STANDARD ALGORITHMS For 7-10 Year Olds Readiness Students need to have sufficient conceptual development of place value prior to using formal algorithm structures. Algorithms An algorithm is a set of rules for solving a math 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 recognize 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 and language for developing each set of rules for the standard algorithms for 7-10 year olds. * A separate PowerPoint presentation is available for the standard algorithms used by 10-13 year olds. * Another PowerPoint presentation is also available for standard fraction computations in addition, subtraction, multiplication and division (for 10-13 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.

STANDARD ALGORITHMS Add No Regrouping Slide 3 Subtract No Regrouping Slide 4 Add With Regrouping Slide 5 Subtract With Regrouping Slide 6 Multiply No Regrouping Slide 7 Divide No Regrouping Slide 8 Multiply With Regrouping Slide 9 Divide With Regrouping Slide 10 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.

45 14 + 5 9 + + Say: We are going to add two numbers, 45 and 14. Say: We can add the ones/units first. Click to show the arrow adding 4+5 or 5+4 Ask: What is 4 plus/add 5? What is 5 plus/add 4? Click to show the total. Say: Now we add the tens. Click to show the arrow adding 1+4 or 4+1 Ask: What is 1 plus/add 4? What is 4 plus/add 1? Ask: What is 14 plus/add 45? What is 45 plus/add 14?

26 - 13 - - 1 3 Say: We are going to subtract 13 from 26. (Or we are going to take 13 from 26. Or we are going to find the difference between 13 and 26.) Say: We can subtract the ones/units first. Click to show 6 take/subtract 3 Ask: What is 6 take/subtract 3? Click to show the remainder. Say: Now we subtract the tens. Click to show 2 take/subtract 1 Ask: What is 2 take/subtract 1? Ask: What is 26 take/subtract 13?

47 + 15 6 2 1 2 + + Say: We are going to add two numbers, 15 and 47. Say: We can add the ones/units first. Click to show the arrow adding 5+7 or 7+5 Ask: What is 5 plus/add 7? What is 7 plus/add 5? Click to show the total 12 above the top number. Say: We have a total of 12. We can’t put both the digits 1 and 2 in the ones/units place. Click to show the total of 2 in the ones/units place. Say: We have put the 2 in the ones/units place. 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/add 4 plus/add 1? Click to show the total of 6 tens. Ask: What is the total when you add 15 and 47?

40 - 15 3 1 - - 2 5 Say: We are going to subtract 15 from 40. (Or we are going to take 15 from 40. Or we are going to find the difference between 15 and 40.) Say: We can subtract the ones first. However, we have zero ones in 40 and we can’t take 5 from zero. Say: We can fix that by taking 10 from 40 and putting it in the ones/units place. Say: Watch carefully while I do this. Click to show the 4 crossed out. Say: We take a 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/units place. Say: We can now take 5 from 10. Click to show the arrows for subtracting subtract 5 from 10. Ask: What is 10 take/subtract 5? Click to show the remainder 5. Say: We can now take 1 ten from 3 tens. Click to show the arrows for subtracting 1 from 3. Ask: What is 3 take/subtract 1? Click to show the remainder 2. Ask: We have subtracted 15 from 40. What is the remainder?

22 X 3 6 6 x x Say: We are going to multiply 22 by 3. Say: We can multiply the ones/units first. Click to show the arrow multiplying 3 x 2 Ask: What is the total/product for 3x2 Click to show the total/product. Say: Now we multiply the tens. Click to show the arrow multiplying 3x2 tens. Ask: What is the total/product for 3x2 tens? Ask: What is the total/product when you multiply 22 by 3?

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 dividend 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 dividend 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?

X 3 7 8 26 6 1 8 + x x Say: We are going to multiply 26 by 3. Say: We can multiply the ones/units first. Click to show the arrow multiplying 3x6 Ask: What is 3x6? Say: 18 can be shown as 8 ones and 1 ten. Click to show the total of 18 as 8 ones and 1 ten. Click to show where to record the 8 ones. Say: Now we multiply the tens. Click to show the arrow multiplying 3x2 tens Ask: What is 3x2 tens? Click to show the total of 6 tens. Say: We now add the 6 tens to the 1 ten for a total of 7 tens. Click to show the addition sign. Say: We now have 7 tens. Click to show where to record the 7 tens. Say: We have multiplied 26 by 3. Ask: What is the product/total when you multiply 26 by 3?

3 642 2 1 4 1 ÷ ÷ ÷ Say: We are going divide to 642 by 3. (Or we are going to find how many sets of 3 we can make from 642. Or we are going to divide 642 into 3 equal groups.) Say: We divide the 6 hundreds by 3 first. Click to show the arrow dividing 6 hundreds by 3. Ask: What is 6 divided by 3? Click to show the quotient of 2 hundreds. Say: Now we divide the 4 tens by 3. Click to show the arrow dividing 4 tens 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 ten still not divided? Click to show the quotient of 1 ten. Say: We can now add the ten to the ones. Click to show 12 ones. Ask: How many ones can we now divide by 3? Click to show the arrow dividing 12 ones by 3. Ask: What is 12 divided by 3? Click to show the quotient of 4 ones. Ask: How many sets of 3 can we make from 642? Ask: If we divide 642 into 3 groups, how many will be in each group?