1. Multiplication

2. Standards Third Grade Common Core 3.3 NBT Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. Third Grade CA Standards NS 2.4 Solve simple problems involving multiplication of multi-digit numbers by one-digit numbers (3,671 x 3 = __). Fourth Grade Common Core 4.5 NBT– Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4.5.1 NBT - Solve problems involving multiplication of multi-digit numbers by two-digit numbers. Fourth Grade CA Standards NS 3.2 Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multi digit number by a two-digit number and for dividing a multi digit number by a one-digit number; use relationships between them to simplify computations and to check results. NS 3.3 Solve problems involving multiplication of multi digit numbers by two-digit numbers.

3. Multiplication Students should use methods they understand and can explain while multiplying. – Visual representations such as area models that students draw and connect to equations are useful for this purpose. By reasoning repeatedly about the connection between math drawings and written numerical work, students can come to see written algorithms as abbreviations or summaries of their reasoning about quantities. In mathematics, an algorithm is defined by its steps and not by the way those steps are recorded in writing. With this in mind, minor variations in methods of recording standard algorithms are acceptable.

4. Area models enhance the understanding of geometry and multiplication. This is an area model of 7x5 using built using base ten blocks. The red base ten blocks represent the factors as if we were making a square with a length of 7 and a width of 5. The product is represented by the blue base ten blocks. Area Models

5. Build an area model of 10 x 5 using base ten blocks. 10 x 5

6. Build an area model of 10x10 using base ten blocks. 10 x 10

7. Build an area model of 12x15 using base ten blocks. 10 x 10 2 x 10 10 x 5 2 x 5

8. 4.5 NBT– Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 10 + 5 10 + 2 10 x 10 = 10010x5 = 50 10x2= 202x5=10 12 15 x 100 + 50 + 20 + 10 = 180

9. 4.5 NBT– Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 30 + 1 40 + 2 1,20040 602 42 31 x 1,200 + 60 + 40 + 2 = 1,302

10. Connecting the area model to the algorithm 200 + 40 + 6 7 246 7 x 2 4 6 7 x 4 2 4 6 7 2 x 4 2 2 8 2 4 6 7 2 x 4 8 2 4 1, 42 280 1,400 2 4 6 7 2 x 4 8 2 4 1, + 2 4 0 2 2 7 1, 1 Two-Step Solution 1)Multiply all the numbers and record the answers. 2)Add the numbers from the top and record the final answer.

11. 3,000 + 200 + 40 + 6 7 3, 246 7 x 3, 2 4 6 7 x 4 2 42 2801,40021,000 3, 2 4 6 7 2 x 4 8 2 3, 2 4 6 7 2 x 4 8 2 4 3, 2 4 6 7 2 x 4 8 2 4 1 1 1, 2 + 1, 2 4 0 1 2 2 72, 2 Connecting the area model to the algorithm Two-Step Solution 1)Multiply all the numbers and record the answers. 2)Add the numbers from the top and record the final answer.

12. 2,000 + 300 + 50 + 8 6 2, 358 6 x 2, 3 5 8 6 x 4 8 48 3001,80012,000 2, 3 5 8 6 8 x 4 0 3 2, 3 5 8 6 8 x 4 0 3 8 2, 3 5 8 6 8 x 4 0 3 8 1 1 2, 1 + 1, 3 4 0 1 8 4 1 4, 1 Connecting the area model to the algorithm Two-Step Solution 1)Multiply all the numbers and record the answers. 2)Add the numbers from the top and record the final answer.

13. 2, 3 5 8 6 x 431 1 + 1, 3 4 0 1 2, 8 0 8 1 4, 1 4 8 2, 3 5 8 6 x 4 8 4 3 1 2 4, 1 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Two-Step Solution 1)Multiply all the numbers and record the answers. 2)Add the numbers from the top and record the final answer. One-Step Solution Multiply each number and add the number from the top before recording a final answer answer. We are multiplying by a one-digit whole number. Mathematicians prefer to complete this problem in one step.

14. 4.5 NBT– Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 20 + 3 30 + 6 60090 12018 36 23 x 600 + 120 + 90 + 18

15. 4.5 NBT– Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 36 23 x Step one: 3 x 6 = 18 Step two: 3 x 30 = 90 Step three: 20 x 6 = 120 Step four: 20 x 30 = 600 Step five: 828 18 (3 x 6) 90 (3 x 30) 120 (20 x 6) 600 (20 x 30) + ____ 828 36 x 23 = (30 + 6) x (20 + 3) 36 x 23 = (30 + 6) x 20 + (30 + 6) x 3 36 x 23 = (30 x 20) + (6 x 20) + (30 x 3) + (6 x 3)

16. 4.5 NBT– Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. llustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Step one: 3 x 6 = 18 Step two: 3 x 30 = 90 Step three: 20 x 6 = 120 Step four: 20 x 30 = 600 Step five: 828 8 1 36 23 x 36 23 x 8 1 9 36 23 x 8 1 9 2 1 36 23 x 8 1 9 2 0 1 6 0 8 1 9 1 6 8 1 7 1 + 0 11 8 28 + 36 23 x Notice how step five was two addition problems. The next slide will show us how to do step five with only one addition problem.

17. 4.5 NBT– Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Step one: 3 x 6 = 18 Step two: 3 x 30 = 90 Step three: 20 x 6 = 120 Step four: 20 x 30 = 600 Step five: 828 8 1 36 23 x 36 23 x 8 1 0 36 23 x 8 1 0 2 1 36 23 x 8 1 0 2 0 1 7 0 8 1 0 1 7 8 28 + 36 23 x 1 11 1 This is the preferred method, and this is how we will do all future multiplication problems.

18. 4.5 NBT– Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Step one: 6 x 8 = 48 Step two: 6 x 40 = 240 Step three: 70 x 8 = 560 Step four: 70 x 40 = 2,800 Step five: 3,648 8 4 48 76 x 48 76 x 8 4 8 48 76 x 8 4 8 6 5 48 76 x 8 4 8 6 0 5 3 0 2 22 3 6 x 40 is 240. Then I add the 40 from step one and I have 280. This is 8 tens and 2 hundreds. Notice how 288 is the total of steps one and two below. Why is that? 70 x 40 is 2800. Then I add the 500 from step three and I have 3,300. This is 3 hundreds and 3 thousands. Notice how 3,360 is the total of steps three and four below. Why is that? 8 4 8 6 0 5 3 8 46 + 48 76 x 2 3 1 3,

19. What is the best method for solving this problem? Why? 368,423 x 7,286