Grade 3
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Developing The Concept

Multi-digit by One-digit Multiplication

When developing multi-digit by one-digit multiplication, it is important to stress place value so students will have a solid foundation when they learn the multiplication algorithm. Materials: Overhead projector or chalkboard. Preparation: Write

 4  2 
 x  3 
on the board or overhead projector.

  • Ask: How many tens are in 42? How many ones are in 42? What is 42 in expanded form?
    The first two questions should be easy for students. There are 4 tens and 2 ones in 42. Some students may need help with the third question. Elicit from them that 4 tens equal 40 and 2 ones equal 2, so the expanded form of 42 is 40 + 2. Write 40 + 2 times 3 on the board next to 42 times 3.

     4  2 
     x  3 
     40 + 2 
     x  3 

  • Say: We'll multiply the ones first. What is 2 times 3?
    Students should know their multiplication facts well enough to promptly say 6.

  • Say: What is 40 times 3? Students should have sufficient experience with multiplying by multiples of ten to know the answer is 120.

  • Write 120 + 6 on the board below 40 + 2 times 3.
     4  2 
     x  3 
     40 + 2 
     x  3 
    120  +  6

  • Say: Now we just have to find the sum of 120 + 6. What is the sum?
    Students will easily answer 126.

  • Continue with additional examples that stress the connection of place value with multiplication. After students comprehend multi-digit multiplication using place value, introduction to a modified version of the standard multiplication algorithm is appropriate.

Wrap-Up and Assessment Hints
Students need time to develop confidence and understanding of multi-digit multiplication. When you assess students' progress, take extra time to ensure that students understand the importance of place value as it relates to multiplication. Be sure to provide enough examples and practice with prior concepts such as multiplying by ten and multiples of ten before introducing additional multi-digit multiplication.

    Multi-digit by one-digit:

    Properties of Multiplication:

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