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Students need to know that six-eighths is equivalent to three-fourths and that four-twelfths is equivalent to one-third.  While they can calculate these, it is very helpful to know the most common equivalent fractions by memory.  One of the most common problems students have in fractions is not “reducing their answers to simplest form.”

Here’s a 5 minute Educreations lessons on How the Equivalent Fractions program works.

Part of the Universal subscription package.

Equivalent fractions will help students commit 100 common equivalent fractions to memory.  Each set (A through Z) has four fractions which are displayed on a fraction number line.  Students frequently learn fractions equivalent to one,such as ten-tenths, as well as fractions that can’t be reduced, for example three-fourths is equivalent to three-fourths.  Using the fraction number line will help with student understanding of why those fractions are equivalent.

Click here for the full sequence of 100 Equivalent fractions that students will learn in this program.

Equivalent fractions, Factors, and Integers, are all pre-algebra programs that are appropriate for middle school students who already know the basic facts.

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The Rocket Math Addition and Multiplication Apps for iPads and iPhones are only available through iTunes.

Please click on this link to see my page with lots of information on these products and links to iTunes.

After becoming fluent with multiplication facts the best way for students to retain the knowledge of those facts is by doing multiplication computation.  If students have not been taught multiplication computation, this program breaks it down into small, easy-to-learn steps that are numbered in a teaching sequence that leaves nothing to chance.

Note that the number for each skill gives the grade level as well as indicating the teaching sequence.  Skill 3b is a 3^rd grade skill and after skill 3e is learned the next in the sequence is skill 4a.  The sequence of skills is drawn from M. Stein, D. Kinder, J. Silbert, and D. W. Carnine, (2006) Designing Effective Mathematics Instruction: A Direct Instruction Approach (4^th Edition) Pearson Education: Columbus, OH.

(3b) Multiplying 1-digit times 2-digit; no renaming

(3c) Multiplying 1-digit times 2-digit; carrying

(3d) Multiplying 1-digit times 2-digit, written horizontally.

(3e) Reading and writing thousands numbers, using commas.

(4a) Multiplying 1-digit times 3-digit

(4b) Multiplying 1-digit times 3-digit; zero in tens column

(4c) Multiplying 1 digit times 3 digit, written horizontally

(4d) Multiplying 2-digits times 2-digits.

(4e) Multiplying 2-digits times 3-digits.

(5a) Multiplying 3-digits times 3-digits.

(5b) Multiplying 3-digits times 3-digits; zero in tens column of multiplier.

For each skill there is a suggested Teaching Script giving the teacher/tutor/parent consistent (across all the skills we use the same explanation) language of instruction on how to do the skill.  The script helps walk the student through the computation process.  For the teacher, in addition to the script, there are answer keys for the five worksheets provided for each skill.

Each worksheet is composed of two parts.  The top has examples of the skill being learned that can be worked by following the script.  After working through those examples with the teacher the student is then asked to work some review problems of addition problems that are already known.  The student is asked to do as many as possible in 3 minutes—a kind of sprint.  If all is well the student should be able to do all the problems or nearly all of them, but finishing is not required.  Three minutes of review is sufficient for one day.

There are five worksheets for each skill.  Gradually as the student learns the skill the teacher/tutor/parent can provide progressively less help and the student should be able to do the problems without any guidance by the end of the five worksheets.  There are suggestions for how to give less help in the teaching scripts.
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Mixed Integers displays problems on a vertical number line and then teaches students two rules about how to solve problems that add or subtract positive and negative numbers.
Rule 1:  When you add a positive number OR subtract a negative number, go UP.
Rule 2:  When you subtract a positive number OR add a negative number, go DOWN.

Students learn how these rules play out when starting with a positive number and a negative number, gradually learn these two variations of all four types of problems.  They learn to solve a problem type using the number line and then to recognize the pattern of each problem type by working several examples of each type.  This practice gives them a chance to build fluency with each problem type as they work with their partner on the top half of the page.  You will probably not be surprised that there is a one-minute test on each set.  The goals are slightly different than before.  Students are to be 100% accurate and to meet or beat their goal from the special writing speed test for mixed integers.

8 online lessons teach students how each type of problem is solved and why it is correct.

(1) Mixed Integers Set A1 Positive add a positive

(2) Mixed Integers Set A2 Positive subtract a positive

(3) Mixed Integers Set D Negative add a positive

(4) Mixed Integers Set G Negative subtract a positive

(5) Mixed Integers Set J Negative subtract a negative

(6) Mixed Integers Set M Positive subtract a negative

(7) Mixed Integers Set P Positive add a negative

(8) Mixed Integers Set S Negative add a negative

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