1. STANDARD ALGORITHMS YEARS 4-7
An algorithm is a set of rules for solving a maths computation which, if done properly, will always give a correct answer.
While an algorithm is an important aspect of mathematical knowledge and skill, students need to recognise that they can choose from mental computation, a written algorithm or a mathematical tool such as a calculator or abacus in solving a problem.
There are many algorithms for each of the four processes and students, through exposure to different models, will eventually adopt models that best suit them. However, it is appropriate for the most efficient algorithm (i.e. standard algorithm) for each of the 4 processes to be a key element of any school mathematics policy.
This presentation provides the structure (on the slides) and language (teacher notes below the slides) for developing each set of rules for the standard algorithms across Years 4, 5, 6, 7. The Guide presents the view that efficiency, simplicity and accuracy are, from Year 5, keys to using written algorithms.
* A separate presentation is available for the standard algorithms across years 2, 3, 4.
* Another presentation is also available for standard fraction computations in addition, subtraction, multiplication and division.
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.
Coming Soon
Interactive PowerPoint activities for many areas of content from the ACM.

2. STANDARD ALGORITHMS Years 4-7
Add Whole Numbers With Regrouping Slides 3-5
Add Decimal Numbers With Regrouping Slides 6-8
Subtract Whole Numbers With Regrouping Slides 9-12
Subtract Decimal Numbers With Regrouping Slides 13-14
Multiply Whole Numbers With Regrouping Slides 15-18
Multiply Decimal Numbers With Regrouping Slides 19-22
Divide Whole Numbers With Regrouping Slides 23-28
Divide Decimal Numbers With Regrouping Slides 29-32
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. 47 + 15 6 2 1 Say: We are going to add two numbers 15 and 47.
Say: We can add the ones first.
Click to show the arrow adding 5+7
Ask: What is 5 plus 7?
Say: We can show 2 in the ones column and place 1 ten in the tens column.
Click to show the 2 in the ones column.
Click to show 1 ten added to the tens column
Say: Now we add the tens.
Ask: Can you tell me the tens we need to add up?
Click to show the arrow adding 1+4+1
Ask: What is 1 plus 4 plus 1?
Click to show the total of 6 tens.
Ask: What is the total when you add 15 and 47?

4. 474 + 158 6 3 2 1 1 Say: We are going to add two numbers 158 and 474.
Say: We can add the ones first.
Click to show the arrow adding 8+4
Ask: What is 8 plus 4?
Say: We can show 2 in the ones column and place 1 ten in the tens column.
Click to show the 2 in the ones column.
Click to show 1 ten added to the tens column.
Say: Now we add the tens.
Ask: Can you tell me the tens we need to add up?
Click to show the arrow adding 5+7+1
Ask: What is 5 plus 7 plus 1?
Say: We can show 3 in the tens column and place 1 hundred in the hundreds column.
Click to show the 3 in the tens column.
Click to show the 1 hundred added to the hundreds column.
Say: Now we add the hundreds.
Ask: Can you tell me the hundreds we need to add up?
Click to show the arrow adding 1+4+1
Ask: What is 1 plus 4 plus 1?
Click to show the total of 6 hundreds.
Ask: What is the total when you add 158 and 474?

5. 474
458
+ 307 1 1
1 2 3 9
Teacher: At this level place value explanations are no longer required as students should be confident with these understandings. The algorithm is described as an adult would solve it.
Say: We are going to add three numbers 307, 458 and 474.
Say: We add the ones first.
Ask: What is 7 plus 8 plus 4?
Click to show the arrow adding 7+8+4
Say: Put 9 in the answer and regroup 1 to the tens.
Click to show the 9 in the answer.
Click to show 1 regrouped to the tens.
Say: Now we add the tens.
Ask: What is 0 plus 5 plus 7 plus 1?
Click to show the arrow adding
Say: Put 3 in the answer and regroup 1 to the hundreds.
Click to show the 3 in the answer.
Click to show 1 regrouped to the hundreds.
Say: Now we add the hundreds.
Ask: What is 3 plus 4 plus 4 plus1?
Click to show the arrow adding
Click to show the total of 12 hundreds.
Ask: What is the total when you add 307, 458 and 474?

6. 4.5 + 1.5 6 . 1 Say: We are going to add two numbers 1.5 and 4.5
Say: We are going to add two numbers 1.5 and 4.5
Say: We can add the tenths first.
Click to show the arrow adding 5+5
Ask: What is 5 plus 5?
Say: We can show 0 in the tenths column and regroup 1 to the ones.
Click to show the 0 in the tenths column.
Click to show 1 regrouped.
Say: The next column shows the decimal points for each number.
Ask: Where should we place the decimal point for the answer?
Click to show the decimal point in the answer line.
Say: Now we add the ones.
Ask: Can you tell me the ones we need to add up?
Click to show the arrow adding 1+4+1
Ask: What is 1 plus 4 plus 1?
Click to show the total of 6.
Ask: What is the total when you add 1.5 and 4.5?

7. 4.32
+ 1.68 1 1 6 .
Say: We are going to add two numbers 1.68 and 4.32.
Say: We can add the hundredths first.
Click to show the arrow adding 8 +2
Ask: What is 8 hundredths plus 2 hundredths?
Say: We can show 0 in the hundredths column and regroup 1 tenth in the tenths column.
Click to show the 0 in the hundredths column.
Click to show 1 tenth regrouped to the tenths column.
Say: Now we add the tenths.
Ask: Can you tell me the tenths we need to add up?
Click to show the arrow adding 6+3+1
Ask: What is 6 tenths plus 3 tenths plus 1 tenth?
Say: We can show 0 in the tenths column and regroup 1 in the ones column.
Click to show the 0 in the tenths column.
Click to show 1 regrouped to the ones column.
Say: The next column shows the decimal points for each number.
Ask: Where should we place the decimal point for the answer?
Click to show the decimal point in the answer line.
Say: Now we add the ones.
Ask: Can you tell me the ones we need to add up?
Click to show the arrow adding 1+4+1
Ask: What is 1 plus 4 plus 1?
Click to show the total of 6 ones.
Ask: What is the total when you add 1.68 and 4.32?

8. 9.74
4.58
+ 0.07 1 1
1 4 . 3 9
Teacher: At this level place value explanations are no longer required as students should be confident with these understandings. The algorithm is described as an adult would solve it.
Say: We are going to add three numbers 0.07, 4.58 and 9.74
Say: We add the hundredths first.
Ask: What is 7 plus 8 plus 4?
Click to show the arrow adding 7+8+4
Say: Put 9 in the answer and regroup 1 to the tenths.
Click to show the 9 in the answer.
Click to show 1 regrouped.
Say: Now we add the tenths.
Ask: What is 0 plus 5 plus 7 plus 1?
Click to show the arrow adding
Say: Put 3 in the answer and regroup 1 to the ones.
Click to show the 3 in the answer.
Say: Now we add the ones.
Ask: What is 0 plus 4 plus 9 plus1?
Click to show the arrow adding
Click to show the total of 14.
Ask: What is the total when you add 0.07, 4.58 and 9.74?

9. 40 - 15 2 5 3 1 - - Say: We are going to subtract 15 from 40.
Say: We can subtract the ones first. However, we can’t take 5 from zero.
Say: We can fix that by taking 10 from 40 and adding it to the ones place.
Say: Watch carefully while I do this.
Click to show the 4 crossed out. Say: We regroup ten from the 4 tens.
Click to show 3 above the tens. Say: We now have 3 tens left.
Click to show 10 above the ones. Say: And now we have 10 in the ones place.
Say: We can now take 5 from 10.
Click to show the arrow for subtracting subtract 5 from 10.
Ask: What is 10 take 5?
Click to show the remainder 5.
Say: We can now take 1 ten from 3 tens.
Click to show the arrow for subtracting 1 from 3.
Ask: What is 3 take 1?
Click to show the remainder 2.
Ask: We have subtracted 15 from 40. What is the remainder?

10. 1
2 365 1 2 1 - - - - 9 9 1
Teacher: At this level place value explanations are no longer required as students should be confident with these understandings. The algorithm is described as an adult would solve it.
Say: We are going to subtract 1374 from 2365.
Say: We can subtract the ones first.
Ask: What is 5 take 4?
Click to show the remainder 1.
Say: We can now subtract the tens. However, 7 is greater than 6. We need to regroup.
Click to show the 3 crossed out.
Say: We regroup to the ones for 16 altogether.
Click to show 1 regrouped to the tens.
Say: We now have 2 hundreds left.
Click to show the 2 hundreds.
Ask: What is 16 take 7?
Click to show the arrow for subtracting 7 from 16.
Click to show the remainder 9.
Say: We can now subtract the hundreds. However, 3 is greater than 2. We need to regroup again.
Click to show the 2 crossed out.
Say: We regroup to the hundreds for 12 altogether.
Click to show 1 regrouped to the hundreds.
Say: We now have 1 thousand left.
Click to show the 1 thousand.
Ask: What is 12 take 3?
Click to show the arrow for subtracting 3 from 12.
Say: We can now take 1 from 1.
Ask: What is 1 take 1?
Click to show the arrow for subtracting 1 from 1.
Say: There are zero thousands so we leave the thousands place in the answer empty.
Ask: We have subtracted 1374 from What is the remainder?

11. 405
- 237 39 1 - - - 1 6 8
Teacher: At this level place value explanations are no longer required as students should be confident with these understandings. The algorithm is described as an adult would solve it.
Say: We are going to subtract 237 from 405.
Say: We can subtract the ones first. However, 7 is greater than 5. We need to regroup.
Say: We can’t take 1 from 0 so we regroup from the 40.
Click to show the 40 crossed out.
Say: We regroup to the ones for 15 altogether.
Say: We now have 39 tens left.
Click to show 39 tens.
Ask: What is 15 take 7?
Click to show the arrow for subtracting 7 from 15.
Click to show the remainder 8.
Say: We can now take 3 from 9.
Click to show the arrow for subtracting 3 from 9.
Ask: What is 9 take 3?
Click to show the remainder 6.
Say: We can now take 2 from 3.
Ask: What is 3 take 2?
Click to show the arrow for subtracting 2 from 3.
Click to show the remainder 1.
Ask: We have subtracted 237 from 405. What is the remainder?

12. 1 4 3
542
- 245 1 - - - 2 9 7
Teacher: At this level place value explanations are no longer required as students should be confident with these understandings. The algorithm is described as an adult would solve it.
Say: We are going to subtract 245 from 542.
Say: We can subtract the ones first. However, 5 is greater than 2. We need to regroup.
Click to show the 4 crossed out.
Say: We regroup 1 to the ones for 12 altogether.
Click to show 1 regrouped to the ones.
Say: We now have 3 tens left.
Click to show the 3 tens.
Ask: What is 12 take 5?
Click to show the arrow for subtracting 5 from 12.
Click to show the remainder 7.
Say: We can now subtract the tens. However, 4 is greater than 3. We need to regroup again.
Click to show the 5 crossed out.
Say: We regroup 1 to the tens for 13 altogether.
Click to show 1 regrouped to the tens.
Say: We now have 4 hundreds left.
Click to show the 4 hundreds.
Ask: What is 13 take 4?
Click to show the arrow for subtracting 4 from 13.
Click to show the remainder 9.
Say: We can now take 2 from 4.
Ask: What is 4 take 2?
Click to show the arrow for subtracting 2 from 4.
Click to show the remainder 2.
Ask: We have subtracted 245 from 542. What is the remainder?

13. 4.0 - 1.9 2 . 1 3 1 - - Say: We are going to subtract 1.9 from 4.0.
Say: We can subtract the tenths first. However, we can’t take 9 tenths from zero tenths.
Say: We can fix that by taking 10 tenths from 4 ones and adding it to the tenths place.
Say: Watch carefully while I do this.
Click to show the 4 crossed out. Say: We take 10 tenths from the 4 ones.
Click to show 3 above the ones. Say: We now have 3 ones left.
Click to show 10 added to the ones. Say: And now we have 10 in the tenths place.
Say: We can now subtract the tenths.
Click to show the arrow subtracting 9 from 10.
Ask: What is 10 take 9?
Click to show the remainder 1.
Say: The next column shows the decimal points for each number.
Ask: Where should we place the decimal point for the answer?
Click to show the decimal point in the answer line.
Say: We can now take 1 from 3.
Click to show the arrow subtracting 1 from 3.
Ask: What is 3 take 1?
Click to show the remainder 2.
Ask: We have subtracted 1.9 from 4.0. What is the remainder?

14. 1 4
4.55
- 3.57 3 1 - - - . 9 8
Teacher: At this level place value explanations are no longer required as students should be confident with these understandings. The algorithm is described as an adult would solve it.
Say: We are going to subtract 3.57 from 4.55.
Say: We can subtract the hundredths first. However, 7 is greater than 5. We need to regroup.
Click to show the 5 crossed out.
Say: We regroup 1 to the hundredths for 15 altogether.
Click to show 1 regrouped to the hundredths.
Say: We now have 4 tenths left.
Click to show the 4 tenths.
Ask: What is 15 take 7?
Click to show the arrow for subtracting 7 from 15.
Click to show the remainder 8.
Say: We can now subtract the tenths. However, 5 is greater than 4. We need to regroup again.
Click to show the 4 ones crossed out.
Say: We regroup 1 to the tenths for 14 altogether.
Click to show 1 regrouped to the tenths.
Say: We now have 3 ones left.
Click to show the 14 tenths.
Ask: What is 14 take 5?
Click to show the arrow for subtracting 5 from 14.
Click to show the remainder 9.
Say: The next column shows the decimal points for each number.
Ask: Where should we place the decimal point for the answer?
Click to show the decimal point in the answer line.
Say: We can now take 3 from 3.
Ask: What is 3 take 3?
Click to show the arrow for subtracting 3 from 3.
Click to show the remainder 0.
Ask: We have subtracted 3.57 from What is the remainder?

15. 45 X 3 13 5 12 + 1 5 x x Say: We are going to multiply 45 by 3.
Say: We can multiply the ones first.
Click to show the arrow multiplying 3x5
Ask: What is 3x5?
Say: 15 can be shown as 5 ones and 1 ten.
Click to show the total of 15 as 5 ones and 1 ten.
Say: The 5 ones are now recorded in the answer.
Click to record the 5 ones.
Say: Now we multiply the tens.
Click to show the arrow multiplying 3x4 tens
Ask: What is 3x4 tens?
Click to show the total of 12 tens.
Say: We now add the 12 tens to the 1 ten.
Click to show the addition sign.
Say: We now have 13 tens.
Say: The 13 tens are now recorded in the answer.
Click to record the 13 tens.
Say: We have multiplied 45 by 3.
Ask: What is the product when you multiply 45 by 3?

16. 326 X 2 6 5 2 1 Say: We are going to multiply 326 by 2.
Say: We can multiply the ones first.
Click to show the arrow multiplying 2x6
Ask: What is 2x6?
Say: 12 is shown as 2 ones and we regroup 1 ten.
Click to show the total of 12 as 2 ones and 1 ten.
Say: Now we multiply the tens.
Click to show the arrow multiplying 2x2.
Ask: What is 2x2?
Say: Now we have 4 tens and add the ten we regrouped for a total of 5 tens.
Click to show the total of 5 tens.
Say: Now we multiply the hundreds.
Click to show the arrow multiplying 2x3.
Ask: What is 2x3?
Click to show the total of 6 hundreds.
Say: We have multiplied 326 by 2.
Ask: What is the product when you multiply 326 by 2?

17. 654
X 5 2 2
3 2 7
Teacher: At this level place value explanations are no longer required as students should be confident with these understandings. The algorithm is described as an adult would solve it.
Say: We are going to multiply 654 by 5.
Say: We can multiply the ones first.
Click to show the arrow multiplying 5x4
Ask: What is 5x4?
Say: We record the 0 and we regroup 2.
Click to show 0 recorded and 2 regrouped.
Say: Now we multiply the tens.
Click to show the arrow multiplying 5x5.
Ask: What is 5x5?
Say: And now we add 2 to the 25.
Say: We record the 7 and we regroup 2.
Click to show 7 recorded and 2 regrouped.
Say: Now we multiply the hundreds.
Click to show the arrow multiplying 5x6.
Ask: What is 5x6?
Say: And now we add 2 to the 30.
Say: We record the 32.
Click to show 32 recorded.
Say: We have multiplied 654 by 5.
Ask: What is the product when you multiply 654 by 5?

18. 64
X 23 1 1 19 2 12 8 1 4 7 2
Teacher: All but one place value explanation have been left out of the description below. At this level place value explanations are no longer required as students should be confident with these understandings. The algorithm is described as an adult would solve it.
Say: We are going to multiply 64 by 23.
Say: We can multiply 64 by 3 first.
Say: Start by multiplying 3x4.
Click to show the arrow multiplying 3x4
Click to fade the arrow.
Ask: What is 3x4?
Say: We record the 2 and we regroup 1.
Click to show 2 recorded and 1 regrouped.
Say: Now we multiply 3x6.
Click to show the arrow multiplying 3x6.
Ask: What is 3x6?
Say: And now we add 1 to the 18.
Click to show 19 recorded.
Say: We have now recorded the product for 3x64.
Ask: What is the product of 3x64?
Say: Next we are going to multiply from the tens column so we enter a zero first.
Say: We now multiply 2x4.
Click to show the arrow multiplying 2x4.
Ask: What is 2x4?
Click to show 8 recorded.
Say: Now we multiply the 2x6.
Click to show the arrow multiplying 2x6.
Ask: What is 2x6?
Click to show 12 recorded.
Say: We have now recorded the product of 20x64.
Ask: What is the product of 20x64?
Say: Now we add the two products to find the total for 23x64.
Say: Watch as the total is added.
Click to add the ones, tens, hundreds and thousands in sequence.
Say: We have multiplied 64x23.
Ask: What is the product when you multiply 64x23?

19. 4.5 X 3 13 . 5 12 1 5 + x x Say: We are going to multiply 4.5 by 3.
Say: We can multiply the tenths first.
Click to show the arrow multiplying 3x.5
Ask: What is 3x.5?
Say: 1.5 can be shown as 5 tenths and 1
Click to show the total of 1.5 as 5 tenths and 1
Say: The 5 tenths are now recorded in the answer.
Say: Next we multiply the ones.
Say: However, before we multiply the ones we need to separate the whole numbers and decimal numbers in the answer with a decimal point.
Ask: Where should the decimal point go in the answer?
Click to show the decimal point.
Say: Now we multiply the ones.
Click to show the arrow multiplying 3x4
Ask: What is 3x4?
Click to show the total of 12.
Say: We now add the 12 to the 1.
Click to show the addition sign.
Say: We now have 13.
Say: 13 is now recorded in the answer.
Click to record 13.
Say: We have multiplied 4.5 by 3.
Ask: What is the product when you multiply 4.5 by 3?

20. 32.6 X 2 6 5 . 2 1 Say: We are going to multiply 32.6 by 2.
Say: We can multiply the tenths first.
Click to show the arrow multiplying 2x6.
Ask: What is 2x.6?
Say: 1.2 is shown as 2 tenths and we regroup 1.
Click to show the total of 1.2 as 2 tenths and 1.
Say: The 2 tenths are now recorded in the answer.
Say: We need to also show the decimal point in our answer.
Click to show the decimal point.
Say: Now we multiply the ones.
Click to show the arrow multiplying 2x2.
Ask: What is 2x2?
Say: Now we have 4 and the 1 we regrouped for a total of 5.
Click to show the total of 5.
Say: Now we multiply the tens.
Click to show the arrow multiplying 2x3.
Ask: What is 2x3?
Click to show the total of 6 tens.
Say: We have multiplied 32.6 by 2.
Ask: What is the product when you multiply 32.6 by 2?

21. 6.54
X 5 2 2 32 . 7
Teacher: At this level place value explanations are no longer required as students should be confident with these understandings. The algorithm is described as an adult would solve it.
Say: We are going to multiply 6.54 by 5.
Say: We can multiply the hundredths first.
Click to show the arrow multiplying 5x4
Ask: What is 5x4?
Say: We record the 0 and we regroup 2.
Click to show 0 recorded and 2 regrouped.
Say: Now we multiply the tenths.
Click to show the arrow multiplying 5x5.
Ask: What is 5x5?
Say: And now we add 2 to the 25.
Say: We record the 7 and we regroup 2.
Click to show 7 recorded and 2 regroup.
Say: Now we multiply the ones.
Say: Before we do that enter the decimal point in the answer.
Click to show the decimal point in the answer.
Click to show the arrow multiplying 5x6.
Ask: What is 5x6?
Click to show the total of 30.
Say: And now we add 2 to the 30.
Say: We record the 32.
Click to show 32 recorded.
Say: We have multiplied 6.54 by 5.
Ask: What is the product when you multiply 6.54 by 5?

22. 6.4
X 2.3 1 1
1 9 2 12 8 1 4 . 7 2
Teacher: Some place value explanations have been left in the description below. However, at this level all place value explanations are not required as students should be confident with these understandings. The algorithm is largely described as an adult would solve it.
Say: We are going to multiply 6.4 by 2.3
Say: We can multiply 6.4 by .3 first.
Say: Start by multiplying .3x.4
Click to show the arrow multiplying 3x4
Click to fade the arrow.
Ask: What is .3x.4?
Say: We record the 2 and we regroup 1.
Click to show 0.02 recorded and 1 regrouped.
Say: Now we multiply .3x6
Click to show the arrow multiplying 3x6.
Ask: What is .3x6?
Say: And now we add 1 to the 18.
Click to show 1.9 recorded.
Say: Next we are going to multiply 2x.4.
Click to show the arrow multiplying 2x4.
Ask: What is 2x.4?
Click to show 0.8 recorded.
Say: Now we multiply the 2x6.
Click to show the arrow multiplying 2x6.
Ask: What is 2x6?
Click to show 12 recorded.
Say: We have recorded the products of 6.4x.3 and 6.4x2
Say: Now we add the two products to find the total for 6.4x2.3
Say: Watch as the total is added.
Click to add the hundredths, tenths, ones and tens in sequence.
Say: Now we need to enter the decimal point in the answer.
Ask: Where does the decimal point go?
Click to show the decimal point.
Say: We have multiplied 6.4x2.3
Ask: What is the product when you multiply 6.4x2.3?

23. 3 69 2 3 ÷ ÷
Say: We are going to divide 69 by 3. (Or we are going to find how many sets of 3 we can make from 69. Or we are going to divide 69 into 3 equal groups.)
Say: We divide the 6 tens by 3 first.
Ask: What is 6 divided by 3?
Click to show the arrow dividing 6 tens by 3.
Click to show the quotient of 2 tens.
Say: We can now divide the 9 ones by 3.
Click to show the arrow dividing 9 by 3.
Ask: What is 9 divided by 3?
Click to show the quotient of 3.
Ask: How many sets of 3 can we make from 69?
Ask: If we divide 69 into 3 groups, how many will be in each group?

24. 3 672 2 2 4 1 ÷ ÷ ÷
Teacher: At this level place value explanations are no longer required as students should be confident with these understandings. The algorithm is described as an adult would solve it.
Say: We are going divide to 672 by 3.
Say: We divide the 6 by 3 first.
Click to show the arrow dividing 6 by 3.
Ask: What is 6 divided by 3?
Click to show the quotient of 2.
Say: Now we divide the 7 by 3.
Click to show the arrow dividing 7 by 3.
Ask: Can 7 be evenly divided by 3? Why not?
Ask: What is 7 divided by 3?
Say: Now regroup the remainder of 1 to the 2.
Click to show 1 regrouped.
Say: Now we divide the 12 by 3.
Ask: What is 12 divided by 3?
Click to show the arrow dividing 12 by 3.
Click to show the quotient of 4.
Ask: What is the answer when we divide 672 by 3?

25. 4 500 1 2 5 1 2 ÷ ÷ ÷
Teacher: At this level place value explanations are no longer required as students should be confident with these understandings. The algorithm is described as an adult would solve it.
Say: We are going divide to 500 by 4.
Say: We divide the 5 by 4 first.
Click to show the arrow dividing 5 by 4.
Ask: What is 5 divided by 4?
Click to show the quotient of 1.
Say: Now regroup the remainder of 1 to the 0.
Click to show 1 regrouped.
Say: Now we divide the 10 by 4.
Click to show the arrow dividing 10 by 4.
Ask: What is 10 divided by 4?
Click to show the quotient of 2.
Say: Now regroup the remainder of 2 to the 0.
Click to show 2 regrouped.
Say: Now we divide the 20 by 4.
Click to show the arrow dividing 20 by 4.
Ask: What is 20 divided by 4?
Click to show the quotient of 5.
Ask: What is the answer when we divide 500 by 4?

26. 4 324 8 1 ÷ ÷ ÷
Teacher: At this level place value explanations are no longer required as students should be confident with these understandings. The algorithm is described as an adult would solve it.
Say: We are going divide to 324 by 4.
Click to show the arrow dividing 3 by 4.
Say: We divide the 3 by 4 first but 4 is greater than 3.
Say: We now divide 32 by 4.
Click to show the arrow dividing 32 by 4.
Ask: What is 32 divided by 4?
Click to show the quotient of 8.
Say: Now we divide the 4 by 4.
Click to show the arrow dividing 4 by 4.
Ask: What is 4 divided by 4?
Click to show the quotient of 1.
Ask: How many sets of 4 can we make from 324?
Ask: If we divide 324 into 4 groups, how many will be in each group?

27. 5 294 5 8 r4 4 ÷ ÷ ÷
Teacher: At this level place value explanations are no longer required as students should be confident with these understandings. The algorithm is described as an adult would solve it.
Say: We are going divide to 294 by 5.
Click to show the arrow dividing 2 by 5.
Say: We divide the 2 by 5 first but 5 is greater than 2.
Say: We now divide 29 by 5.
Click to show the arrow dividing 29 by 5.
Ask: What is 29 divided by 5?
Click to show the quotient of 5.
Say: Now regroup the remainder of 4 to the 4.
Click to show 4 regrouped.
Say: Now we divide the 44 by 5.
Click to show the arrow dividing 44 by 5.
Ask: What is 44 divided by 5?
Click to show the quotient of 8.
Say: Now we have a remainder of 4.
Click to show the 4 as a whole number remainder.
Ask: What is the answer when we divide 294 by 5?

28. 1 9 6 r6 14 9
9 x 15 = 135 ÷ ÷ ÷ ÷
6 x 15 = 90
Teacher: Double digit divisors can be explored by students but it should not take too much of your teaching time as it is more efficient to solve these problems using a calculator.
At this level place value explanations are no longer required as students should be confident with these understandings. The algorithm is described as an adult would solve it.
Say: We are going to divide 2946 by 15.
Click to show the arrow dividing 2 by 15.
Say: We divide the 2 by 15 first but 15 is greater than 2.
Say: We now divide 29 by 15.
Click to show the arrow dividing 29 by 15.
Ask: What is 29 divided by 15?
Click to show the quotient of 1.
Say: Now regroup the remainder of 14 to the 4.
Click to show 14 regrouped.
Say: Now we divide the 144 by 15.
Click to show the arrow dividing 144 by 15.
Ask: What is 144 divided by 15?
Say: To find the nearest number to 144 that is divisible by 15 you can do a multiplication sum. For example, 10x15 is 150 but that is greater than 144.
Try 9x15 and the total is 135.
Click to show 9x15=135
Say: This is the closest number to 144 that is divisible by 15.
Click to show the quotient of 9.
Say: Now regroup the remainder of 9 to the 6.
Click to show 9 regrouped.
Say: Now we divide the 96 by 15.
Click to show the arrow dividing 96 by 15.
Ask: What is 96 divided by 15?
Say: To find the nearest number to 96 that is divisible by 15 you can do a multiplication sum. For example, try 6x15 and the total is 90.
Click to show 6x15=90
Say: This is the closest number to 96 that is divisible by 15.
Click to show the quotient of 6.
Say: Now we have a remainder of 6.
Click to show the 6 as a whole number remainder.
Ask: What is the answer when we divide 2946 by 15? What is the remainder?

29. 3 64.2 2 1 . 4 1 ÷ ÷ ÷
Teacher: At this level place value explanations are no longer required as students should be confident with these understandings. The algorithm is described as an adult would solve it.
Say: We are going divide to 64.2 by 3.
Say: We divide the 6 by 3 first.
Click to show the arrow dividing 6 by 3.
Ask: What is 6 divided by 3?
Click to show the quotient of 2.
Say: Now we divide the 4 by 3.
Click to show the arrow dividing 4 by 3.
Ask: Can 4 be evenly divided by 3? Why not?
Ask: What is 4 divided by 3? What can we do with the 1 remainder?
Say: Now regroup the remainder of 1 to the 2.
Click to show 1 regrouped.
Say: Now we are dividing after the decimal point. The decimal point also needs to be shown in the answer.
Click to show the decimal point.
Ask: What is 12 divided by 3?
Click to show the quotient of 4.
Ask: What is the answer when we divide 64.2 by 3?

30. 4 $5 $ 1 . 2 5
.00 1 2 ÷ ÷ ÷
Teacher: At this level place value explanations are no longer required as students should be confident with these understandings. The algorithm is described as an adult would solve it.
Say: We are going divide to $5 by 4.
Say We place the dollar sign in the answer first.
Click to show the $ sign.
Say: Now we divide the 5 by 4.
Click to show the arrow dividing 5 by 4.
Click to show the quotient of 1.
Ask: What can we do with the 1 remainder?
Say: We need to use zeros to create place holders for the cents.
Say: Now we can regroup the remainder of 1 to the 0.
Click to show 1 regrouped.
Say: As we are now we are dividing after the decimal point, the decimal point also needs to be shown in the answer.
Click to show the decimal point.
Say: Now we divide the 10 by 4.
Ask: What is 10 divided by 4?
Click to show the arrow dividing 10 by 4.
Click to show the quotient of 2.
Ask: What can we do with the 2 remainder?
Say: Now regroup the remainder of 2 to the 0.
Click to show 2 regrouped.
Say: Now we divide the 20 by 4.
Ask: What is 20 divided by 4?
Click to show the arrow dividing 20 by 4.
Click to show the quotient of 5.
Ask: What is the answer when we divide $5 by 4?

31. 5 2.94 . 5 8 8 2 4 4 ÷ ÷ ÷ ÷
Teacher: At this level place value explanations are no longer required as students should be confident with these understandings. The algorithm is described as an adult would solve it.
Say: We are going divide to 2.94 by 5.
Click to show the arrow dividing 2 by 5.
Say: First we divide the 2 by 5 but 5 is greater than 2.
Say: We enter a zero place holder to show 2 can’t be divided by 5.
Click to show the zero place holder.
Say: Now we need to regroup the 2 to the 9.
Say: As we are now dividing after the decimal point a decimal point also needs to be shown in the answer.
Click to show the decimal point.
Say: We now divide 29 by 5.
Click to show the arrow dividing 29 by 5.
Ask: What is 29 divided by 5?
Click to show the quotient of 5.
Ask: What can we do with the 4 remainder?
Click to regroup the remainder of 4 to the 4.
Say: Now we divide the 44 by 5.
Click to show the arrow dividing 44 by 5.
Ask: What is 44 divided by 5?
Click to show the quotient of 8.
Say: We need to add a zero place holder so we can regroup the 4.
Click to add in the zero place holder.
Say: Now we regroup the remainder 4 to the 0.
Click to show 4 regrouped.
Say: Now we divide the 40 by 5.
Click to show the arrow dividing 40 by 5.
Ask: What is 40 divided by 5?
Ask: What is the answer when we divide 2.94 by 5?

32. . 8 25 20 .0 20 ÷ ÷
Teacher: Double digit divisors can be explored by students but it should not take too much of your teaching time as it is more efficient to solve these problems using a calculator.
At this level place value explanations are no longer required as students should be confident with these understandings. The algorithm is described as an adult would solve it.
Say: We are going to divide 20 by 25.
Click to show the arrow dividing 20 by 25.
Say: First we divide the 20 by 25 but 25 is greater than 20.
Say: Now we need to add a zero place holder in the tenths place so we can regroup the 20.
Click to add in the decimal point and zero place holder.
Say: Now we regroup the 20 to the tenths.
Click to show 20 regrouped as 200 tenths.
Say: As we are now dividing after the decimal point a decimal point also needs to be shown in the answer.
Click to show the decimal point and zero as a place holder in the ones place.
Say: Now we divide the 200 tenths by 25.
Click to show the arrow dividing 200 by 25.
Ask: What is 200 tenths divided by 25?
Click to show the quotient of 8 tenths.
Ask: What is the answer when we divide 20 by 25?