Algebra is not a dirty word!

algebra

So far you have learned some really good skills that contribute to your developing understanding of algebra. Most of you are able to do the first four or five activities:

  • Recognizing and continuing number patterns – using positive and negative integers, fractions and decimals.
  • Identifying and combining like terms.
  • Substitution – replacing a number for a letter in an equation.
  • Finding the missing number in a simple equation.
  • Backtracking to solve two-step and three-step equations.

Here are some digital resources that I would like you to use to practise these skills:

Hey teacher – there’s letters in my Maths!


Learning Intention: Students should understand that pronumerals represent variable numbers in expressions and equations. They will also understand what “like” and “unlike” terms are and some of the simple algebraic conventions that mathematicians use.

Success Criteria: You will complete a series of tasks, including identifying like and unlike terms and simplifying expressions.

This week we will continue our introduction to algebra. You have already done lots of algebra without knowing it – recognizing and continuing number patterns, finding the missing angle or number and substituting values into equations.

A = the number of letters in your first name (Britt = 5)
B = the number of letters in your family name (Gow = 3)

What does A + B = ? (Britt Gow = 8) See if you can find someone in the class with the same answer as you. Did you both have the same equation?

Now see if you can make A and B equal your age. I am 46 years old, so
8A + 2B = 46. Are there other ways you can make the answer equal your age?

How could you make A and B equal today’s date? Can you make A and B equal your birthdate (day of the month you were born).

Some more algebra for beginners:

Shape times Shape is an activity where you discover which shapes represent which numbers, using a series of multiplication problems.

BBC Bitesize has an introduction to algebra using formulae.

Maths is Fun also has an introduction to algebra which includes a brief explanation with some examples.

Students then need to be able to recognise like and unlike terms. There are some more practise questions at MCA Online: Like and Unlike TermsAlgebra for Children is another site that may assist you to work with like and unlike terms.

Later in the term we will access some more difficult problems:

As each of you have netbooks to use at school and at home, you may like to access the National Library of Virtual Manipulatives site, which has a great range of interactive tasks for year 6 to 8 Algebra. I like the “Coin Problem”;“Factor Tree” and “Function Machine”.

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.

Algebra Balance Scales

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.

New Unit on Algebra next term


Prior to starting this unit students should be able to recognise simple number patterns (addition, subtraction, multiplication, division and indices) and understand that (multiplication and division) and (addition and subtraction) are opposite terms. We will start with an activity to reinforce working with positive and negative numbers at Algebasics.
“Maths is Fun” has a good Introduction to Algebra, that we will go through in class. Students then need to be able to recognise like and unlike terms. There are some more practise questions at MCA Online: Like and Unlike Terms Algebra for Children is another site that may assist you to work with like and unlike terms.

As each of you have netbooks to use at school and at home, you may like to access the National Library of Virtual Manipulatives site, which has a great range of interactive tasks for year 6 to 8 Algebra. I like the “Coin Problem”; “Factor Tree” and “Function Machine”.

I would like to be basing this unit of work on some of Dan Meyer’s Resources at “Algebra: The Supplement”. Dan Meyer has curated 40 weeks of algebra learning activities, while we have just ten weeks until the end if term, so we will try to do some of the most powerful problems that have been posed.

Sketching Linear Graphs

Miss Tara Richardson has produced another video “Sketching Linear Graphs” – her blog is at “My Blog”

Learning Intention:
Students will learn how to sketch linear graphs.
Success Criteria:
There are three different methods you can use to draw a linear graph
1. You can identify the y-intercept and gradient (rise over run) from an equation.
2. You can substitute values into an equation to find at least two co-ordinates.
3. You can use the intercept method to plot two points on the x and y axis. Plot the graph by substituting x=0 (the y-intercept) into the equation as the first point and substitute y=0 into the equation to find the second point.
Tell me which method you prefer to use and why?

Calculating Gradient on YouTube!

Learning Intention:
Students will understand how to calculate the gradient of a straight line using three different methods.
Success Criteria:
You will be able to calculate the gradient of a line when given the linear equation, the graph or two sets of co-ordinates on the line.

Over the next five weeks, Miss Tara Richardson will be taking your Maths and Science classes as part of her teaching rounds in her final year of a Graduate Diploma of Education. She has created these great videos for YouTube to assist your learning about linear equations. Do they help you to understand gradient and y-intercepts and equations? Let her know what you think about them by clicking on the ‘like’ or ‘dislike’ buttons.

Algebra versus Cockroaches

This fun game from HotMaths requires you to use linear equations to knock out cockroaches on a cartesian plane. Choose a weapon and determine the equation of the line, which represents the path of a weapon, that is used to destroy cockroaches. Draw on your knowledge of the gradient and y-intercept of a line. There are different levels which get progressively harder as you move through the levels. Hints and a printable report, outlining your progress, are also available. Let me know what you learnt in the comments below.

Slopes and Equations of lines from Geogebra  has a series of five activities which begin with asking you to choose two points on the given line, then following the instructions and using the rule for gradient, calculate the gradient. The next activities ask you to find the gradient from a line you create and the last two activities require you to find the equation of the line. Good luck and have fun! Let me know how you go in the comment section. Which of the two sites helped you to learn more about gradient and linear equations?

Gradient

The gradient of a ramp is very important if you are a builder or in a wheelchair – too steep and it is too difficult to wheel up and too shallow and it is very long and expensive to build. The Australian Standard (AS1428.1) requires that
ramps should be of a gradient of 1:14 (if over 1250mm in length) and 1:8 if less than 1250mm in length. The ramps at school were built 15 years ago; measure them and determine if they meet the current Australian Standards.

Take a photograph and measure the slope of the slide (or another example of gradient) in the playground. What is it’s gradient? (rise divided by run). Label your image (in Paint) and send it to my email address. The following screenshot shows the slopes generated in Graphmatica (Free download here). The pink line is the slope of the ramps inside our old school building. It sits between the recommended Australian standard (white) and the maximum Australian Standard (red). The new building has a wooden ramp with a slope of 1:14, which is the recommended Australian standard. Choose one of the slopes we measured and describe it in the comments below.

 

GeoGebra – Free maths software for teaching and learning

Snoopy_Geogebra

Image Source – Screenshot from Plotting Points – GeoGebra – Snoopy

GeoGebra is free mathematics software for teaching and learning originally developed as a Phd project in 2002. You can download the free program or use it online. As well as the activity above (getting practise plotting the points around the perimeter of Snoopy), there are two more cartesian plane plotting activities at Co-ordinate System. There are lots more middle school activities including Linear Equations, Transformations and Proportions. This might be a good tool for use with our on-line class in the last week of October. We could use GeoGebra to plot the points of ‘mystery’ pictures.

Today when I was in Warrnambool, I spoke to several people about how they use maths in their jobs and why they think maths is important.

 Nicole from St John of God Pathology

Maria from Cafe 103 in Warrnambool

Alan from Soulsby and Struth Pharmacy

Denise from Trewartha’s