At first, students could not think of any examples of inequalities in real life. With an example of  children as age < 13, however, they were soon off to name several. We even had a few fun digressions as we explored some "stories" behind the examples. Here are some of them:
  1. speed > 40 at school zones is speeding - somebody told a story of her granddad being booked for driving too slow (concept of minimum is important, too)
  2. senior age > 50, it brought a discussion that this is too young
  3. marrying age >= 16, too young again
  4. 13 <= teen <= 19 
  5. wins > 4 to qualify to next debating round - and a nod to one of the members of the debating team!

It soon became clear that inequalities are just as present in real life as equations are.A quick revision of step graphs showed the students that they have also seen the graphing of inequalities before.


Students were again reminded of the guiding principles regarding working with equations with the addition of:
  • with inequalities, multiplying or dividing by a negative number means reversing the sign

I believe the constant focus on the big picture with regards to equations is starting to pay off as the students are working more confidently.
 
 
The class is working with equations and have to remember these 5 points or guidelines:
  1. There is an = sign (expressions don't)
  2. LHS = RHS (balancing strategy)
  3. to solve for x, isolate it (make it the subject)
  4. use inverse or opposite operations to help isolate x
  5. during, check using points above; after, check by substitution
These points are revised in every lesson. The idea is that if they stick to these points, they can solve any type of equation: 1-step, 2-step, x on both sides, equations with fractions and directed numbers and grouping symbols.


Students have had a chance to practice using computers - see Interactives page as well as on paper. This is critical to increase proficiency in solving equations. 

 
 
We've just finished Percentages and have started Algebra. 

We are refining our algebraic techniques which we've started learning in year 7. These include the four operations (add, subtract, multiply, divide) as well as basic Index Laws and expansion of expressions, possibly even factorising...maybe.

Some very basic things to remember are:
  • pronumerals (the letters) represent numerical values - numbers in disguise; also known as variables (opposite of constant), because the values they represent can change 
  • numbers before letters (coefficient then pronumeral) when writing terms, e.g. 2y
  • numbers before letters when multiplying and dividing pronumerals, e.g. 3b x 4c = 3 x 4 and b x c = 12bc
  • no need to write 1, e.g. write b, instead of 1b
  • invisible operation means to multiply, e.g. 8m or 9(n+ 1) both mean multiply
  • like terms (matching pronumerals) apply to addition and subtraction, e.g. 4a + 5a, and 6mn - 2mn
  • x and x-squared are not like terms
  • b + b is not the same as b x b, b + b = 2b but b x b = b^2; ^ means raised to the power of 
  • rule means formula or equation or number sentence, i.e. expect to see the = sign, e.g. A = bh, t = 2m + 1. Rules can have variables and/or constants.
  • algebraic expressions do not have the = sign, e.g. 3a + 5
  • in Algebra, use what you learned about operating with whole numbers, directed numbers, fractions, decimals and percentages as well as order of operations

It's hard to believe that we've actually covered all of the above already.