Two+Step+Equations+and+Backtracking

=Two Step Equations= In this lesson we look at solving two step equations using back tracking flowcharts.

Equations involve using backtracking. Watch the youtube video for an initial overview of the process of backtracking.

media type="youtube" key="w49gh915Cko" height="345" width="420" Here are the main steps involved with Back Tracking using Flowcharts:

The first step involves working out the order of the operations that are applied to our letter variable. The “Order of Operations” is called “BODMAS” in Australia. The following PDF file will give you good practise in doing backtracking activities. == = In 2N + 5 = 11 there is adding of 5, and also multiplying by 2. = = The Order of Operations tells us that multiplying by 2 happens before the adding of 5. =

Here is a video about using the Balance Beam concept to solve a basic Two Step Equation. media type="youtube" key="NbrH8VkFGUk" height="360" width="640"

Here is a similar video that involves negative numbers in equations. media type="youtube" key="Kju3n32PYpU" height="360" width="640" Here is a slightly different kind of balancing problem, called a “Pan Balance” problem. media type="youtube" key="vbX83p0xJ9c" height="360" width="640"

=Lets return to our equation: 2N + 5 = 11= To make a Forward Flowchart to represent “N”, and the multiplying by 2 followed by the adding of 5, we need to draw three rectangles. In between the rectangles we place two arrows, because this equation has two operations (x2 and +5) performed in it. The resulting Forward Flowchart looks like this:

Back Tracking Flowcharts

Let’s now look at how we can add more boxes and arrows onto our Forward Flowchart, to make a full “Back Tracking Flowchart”. This flowchart will solve the equation for us. We add extra boxes under each of our Forward boxes, and also add back tracking arrows onto our diagram. Whenever we make a Back Tracking Flowchart, we always create the same overall structure. This may look very complicated at first, but things will become much clearer when we do some number examples. The following “Opposite” operations are always used for solving equations. Let’s return to our first example equation: 2N + 5 = 11, and see how its solution of N=3 can be worked out using Back Tracking. Checking Solutions Using Substitution We can always check the solution to any equation by substituting the number answer we obtained back into the original equation. Here is how we can check the N=3 solution for the equation 2N + 5 = 11.

=SUMMARY=

We need to set up three double box rectangles, with arrows in between them.

The letter variable always goes on its own in the top left hand box

The whole left hand “Algebra” side of the equation always goes in the third and final top box.

The Right hand side number for the equation always goes in the very right hand bottom box.

The Operations that were done on the variable letter go onto the arrows, in BODMAS or PEMDAS order on the top, and in Opposite order on the bottom.

The number answer always ends up in the bottom left hand side box.

The flowcharts for two step equations are always set up using the structure shown in the following diagram.



Online Activities and Games Interactive Equation Balancing This activity is really cool. We can click on the purple buttons to add or remove x’s or ones. As we do this, the items are added or removed from both sides of the balance. The idea is to reduce the items on the balance down until we just have one “x” on the balance. The remaining numbers on the other side of the balance tell us what the answer for the value of “x” is. This activity can be found at the following link. @http://www.mathsisfun.com/algebra/add-subtract-balance.html Poodle Weigh In This game involves putting number weights on the balance to match the weight of the strange looking Poodle. Hover the mouse over the bottom right hand corner “Help” button, to get instructions on how to play the game. Hover the mouse over the bottom left hand corner “Hint” button, to reveal the number equation which needs solving. Then click on the number weights to make them go onto the balance and add up to the required answer. To remove a number off the balance, simply click the number on the right hand side of the balance that we want to remove. The game can be played at the following link. @http://pbskids.org/cyberchase/games/algebra/algebra.html Algebraic Reasoning Here is an online puzzle Game that involves working out how much one item is, and then using this information to work out a second item. The game can be played at the following link. @http://www.mathplayground.com/algebraic_reasoning.html