1. STANDARD COMPUTATION FOR FRACTIONS
For Year Olds
Students will require a sound understanding of fractions and related concepts such as equivalence prior to working with these computations.
This presentation provides the structure (on the slides) and language (teacher notes below the slides) for developing each set of rules for the standard computational strategies with fractions. The Guide presents the view that efficiency, simplicity and accuracy are keys to using standard computations.
There are different computational strategies available for each of the four processes and students, through exposure to different models, will eventually adopt strategies that best suit them. However, it is appropriate for the most efficient computation (i.e. standard computation) for each of the 4 processes to be a key element of any school mathematics policy.
* A separate presentation is available for the standard written algorithms for 7-10 year olds.
* A separate presentation is available for the standard written algorithms for year olds.
Teachers
Some computers with earlier versions of PowerPoint may not form the algorithms correctly.
To view the slides interactively: Click on ‘Slide Show’. Click ‘From Beginning’.
Hints For Use in the Class
Coordinate your language (and student language) to the actions occurring onscreen.
To start at a specific slide: Click on Slide Show. Scroll to the Slide you want. Click From Current Slide.

2. STANDARD ALGORITHMS Add Fractions With Like Denominators Slides 3-5
Add Fractions With Unlike Denominators Slides 6-7
Subtract Fractions With Like Denominators Slides 8-9
Add and Subtract Fractions With Like Denominators Slide 10
Subtract Fractions With Unlike Denominators Slides 11-12
Multiply Whole Numbers by a Fraction or Mixed Numeral Slides 13-14
Multiply a Fraction by a Fraction or a Mixed Numeral by a Fraction Slides 15-17
Divide a Whole Number by a Fraction or a Mixed Numeral by a Fraction Slides 18-20
Divide a Fraction by a Fraction or Mixed Numeral; or a Mixed Numeral by a Fraction Slides 21-22
Find the Percentage of a Whole Slide 23
Teacher
(1) To start at a specific slide: Click on Slide Show. Scroll to the Slide you want. Click From Current Slide.
(2) To print the teacher notes for any slide: Copy and paste them into a Word doc and print.

3. 1 = + = 12 12 2 2 Say: Here we are adding a half plus a half.
Ask: Are the denominators the same?
Click once to arrow the denominators.
Click a second time to highlight the denominators.
Say: The denominators are the same so we write the denominator we will need in the answer.
Click to show the denominator of 2.
Ask: What is the total for the numerators?
Click to show the arrow adding the numerators.
Click to show the total.
Ask: Can we simplify the answer? What is another name for two halves?
Click to show the answer as 1.

4. 3 + 2 3 2 5 = 5 34 14 + 24 = 3 4 +
1 + 2
4 4
Say: Here we are adding two mixed numerals: three and a quarter plus two and two quarters.
Say: First we add the whole numbers in our head.
Click to show the addition in the thought cloud.
Click to show the total for the whole numbers.
Ask: Are the denominators the same?
Click to arrow the denominators.
Click a second time to fade the arrows.
Say: The denominators are the same so we can add the numerators in our head.
Click to show the total for the fractions.
Ask: What is the total for the whole number and the fraction?
Click to show the answer.

5. 2 = + + = 35 15 45 45 11 5 Say: Here we are adding three fractions.
Ask: Are the denominators the same?
Click to arrow the denominators.
Click a second time to highlight the denominators.
Say: The denominators are the same so we can add the numerators in our head.
Ask: What is 3+4+4?
Ask: How many fifths have we added?
Click to show the total for the fractions as an improper fraction.
Say: You can see the numerator is greater than the denominator.
Ask: What is 11 fifths as a mixed numeral?
Click to show 11 divided by 5.
Ask: What is the total for the whole number and the fraction?
Click to show the answer.

6. 1
+ 2 14 12 34 = + = 4
LCD 4
Teacher: At this level equivalence explanations are no longer required as students should be confident with these understandings. The computation is described as an adult would solve it.
Say: Here we are adding two fractions.
Ask: Are the denominators the same?
Say: The denominators are different so we need a way to make them the same.
Ask: What is the lowest common denominator or number that 4 and 2 will divide into evenly?
Click to show the term: LCD.
Click to show 4 as the lowest common denominator.
Say: We can now write 4 as the common denominator in the answer.
Click to show 4 as the common denominator.
Say: One quarter can be placed over the denominator of 4.
Click to show one quarter on the vinculum (the divider between the numerator and denominator).
Say: Now we change the half to quarters.
Ask: What is one half as quarters?
Click to show one half as two quarters on the vinculum.
Ask: What is the total for the two fractions?
Click to show the answer.

7. 4
+ 3
+ 6 = 1 12 13 14 12
1312 = = + + 12
LCD 12
Teacher: At this level equivalence explanations are no longer required as students should be confident with these understandings. The computation is described as an adult would solve it.
Say: Here we are adding three fractions.
Ask: Are the denominators the same?
Say: The denominators are different so we need a way to make them the same.
Ask: What is the lowest common denominator or number that 3, 4 and 2 will divide into evenly?
Click to show 12 as the lowest common denominator.
Say: We can now write 12 as the common denominator in the answer.
Click to show 12 as the common denominator.
Say: Now we change one third to twelfths.
Ask: What is one third as twelfths?
Click to show one third as 4 twelfths on the vinculum.
Say: Now we change one quarter to twelfths.
Ask: What is one quarter as twelfths?
Click to show one quarter as 3 twelfths on the vinculum.
Say: Now we change one half to twelfths.
Ask: What is one half as twelfths?
Click to show one half as 6 twelfths on the vinculum.
Say: You can see the numerator is greater than the denominator.
Ask: What is 13 twelfths as a mixed numeral?
Click to show the answer.

8. 46 16 3 1 2 = - = 6
Say: Here we are subtracting one sixth from four sixths.
Ask: Are the denominators the same?
Click once to arrow the denominators.
Click a second time to highlight the denominators.
Say: The denominators are the same so we write the denominator we will need in the answer.
Click to show the denominator of 6.
Ask: What is the remainder for the numerators?
Click to show the arrow subtracting the numerators.
Click to show the remainder.
Ask: What is the answer?
Ask: Can we simplify the answer? What is another name for three sixths?
Click to show the answer as 1/2.

9. 3 - 2 3 2 1 = 1 14 34 - 24 = 1 4 +
3 - 2
4 4
Say: Here we are subtracting mixed numerals: three and three quarter subtract two and two quarters.
Say: First we subtract the whole numbers in our head.
Click to show the subtraction in the thought cloud.
Click to show the remainder for the whole numbers.
Ask: Are the denominators the same?
Click to arrow the denominators.
Click a second time to fade the arrows.
Say: The denominators are the same so we can subtract the numerators in our head.
Click to show the remainder for the fractions.
Ask: What is the total emainder for the whole number and the fraction?
Click to show the answer.

10. 35 45 25 - + 35 + 25 45 - = 55 = 1 5
Teacher: The computation is described as an adult would solve it.
Say: Here we are adding and subtracting fractions.
Ask: Are the denominators the same?
Say: As the denominators are the same we can rearrange the fractions to make two small fraction sums.
Say: First we do the addition of fractions.
Click 3 times to show three fifths and two fifths being added.
Say: Now we can subtract four fifth from five fifths.
Click 2 times to show five fifths subtract four fifths.

11. 6
- 5 35 12
1 10 = - = 10
LCD 10
Teacher: At this level equivalence explanations are no longer required as students should be confident with these understandings. The computation is described as an adult would solve it.
Say: Here we are subtracting fractions.
Ask: Are the denominators the same?
Say: The denominators are different so we need a way to make them the same.
Ask: What is the lowest common denominator or number that 5 and 2 will divide into evenly?
Click to show the term: LCD.
Click to show 10 as the lowest common denominator.
Say: We can now write 10 as the common denominator in the answer.
Click to show 10 as the common denominator.
Say: Now we change the three fifths to tenths.
Ask: What is three fifths as tenths?
Click to show six tenths on the vinculum (the divider between the numerator and denominator).
Say: Now we change the half to tenths.
Ask: What is one half as tenths?
Click to show one half on the vinculum.
Ask: What is the remainder?
Click to show the answer.

12. 14 - 23 = 3 2 39
- 24 = 3 12 1 = 1 4 13 4 - 8 3 = = 15 12 12
LCD 12
Teacher: At this level equivalence explanations are no longer required as students should be confident with these understandings. The computation is described as an adult would solve it.
Say: Here we are subtracting fractions.
Say: We start by changing both mixed numerals to improper fractions.
Ask: What is three and a quarter as an improper fraction?
Click to show thirteen quarters.
Click to show the subtraction sign.
Ask: What is two and two thirds as an improper fraction?
Click to show eight thirds.
Click to show the equal sign.
Ask: Are the denominators the same?
Say: The denominators are different so we need a way to make them the same.
Ask: What is the lowest common denominator or number that 4 and 3 will divide into evenly?
Click to show the term: LCD.
Click to show 12 as the lowest common denominator.
Say: We can now write 12 as the common denominator in the answer.
Click to show 12 as the common denominator.
Say: Now we change the thirteen quarters to twelfths.
Ask: What is thirteen quarters as twelfths?
Click to show 39 twelfths on the vinculum (the divider between the numerator and denominator).
Say: Now we change the eight thirds to twelfths.
Ask: What is eight thirds as twelfths?
Click to show 24 twelfths on the vinculum.
Ask: What is the remainder in twelfths?
Click to show fifteen twelfths.
Ask: Is fifteen twelfths an improper fraction?
Ask: What is fifteen twelfths as a mixed numeral?
Click to show the answer.

13. 3 23 9 6 x = 1
Teacher: At this level equivalence explanations (including simplification) are no longer required as students should be confident with these understandings. The computation is described as an adult would solve it.
Say: Here we are finding two thirds of 9.
Ask: Can we simplify this problem?
Click to show division of 3 and 9 by 3.
Ask: Can we simplify any further?
Say: Now we multiply the top numbers.
Click to show the arrow multiplying 2x3.
Ask: What is 2 by 3?
Click to show the answer as 6.
Ask: What is two thirds of 9?

14. 1 3 2 8 12 3 x = 4 1
Teacher: At this level equivalence explanations (including simplification) are no longer required as students should be confident with these understandings. The computation is described as an adult would solve it.
Say: Here we are finding two eighths of 12.
Ask: Can we simplify the 2 and 8?
Click to show division of 2 and 8 by 2.
Ask: Can we simplify the 4 and 12?
Click to show division of 4 and 12 by 4.
Say: Now we multiply the top numbers.
Click to show the arrow multiplying 1x3.
Ask: What is 1 by 3?
Click to show the answer as .
Ask: What is two eighths of 12?

15. 1 2 1 2 1 x = 4
Teacher: At this level equivalence explanations (including simplification) are no longer required as students should be confident with these understandings. The computation is described as an adult would solve it.
Say: Here we are finding a half of a half.
Ask: Can we simplify the fractions?
Say: Now we multiply the top numbers or numerators.
Click to show the arrow multiplying 1x1.
Ask: What is 1 by 1?
Click to show the numerator 1.
Say: Now we multiply the bottom numbers or denominators.
Click to show the arrow multiplying 2x2.
Ask: What is 2 by 2?
Click to show the denominator 4.
Ask: What is a half of a half?

16. 1 1 3 4 2 3 1 x = 2 2 1
Teacher: At this level equivalence explanations (including simplification) are no longer required as students should be confident with these understandings. The computation is described as an adult would solve it.
Say: Here we are finding three quarters of two thirds.
Ask: Can we simplify the fractions?
Click to show division of 3 and 3 by 3.
Ask: Can we simplify any further?
Click to show division of 2 and 4 by 2.
Say: Now we multiply the top numbers or numerators.
Click to show the arrow multiplying 1x1.
Ask: What is 1 by 1?
Click to show the numerator 1.
Say: Now we multiply the bottom numbers or denominators.
Click to show the arrow multiplying 2x1.
Ask: What is 2 by 1?
Click to show the denominator 2.
Ask: What is three quarters of two thirds?

17. 2 2 5 2 3 x 4 12 5 2 3 8 = = 3 5 1 x 5 1
Teacher: At this level equivalence explanations (including simplification) are no longer required as students should be confident with these understandings. The computation is described as an adult would solve it.
Say: Here we are multiplying two and two fifths by two thirds.
Say: First we change the mixed numeral to an improper fraction.
Ask: What is two and two fifths as an improper fraction?
Click to show 12 fifths.
Say: Now we complete the new sum.
Click to move the x sign.
Click to move the two thirds.
Ask: Can we simplify the fractions?
Click to show division of 12 and 3 by 3.
Ask: Can we simplify any further?
Say: Now we multiply the top numbers or numerators.
Click to show the arrow multiplying 4x2.
Ask: What is 4 by 2?
Click to show the numerator 8.
Say: Now we multiply the bottom numbers or denominators.
Click to show the arrow multiplying 5x1.
Ask: What is 5 by 1?
Click to show the denominator 5.
Ask: Is eight fifths an improper fraction?
Ask: What is eight fifths as a mixed numeral?
Click to show the answer.

18. 1 2 12 ÷ 12 2 1 = 24 x
Teacher: At this level explanations of equivalence, simplification and reciprocals are no longer required as students should be confident with these understandings. The computation is described as an adult would solve it.
Say: Here we are dividing 12 by a half. We can also say that we are looking to see how many halves are in 12.
Say: First we rewrite the sum as a fraction multiplication sum.
Click to move the 12.
Say: We now change the division sign to its reciprocal, multiplication.
Click to change the division sign.
Say: Now we need to find the reciprocal of the divider one half.
Ask: What is the reciprocal of one half?
Click to show two over one.
Say: Now we have completed the new sum.
Ask: What is 12 by 2?
Click to show 24.
Ask: What is 12 divided by a half?
Ask: How many halves are in 12?

19. 8 10 20 ÷ 5 5 20 10 8 = 25 x 2 1
Teacher: At this level explanations of equivalence, simplification and reciprocals are no longer required as students should be confident with these understandings. The computation is described as an adult would solve it.
Say: Here we are dividing 20 by 8 tenths.
Say: First we rewrite the sum as a fraction multiplication sum.
Click to move the 20.
Say: We now change the division sign to its reciprocal, multiplication.
Click to change the division sign.
Say: Now we need to find the reciprocal of the divider 8 tenths.
Ask: What is the reciprocal of 8 tenths?
Click to show 10 over 8.
Say: Now we have completed the new sum.
Ask: Can we simplify the problem?
Click to show the division of 20 and 8 by 4.
Ask: Can we simplify any further?
Click to show the division of 10 and 2 by 2.
Say: Now we multiply 5 by 5.
Click to show the arrow multiplying 5x5.
Ask: What is 5 by 5?
Click to show the answer 25.
Ask: What is 20 divided by a 8 tenths?

20. 20 2 1 2 ÷ 4 20 2 5 = 8 x 1
Teacher: At this level explanations of equivalence, simplification and reciprocals are no longer required as students should be confident with these understandings. The computation is described as an adult would solve it.
Say: Here we are dividing 20 by two and a half. We can also say that we are finding how many two and a halves in 20.
Say: First we rewrite the sum as a fraction multiplication sum.
Click to move the 20.
Say: We now change the division sign to its reciprocal, multiplication.
Click to change the division sign.
Say: Now we need to find the reciprocal of the two and a half.
Ask: What is two and a half as an improper fraction?
Ask: If two and half is five halves as an improper fraction, what is the reciprocal of five halves?
Click to show 2 over 5.
Say: Now we have completed the new sum.
Ask: Can we simplify the problem?
Click to show the division of 20 and 5 by 5.
Say: Now we multiply 4 by 2.
Click to show the arrow multiplying 4x2.
Ask: What is 4 by 2?
Click to show the answer 8.
Ask: What is 20 divided by two and a half?
Ask: How many two and a halves in 20?

21. 3 5 3 2 2 3 9 x = ÷ 10
Teacher: At this level explanations of equivalence, simplification and reciprocals are no longer required as students should be confident with these understandings. The computation is described as an adult would solve it.
Say: Here we are dividing three fifths by two thirds.
Say: First we rewrite the sum as a fraction multiplication sum.
Say: We first change the division sign to its reciprocal, multiplication.
Click to fade the division sign.
Click to show the multiplication sign.
Say: Now we need to find the reciprocal of two thirds.
Ask: What is the reciprocal of two thirds?
Click to fade two thirds.
Click to show 3 over 2 or three halves.
Ask: Can we simplify the problem?
Say: Now we multiply the numerators.
Ask: What is 3 by 3?
Click to show the numerator in the answer.
Say: Now we multiply the denominators.
Ask: What is 5 by 2?
Click to show the denominator in the answer.
Ask: What is three fifths divided by two thirds?

22. 1 2 ÷ 3 = 7 1 2 5 2 3 1 15 = x 2
Teacher: At this level explanations of equivalence, simplification and reciprocals are no longer required as students should be confident with these understandings. The computation is described as an adult would solve it.
Say: Here we are dividing two and a half by one third.
Say: First we rewrite the sum as a fraction multiplication sum.
Ask: What is two and a half as an improper fraction?
Click to show 5 over 2.
Say: Now we change the division sign to its reciprocal, multiplication.
Click to change the division sign to the multiplication sign.
Say: Now we need to find the reciprocal of one third.
Ask: What is the reciprocal of one third?
Click to change one third to 3 over 1.
Ask: Can we simplify the problem?
Say: Now we multiply the numerators.
Ask: What is 5 by 3?
Click to show the numerator in the answer.
Say: Now we multiply the denominators.
Ask: What is 2 by 1?
Click to show the denominator in the answer.
Ask: Is 15 over 2 an improper fraction?
Ask: What is 5 over 2 as a mixed numeral?
Click to show the answer.

23. 10% of 60 1 x 6 10
100 60 6 = x 10 1
Teacher: At this level explanations of simplification are no longer required as students should be confident with these understandings. The computation is described as an adult would solve it.
Say: Here we are finding 10% of 60.
Say: First we write the problem as a fraction problem.
Click to show 10% as a fraction of 100.
Click to show the x sign.
Click to show 60 and = sign.
Ask: Can we simplify the problem?
Click to show the division of 10 and 100 by 10.
Ask: Can we simplify the problem any further?
Click to show the division of 10 and 60 by 10.
Say: Now we multiply 1 by 6.
Click to show the arrow multiplying 1x6.
Ask: What is 1 by 6?
Click to show the answer 6.
Ask: What is 10 percent of 60?