More Multiplication Math Resources

If you are looking of  a simple grid to help students learn their multiplication or addition tables check out this PDF file that I've created. Students fill in the answers for each of the squares. This worksheet would work well with Salman Khan's Multiplication 2: The Multiplication Tables tutorial shown below.

Addition and Multiplication Grid (download)
 

Math Facts Demo Version

I expect Math Facts to be ready to come out of beta version by the end of the summer 2010. If you are interested in signing up for beta account now which will get you a discounted price for as long as you keep your account. Now is the time to sign up!

Here is a demo of multiplication problems up to 6x6. The full version allows students to save their scores and keep track of which multiplication tables they have complete and how quickly they have completed them.

Graphing Inequalities With One Variable

It is easy to get confused when graphing equations with one variable. The first thing that you need to determine is if the question is asking for the equation to be graphed on a number line or in the coordinate plane. Lets take the example mentioned in a comment on the previous post How to Graphing Inequalities in the Coordinate Plane.

x > 6 and x > 2.

First we need to recognize the inequality that answers the problem. Any x value that will correctly solve x > 6 will also work for x > 2. This means that x > 6 is a subset of x > 2. Since this is an and problem that is a solution has to work for both inequalities to be part of the solution set. This makes x > 6 the answer since it everything that works for x > 6 will also work for x > 2.

With that said we now need to determine which type of graph we need to create, assuming that you have to graph your answer. Note that in the graphs below each grid line represents 2.

If you are asked to graph the inequality on a number line your answer would be the red line, the one on top, of the graph below. I've drawn both lines so that you can see everywhere the red line is the orange is also.
Remember to make your left end points empty since the inequality is greater than but not equal to.


If you are asked to graph the inequality in the coordinate plane your answer should look like the yellowish/greenish area on the right side of the yellow line in the graph below. Like the graph above everywhere the yellow area is the green area is also.
Remember to dash your lines since this a greater than but not equal to.

Now if the problem as or instead of and you would the green and orange lines would be your answer since your solutions in the solution set would only have to answer one of the equations. Everything that works in x > 6 also works for x > 2.

Flash Muliplication Resource: 4-digit by 1-digit

I'm working with my lower grade students to help them learn to multiply larger numbers than just the simple math facts. I wanted a way to help them get lots of practice without having to grade lots of problems and still help them get the immediate feedback on how they are doing.



If you are having problems with the applet above visit the original site: 4-digit by 1-digit multiplication practice at woehler.us.

Inkscape Clock

If you are ever wanting to use an analog clock image check out file available from TpT. It was made using Inkscape and saved as a scalable vector graphic file or svg and can be easily adjusted to say whatever time you want it to. I've used it to create worksheets helping my students learn how to read time on analog clock. The hands are setup so that all you have to do is rotate them, everything else is locked by default so you will not accidentally move it. You can change any of the items in clock to personalize it to meet your needs. The image at the right is an example of what it looks like. If you want to be very precise with your settings rotate the minute hand 6 degrees equals one minute and the rotating the hour hand 0.5 degrees for one minute.

Quickly Drawing a Figure in Inkscape

Introduction:
In this lesson we will create a simple figure by creating a bunch of shapes and then combine them together. This is a technique used by many traditional drawing books that helps students see the fundamental shapes within an object.

Learning Objectives:
Learn how to use the:

• Shape tools
• Selection tool
• Edit Path tool
• Combining shapes
• Object order

Figure 1


Figure 2


Figure 3

Directions:

• Select the rectangle tool and draw a rectangle for the body by clicking and dragging the mouse with the button held down until you get the size of the body that you want. Don't worry if it is not exactly like you want you can come back and change it easily later.
• The color and outline or stroke of the body may not be want you want to change that click the fill/stroke button (the paint brush) in the tool bar at the top.
• Now remove the fill by selecting the x. Click the stroke tab and set the outline color.
  
• Now draw rectangle for the arms and legs.
• Use the circle/oval tool to draw an oval for the head.
• Use the selection tool (the arrow pointer) to make sure that all of the shapes overlap and are about the right size that you wan them to be. Now your drawing should look something like figure one.
  
• Select all of the shapes by pressing ctrl-a and select union from the objects menu. This will combine them all into one shape. Now your figure should look something like figure 2.
  
• Now click the Edit Path tool and then click the outline of your figure. You should now see the notes that control the lines. To change the location of a node click it and move it or its handles to the desired location. When you are finished your figure should look something like figure 3.
  
• Add extra features such as eyes, mouth, hair, etc.... feel free to explore the tools and add extra details.
  

Another Example:
In the cat example below I only used ovals and decided not to join all of the shapes together to give it a little bit of perspective.

How to Solve Absolute Value Inequalities

Objective:

• Find the solution of a single variable inequality equation.
  

Assumptions:

• The at you know how find the value of an inequality equation with a single variable.
  

Concepts:

• Write the problem as two variations to remove the absolute value.
• Solve as normal.
  

Directions:
Since absolute values can contain either a positive or negative number that is always evaluated to a positive number. We need to write the equation twice since we don't know if it is positive or negative. Let's use the example:
| 9 + x | < 7

| 9 + x | < 7
(9 + x ) < 7 9 - 9 + x > 7 - 9 x > -2	-(9 + x ) < 7 -(9 + x )/-1 < 7/-1 (9 + x ) > -7 9 + x > -7 9 - 9 + x > -7 - 9 x > -16
x < -2 and x > -16 -16 < x > -2

Many text books have students memorize the fact that you change the inequality sign and make the right side negative and positive but I have found that the method shown here helps students to make fewer mistakes.

Things to remember when solving absolute value inequalities.

• Isolate the absolute value to one side of the equation first.
• Remember to change the inequality sign when multiplying or dividing by a negative number.
• Less than (<) are usually and statements.
• Greater than (>) are usually or statements.
• Watch out for the exceptions such as |x| < 0 or any other value less than 0, since absolute values always evaluate to be positive it will never be less than 0.
• Watch out for the exception |x| > -1 which is all values of x. Again since the absolute value always evaluates to be positive any number that you insert will always work.
• And statements may be written two different ways whereas or statements may only be written one way.