Free short notes and revision cards
Grade 6 Mathematics on Temari has 24 revision cards, arranged by the chapters of the Ethiopian national curriculum. Every card says when the rule applies, what each symbol in it stands for, and the mistake students most often make with it. They are free to read and need no account.
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When you use it
Use to avoid incorrectly assuming that divisibility by a factor guarantees divisibility by its multiples.
Watch out
A number divisible by 3 is not necessarily divisible by 9, just as a number divisible by 2 is not necessarily divisible by 4 or 8.
Drafted from Grade 6 Mathematics, pages 4-23, then checked twice before it went up
When you use it
Use to check if a large whole number is divisible by 3 or by 9 without performing long division.
Watch out
Sum all digits together. A number is divisible by 9 only if the sum is divisible by 9, not merely divisible by 3.
Drafted from Grade 6 Mathematics, pages 4-23, then checked twice before it went up
When you use it
Use to determine divisibility by 4 or 8 by inspecting only the last digits.
Watch out
Check the number formed by the last two digits for 4, and the last three digits for 8. Do not add the digits.
Drafted from Grade 6 Mathematics, pages 4-23, then checked twice before it went up
When you use it
Use to verify whether a two-digit or multi-digit whole number is divisible by 7 without standard long division.
Watch out
For numbers with three or more digits, multiply the leading number (excluding tens and ones) by 2, then add the number formed by the last two digits.
Drafted from Grade 6 Mathematics, pages 4-23, then checked twice before it went up
When you use it
Use when determining if a factor of two numbers also divides their sum or difference.
Watch out
Both numbers must be divisible by the divisor. If only one number is divisible, the sum or difference is not divisible.
Drafted from Grade 6 Mathematics, pages 4-23, then checked twice before it went up
When you use it
Use when finding the GCD and LCM of numbers written as products of prime factors.
Watch out
For GCD take only common prime bases with their smallest exponent. For LCM take all prime bases appearing in any factorization with their largest exponent.
Drafted from Grade 6 Mathematics, pages 24-58, then checked twice before it went up
When you use it
Use to instantly find GCD or LCM when one number divides another or when numbers are relatively prime.
Watch out
If a divides b, then GCD(a, b) = a and LCM(a, b) = b. If a and b are relatively prime, GCD(a, b) = 1 and LCM(a, b) = a multiplied by b.
Drafted from Grade 6 Mathematics, pages 24-58, then checked twice before it went up
When you use it
Use when finding an unknown number, GCD, or LCM given three of these values.
Watch out
This relation applies directly to pairs of numbers, not to three or more numbers together.
Drafted from Grade 6 Mathematics, pages 24-58, then checked twice before it went up
When you use it
Use when identifying prime numbers or determining the least common multiple of a set of numbers.
Watch out
Zero is a multiple of every whole number, but LCM is strictly the smallest non-zero common multiple. Also remember that 1 is neither prime nor composite.
Drafted from Grade 6 Mathematics, pages 24-58, then checked twice before it went up
When you use it
Use when an expression contains both a fraction and a decimal to be added or subtracted.
Watch out
Convert all terms to the same format, either all fractions with a common denominator or all decimals, before calculating.
Drafted from Grade 6 Mathematics, page 59 onwards, then checked twice before it went up
When you use it
Recognize this error when adding or subtracting fractions obtained after converting from decimals.
Watch out
Never add numerators directly while denominators are different. Always find the lowest common multiple of the denominators first.
Drafted from Grade 6 Mathematics, page 59 onwards, then checked twice before it went up
When you use it
Use when finding the product of a fraction or mixed number and a decimal.
Watch out
Convert mixed numbers into improper fractions first. When multiplying as decimals, count the total number of decimal digits in both factors to place the decimal point.
Drafted from Grade 6 Mathematics, page 59 onwards, then checked twice before it went up
When you use it
Use when writing the relationship showing that b divides a, denoted as b|a.
Watch out
Zero cannot divide any number, but zero is divisible by every non-zero whole number.
Drafted from Grade 6 Mathematics, page 6 onwards, then checked twice before it went up
When you use it
Use to determine if a divisor divides the sum or difference of two numbers, or to apply factors of a divisor.
Watch out
If a number is divisible by 3, it is not necessarily divisible by 9. But if it is divisible by 9, it is always divisible by 3.
Drafted from Grade 6 Mathematics, page 6 onwards, then checked twice before it went up
When you use it
Use to test if a whole number is divisible by 7. For a 2-digit number, multiply the tens digit by 3 and add the units digit. For 3 or more digits, multiply the number before the last two digits by 2 and add the last two digits.
Watch out
For numbers with 3 or more digits, multiply the leading block by 2 and add the entire two-digit ending as a number, not digit by digit.
Drafted from Grade 6 Mathematics, page 6 onwards, then checked twice before it went up
| Divisor | Divisibility Condition |
|---|---|
| Last digit is or | |
| Sum of all digits is divisible by | |
| Number formed by last two digits is divisible by | |
| Last digit is or | |
| Number is divisible by both and | |
| Number formed by last three digits is divisible by | |
| Sum of all digits is divisible by | |
| Last digit is |
When you use it
Use to quickly check whether a whole number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10 without using long division.
Watch out
Rules for 3 and 9 require summing all digits, while rules for 4 and 8 only check the last 2 or 3 digits.
Drafted from Grade 6 Mathematics, page 6 onwards, then checked twice before it went up
When you use it
Use this when a transversal cuts two lines and you want to say a pair of alternate or corresponding angles is equal.
Watch out
These angles are equal only when the two cut lines are parallel. If the question does not state or show that the lines are parallel, do not assume the angles are equal.
Drafted from Grade 6 Mathematics, pages 106-151, then checked twice before it went up
When you use it
Use this when two angles together make a right angle, for example to find a missing angle from one that is given.
Watch out
The sum must be 90°, not 180°. For 58° the partner is 32°, not 122°.
Drafted from Grade 6 Mathematics, pages 106-151, then checked twice before it went up
When you use it
Use this to find the diameter from the radius, or the radius from the diameter, before drawing a circle with a compass.
Watch out
When you use the compass, set the opening to the radius, not the diameter. For a 6 cm diameter, the compass opening is 3 cm.
Drafted from Grade 6 Mathematics, pages 106-151, then checked twice before it went up
When you use it
Use this when two angles sit side by side on a straight line, or when their sum is a straight angle, to find a missing angle.
Watch out
The sum is 180°, not 90°. Do not mix this with the complementary rule. For a missing angle, subtract from 180°.
Drafted from Grade 6 Mathematics, pages 106-151, then checked twice before it went up
When you use it
Use this when a question asks for the middle value of a data set once the values are put in order.
Watch out
Arrange the values from smallest to largest before choosing the middle. If there is an even number of values, add the two middle values and divide by 2, rather than picking just one of them.
Drafted from Grade 6 Mathematics, pages 152-179, then checked twice before it went up
When you use it
Use this when a question asks for the average of a set of values, by adding all the values and dividing by how many there are.
Watch out
Divide the total sum by the number of values, not by the largest value or by a number you chose. Count the values again before dividing.
Drafted from Grade 6 Mathematics, pages 152-179, then checked twice before it went up
When you use it
Use this when a question asks for the value that appears most often in a data set.
Watch out
If every value appears only once, there is no mode, so say so. Do not write the largest or the smallest value as the mode.
Drafted from Grade 6 Mathematics, pages 152-179, then checked twice before it went up
When you use it
Use this when you draw a pie chart from a table of values and need the angle in degrees for each sector.
Watch out
Divide each value by the total of all the values, not by the number of categories. The angles of all sectors must add up to 360 degrees.
Drafted from Grade 6 Mathematics, pages 152-179, then checked twice before it went up
The student textbook for the new curriculum, free as a PDF. The cards on this page follow its chapters.
Ministry of Education edition, Amharic
184 pages
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