Math Strategy: Repeated Addition

What is the math strategy, Repeated Addition?

Math Strategy: Repeated Addition
Strand: Number Sense



Overview:
Repeated addition is adding the same number again and again to get the answer to a multiplication problem. It is an entry-level strategy for multiplication and will naturally occur when students are first presented with multiplication problems.

Guide to Effective Instruction in Mathematics Grades 4 to 6 Volume 3 Multiplication page 14-18 http://www.eworkshop.on.ca/edu/resources/guides/NSN_vol_3_Multiplication.pdf



Eventually, students will regroup the groups of repeated additions. 

How to Support Student Learning:
Using student examples of repeated addition can serve as an excellent vehicle for discussion efficiency. It is not efficient to repeatedly add 37 groups of 28.

As students develop concepts about multiplication, and as their knowledge of basic facts increases, they begin to use multiplicative rather than additive strategies to solve multiplication problems.

It is important that a variety of models both concrete and pictorial representations be explored with students.

Where to Next?



- 10X

Because many strategies for multi-digit multiplication depend on decomposing numbers to hundreds, tens, and ones, it is important that students develop skill in multiplying numbers by multiples of 10. For example, students in the junior grades should recognize patterns such as 7 × 8 = 56, 7 × 80 = 560, 7 × 800 = 5600, and 7 × 8000 = 56 000. Students can use models to develop an understanding of why patterns emerge when multiplying by multiples of 10.

Students can also use base ten materials to model the effects of multiplying by multiples of 10. The following example illustrates 3 × 2, 3 × 20, and 3 × 200.



Understanding the effects of multiplying by multiples of 10 also helps students to solve problems such as 30 × 40, where knowing that 3 × 4 =12 and 3 × 40 =120 helps them to know that 30 × 40 = 1200.



- 10X and familiar facts

28 X 37 could be thought of as 3 groups of 28 X 10 plus 20 X 7 plus 8 X 7:





- Partial Products GEIM Volume 3 page 19-23
With partial product strategies, one or both factors in a multiplication expression are decomposed into two or more numbers, and these numbers are multiplied by the other factor. The partial products are added to determine the product of the original multiplication expression. Partial product strategies are applications of the distributive property of multiplication; for example, 5 ×19 = (5×10) + (5× 9).





An open array provides a model for demonstrating partial product strategies, and gives students a visual reference for keeping track of the numbers while performing the computations. The following example shows how 7× 42 might be represented using an open array.

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