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lesson 5
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.
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5. What is the value of point d ? In symbols, this translates to:
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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
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 ).
Editor's Notes
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Page 43 - This diagram shows that we add +2 a total of 5 times.
Page 43 -We can count up the ones to find that:
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Page 44 - In general, all multiples of 2 are illustrated by the following diagram:
Page 44 -The x is called the multiplication symbol . -We read 7 x 2 as “seven times two”.
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Page 44 -Does multiplication always make things bigger? - Not always. Let’s look at this example.
Page 44 -Multiplying by 1 doesn’t change the value. Since this is always true, this is an identity.
Page 45 -In the last lesson, we saw that adding 0 doesn’t change the value of an expression.
Page 45 -What happens when we multiply by zero?
Page 45 -For this reason, 0 x k always equals zero.
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Page 45 -Multiplication is a more efficient way to express repeated addition. -Here is how it is shown on the number line.
Page 46 -The expression b + m is grouped by a dashed curve to show that b + m repeats as a group. - When represented as multiplication, we write:
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Page 46- 47 -When adding a sequence of jumps, grouping doesn’t change the final value. -In symbols the identity is written: -Here the word associate means to form a group.
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Page 47 -Sometimes we might see expressions that don’t look like repeated addition. -Since ( V + Z ) is added repeatedly 4 times, we can simplify it using multiplication.
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