Answer to Question #196999 in Algebra for Ntombikayise

Question

6.2 Use the factor tree to determine the prime factors of 135. (3)

7 Use the vertical and horizontal algorithms to find the sum or difference of the following. (Explain the "borrow and carry" concepts.)

a) 587 +620

b) 749 − 568 (2)

8 How do standard algorithms differ from student-invented strategies? Explain the benefits of invented strategies over standard algorithms (give at least two valid points). (4)

9 Draw pictures showing how 39 × 6 could be modelled with base-10 blocks or with areas on base-10 grids. (Use at least two of the methods.) (3)

10 Use the method of compensation to show how you can make the subtraction of 563 − 79 easier.

Answer 1

8. (a) Students who use invented strategies use mental computation and estimation regularly. It creates a sense of confidence in their ability to learn math and builds their sense-making and reasoning.

(b) They are efficient because they use place-value knowledge and single-digit computations that have already been developed. Because of the consistent one-for-ten structure across all whole number and decimal places, these algorithms thus generalize to large whole numbers and to decimals

9.. First, start by modeling the number 39 with base 10 blocks. We have three tens and nine ones

Since we are multiplying 39 by 6, using definition of multiplication, we are adding 39 six times

making 39 using 10 blocks and showing it 9 times, we have

Therefore (three tens nine ones) + (three tens nine ones) + (three tens nine ones) + (three tens nine ones) + (three tens nine ones) + (three tens nine ones) + (three tens nine ones) + (three tens nine ones) + (three tens nine ones) = 234

10 ) 563-79

add 1 to both sides to get

564-80

subtract 64 from 564 to get 500

Therefore 500-80 = 420

Add back 64 to get

420+64= 484