) " But in all things approving ourselves as the ministers of God..." 2Corinthians 6:4
8) "Blessed are those servants, whom the lord when he cometh shall find watching..." Luke 12:37
9) " And all thy children shall be taught of the LORD..." Isaiah 54:13
10) " For thou art an holy people unto the LORD thy God..." Deuteronomy 7:6
So that is pretty much our focus for the week...identifying God's creation, including His faithful servants, by their attributes.
Here is a great blog about unit studies...complete with a unit study to get you started, so run over to Janne's place and check it out!
Is anyone else posting lesson plans today? If so, let me know so I can link to your blog and enter you in my blogroll! Click here for more information!
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Nov. 15, 2005 Measurement and fractions
Having your young children help you in the kitchen is beneficial in so many ways...it far outweighs the drawbacks of 1) mess and 2) time it takes to get things done. You are training them to be an actual help to you and to be independent later in life, you are helping them see themselves as a valuable member of the family, you are sharing quality time working together, and their are numerous opportunities to teach academic skills, whether it be in science, reading, mathematics, etc.
This is an early lesson in fractions.
Principle: God is just.
Leading Idea: God expects us to be accurate in all we do.
Definitions:
A fraction is a part of a whole.
Scripture:
Pro 16:11 A just weight and balance are the LORD'S...
Reasoning:
When we measure accurately, we are following God's will. "Tipping the scale" to gain an advantage is the same as stealing and is against God's law. Luke 6:38 tells us: "For with the same measure that ye mete withal it shall be measured to you again."
This is applicable in all we do. We should never lie about age in order to get cheaper movie tickets or buffet prices. In cooking, measuring accurately gives us a better end product.
Activity:
Show common fractions, such 1/2, 1/3 and 1/4. Demonstrate how to read these fractions. In the beginning, I always say, "1 over 2, or one half, 1 over 3, or one third." Tell the child what it means (I say, "1 over 2 is a way to write one out of two equal parts") and demonstrate. Two halves make one whole. Three thirds make one whole. Four fourths make one whole. This does not have to be a long drawn out thing. I recommend just going over it so the child has some notion of what's going on, and make sure to use the vocabularly repeatedly while baking with your child. They do not have to have a complete understanding of fractions the first lesson.
Choose a simple recipe and allow your child to make it independently. Provide supervision and assistance where necessary, but let him read the recipe, assemble the ingredients and everything needed to make it. We do this a lot, and now my almost 7yo daughter can make muffins, pancakes, macaroni and cheese and similar items on her own (of course I help her with the cooking part.). And she knows what fractions represent.
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Nov. 15, 2005 Comparing and Ordering Numbers
The basic skills associated with comparing and ordering numbers are identifying which of two numbers is greater and which is less, putting numbers in order from least to greatest and also from greatest to least.
Principle: God's ways are greatest
Leading Idea: God lifts up those who humble themselves. Those who recognize their need for a savior the most will be the greatest in the kingdom of heaven.
Scripture:
Mat 18:4 Whosoever therefore shall humble himself as this little child, the same is greatest in the kingdom of heaven.
Reasoning:
People like to be noticed for the good things they do. We like attention and recognition. When we succeed, it is easy to take the credit and minimize our failures. We also like to think that we are not so bad, and can think of other people who are in a worse moral state than we are. But to be recognized as great by God, we must humble ourselves, and think of ourselves last. We must see our sins as God sees them, and remember to compare ourselves to His perfect standard rather than other men.
Definitions:
"Greater than" means "more than" or "bigger than." It's symbol looks like this: >
"Less than" means "fewer than" or "smaller than." It's symbol looks like this: <
"Equal to" means the "same as." It's symbol looks like this: =
Activity:
For this lesson, we are going to compare numbers to see which are greater and which are less. (Numbers are nice...they don't think they are any greater than they really are!) Young children have a difficult time with symbols as similar as < and > because they often flip these symbols in their minds. To help, I begin by drawing an alligator with a big open mouth and saying that the alligator always eats the bigger number, showing his wide open chompers devouring a big number. My daughter likes to draw teeth in her symbol, and that is fine for young children.
After discussing the vocabulary, and doing some practice problems orally, I got out the dominoes. This is similar to "domino addition" except now we are comparing the two sides of the domino. Draw out one domino and lay it horizontally on the paper. Write the two numbers represented by the dots on the paper and the appropriate sign in between.
For activities like this, I often set a timer and see how many she can do in five minutes. This keeps her focused and engaged, and is really all that is necessary. A child does not NEED to do 100 problems to prove how well they know something. In five minutes, she typically does 8 - 10 problems. If she gets them all right, I know that she gets the concept and there is no need to drill further. If she gets them all wrong, I know that she does not get the concept and I need to back up and re-explain. If she misses a couple, I know that we need to continue this practice...and five minutes a day will be fine.
This can also be done by drawing two cards from a deck, or rolling two dice. At this point, I would not do it by rolling one die twice. It really does help the child to be able to see the numbers side by side...the written number itself is an abstract concept, and it is beneficial to have it tied to something more concrete while working with these skills.
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Nov. 13, 2005 Raceway To Addition
This is a fun game which can be modified easily for any skill level. All you need is a die, a numberline, and place markers. This is orinally written with the TX first grade math objectives in mind, which included sums and differences to 18. You can easily go higher or lower to suit your child's ability level.
Principle: God is infinite. He has no beginning and no end.
Leading idea: God created numbers to also be infinite. No matter how high a number is, there is always one higher.
Definitions:
Arithmetic is counting.
Addition is counting forward.
Subtraction is counting backward.
A numberline shosws the order of numbers from least to greatest. It goes forever in both directions and has no end. A numberline can be helpful to add and subtract quickly.
Infinite means (literally) "no end."
Scripture:
Psa 147:5 Great is our Lord, and of great power: his understanding is infinite.
Reasoning:
God's knowledge is infinite. There is nothing He does not know. He knows the hairs on your head and the number of the stars. He knows all our thoughts. Our knowledge is finite. Therefore, we do better to trust God, who knows all.
Activity:
To play this, you need a die, a game board and a place marker for each player. This is really practice adding and subtracting on a number line. Take a moment to explain the numberline, and that it really goes on forever. This is just a small part you are taking for this game. To play, you need the game board with 19 spaces numbered 0-18. Each player begins on 0. Take turns rolling the die and advancing the marker that many spaces. Spaces only count if the child says the number sentence (for example, 0 + 4 = 4). Then the next player goes. I recommend having the child get an exact match to 18 before being able to land on 18. Once the player lands on 18, s/he begins subtracting each roll of the die until getting back to 0. Whoever gets all the way to 18 and back to 0 first wins.
You can start just with addition and stop at 18 if you have not worked on subtraction yet.
Here is a numberline from 0 to 10.
Here is a numberline from 11 to 20.
You can cut them and paste together for an easy gameboard.
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Nov. 12, 2005 Number Recognition
This is another activity for the hundreds chart, but is geared toward children who still struggle some reading large numbers. Again, if you do not have a hundreds chart, one can be printed off here:
http://www.abcteach.com/Math/hundchart.htm
Principle: God gave man the gift of language, including mathematical language, for His glory.
Leading Idea: We are responsible to speak accurately. Describing things accurately and using the proper words aids communication.
Scripture:
Gen 1:3 And God said, Let there be light: and there was light.
Reasoning:
God spoke all things into existence by His word. He had language from the beginning, and gave it as a gift to humans. Because His word is true, ours should be true. We should strive to speak the truth, and to use precise, accurate terms in our speech.
Activity:
Give the child a numbers chart and several counters or other small objects which will fit in the squares. Allow the child to place the counters in the spaces to create pictures, shapes, and/or patterns. When he is finished, have him read the numbers he covered as he removes the counters. Color in the numbers as he says them on your own number chart until you have a copy of what he did on his. This gives practice in number recognition, but also in the importance of precise speech. Our speech should create an image in the listener's mind akin to what we are trying to say.
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Nov. 12, 2005 Guess My Number
This is another challenging game to play with a hundreds chart. It helps build mathematical vocabulary and reasoning, while learning about numbers.
If you do not have a hundreds chart, you can print one off here:
http://www.abcteach.com/Math/hundchart.htm
Principle: God is just.
Mathematics operates by properties and principles which are always true, because God is just.
Leading Idea: Numbers do not change. They have properties, or characteristics, that never change.
Definitions:
Even numbers can be divided equally with no remainders. Two people can share that amount fairly without breaking any up.
Odd numbers cannot be divided equally with no remainders. If two people shared that amount, there would be some left over.
Greater than means more than. If a number is greater, it is bigger.
Less than means fewer than. If a number is less, it is smaller.
Scripture:
Deu 32:4 He is the Rock, his work is perfect: for all his ways are judgment: a God of truth and without iniquity, just and right is he.
Reasoning: God is constant. He is perfect. He is without fault and just. Our actions are measured against His perfect standard.
Because God operates on principles, His creation also operates according to principles. Numbers have properties, and by describing properties, we can tell what kind of a number we are looking for. If I say I have an even number of cookies, you know I cannot have three.
Activity:
For this, each child need a hundreds board and something to write with. I prefer using a laminated one and markers, but paper and pencil is fine. This game is somewhat like 20 questions, only with numbers. You pick a number and the children ask questions about it until they narrow it down. I introduce this by telling the children what to cross out until they are familiar with the vocabulary and the process and then they begin asking me questions.
For example: My number is odd (they cross out all the even numbers). My number is greater than 40 (they cross out all the numbers 40 and below). My number is less than 50 (they cross out all the numbers greater than 50). Now all they should have left is 41, 43, 45, 47 and 49. They can guess from here. Later, I just answer yes or no to their questions as they ask me if it is even, odd, greater, less than, etc.
Similarly, you can make up riddles. For example, I am a number between 40 and 50. Both my ones and tens digits are even. My ones digit is greater than my tens digit. The ones digit is not 6. What number am I? (48)
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Nov. 12, 2005 Speed Addition
This activity is designed to help children understand how the hundreds chart is set up. For it, you need only a hundreds chart. It is motivating for most children because it moves quickly, most pick up the pattern easily, and they are adding large numbers, which for some reason most seem to enjoy. It helps get a child's attention when transitioning from one subject into math and gets them thinking for the upcoming lesson.
If you do not have a hundreds chart, you can print one off here:
http://www.abcteach.com/Math/hundchart.htm
Principle: God is immutable. He is constant and unchanging. From the beginning, He has had a plan for salvation which He works out through individuals.
Leading Idea: Numbers do not change. When you add two and two, the answer is always four.
Definitions:
Arithmetic is counting.
Addition is counting forward.
Subtraction is counting backward.
Scripture:
Act 16:5 And so were the churches established in the faith, and increased in number daily.
Reasoning:
The churches were established on the word of God. Despite persecution, they showed quick increase. When we obey God, we can be used to have a great impact on our communities, both local and national.
Activity:
This basically helps reinforce adding tens and the way the hundreds chart is set up. Start with a number from 1 to 10 and add ten to it then to that number, each time moving your finger down the appropriate column. Children pick this up quickly and enjoy seeing how fast they can go. For example, put your finger on the 2 and say, "2 + 10 = 12 +10 = 22 + 10 = 32, and so on, moving your finger down each time. Start slow, but pick up the pace quickly, to match what your child is capable of. If he can read numbers, he'll quickly see that the next answer is straight down in the column.
Once they have this down, you can do the same thing with subtraction, but moving from the bottom of the chart to the top.
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Nov. 12, 2005 Domino Trains
Here is another fun game with dominoes which helps to practice number bonds, or number families as some texts call them.
Principle: God is immutable.
Leading Idea: Numbers are immutable. No matter how you divide up a number, it equals the same when you put the parts back together.
Definitions:
Immutable means unchangeable.
A bond is something that connects.
Scripture:
Heb 13:8 Jesus Christ the same yesterday, and to day, and for ever.
Reasoning:
If Jesus is always the same, He can be trusted. Numbers are similar. No matter how you break up a number, when you put it back together, it will be the same number. Numbers have properties which never change.
Activity:
Introduce the dominoes as cars on a train. Each car has a value equivalent to the number of dots on it. Say a number, for example 10. Have the child build trains that will total 10, such as a domino with double fives, a four and a six, etc. Challenge your child to make as long of a train as possible...perhaps with a double blank, double ones, two and one and so forth until it adds up to one. Try to make long trains, short trains and trains with a specific number of cars (can you make ten with three dominoes?) Start simple, but don't be afraid to just let your child struggle with a problem for awhile. Let them get those gears going. But do start with small numbers until the child understands the game and then you can start challenging as the child is ready.
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No homeschool should be without dominoes, dice and/or cards. They are great manipulatives for math practice and provide some drill without the tediousness of worksheets. Research suggests that some of the problems our kids are having in math today is due to children NOT playing games with dominoes, dice and cards. Think about it. When we were kids, we saw the configuration of dots and knew the number without counting. This recognition of sets is a critical early math concept upon which others are built. Some of these games also require mathematical reasoning which cannot be found playing Tombraider.
Principle: God is infinite.
Leading Idea: No matter how high you count, you can always add one more to get a higher number.
Definitions:
Arithmetic is counting.
Addition is counting forward.
The addends are the numbers we add together to get the answer.
The sum is the total number, or answer, in an addition sentence.
Scripture:
Num 1:2 Take ye the sum of all the congregation of the children of Israel...
Reasoning:
Taking the sum of the people means they were to add them up. They would need to count forward to know how many people were in the congregation.
Activity:
Use a set of dominoes to generate number sentences. Double nines are best, because they provide more opportunity for practice with higher numbers. If you want to focus on the smaller numbers for younger children, you can always take out the higher number ones.
Have the child draw a domino and place it horizontally on the paper. Have him count the dots on the left and write the number on his paper under the dots. Have him put a plus under the line and then write the number from the right side of the domino and then an equal sign. He then can count up all the dots and write the answer. This provides the same practice as a worksheet, but is more interesting. It has the added benefit of keeping the addition problems fairly concrete, by having the dots to count. It also helps students to begin to recognize sets of numbers. After awhile, the child will see those two parallel rows of three and automatically know there is six. Use mathematical vocabulary to describe to him what he is doing as he is doing it. End the activity before he is ready to end. If he is still enjoying it when you stop, he will look forward to this activity in the future.
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