1. CONFIDENTIAL1 Today our topic of discussion will be: Multiply 2-4 digit by 2 digit Good Afternoon! Let’s Warm up:. 1) (2 x 6) x 3 = 3) Estimate 5 x 73. 2) (8 x 2) x 6 = Find the product: 573 X 3 4)

2. CONFIDENTIAL2 REVIEW Let’s discuss what we did in the last session. ASSOCIATIVE PROPERTY of Multiplication: While multiplying, we can change the grouping of the factors and the product stays the same. EXAMPLE: 2 x (3 x 4) = (2 x 3) x 4 2 x (3 x 4) = 2 x 12 = 24 (2 x 3) x 4 = 6 x 4 =24 Associative Property of Multiplication can be used to multiply the three factors. The grouping of the numbers does not affect the answer. Multiplication is an operation on two numbers to find a product. Like 3 x 4 = 12.

3. CONFIDENTIAL3 You can use pattern of factors and products to multiply mentally. 3 x 2 = 6 3 x 20 = 60 3 x 200 = 600 3 x 2,000 = 6,000 REVIEW We multiply numbers by first lining up the digits. 236 X 6 First multiply 6 with 6 to obtain 36. 6 3 STEP 1: Regroup 36 as 3 tens and 6 ones.

4. CONFIDENTIAL4 REVIEW 236 X 6 Again, multiply 6 with 3 at the tens place to obtain 18. Then, add 3 and 18 to obtain 21. 16 2323 STEP 2: Regroup 21 as 2 hundreds and 1 tens. 236 X 6 Then, multiply 6 with 2 at the hundreds place to obtain 12. Then, 2 and 12 to obtain 14. 1416 2323 STEP 3: Hence, the result.

5. CONFIDENTIAL5 REVIEW Estimate 6 x 44.  By Estimate, we mean an answer that is close to the exact answer. While estimating products, we round the greater factor. 6 x 44. 6 x 40 =240 Round to the nearest tens.  Overestimate: It is estimate greater than the exact answer.  Underestimate: It is estimate less than the exact answer.

6. CONFIDENTIAL6 REVIEW We also use the Distributive Property to multiply. Split 3,839 into 4 parts: 3,000 + 800 + 30 + 9 5 x 3,000 =15,000 5 x 800 = 4,000 5 x 30 = 150 5 x 9 = 45 Then finally add each part: 15,000 + 4,000 + 150 + 45 = 19,195 Multiply: 5 x 3,839 Then multiply each part by 5:

7. CONFIDENTIAL7 Let’s start now Find 20 x 23. Multiply by the multiples of 10. For this we can break apart the factors and then add the parts. 3 blocks 20 blocks 20 x 20 20 x 3 Hence a total of 460 blocks.

8. CONFIDENTIAL8 Find 20 x 23. We can do it in the other way also. 23 can also be written in the Expanded Form as: 20 + 3. Now, we multiply each part by 20. 20 X 20 400 20 X 3 60 Hence, 400 + 60 = 460

9. CONFIDENTIAL9 Now, we will see the multiplication of any 2-digit numbers. Find 16 x 19 We will first use models to find the solution:  Use one factor as width and the other factor as the length. The order does not matter.  Count the blocks. 16 blocks 19 blocks  The product is 304.

10. CONFIDENTIAL10 DISTRIBUTIVE PROPERTY of Multiplication: To multiply a sum by a number, You can multiply each addend by the number and add the product. EXAMPLE: 3 x (9 + 7) = (3 x 9) + (3 x 7) = 27 + 21 = 48 Here we look at one more property of multiplication.

11. CONFIDENTIAL11 Find 236 x 46 We now see the other way of multiplication. We multiply numbers by first lining up the digits in the following manner: 236 X 46 1416 2323 Multiply by the ones. STEP 1: Regroup Whereve r necessar y.

12. CONFIDENTIAL12 STEP 2: Multiply by the tens. Regroup Whereve r necessar y. 236 X 46 1416 2323 9440 1212

13. CONFIDENTIAL13 236 X 46 1416 2323 +9440 1212 10856 STEP 3: Then, add the products. Hence, 236 x 46 = 10,856

14. CONFIDENTIAL14 Some multiplication problems involves multisteps. By MULTISTEP we mean those problems consisting of multiplications at more than one step. Solve: Ronny can read 6 pages in hour. He reads 4 hours in one day. How many pages does he reads in 12 days? Here, we see that we have to fine the solution in 2 steps.  First step would be to find the number of pages that Ronny reads in 1 day.  Second step would be to find the number of pages that Ronny reads in 12 days. So, we move stepwise.

15. CONFIDENTIAL15 STEP 1: STEP 2: The number of pages that Ronny reads is 1 day will be: = 6 x 4 = 24 pages Now, we calculate the number of pages that Ronny reads is 12 days will be: = 12 x 24 = 288 pages. Hence, we see that Ronny reads 288 pages in 12 days.

16. CONFIDENTIAL16 Estimating Products: Estimate: 36 x 54  By Estimate, we mean an answer that is close to the exact answer. While estimating products, we round each factor. 36 x 54. 40 x 50 =2,000 Round to the nearest tens. Hence, the estimated value of 40 x 50 is 2,000. Round to the nearest tens.

17. CONFIDENTIAL17 Estimate to the Nearest Hundred or Thousand Estimate: 48 x 278 48 x 278. 50 x 300 =15,000 Round to the nearest Hundreds. Hence, the estimated value of 40 x 300 is 15,000. Round to the nearest tens. Estimate: 62,964 x 329

18. CONFIDENTIAL18 BREAK

19. CONFIDENTIAL19 GAME Click on the link below for some exciting puzzle http://www.thekidzpage.com/onlinejigsawpuzzles/jigsaw- puzzles/12-piece-jigsaw/050205food.html

20. CONFIDENTIAL20 Assessment Multiply: 1) 20 x 37 =2) 32 x 50 = Using the Distributive Property of Multiplication, find the product: 3) 5 x (6 + 7) = 4) 5 x (6 + 7) =

21. CONFIDENTIAL21 5) 742 X 37 Find the values of the following. 6) 935 X 33

22. CONFIDENTIAL22 7) Vivian teaches 16 students in one hour. She teaches for 3 hours each day. How many students does she teach in 23 days?

23. CONFIDENTIAL23 8) 45 x 320 Estimate: 9) 683 x 7,629

24. CONFIDENTIAL24 10) Lisa has 4 boxes of chocolates. Each box has 35 chocolates. How many chocolates does she have in all?

25. CONFIDENTIAL25 Very Good! Let's Review Find 20 x 23. 32 can also be written in the Expanded Form as: 20 + 3. Now, we multiply each part by 20. 20 X 20 400 20 X 3 60 Hence, 400 + 60 = 460  We saw the multiplication of 2-digit numbers with the help of models.  We saw the other way of multiplication also.

26. CONFIDENTIAL26 DISTRIBUTIVE PROPERTY of Multiplication: To multiply a sum by a number, You can multiply each addend by the number and add the product. EXAMPLE: 3 x (9 + 7) = (3 x 9) + (3 x 7) = 27 + 21 = 48 Find 236 x 46 We saw more ways of multiplication. We multiply numbers by first lining up the digits in the following manner: 236 X 46 1416 2323 Multiply by the ones. Regroup Whereve r necessar y. STEP 1:

27. CONFIDENTIAL27 STEP 2: Regroup Whereve r necessar y. 236 X 46 1416 2323 9440 1212 Multiply by the tens. 236 X 46 1416 2323 +9440 1212 10856 STEP 3: Then, add the products. Hence, 236 x 46 = 10,856

28. CONFIDENTIAL28  By MULTISTEP we mean those problems consisting of multiplications at more than one step. Estimate: 36 x 54  By Estimate, we mean an answer that is close to the exact answer. While estimating products, we round each factor. 36 x 54. 40 x 50 =2,000 Round to the nearest tens. Hence, the estimated value of 40 x 50 is 2,000. Round to the nearest tens.

29. CONFIDENTIAL29 You have done a nice job. See you in the next session.