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Multiplying 2-digit Numbers Maggie Martinez Summer 2005 Reusable Learning Object
Overview Multiplication is used everyday in life. By using two-digit multiplication, we can find the product of an equation a lot faster than counting each individual piece. Learning how to multiply is critical in doing higher math such as division, fractions and algebra. Overview – Introduction and Importnace
After completing this lesson, you will be able to correctly multiply two factors when one of the factors has 2-digits. Overview – Objectives and Prerequisites Prerequisites • Before proceeding with this lesson, you should have a basic understanding of the following math concepts: • Place value • Addition • Number sentences
Overview – Scenario Today is your lucky day! Ms. Martinez is going to order pizza for the whole class! Before she can do so, she needs YOU to find out how many slices of pizza the students will eat. There are 23 students in the class. If each student eats 2 slices, how many slices does Ms. Martinez have to order?
Outline Overview - Outline What are the parts of a place value chart? What are the different symbols that can be used in a number sentence? What is a factor? What is a product? In what way are addition and multiplication related? How to multiply by 2-digits
An equation is a mathematical number sentence where the left side of the equal sign has the same value as the right side. There are so many different symbols in a math equation. What are they? Concept RIO – Symbols in a Number Sentence
All multiplication number sentences contain factors and products. You will need to identify the parts of a multiplication number sentence Concept RIO - Factors and Products 8 Factor 8 Factor 64 Product x = A product is the answer to a multiplication equation; it is the result of multiplying two numbers A factor is a whole number that multiplies with another number
Factors Product Concept RIO – Factors and Products EXAMPLE 2 x 3 6 Multiplication symbol
2 Addend 2 Addend 4 Sum + = 12 Dividend 3 Divisor 4 Quotient / = NON-EXAMPLES Concept RIO – Factors and Products These are not examples of the use of factors and products. Notice that the number sentences do not use a multiplication symbol.
8 8 Factor 5 8 3 2 Factor 64 15 Product 10 x + x = = = Equation, Symbols, Factors, and Products Practice Exercises For each equation, determine whether number sentence is correctly identified. Concept Practice Factors and Products Example CORRECT or INCORRECT This number sentence is correct because the 8 is a factor in the multiplication PRACTICE EXERCISES 1.CORRECT or INCORRECT This number sentence is not correct because the 2 is an addend. This is an addition equation. 2. CORRECT or INCORRECT This number sentence is correct because the 15 is a product; it is an answer in the multiplication equation.
PLACE VALUE CHART , Each digit has a value depending on its place in a number. The place value chart helps us to understand the value of each number. In order to complete a multiplication problem, you will need to know the place value of each digit. Fact RIO - Place Value Chart Thousands 1,000 Hundreds 100 Tens 10 Ones 1
Thousands 1,000 Hundreds 100 Tens 10 Ones 1 The number 235 can be put into the chart, then I can figure out how much each digit is worth. Fact RIO - Place Value Chart , 2 3 5 Notice that the value increases as we move to the left
PRACTICE EXERCISE A Drag and drop the name and place value block in the correct column. Fact PracticePlace Value Chart Ones _______ _________ ________ _______ Hundreds Tens Thousands PRACTICE EXERCISE B Given the following numbers, click on the the correct place value that names the underlined digit. 8 , 1 5 6 Ones Tens Hundreds Thousands 3 , 2 9 8 Ones Tens Hundreds Thousands 4 , 6 7 2 Ones Tens Hundreds Thousands
Multiplication is just a very quick way of adding numbers together.2+2+2+2+2+2 = 12 Process RIO – Addition and Multiplication How many twos are in the problem? 6 So a quicker way of saying 2+2+2+2+2+2 is 2 X 6 Multiplication and addition are very closely related. You can change a long addition number sentence into a very short multiplication number sentence.
Directions: Decide whether you can use a multiplication number sentence as a faster way to solve the problem. If so, then solve the problem. If not, provide a reason.You are opening up a dog walking business. Every day of the week, you are to walk 3 dogs. How many dogs will you have walked at the end of the week? Sunday Monday Tuesday Wednesday Thursday Friday Saturday Click for answer You CAN solve this problem with multiplication! 3 dogs X 7 days in the week 3 X 7 = 21 Process Practice Addition and Multiplication
Now that you can correctly identify the parts of a multiplication number sentence, we can learn how to multiply when one of the factors has 2-digits. There are 4 steps. Procedure RIO - How to Multiply by 2-digits (without regrouping) We’ll be using this multiplication problem 3 4 x 2
Step Action Example 1 Begin by multiplying the digits in the ones place value T O 3 4 x 2 2 Put the product in the ones place T O 3 4 x 2 8 3 Multiply the bottom factor by the top factor that is in the tens place T O 3 4 x 2 8 4 Place the product in the tens place value column T O 3 4 x 2 6 8 Procedure RIO – How to Multiply by 2-digits
Procedure PracticeHow to Multiply by 2-digits You have decided that now you can start to solve the pizza problem that will allow Ms. Martinez to order for the whole class. In order to do so, you have to multiply 23 X 2. Number the steps to solving the equation correctly. Multiply the digits in the ones place value Place the product in the tens place value column Put the product in the ones place Multiply the bottom factor by the top factor that is in the tens place 1 2 3 4
Review This completes the lesson on how to multiply with a 2-digit factor. You should be able to label the parts of a place value chart, identify symbols, factors and products in a number sentence, and be able to solve a 2-digit multiplication equation. Summary T O 2 3 X 2 4 6 You should now be able to tell Ms. Martinez how many slices of pizza to order for the class by solving 23 x 2. Ms. Martinez should order 46 slices!
Next Steps • It is recommended that you research the items listed below to gain a fuller understanding of this subject. • Place value • Expanded Form of a number • Multiplying using partial-product Additional Resources • The following item will provide more information on the topics that were covered in this lesson. • A Math Dictionary for Kids, Jenny Eather. An animated interactive dictionary for kids. http://www.teachers.ash.org.au/jeather/indexmdfk.html
Number Visual 3 , 2 9 8 4 , 6 7 2 7 3 4 Product - = Quiz Exercise A CORRECT or INCORRECT This number sentence is NOT correct because the 4 is the difference; it is an answer in a subtraction equation. Exercise B For each number drag and drop blocks to make a visual representation using place value blocks. Use as many blocks of each as needed.
Step Action 1 Begin by multiplying the digits in the ones place value 2 Put the product in the ones place 3 Multiply the bottom factor by the top factor that is in the tens place 4 Place the product in the tens place value column Quiz Exercise C Solve the following problems. If necessary, refer to the action table to the right. T O T O T O 9 2 3 4 4 3 x 1x 2x 2
Reusable Learning Object Multiplying 2-digit Numbers Maggie Martinez Summer 2005