The document provides lesson content on multiplication as repeated addition. It defines multiplication of whole numbers, represents multiplication on a number line, and discusses properties like the commutative property of addition, additive property of zero, and multiplicative properties of zero and one. Examples are provided to check understanding of rewriting addition expressions using multiplication and applying properties like the associative property of addition.

1. Chapter 1 Lesson 5 Multiplication by a Whole Number Copyright 2010 MIND Research Institute For use only by licensed users WO.6 Understand multiplication as repeated addition. Represent multiplication of whole numbers on the number line. PR.1 Understand and identify the associative property of addition. PR.2 Understand and identify the commutative property of addition. PR.6 Understand and identify the additive property of 0. PR.7 Understand and identify the special properties of 0 and 1 in multiplication and division.

5. What is the value of point d ? In symbols, this translates to:

7. Now that we know the exact location of d we can illustrate it on the number line like this:

8. Check for Understanding 1. What are the values of the variables v and m in the following equations? m = 6 v = 8

9. When n = 7, the expression represents: Instead of writing “2” seven times, we can rewrite it using multiplication.

10. What expression does the diagram represent when n = 3? How do we rewrite it using the multiplication symbol?

11. v Check for Understanding 2. Rewrite the following expressions using the multiplication symbol: 3 × c p × s 4 × h 8 × 5

12. This means that we repeat the jump + k only once. This means that

13. Multiplicative Property of One This identity is called the Multiplicative Property of One.

15. What is the value of this expression? This means we don’t make any + k jumps and we stay at 0.

16. Multiplicative Property of Zero This is known as the Multiplicative Property of Zero.

17. Check for Understanding 3. What are the values of j , m , n and p in the following equations? Explain your reasoning. j = 0 Additive property of zero m = 0 Multiplicative property of zero n = 1 Multiplicative property of one p = 3 Multiplicative property of one

18. Sometimes we will see repeated addition of an expression. Here is b + m added repeatedly 4 times.

19. With symbols, we indicate a group by using parentheses , like this:

20. Check for Understanding 4. Use parentheses to write the following expressions: z × (1+ a ) v + ( h + 1) + h 5 × ( k + d ) t + ( w + s )

21. Check for Understanding 5. Use parentheses and multiplication to rewrite the following addition expressions: a. r + t + w + r + t + w + r + t + w b. z + 6 + z + 6 + z + 6 + z + 6 c. a + y + a + y d. p + 3 + p + 3 + p + 3 + p + 3 3 × ( r + t + w ) 4 × ( z + 6) 2 × ( a + y ) 3 × ( p + 3)

22. Associative Property of Addition This identity is called the Associative Property of Addition .

23. Check for Understanding 6. Use symbols to write the following identities: ( r + s ) + t = r + ( s + t ) ( c + d + e ) = c + ( d + e ) a + b + k = a + ( b + k ) ( w + 2) + 3 + 2 = w + 2 + (3 + 2)

24. We can use the Commutative Property of Addition to reorder the expression so it is a repeated addition of .

25. Check for Understanding 7. Simplify the following expressions using multiplication: 3 × ( d + e + f ) 2 × ( p + 8) 5 × ( a + b ) 4 × (7 + g ) 3 × h + 3 × y or 3 × ( h + y )

26. Multiple Choice Practice 1. What property is represented by the following identity? b = b × 1 2. True or false: The value of n × 5 is always greater than the value 5.

27. Find the Errors Correct. Correct. This should be m = 0. This should be 4 × (8 + k ).