Mrs. Dhillon’s Classroom An Introduction to Multiplication Algorithms Home Overview Partial Product Lattice Traditional Assessment An Introduction to Multiplication Algorithms Ramneek Dhillon

Mrs. Dhillon’s Classroom In this tutorial you will be introduced to three different multiplication algorithms. Remember, an algorithm is a step by step procedure for calculations that work every time when followed correctly. Prior to learning the algorithms shown below you will be introduced to some multiplications basics. Partial Product Lattice Method Traditional Please use the navigation arrows at the bottom of the screen to advance the slides. Alternatively, you have the option to use the navigation bar on the left to go to a particular section of the tutorial. At the end of the tutorial you will be required to complete an assessment. You need a minimum score of 80% to pass. If you do not pass, return to the tutorial to review the information presented. Should additional guidance be required, kindly ask the teacher for help. Home Overview Partial Product Lattice Traditional Assessment

Mrs. Dhillon’s Classroom Multiplication is often described as repeated addition. For example the product of 3×4 is equal to the sum of 4+4+4 . In multiplication there are 3 terms that a required to be known to describe the problem; multiplicand, multiplier, and product. The multiplicand and multiplier are also referred to as factors, the two numbers that are being multiplied together. The answer is referred to as the product. Refer to the following example. Home Overview Partial Product Lattice Traditional Assessment 152 × 3 456 Multiplicand Multiplier Product In the above example, the multiplication column was written in a vertical format. However, multiplication problems can also be written in a linear format. Refer to the example below. 152×3=456 Also, it’s important to note that the product of two factors is the same regardless of how the problem is visually written. For example, the product of 4×3 is the same as 3×4. Which number is the multiplier and the multiplicand is not important. The answer to both multiplication problems is 12.

Mrs. Dhillon’s Classroom When solving multiplication problems it is often helpful to set up the problem vertically. Furthermore, it is normal practice to write the larger number as the multiplicand and the smaller number as the multiplier. Most important, however, is to align the units of each factor in the ones, tens, hundreds, and so forth units. For example, the multiplication problem 354×52 should be written as the following Home Overview Partial Product Lattice Traditional Assessment 3 5 4 × 2 Multiplicand (Large Number) Multiplier (Small Number) Product 7 0 8 7 0 8 3 5 4 × 2 Ones Tens Hundreds

Mrs. Dhillon’s Classroom 234 × 8 1600 234 × 8 1600 240 234 × 8 1600 240 + 32 1872 234 × 8 1600 240 + 32 1872 Home Overview Partial Product Lattice Traditional Assessment In the partial products algorithm, the tens partial (part of something) and the ones partial product are found and than added to find the whole product. Follow the directions below to see how it’s done. Step 1 (red): We start with going from left to right. The first thing you need to do when solving the partial products method is, multiply 8[200s] (8 times 200). This will give you the answer of 1600. Step 2 (green): Next, you need to multiply 8[30s] (8 times 30). This will give you the answer of 240. Step 3 (blue): Than you multiply 8[4s] (8 times 4). This will give you the answer of 32. Step 4 (orange): Finally, you add all 3 answers (1600, 240, and 32) together to get your final product.

Mrs. Dhillon’s Classroom Once you’ve solved the following problems, add the 3 products together for your answer. HINT Partial products practice: Solve the problem below using the partial product algorithm. Show all your work in the box and than check your answer. Home Overview Partial Product Lattice Traditional Assessment 671 × 4 2,684 ANSWER

Mrs. Dhillon’s Classroom In math, a lattice is a box with squares and diagonals that is used for multiplication. To multiply using the lattice method, first, write the factors on the outside of the box, one across the top and one down the right side. Second, multiply each digit in one factor by each digit in the other factor. If you end up with a 1 digit product, you must add a 0 and than the product (see example below). Third, add the numbers inside the lattice within each diagonal. If the sum on a diagonal exceeds 9, the excess 10’s are added in the next diagonal. See the next slide for a step-by-step visual of how to fill out the lattice boxes. Note that is does not matter if you begin multiplying form right to left or left to write. Home Overview Partial Product Lattice Traditional Assessment 2 8 4

Mrs. Dhillon’s Classroom 2 3 4 8 1 6 Create a lattice box. For each place value of the factor create a box. Write the multiplicand place value on top of each box. Write the multiplier place value on the side of the box. Only one digit is allowed for each box. Home Overview Partial Product Lattice Traditional Assessment Multiple the multiplicand by the multiplier for the ones place value and write the product within the first box. 4×8=32 Continue the above process for the remaining place values. 3×8=24 2×8=16

Mrs. Dhillon’s Classroom Next, add the numbers within each diagonal column. Remember, if the sum of the product within each diagonal exceeds 9, the excess 10’s are added in the next diagonal. Home Overview Partial Product Lattice Traditional Assessment 6 1 2 3 4 8 71 21 7 Once you have completed the addition of the diagonal columns, the value displaced underneath the lattice box will be the product of the problem (blue). 6 1 2 3 4 8 7

Mrs. Dhillon’s Classroom Lattice method practice: Solve the problem below using the lattice method. Show all your work in the box and than check your answer. HINT 4 9 2 Home Overview Partial Product Lattice Traditional Assessment 492 × 4 ANSWER 6 1 3 8 4 9 2 1

Mrs. Dhillon’s Classroom The traditional method of multiplication is familiar to most adults and many children. When you use the algorithm you multiply from left to right, regrouping as necessary. Follow these steps when using this algorithm. First, multiply the ones digit in the bottom factor by the ones digit in the top factor. Record any regrouping at the top of the next place-value column. Then, multiply each of the remaining digits in the bottom factor by each of the remaining digits in the top factor, moving from right to left. Finally, if you have partial products, add them to find the total product. Home Overview Partial Product Lattice Traditional Assessment × 8 4 7 3

Mrs. Dhillon’s Classroom × 8 4 7 3 Set up the problem vertically and align each unit for the factors. Home Overview Partial Product Lattice Traditional Assessment × 8 4 7 3 1 Multiple the factors in the ones column. 7×3=21 × 8 4 7 3 1 2 From the product, add the value from the ones column and carry the two.

Mrs. Dhillon’s Classroom Continue to follow the same steps for the tens and hundreds place value. Make sure to carry the excess 10’s to the following column if the value exceeds 9. Home Overview Partial Product Lattice Traditional Assessment × 8 4 7 3 1 2 × 8 4 7 3 1 × 8 4 7 3 1 × 8 4 7 3 5 1 2

Mrs. Dhillon’s Classroom Traditional method practice: Solve the problem below using the traditional method. Show all your work in the box and than check your answer. Keep your place values aligned and remember to carry your remainder. HINT Home Overview Partial Product Lattice Traditional Assessment 632 × 7 ANSWER 3 7 × 6 2 4 1

Mrs. Dhillon’s Classroom There are a total of 5 questions within this assessment. You must correctly answer 4 for a passing score of 80%. Note during this assessment you will be required to show your work. Use the PowerPoint built in pen tool to show your work if needed. To access the pen tool follow the following steps. Right click on the presentation. Select the Pointer Option Select Pen Should you need to erase perform the above 2 steps, however for step 3, select eraser. Home Overview Partial Product Lattice Traditional Assessment

Mrs. Dhillon’s Classroom Question 1: Home Overview Partial Product Lattice Traditional Assessment 1 6 8 × 5

Mrs. Dhillon’s Classroom Question 2: Home Overview Partial Product Lattice Traditional Assessment 3 5 9 × 2

Mrs. Dhillon’s Classroom Question 3: Home Overview Partial Product Lattice Traditional Assessment 9 1 6 × 8

Mrs. Dhillon’s Classroom Question 4: Home Overview Partial Product Lattice Traditional Assessment 4 3 9 × 6

Mrs. Dhillon’s Classroom Question 5: Home Overview Partial Product Lattice Traditional Assessment 7 7 3 × 6

Mrs. Dhillon’s Classroom Open Response: In the box below explain one multiplication algorithm and how it works. You can give an example, however, be sure to use your words and write in complete sentences. Home Overview Partial Product Lattice Traditional Assessment