When I returned to teaching a year 7 Maths class, after a break of two years, I went searching for a virtual manipulative that I had used to improve understanding of algebra concepts. The National Library of Virtual Manipulatives has a great range of visuals, but unfortunately, most rely on Java, which is not supported by any current browser. Luckily, someone over at Hood Math has converted or upgraded the applet, so Algebra Balance Scales can be used by students in class.
There are many skills to learn to master Algebra, but we have already made a great start – You :
1. Can recognise and continue a pattern
2. Understand that a pro-numeral (a letter) represents a variable (changing number)
3. Understand that it is mathematical convention to leave out the multiplication sign in expressions and equations involving pro-numerals.
4. Can substitute positive and negative numbers into an equation
5. Can plot points on a cartesian plane
6. Can determine the equation from a table of values
7. Can solve an equation using backtracking
The next step is to be able to solve an equation by doing the same operation to both sides. Try these online activities:
Algebra Balance Scales (a virtual manipulative from Utah State University)
Algebra Balance Scales with negatives (same as above, but with negative numbers)
Equation Buster – from MathsNet
Tell me what you think about Dragon Box! Did you find it interesting, curious, fun, weird, exciting or not? What do you think you learnt about equations? Do you think this app will help you learn algebra? Would you like to play this app more often?
So far we have looked at the basic rules for algebra in expressions – leaving out the multiplication sign and the ‘1’ in front of a pronumeral, adding and subtracting ‘like terms’ and multiplying and dividing with pronumerals. Next we will look at multiplying and dividing with indices and then using equations.
Maths is Fun has a quick tutorial on how to use exponents with six questions you can try online.
The Algebra Balance Scales are all about doing the same thing to both sides. So if you remove to blocks from one side do the same to the other side.
Algebra Balance Scales with Negatives is a little more difficult – balloons act as negative numbers to counter-act the weights.
When you have spent about 15 minutes on each activity, leave me a comment to let me know what you found easy, what you found difficult and what you learnt from these two interactive learning objects.
This virtual manipulative from the National Library, Algebra Scales, helps you to solve equations using a balance scales. This one is a little more difficult, Algebra Scales using negative numbers. Remember to do the same thing to both sides of the equation. Maths300 also has some good activities building equations. Try “Algebra Charts” and “What’s my Rule?”. When you have finished leave me a comment under this post about which activity helped you learn the most.
This week we started learning about algebra – using pronumerals in equations to represent numbers. Algebra is very useful for writing relationships between numbers. For example, if the cost of an adult movie ticket is “A” and the cost of a child’s ticket is “C”, then if we take 2 adults and 3 children to the movies, the total cost will be 2A + 3C. We substitute the value of each ticket into the equation. There are several rules when we use algebra – we leave out the multiplication sign and always write the number before the pronumeral. If there is no number before the pronumeral, that means ‘one multiplied by’ the pronumeral (we leave the 1 out).
Algebra is also useful for representing number patterns – the number of rails in a fence, the number of chairs around tables or the number of matches in a pattern of rectangles. One of my students asked “Why do we need to know algebra? My mum said she can’t do it!” Well, my response was that she does algebra every day without even knowing it! When baking, we double the recipe. So, we multiply every amount (butter, sugar, eggs, flour and milk) by two. When buying petrol, we need to multiply the amount of petrol by the cost per litre. If it costs $60.00 to fill the tank, how much does it cost for half a tank of petrol? When calculating a taxi fare we need to add the flagfall (cost for hiring the cab) to the cost per kilometre, multiplied by the number of kilometres travelled. What other professions use algebra?
Screenshot from Learning Today
This maths game is about a machine that changes numbers – what has happened to the numbers in the table above? We will also be using balance scales as a model for algebra learning. This virtual manipulative shows how to add and subtract from both sides of the equation to find an unknown. Over the next few weeks in Term 4 you will be learning algebra – using letters to represent numbers in equations. As always, the BBC KS3 Bitesize site has excellent activities and games to help you learn about algebra, including formulas, equations, graphs, number patterns and linear sequences. I would like you to work through these activities at your own pace and ask questions as required. When you do the tests, take a screen shot and email your results to me at my gmail address. If you are finding the problems too difficult, try the BBC KS2 activities (Number) or some of the activities from the National Library of Virtual Manipulatives instead.
Another interesting maths game is at MathMovesU. “MathMovesU is an interactive virtual world where middle school students can interact with algebra, geometry, decimals, fractions, and word problems through topics they are passionate about like sports, music, and fashion. As students navigate through MathMovesU they will encounter math problems delivered through games, polls, and fun facts. The site is a great supplement to curriculum and will help students practice and improve their math skills in a fun, engaging manner.” from iLearn Technology.
